1 10 12 https://lis5472.cci.fsu.edu/sp19/group8/files/original/08d7f698d8bdb17027f044495038df00.pdf e7676528cf239ecfb6a18e3b1d62ea94 PDF Text Text Trends in High School Dropout and Completion Rates in the United States: 1972–2008 Compendium Report DECEMBER 2010 Chris Chapman National Center for Education Statistics Jennifer Laird MPR Associates, Inc. Angelina KewalRamani Education Statistics Services Institute American Institutes for Research NCES 2011-012 U.S. DEPARTMENT OF EDUCATION �U.S. Department of Education Arne Duncan Secretary Institute of Education Sciences John Q. Easton Director National Center for Education Statistics Stuart Kerachsky Acting Commissioner The National Center for Education Statistics (NCES) is the primary federal entity for collecting, analyzing, and reporting data related to education in the United States and other nations. It fulfills a congressional mandate to collect, collate, analyze, and report full and complete statistics on the condition of education in the United States; conduct and publish reports and specialized analyses of the meaning and significance of such statistics; assist state and local education agencies in improving their statistical systems; and review and report on education activities in foreign countries. NCES activities are designed to address high-priority education data needs; provide consistent, reliable, complete, and accurate indicators of education status and trends; and report timely, useful, and high-quality data to the U.S. Department of Education, the Congress, the states, other education policymakers, practitioners, data users, and the general public. Unless specifically noted, all information contained herein is in the public domain. We strive to make our products available in a variety of formats and in language that is appropriate to a variety of audiences. 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Suggested Citation Chapman, C., Laird, J., and KewalRamani, A. (2010). Trends in High School Dropout and Completion Rates in the United States: 1972–2008 (NCES 2011-012). National Center for Education Statistics, Institute of Education Sciences, U.S. Department of Education. Washington, DC. Retrieved [date] from http://nces.ed.gov/pubsearch. Content Contact Chris Chapman (202) 502-7414 chris.chapman@ed.gov �Acknowledgments The authors would like to recognize the time and effort volunteered by household respondents to the Current Population Survey (CPS). The report also relies on voluntary reporting by local and state officials to compile the rates reported through the Common Core of Data on public schools. iii ��Contents Page Acknowledgments ...................................................................................................................... iii List of Tables .............................................................................................................................. vi List of Figures............................................................................................................................. ix Introduction ................................................................................................................................ 1 Findings....................................................................................................................................... National Event Dropout Rates ............................................................................................... State Event Dropout Rates for Public High School Students ................................................ National Status Dropout Rates ............................................................................................... National Status Completion Rates ......................................................................................... General Educational Development (GED) Credentials and National Status Completion Rates................................................................................................................ Averaged Freshman Graduation Rates for Public School Students....................................... 5 5 7 8 10 11 12 References ................................................................................................................................... 15 Figures......................................................................................................................................... 21 Tables .......................................................................................................................................... 29 Appendix A—Technical Notes..................................................................................................A-1 Appendix B—Glossary ..............................................................................................................B-1 Appendix C—Standard Error Tables......................................................................................C-1 v �List of Tables Table Page 1 Event dropout rates and number and distribution of 15- through 24-year-olds who dropped out of grades 10–12, by selected characteristics: October 2008 ........................ 30 2 Event dropout rates of 15- through 24-year-olds who dropped out of grades 10–12, and number of dropouts and population of 15- through 24-year-olds who were enrolled: October 1972 through October 2008 ................................................................ 32 3 Event dropout rates of 15- through 24-year-olds who dropped out of grades 10–12, by sex and race/ethnicity: October 1972 through October 2008 ..................................... 34 4 Event dropout rates of 15- through 24-year-olds who dropped out of grades 10–12, by family income: October 1972 through October 2008 ................................................. 36 5 Event dropout rates for public school students in grades 9–12, by state: School years 1993–94 through 2007–08...................................................................................... 38 6 Status dropout rates and number and distribution of dropouts of 16- through 24-year-olds, by selected characteristics: October 2008.................................................. 40 7 Status dropout rates, number of status dropouts, and population of 16- through 24-year-olds: October 1972 through October 2008 ......................................................... 42 8 Status dropout rates of 16- through 24-year-olds, by sex and race/ethnicity: October 1972 through October 2008 ............................................................................................. 44 9 Status completion rates, and number and distribution of completers ages 18–24 not currently enrolled in high school or below, by selected characteristics: October 2008.................................................................................................................................. 46 10 Status completion rates, number of completers, and population of 18- through 24-year-olds: October 1972 through October 2008 ......................................................... 48 11 Status completion rates of 18- through 24-year-olds not currently enrolled in high school or below, by sex and race/ethnicity: October 1972 through October 2008 .......... 50 vi �List of Tables Table Page 12 Averaged freshman graduation rate of public high school students, by state: School year 2007–08........................................................................................................ 52 13 Averaged freshman graduation rates of public high school students and change in rates, by state: School years 2001–02 through 2007–08.................................................. 54 Appendix A A-1 Summary table of high school dropout, completion, and graduation rates .................. A-6 A-2 Percentage distribution of persons who passed the General Educational Development (GED) exam outside of federal and state contract facilities, by age group: 1998–2008..................................................................................................................... A-16 A-3 Percentage distribution of persons who passed the General Educational Development (GED) exam at federal or state contract facilities, by age group: 1998–2008 .............. A-17 Appendix C C-1 Standard errors for table 1: Event dropout rates and number and distribution of 15- through 24-year-olds who dropped out of grades 10–12, by selected characteristics: October 2008........................................................................................ C-2 C-2 Standard errors for table 2: Event dropout rates of 15- through 24-year-olds who dropped out of grades 10–12, and number of dropouts and population of 15- through 24-year-olds who were enrolled: October 1972 through October 2008.......... C-3 C-3 Standard errors for table 3: Event dropout rates of 15- through 24-year-olds who dropped out of grades 10–12, by sex and race/ethnicity: October 1972 through October 2008................................................................................................................. C-5 C-4 Standard errors for table 4: Event dropout rates of 15- through 24-year-olds who dropped out of grades 10–12, by family income: October 1972 through October 2008............................................................................................................................... C-7 C-5 Standard errors for table 6: Status dropout rates and number and distribution of dropouts of 16- through 24-year-olds, by selected characteristics: October 2008 ....... C-9 C-6 Standard errors for table 7: Status dropout rates, number of status dropouts, and population of 16- through 24-year-olds: October 1972 through October 2008 ............ C-10 vii �List of Tables Table Page Appendix C C-7 Standard errors for table 8: Status dropout rates of 16- through 24-year-olds, by sex and race/ethnicity: October 1972 through October 2008 ....................................... C-12 C-8 Standard errors for table 9: Status completion rates, and number and distribution of completers ages 18–24 not currently enrolled in high school or below, by selected characteristics: October 2008.......................................................................... C-14 C-9 Standard errors for table 10: Status completion rates, number of completers, and population of 18- through 24-year-olds: October 1972 through October 2008 ............ C-15 C-10 Standard errors for table 11: Status completion rates of 18- through 24-year-olds not currently enrolled in high school or below, by sex and race/ethnicity: October 1972 through October 2008 .......................................................................................... C-17 C-11 Standard errors for figure 3: Status dropout rates of 16- through 24-year-olds, by race/ethnicity and sex: October 2008 ............................................................................ C-18 C-12 Standard errors for figure 5: Status completion rates of 18- through 24-year-olds not currently enrolled in high school or below, by race/ethnicity and sex: October 2008............................................................................................................................... C-18 viii �List of Figures Figure Page 1 Event dropout rates of 15- through 24-year-olds who dropped out of grades 10–12, by family income: October 1972 through October 2008 ................................................. 22 2 Status dropout rates of 16- through 24-year-olds, by race/ethnicity: October 1972 through October 2008 ...................................................................................................... 23 3 Status dropout rates of 16- through 24-year-olds, by race/ethnicity and sex: October 2008.................................................................................................................... 24 4 Status completion rates of 18- through 24-year-olds not currently enrolled in high school or below, by race/ethnicity: October 1972 through October 2008 ....................... 25 5 Status completion rates of 18- through 24-year-olds not currently enrolled in high school or below, by race/ethnicity and sex: October 2008 .............................................. 26 6 Averaged freshman graduation rates of public high school students, by state: School year 2007–08.................................................................................................................... 27 ix ��Introduction Dropping out of high school is related to a number of negative outcomes. For example, the median income of persons ages 18 through 67 who had not completed high school was roughly $23,000 in 2008.1 By comparison, the median income of persons ages 18 through 67 who completed their education with at least a high school credential, including a General Educational Development (GED) certificate, was approximately $42,000. Over a person’s lifetime, this translates into a loss of approximately $630,000 in income for a person who did not complete high school compared with a person with at least a high school credential (Rouse 2007).2 Among adults ages 25 and older, a lower percentage of dropouts are in the labor force compared with adults who earned a high school credential. Among adults in the labor force, a higher percentage of dropouts are unemployed compared with adults who earned a high school credential (U.S. Department of Labor 2010). Further, dropouts ages 25 or older reported being in worse health than adults who are not dropouts, regardless of income (Pleis, Lucas, and Ward 2009). Dropouts also make up disproportionately higher percentages of the nation’s prison and death row inmates.3 Comparing those who drop out of high school with those who complete high school, the average high school dropout is associated with costs to the economy of approximately $240,000 over his or her lifetime in terms of lower tax contributions, higher reliance on Medicaid and Medicare, higher rates of criminal activity, and higher reliance on welfare (Levin and Belfield 2007).4 This report builds upon a series of National Center for Education Statistics (NCES) reports on high school dropout and completion rates that began in 1988. It presents estimates of rates in 2008, provides data about trends in dropout and completion rates over the last three and a half decades (1972–2008), 5 and examines the characteristics of high school dropouts and high school 1 U.S. Department of Commerce, Census Bureau, Current Population Survey (CPS), March 2009. These are not all high school dropouts: 1.0 percent of persons ages 18 through 67 were enrolled in high school in 2008 (U.S. Department of Commerce, Census Bureau, Current Population Survey [CPS], October 2008). 2 Rouse estimates a lifetime loss of $550,000 using 2004 March CPS data. The estimate here is adjusted for inflation between March 2004 and March 2008 using March-to-March consumer price index adjustments. 3 Estimates from the most recent data available indicate that approximately 34 percent of federal and state inmates (data from 2004) and 50 percent of persons on death row (data from 2008) lack a high school credential (U.S. Department of Justice 2004, 2009). Although not strictly comparable because of different age ranges considered, estimates for those 25 and older in the general population during the same years indicate that about 15 percent were dropouts (U.S. Department of Commerce, Census Bureau 2004, 2007). 4 Levin and Belfield estimate costs at $209,000 as of 2004. The estimate here is adjusted for inflation between 2004 and 2008 using March 2004 and March 2008 consumer price indexes. 5 Trend analyses have shown a pattern of decline in event dropout rates prior to 1990, a brief upward trend from 1991 through 1995, and then another decline through 2008. As a result, in this report, overall trends from 1972 to 2008 are reported, as well as separate trends from 1972 through 1990, 1990 through 1995, and 1995 through 2008, to increase the understanding of patterns over time in these rates. 1 �Introduction completers in 2008. Four rates are presented to provide a broad picture of high school dropouts and completers in the United States, with the event dropout rate, the status dropout rate, the status completion rate, and the averaged freshman graduation rate each contributing unique information. • The event dropout rate estimates the percentage of high school students who left high school between the beginning of one school year and the beginning of the next without earning a high school diploma or an alternative credential (e.g., a GED). This report presents a national event dropout rate for students attending both public and private schools using the Current Population Survey (CPS), and state event dropout rates for public high school students using the Common Core of Data (CCD).6 Event dropout rates can be used to track annual changes in the dropout behavior of students in the U.S. school system. • The status dropout rate reports the percentage of individuals in a given age range who are not in school and have not earned a high school diploma or an alternative credential. The rate is calculated using CPS data. It focuses on an overall age group as opposed to individuals in the U.S. school system, so it can be used to study general population issues. • The status completion rate indicates the percentage of individuals in a given age range who are not in high school and who have earned a high school diploma or an alternative credential, irrespective of when the credential was earned.7 The rate is calculated using CPS data. It focuses on an overall age group as opposed to individuals in the U.S. school system, so it can be used to study general population issues.8 • The averaged freshman graduation rate estimates the proportion of public high school freshmen who graduate with a regular diploma 4 years after starting 9th grade. The rate is calculated using data from the CCD. It focuses on public high school students as opposed to all high school students or the general population and is designed to provide an estimate of on-time graduation from high school. Thus, it provides a measure of the extent to which public high schools are graduating students within the expected period of 4 years. Data presented in this report are drawn from the annual October Current Population Survey (CPS), the annual Common Core of Data (CCD) collections, and the annual General Education Development Testing Service (GEDTS) statistical reports. Data in the CPS files are collected through household interviews and are representative of the civilian, noninstitutionalized population in the United States, including students attending public and private schools. The CCD data are collected from state education agencies about all public schools and school systems in the United States, and contain aggregates of administrative record data kept by these agencies that are representative of all public school students in this country. The GEDTS data are also built from administrative record data kept by the testing service, and contain information 6 These datasets are described briefly in the main text and in more detail in appendix A. The status completion rate is not the inverse of the status dropout rate (i.e., status completion does not equal 100 minus the status dropout rate). The rates are based on different age ranges, and the completion rate excludes high school students from its denominator, whereas high school students are included in the denominator of the status dropout rate. 8 Seastrom et al. (2006a) refer to this rate as the “Current Population Survey High School Completion Indicator.” 7 2 �Introduction about all GED test takers (data presented in this report are only for individuals in the 50 states and the District of Columbia).9 As with all data collections, those used in this report are useful for calculating some types of estimates, but poorly suited for calculating other types. For example, CPS data are well suited for studying the civilian, noninstitutionalized population in the United States, including students attending public and private schools, but do not provide information about military personnel or individuals residing in group quarters, such as prison inmates or patients in long-term medical facilities. Data from the CCD are appropriate for studying public school students in a given year, but do not provide information on private school students. GEDTS data are helpful for identifying the number of people who take and pass the GED examination in a given year, but do not contain information about schools that GED test takers attended before taking the GED test. In addition, none of the datasets track individual students over time, limiting their usefulness for studying processes and precise time lines associated with completing high school or dropping out.10 All changes or differences noted in this report were tested using Student’s t statistic and are statistically significant at the p ≤ .05 level. When significance tests fail to meet the p ≤ .05 criterion and the comparison is of substantive interest, terminology such as “no measurable difference was found” is used in this report. Regression analysis was used to test for trends across age groups and over time. Analyses did not include any adjustments for multiple comparisons. Standard error tables are available in appendix C. 9 Appendix A of this report contains information about the three data collections and describes in detail how the rates reported here were computed. 10 Several states have student-level administrative record systems that follow student progress over time that can be used for this kind of analysis. NCES is supporting the development of similar systems across additional states (see http://nces.ed.gov/programs/slds/ for details), and periodically conducts national-level longitudinal studies of high school students that can be used for such analysis, as in the High School Longitudinal Study. 3 ��Findings National Event Dropout Rates The national event dropout rate presented here is based on data from the CPS and is an estimate of the percentage of both private and public high school students who left high school between the beginning of one school year and the beginning of the next without earning a high school diploma or an alternative credential (e.g., a GED). Specifically, the rate describes the percentage of youth ages 15 through 24 in the United States who dropped out of grades 10–12 from either public or private schools in the 12 months between one October and the next (e.g., October 2007 to October 2008).11 The measure provides information about the rate at which U.S. high school students are leaving school without a successful outcome. As such, it can be used to study student experiences in the U.S. secondary school system in a given year. It is not well suited for studying how many people in the country lack a high school credential irrespective of whether they attended U.S. high schools, nor does it provide a picture of the dropout problem more generally because it only measures how many students dropped out in a single year, and students may reenter the school system after that time. More detail about the definition and computation of the event dropout rate and other rates in this report can be found in appendix A. • Event dropout rates: On average, 3.5 percent of students who were enrolled in public or private high schools in October 2007 left school before October 2008 without completing a high school program (table 1). No measurable change was detected in the event dropout rate between 2007 and 2008 (3.5 percent in both years); however, since 1972, event dropout rates have trended downward, from 6.1 percent in 1972 to 3.5 percent in 2008 (figure 1 and table 2).12 Declines occurred primarily from 1972 through 1990, when the rate reached 4.0 percent. From 1990 through 1995, event rates increased, but then trended downward again from 1995 through 2008. These fluctuations during the 1990s and early to mid-2000s resulted in no measurable difference between the 1990 and 2008 event dropout rates. • Event dropout rates by sex: There was no measurable difference in the 2008 event dropout rates for males and females, a pattern generally found since 1972 (tables 1 and 3). Exceptions to this pattern occurred in 4 years—1974, 1976, 1978, and 2000—when males had measurably higher event dropout rates than females. 11 Data about 9th-grade dropouts are not available in the Current Population Survey (see appendix A for more information). The state event dropout rates for public high school students presented later in this report are based on the Common Core of Data, which includes 9th-graders. 12 Trend analyses were conducted using regressions. See appendix A for more details. 5 �Findings • Event dropout rates by race/ethnicity:13 Between October 2007 and October 2008, Black and Hispanic students in public and private high schools had higher event dropout rates than White students (table 1). The event dropout rate was 6.4 percent for Blacks and 5.3 percent for Hispanics, compared with 2.3 percent for Whites. The general downward trend in event dropout rates over the three and a half decade period from 1972 through 2008 observed in the overall population was also found among Whites, Blacks, and Hispanics (table 3).14 However, the decreases happened at different times over this 36-year period for these racial/ethnic groups. The pattern found among Whites mirrored the overall population: a decrease in event rates from 1972 through 1990, an increase from 1990 through 1995, and another decrease from 1995 through 2008. Blacks also experienced a decline from 1972 through 1990, and an increase from 1990 through 1995, but their event dropout rates fluctuated and no measurable trend was found between 1995 and 2008. Hispanics, on the other hand, experienced no measurable change in their event dropout rates from 1972 through 1990, and no measurable change from 1990 through 1995, but did experience a decline from 1995 through 2008. • Event dropout rates by family income: In 2008, the event dropout rate of students living in low-income families was about four and one-half times greater than the rate of their peers from high-income families (8.7 percent vs. 2.0 percent) (table 1).15 Students from low-, middle-, and high-income families experienced an overall decline in event dropout rates during the three-decade period of the mid-1970s through 2008 (figure 1 and table 4). All three groups of students experienced declines in event dropout rates from 1975 through 1990. Those from low-income families had rates that fell from 15.7 percent to 9.5 percent. Students from middle-income families had rates fall from 6.0 percent to 4.3 percent and those from high-income families had rates fall from 2.6 percent to 1.1 percent. From 1990 to 1995, students from low-income families experienced an upward trend in rates from 9.5 percent to 13.3 percent, while their peers from middle- and high-income families experienced no measurable change. In the last 13 years (1995–2008), the event rates for lowincome and middle-income families trended downward. While event dropout rates for students from high-income families fluctuated and no measurable trend was found during the 13 All of the 2008 tables report data for the following four racial/ethnic categories: White (non-Hispanic), Black (non-Hispanic), Asian/Pacific Islander (non-Hispanic), and Hispanic. The first three categories consist of individuals who identified as only one race, and who did not identify as Hispanic. A fourth category consists of Hispanics of all races and racial combinations. For 2008 status dropouts and status completion rates (tables 6 and 9), results for two additional race/ethnic groups are presented: American Indian/Alaska Native (non-Hispanic) and persons of two or more races (non-Hispanic). Because of small sample sizes, American Indians/Alaska Natives and persons of two or more races are included in the total but not shown separately for 2008 event dropout rates and event dropout, status dropout, and status completion results for prior years. For simplicity, the terms “Black,” “Hispanic,” “Asian/Pacific Islander,” “American Indian/Alaska Native,” and “two or more races” are used in the text of this report without the “(non-Hispanic)” label. 14 The trend analyses conducted to examine this three-and-a-half-decade period are based on annual rate estimates for each year from 1972 through 2008. Separate trend analyses were also conducted for each racial/ethnic group separately for trends across the three shorter time periods indicated in the bullet: 1972–1990, 1990–1995, and 1995–2008. Because of small sample sizes for many of the earlier years, reliable trend analyses could not be conducted for Asians/Pacific Islanders, American Indians/Alaska Natives, and persons of two or more races. 15 “Low income” is defined here as the lowest 20 percent of all family incomes, while “high income” refers to the top 20 percent of all family incomes. In 2008, low-income families included those with $18,985 or less in family income, while high-income families included those with $88,080 or more in family income. For respondents missing data for family income (17.4 percent of the weighted sample in table 1), cold-deck procedures were used to impute data. 6 �Findings same 13-year period, there was no measurable difference between their 1995 and 2008 rates (2.0 percent in both years). • Event dropout rates by age: Students who pursued a high school education past the typical high school age were at higher risk than others of becoming an event dropout (table 1). The 2008 event dropout rates for students in the typical age range for fall high school enrollment (ages 15 through 17) were lower than those for older students (ages 20 through 24). Specifically, 2.4 percent of 15- through 16-year-olds and 3.1 percent of 17-year-olds dropped out in the 1-year reference period, compared with 14.9 percent of 20- through 24-year-olds. • Event dropout rates by region: In 2008, the event dropout rates for high school students in the South (4.3 percent) were higher than for their peers in the Northeast (2.3 percent) and Midwest (2.7 percent), and event dropout rates for students in the West (4.1 percent) were higher than those for students in the Northeast (table 1). State Event Dropout Rates for Public High School Students State-level event dropout rates for public high school students are calculated using data from 1993 through 2008 from the CCD. The rates reported in this publication reflect the percentage of public school students who were enrolled in grades 9–12 at some point during the 2007–08 school year but were not enrolled in school in October 2008 and had not earned a high school diploma or completed a state- or district-approved education program.16 Some state or district education programs include special education programs and district- or state-sponsored GED programs. State event dropout rates are useful for evaluating the performance of public high school systems in reporting states. They do not include information about individuals outside the public school system. Rates are presented for the District of Columbia and 49 states that submitted data that could be reported for the 2007–08 school year; a “reporting states” rate was calculated based on data from the reporting states (table 5). Dropout counts from Vermont were suppressed due to a high frequency of missing data. • State event dropout rates for 9th- through 12th-grade public high school students: The 2007–08 CCD event dropout rates ranged from 1.7 percent in Indiana and New Jersey to 7.5 percent in Louisiana (table 5). In all, event dropout rates for public school students in grades 9–12 were lower than 3 percent in fifteen states: Indiana and New Jersey, 1.7 percent; Idaho, 2.0 percent; Alabama, 2.2 percent; South Dakota and Wisconsin, 2.3 percent; North Dakota, 2.4 percent; Kansas and Nebraska, 2.5 percent; Pennsylvania, 2.6 percent; Virginia, 2.7 percent; Connecticut, Kentucky, and Minnesota, 2.8 percent; and Iowa, 2.9 percent. Six states had event dropout rates of 6 percent or more: Delaware, 6.0 percent; Michigan, 6.2 percent; Colorado, 6.4 percent; Arizona, 6.7 percent; Alaska, 7.3 percent; and Louisiana, 7.5 percent. 16 Some states report using an alternative 1-year period from one July to the next. Rates for those states are presented because event dropout rates based on the July-to-July calendar are comparable to those calculated using an October-to-October calendar (Winglee et al. 2000). 7 �Findings • Combining data from the 49 reporting states and the District of Columbia, approximately 613,000 public school students dropped out of grade 9–12 during the 2007–08 school year (data not shown in tables). This translates into an event dropout rate of 4.1 percent.17 National Status Dropout Rates The status dropout rate measures the percentage of individuals who are not enrolled in high school and who do not have a high school credential. The status dropout rate is higher than the event rate in a given year because the status dropout rate includes all dropouts in a particular age range, regardless of when or where they last attended school, including individuals who may have never attended school in the United States. Based on the 16- through 24-year-old age range, the measure provides an indicator of the proportion of young people who lack a high school credential. While useful for measuring overall educational attainment among young adults in the United States, the status dropout rate is not useful as an indicator of the performance of schools because it includes those who never attended school in the United States. Using data from the CPS, the status dropout rate in this report shows the percentage of young people ages 16 through 24 who are out of school and who have not earned a high school diploma or equivalency credential (e.g., a GED). • Status dropout rates: In October 2008, approximately 3.0 million 16- through 24-year-olds were not enrolled in high school and had not earned a high school diploma or alternative credential (table 6). These status dropouts accounted for 8.0 percent of the 38 million noninstitutionalized, civilian 16- through 24-year-olds living in the United States. Among all individuals in this age group, status dropout rates trended downward between 1972 and 2008, from 14.6 percent to 8.0 percent (figure 2 and table 7). The status dropout rate of 2008 was lower than that of 1990, unlike the event dropout rate where no differences were detected between these 2 years. • Status dropout rates by sex: Males ages 16–24 had higher status dropout rates than females in 2008 (8.5 percent vs. 7.5 percent) (table 6). • Status dropout rates by race/ethnicity: The 2008 status dropout rates for persons of two or more races (4.2 percent), Asian/Pacific Islanders (4.4 percent), and Whites (4.8 percent) were the lowest among the racial/ethnic groups considered in this report. The Black status dropout rate was lower than the rate for Hispanics (9.9 percent and 18.3 percent, respectively) (table 6). 17 The number of event dropouts based on CCD data is significantly higher than the number of event dropouts based on CPS data, after restricting CCD counts to grades 10–12 to align with grade-ranges used in CPS estimates. This may be due in part to how the different sources of data account for alternative credentials like the GED. Students earning GEDs through public school systems are generally not counted as dropouts in the CCD, while students who leave the public school system are considered dropouts. Irrespective of how a GED is obtained, CPS data do not count them as dropouts. When this reporting difference is accounted for, estimates from both sources are not detectably different. 8 �Findings Since 1972 the difference between the status dropout rates of Whites and Blacks has narrowed (figure 2 and table 8). This narrowing of the gap occurred during the 1980s, with no measurable change during the 1970s or between 1990 and 2008. The percentage of Hispanics ages 16–24 who were dropouts was consistently higher than that of Blacks and Whites throughout the 36-year period of 1972–2008 (figure 2 and table 8). White and Black status dropout rates have fallen significantly since 1972; the rates for Whites fell from 12.3 to 4.8 percent and the rates for Blacks declined from 21.3 to 9.9 percent. Between 1972 and 1990, Hispanic status dropout rates were generally consistent, but since 1990 they have demonstrated a downward trend, falling from 32.4 percent to 18.3 percent. In 2008, some 32.8 percent of Hispanic 16- through 24-year-olds born outside the United States were status high school dropouts (table 6). Hispanics born in the United States had lower status dropout rates than immigrant Hispanics (10.5 percent and 10.8 percent for “first generation” and “second generation or higher,” respectively).18 In each “recency of immigration” category in table 6, Hispanic youth had higher status dropout rates than nonHispanic youth. • Status dropout rates by sex and race/ethnicity: Dropout rates for Whites and Hispanics varied by sex (figure 3). Among White students, 5.4 percent of males were status dropouts in 2008 compared with 4.2 percent of females. Hispanic males also had higher status dropout rates than their female counterparts (19.9 percent vs. 16.7 percent, respectively). No differences by sex were detected in status dropout rates for Blacks, Asian/Pacific Islanders, American Indian/Alaska Natives, or persons of two or more races. • Status dropout rates by age: Persons ages 16 and 17 had lower status dropout rates in 2008 (2.2 percent and 5.0 percent, respectively) than 18- through 24-year-olds (7.8 percent to 9.9 percent), at least in part because most 16- and 17-year-olds were still actively pursuing a high school diploma (table 6).19 • Status dropout rates by region: In 2008, the Northeast had the lowest status dropout rates (5.6 percent) and the South and the West had the highest (8.8 percent and 9.1 percent, respectively) (table 6). Dropouts were disproportionately concentrated in the South and the West. In 2008, some 35.9 percent of 16- through 24-year-olds lived in the South while 39.6 percent of all status dropouts lived there. Similarly, 23.8 percent of the 16- through 24-yearold population lived in the West but 27.0 percent of status dropouts lived there. In contrast, dropouts were underrepresented in the Northeast. Some 17.9 percent of 16- through 24-yearolds lived in the Northeast, but 12.5 percent of status dropouts lived there. 18 Individuals defined as “first generation” were born in the 50 states or the District of Columbia, and one or both of their parents were born outside the 50 states or the District of Columbia. Individuals defined as “second generation or higher” were born in the 50 states or the District of Columbia, as were both of their parents. 19 In 2008, data from the CPS show that high school enrollment rates by age group were 95.2 percent for 16-year-olds, 88.8 percent for 17-year-olds, 27.7 percent for 18-year-olds, 6.6 percent for 19-year-olds, and 0.9 percent for 20- through 24-year-olds (estimates not shown in tables). 9 �Findings National Status Completion Rates The status completion rate indicates the percentage of young people who have left high school and who hold a high school credential. The rate reported here is based on CPS data and represents the percentage of 18- through 24-year-olds who are not enrolled in high school and who have earned a high school diploma or an alternative credential, including a GED certificate. The status completion rate includes individuals who may have completed their education outside the United States, so the rate is not suited for measuring the performance of the education system in this country. The status completion rate is not the inverse of the status dropout rate (i.e., status completion does not equal 100 minus the status dropout rate). The rates are based on different age ranges, with the status dropout rate reported for 16- through 24-year-olds and the status completion rate reported for 18- through 24-year-olds. The completion rate excludes high school students from its denominator, whereas high school students are included in the denominator of the status dropout rate. • Status completion rates: In 2008, some 89.9 percent of 18- through 24-year-olds not enrolled in high school had received a high school diploma or equivalency credential (table 9).20 Overall, status completion rates have increased since 1972 (figure 4 and table 10), but during the 1970s they remained largely flat. Since 1980, the rate has shown an upward trend, starting at 83.9 percent in 1980 and rising to 89.9 percent in 2008. • Status completion rates by sex: Females ages 18–24 who were not enrolled in high school in 2008 had a higher status completion rate (90.5 percent) than their male counterparts (89.3 percent) (table 9). • Status completion rates by race/ethnicity: In 2008, among 18- through 24-year-olds not currently enrolled in high school, Asians/Pacific Islanders (95.5 percent), Whites (94.2 percent) and persons of two or more races (94.2 percent) had status completion rates of over 90 percent. All three had rates that were higher than those for Blacks (86.9 percent), American Indians/Alaska Natives (82.5 percent), and Hispanics (75.5 percent) (table 9). Status completion rates for Whites, Blacks, and Hispanics exhibited no general patterns of change during the 1970s, but rates trended upward for each group between 1980 and 2008 (figure 4 and table 11). In 2008, some 59.8 percent of foreign-born21 Hispanics ages 18–24 who were not currently enrolled in high school had completed high school (table 9). Compared to foreign-born Hispanics, status completion rates were higher for Hispanics born in the United States (85.1 percent for “first generation” and 85.8 percent for “second generation or higher”), although in each immigrant category Hispanics had higher status completion rates than non-Hispanics. 20 Considering all 18- through 24-year-olds, irrespective of enrollment status, 84.7 percent held a high school credential in October 2008 (estimates not shown in tables). 21 Foreign-born refers to people who were born outside of the 50 states and the District of Columbia. 10 �Findings • Status completion rates by sex and race/ethnicity: For Whites, Blacks, and Hispanics, status completion rates differed by sex (figure 5). In 2008, White and Hispanic females had higher status completion rates than their male counterparts. Specifically, 94.9 percent of White females and 77.9 percent of Hispanic females had completed high school in 2008, compared with 93.6 percent of White males and 73.2 percent of Hispanic males, respectively. Among Blacks, males had higher status completion rates (89.1 percent vs. 85.0 percent). No measurable differences by sex were detected between the status completion rates of American Indians/Alaska Natives, Asians/Pacific Islanders, and persons of two or more races. • Status completion rates by region: Consistent with status dropout data by region, 18through 24-year-olds in the West, South, and Midwest had lower status completion rates (88.7 percent, 89.1 percent, and 90.3 percent, respectively) than their contemporaries in the Northeast (92.7 percent). Additionally, the West had lower rates than the Midwest (table 9). General Educational Development (GED) Credentials and National Status Completion Rates General Educational Development (GED) programs allow individuals who would otherwise lack a high school credential because they did not complete a regular high school program of study, to obtain an alternative credential. Not completing a regular high school program can occur for several reasons including dropping out of high school and immigrating into the country without ever enrolling in U.S. high schools. The GED is accepted by most colleges and universities that require a high school diploma for admission, and most companies that have positions requiring a high school diploma accept the GED as an alternative credential (American Council on Education 2009). While GEDs provide an important opportunity for those who do not earn a regular high school diploma to obtain a high school credential, GED recipients tend to fare significantly worse than those holding regular diplomas across a range of measures. For example, while GED recipients and regular diploma recipients who complete postsecondary programs experience the same economic benefits from the programs, GED recipients attend and complete postsecondary programs at much lower rates than regular diploma holders. Also, while high school dropouts with relatively low cognitive skills experience improved incomes if they earn a GED, dropouts with relatively high cognitive skills do not experience increased earnings after earning a GED (see Boesel, Alsalam, and Smith 1998, and Tyler 2003 for overviews of GED research). To better understand how the rate of GED receipt relates to different rates presented in this report, data from the GED Testing Service are used to estimate the number of GED holders in 11 �Findings the civilian, noninstitutionalized population in 2008.22 Estimates are provided for 18- through 24year-olds to correspond to age ranges used for the status completion rates.23 • National estimates of 18- through 24-year-olds with a GED in 2008: There were approximately 1,500,000 persons ages 18 through 24 in 2008 who had passed the GED exam in 2008 or in prior years (data not shown in tables). This represents 5.5 percent of the civilian, noninstitutionalized population of 18- through 24-year-olds who were not in high school in 2008. Subtracting out those who passed the GED exam, the status completion rate in 2008 for regular high school diploma holders and those holding alternative credentials other than a GED was 84.4 percent (data not shown in tables).24 Focusing on the 18- through 24-year-old population without consideration of high school enrollment, approximately 84.7 percent held some form of high school credential in 2008 with 5.2 percent holding a GED and 79.5 percent holding a regular high school diploma or other alternative credential (data not shown in tables).25 Averaged Freshman Graduation Rates for Public School Students The averaged freshman graduation rate (AFGR) provides an estimate of the percentage of public high school students who graduate on time—that is, 4 years after starting 9th grade—with a regular diploma. The rate uses aggregate student enrollment data to estimate the size of an incoming freshman class and aggregate counts of the number of diplomas awarded 4 years later. The incoming freshman class size is estimated by summing the enrollment in 8th grade for 1 year, 9th grade for the next year, and 10th grade for the year after and then dividing by 3. The averaging is intended to account for higher grade retention rates in the 9th grade. Although not as accurate as an on-time graduation rate computed from a cohort of students using individual student record data, this estimate of an on-time graduation rate can be computed with currently available data. The AFGR was selected from a number of alternative estimates that can be 22 The number of GED holders was based on counts of those who passed the GED exam. Counts of successful GED examinees each year are published by GEDTS. It is possible to pass the GED exam and not obtain a GED, so estimates here represent an upper bound of GED holders in the population. To determine how many people in a given age range have earned a GED requires summation of reported data over multiple years of GEDTS reports. For example, the number of 18- through 24-year-olds in 2008 who had passed the GED exam was estimated by taking the sum of those who passed the exam in 2008 at ages 18–24 plus those who passed the exam in 2007 at ages 17–23 plus those who passed the exam in 2006 at ages 16–22, and so on. See appendix A of this report for details of this calculation. 23 Civilians in the noninstitutionalized population are the focus of the status dropout and completion rates. To align the GED estimates with this population, data from the Survey of Inmates in State and Federal Correctional Facilities, 2004 prorated to 2008 and data provided by the Defense Manpower Data Center for active duty military personnel in 2008 were used. See appendix A of this report for details of how the GED estimates were aligned with the noninstitutionalized population. 24 The CPS data used for the status completion rate include those holding alternative credentials such as a GED in the count of completers. Other alternative credentials exist so removing GED counts from the counts of completers does not result in a count of regular high school diploma holders. 25 Similar estimates could be made in reference to the 16- through 24-year-old population, which is the focus of the status dropout rate. There were approximately 1,597,000 persons ages 16 through 24 in 2008 who had passed the GED exam in 2008 or prior years (data not shown in tables). This represents 4.3 percent of the civilian, noninstitutionalized population of 16- through 24-year-olds in 2008. 12 �Findings calculated using cross-sectional data based on a technical review and analysis of a set of alternative estimates (Seastrom et al. 2006a, 2006b). AFGR estimates are based on the CCD “State Nonfiscal Survey of Public Elementary/Secondary Education,” with ungraded26 enrollments distributed proportional to reported enrollments by grade. Rates are presented for the 49 states and the District of Columbia that submitted data necessary to estimate AFGR for the 2007–08 school year; a national-level rate was calculated for reporting states based on data from the 49 states and the District of Columbia. Diploma count data for 2007–08 are missing for South Carolina. • National averaged freshman graduation rate for public school students: The AFGR among public school students in the United States for the class of 2007–08 was 74.9 percent (table 12). • State averaged freshman graduation rates for public school students: For the class of 2007–08, the AFGR ranged from 51.3 percent in Nevada to 89.6 percent in Wisconsin (figure 6 and table 12). Seventeen states had rates of 80.0 percent or higher—Connecticut, Idaho, Illinois, Iowa, Maryland, Massachusetts, Minnesota, Missouri, Montana, Nebraska, New Hampshire, New Jersey, North Dakota, Pennsylvania, South Dakota, Vermont, and Wisconsin. Eight states had rates below 70.0 percent—Alabama, Alaska, Florida, Georgia, Louisiana, Mississippi, Nevada, and New Mexico—as did the District of Columbia. • Changes in rates from 2006–07 to 2007–08: The AFGR among public school students in the graduating class of 2007–08 was higher than the rate for the class of 2006–07 (74.9 percent versus 73.9 percent) (table 13).27 A comparison of data from 2007–08 to data from the prior school year, 2006–07, shows a percentage point or greater increase in the AFGR for 16 states and the District of Columbia. The AFGR decreased by a percentage point or more for six states during that same time period. 26 Ungraded students are those who are assigned to a class or program that does not have standard grade designations. 27 South Carolina did not report diploma information for 2007–08. Data were available to estimate the number of first-time freshmen in 2004–05 (the graduating class of 2007–08). If the AFGR for 2006–07 in South Carolina were applied to the estimate of first-time freshmen in 2004–05, and the freshmen count and resulting diploma count added to national totals, the AFGR for the United States would have been 74.7 percent in 2007–08. 13 ��References American Council on Education, GED Testing Service. (1991–2002). Who Took the GED? GED Annual Statistical Report. Washington, DC: Author. American Council on Education, GED Testing Service. (2003–06). Who Passed the GED Tests? Annual Statistical Report. Washington, DC: Author. American Council on Education, GED Testing Service. (2007). 2006 GED Testing Program Statistical Report. Washington, DC: Author. American Council on Education, GED Testing Service. (2008). 2007 GED Testing Program Statistical Report. Washington, DC: Author. American Council on Education, GED Testing Service. (2009). 2008 GED Testing Program Statistical Report. Washington, DC: Author. Boesel, D., Alsalam, N., and Smith, T.M. (1998). Educational and Labor Market Performance of GED Recipients. U.S. Department of Education. Washington, DC. Cahoon, L. (2005). Source and Accuracy Statement for the October 2004 CPS Microdata File on School Enrollment. Washington, DC: U.S. Department of Commerce, Census Bureau. Chapman, C., and Hoffman, L. (2007). Event Dropout Rates for Public School Students in Grades 9–12: 2002–03 and 2003–04 (NCES 2007-026). National Center for Education Statistics, Institute of Education Sciences, U.S. Department of Education. Washington, DC. Gujarati, D. (1998). Basic Econometrics (2nd ed.). New York: McGraw Hill, Inc. Kaufman, P., Alt, M.N., and Chapman, C. (2004). Dropout Rates in the United States: 2001 (NCES 2005-046). National Center for Education Statistics, Institute of Education Sciences, U.S. Department of Education. Washington, DC. Laird, J., DeBell, M., Kienzl, G., and Chapman, C. (2007). Dropout Rates in the United States: 2005 (NCES 2007-059). National Center for Education Statistics, Institute of Education Sciences, U.S. Department of Education. Washington, DC. 15 �References Levin, H.M., and Belfield, C.R. (2007). Educational Interventions to Raise High School Graduation Rates. In C.R. Belfield and H.M. Levin (Eds.), The Price We Pay: Economic and Social Consequences of Inadequate Education (pp. 177–199). Washington, DC: Brookings Institution Press. Mishel, L., and Roy, J. (2006). Rethinking High School Graduation Rates and Trends. Washington, DC: Economic Policy Institute. No Child Left Behind Act of 2001, P.L. 107-110, 115 Stat. 1425 (2002). Pleis, J.R., Lucas, J.W., and Ward, B.W. (2009). Summary Health Statistics for U.S. Adults: National Health Interview Survey, 2008. Vital Health Stat, 10(242). National Center for Health Statistics. Rouse, C.E. (2007). Quantifying the Costs of Inadequate Education: Consequences of the Labor Market. In C.R. Belfield and H.M. Levin (Eds.), The Price We Pay: Economic and Social Consequences of Inadequate Education (pp. 99-124). Washington, DC: Brookings Institution Press. Sable, J., and Garofano, A. (2007). Public Elementary and Secondary School Student Enrollment, High School Completions, and Staff From the Common Core of Data: School Year 2005–06 (NCES 2007-352). National Center for Education Statistics, Institute of Education Sciences, U.S. Department of Education. Washington, DC. Sable, J., and Naum, J. (2004a). Documentation to the NCES Common Core of Data Local Education Agency Universe Survey Dropout and Completion Data File: School Year 1997–98 (NCES 2001-302R). National Center for Education Statistics, Institute of Education Sciences, U.S. Department of Education. Washington, DC. Sable, J., and Naum, J. (2004b). Documentation to the NCES Common Core of Data Local Education Agency Universe Survey Dropout and Completion Data File: School Year 1998–99 (NCES 2002-310R). National Center for Education Statistics, Institute of Education Sciences, U.S. Department of Education. Washington, DC. Sable, J., and Naum, J. (2004c). Documentation to the NCES Common Core of Data Local Education Agency Universe Survey Dropout and Completion Data File: School Year 1999–2000 (NCES 2002-384R). National Center for Education Statistics, Institute of Education Sciences, U.S. Department of Education. Washington, DC. 16 �References Sable, J., and Naum, J. (2004d). Documentation to the NCES Common Core of Data Local Education Agency Universe Survey Dropout and Completion Data File: School Year 2000–01 (NCES 2002-315R). National Center for Education Statistics, Institute of Education Sciences, U.S. Department of Education. Washington, DC. Sable, J., Naum, J., and Thomas, J.M. (2004). Documentation to the NCES Common Core of Data Local Education Agency Universe Survey Dropout and Completion Data File: School Year 2001–02 (NCES 2005-349). National Center for Education Statistics, Institute of Education Sciences, U.S. Department of Education. Washington, DC. Seastrom, M., Chapman, C., Stillwell, R., McGrath, D., Peltola, P., Dinkes, R., and Xu, Z. (2006a). User’s Guide to Computing High School Graduation Rates, Volume 1: Review of Current and Proposed Graduation Indicators (NCES 2006-604). National Center for Education Statistics, Institute of Education Sciences, U.S. Department of Education. Washington, DC. Seastrom, M., Chapman, C., Stillwell, R., McGrath, D., Peltola, P., Dinkes, R., and Xu, Z. (2006b). User’s Guide to Computing High School Graduation Rates, Volume 2: Technical Evaluation of Proxy Graduation Indicators (NCES 2006-605). National Center for Education Statistics, Institute of Education Sciences, U.S. Department of Education. Washington, DC. Seastrom, M., Hoffman, L., Chapman, C., and Stillwell, R. (2005). The Averaged Freshman Graduation Rate for Public High Schools From the Common Core of Data: School Years 2001–02 and 2002–03 (NCES 2006-601). National Center for Education Statistics, Institute of Education Sciences, U.S. Department of Education. Washington, DC. Seastrom, M., Hoffman, L., Chapman, C., and Stillwell, R. (2007). The Averaged Freshman Graduation Rate for Public High Schools From the Common Core of Data: School Years 2002–03 and 2003–04 (NCES 2006-606rev). National Center for Education Statistics, Institute of Education Sciences, U.S. Department of Education. Washington, DC. Stillwell, R., and Hoffman, L. (2009). Public School Graduates and Dropouts From the Common Core of Data: School Year 2005–06 (NCES 2008-353rev). National Center for Education Statistics, Institute of Education Sciences, U.S. Department of Education. Washington, DC. 17 �References Stillwell, R. (2010). Public School Graduates and Dropouts From the Common Core of Data: School Year 2007–08 (NCES 2010-341). National Center for Education Statistics, Institute of Education Sciences, U.S. Department of Education. Washington, DC. Tyler, J. (2003). Economic Benefits of the GED: Lessons From Recent Research. Review of Educational Research, 73(3): 369–403. U.S. Department of Commerce, Census Bureau. (2004). Educational Attainment in the United States: 2004. Detailed Tables. Table 10. Washington, DC: Author. Retrieved April 20, 2009, from http://www.census.gov/population/www/socdemo/education/cps2004.html. U.S. Department of Commerce, Census Bureau. (2007). Educational Attainment in the United States: 2006. Detailed Tables. Table 10. Washington, DC: Author. Retrieved April 20, 2009, from http://www.census.gov/population/www/socdemo/education/cps2006.html. U.S. Department of Commerce, Census Bureau. (2009). Current Population Survey, October 2008: School Enrollment and Internet Use Supplement File (Technical Documentation CPS-09). Washington, DC: Author. U.S. Department of Commerce, Census Bureau, Current Population Survey (CPS), October 1972–2007. U.S. Department of Education, National Center for Education Statistics. (n.d.). Documentation to the NCES Common Core of Data Local Education Agency Universe Dropout and Completion Data File: School Years 1991–92 through 1996–97. Washington, DC. Retrieved August 6, 2007, from http://www.nces.ed.gov/ccd/drp7yrag.asp. U.S. Department of Justice, Bureau of Justice Statistics. (2004). Survey of Inmates in State and Federal Correctional Facilities, 2004. Unpublished estimates. ICPSR04572-v1. Ann Arbor, MI: Inter-university Consortium for Political and Social Research [producer and distributor], 2007-02-28. doi:10.3886/ICPSR04572. U.S. Department of Justice, Bureau of Justice Statistics. (2009). Capital Punishment, 2008—Statistical Tables (NCJ-228662). Washington, DC. Retrieved March 4, 2010, from http://bjs.ojp.usdoj.gov/index.cfm?ty=pbdetail&iid=1757. U.S. Department of Labor, Bureau of Labor Statistics. (2010). Tabulations retrieved March 4, 2010, from http://www.bls.gov/cps/cpsa2009.pdf. 18 �References Winglee, M., Marker, D., Henderson, A., Aronstamm Young, B., and Hoffman, L. (2000). A Recommended Approach to Providing High School Dropout and Completion Rates at the State Level (NCES 2000-305). National Center for Education Statistics, U.S. Department of Education. Washington, DC. 19 ��Figures 21 �Figures Figure 1.—Event dropout rates of 15- through 24-year-olds who dropped out of grades 10–12, by family Figure 1.—income: October 1972 through October 2008 Percent 20 20 18 18 16 16 14 Low income 14 12 12 10 10 8 Middle income 8 6 6 4 2 0 1972 Total 4 2 High income 1975 1978 1980 1981 0 1984 1985 1987 1990 1993 1995 1996 1999 2000 2002 2005 2008 Year NOTE: The event dropout rate indicates the percentage of youth ages 15 through 24 who dropped out of grades 10–12 between one October and the next (e.g., October 2007 to October 2008). Dropping out is defined as leaving school without a high school diploma or equivalent credential, such as a General Educational Development (GED) certificate. Low income is defined as the bottom 20 percent of all family incomes for the year; middle income is between 20 and 80 percent of all family incomes; and high income is the top 20 percent of all family incomes. Data on family income are missing for 1974. Estimates beginning with 1987 reflect new editing procedures for cases with missing data on school enrollment items. Estimates beginning with 1992 reflect new wording of the educational attainment item. Estimates beginning with 1994 reflect changes due to newly instituted computer-assisted interviewing. For details about changes in the Current Population Survey (CPS) over time, please see Kaufman, P., Alt, M.N., and Chapman, C. (2004). Dropout Rates in the United States: 2001 (NCES 2005-046). National Center for Education Statistics, Institute of Education Sciences, U.S. Department of Education. Washington, DC. SOURCE: U.S. Department of Commerce, Census Bureau, Current Population Survey (CPS), October 1972–2008. 22 �Figures Figure 2.—Status dropout rates of 16- through 24-year-olds, by race/ethnicity: October 1972 through Figure 2.—October 2008 Percent 40 40 35 35 Hispanic 30 25 30 25 Black, non-Hispanic 20 15 10 20 Total 15 10 White, non-Hispanic 5 0 1972 5 1975 1978 1980 1981 1984 1985 1987 1990 1993 1995 1996 1999 2000 2002 2005 0 2008 Year NOTE: The status dropout rate indicates the percentage of 16- through 24-year-olds who are not enrolled in high school and who lack a high school credential. High school credentials include high school diplomas and equivalent credentials, such as a General Educational Development (GED) certificate. Beginning in 2003, respondents were able to identify themselves as being two or more races. The 2003 through 2008 categories for White (non-Hispanic) and Black (non-Hispanic) contain only respondents who indicated just one race. The Hispanic category includes Hispanics of all races and racial combinations. Due to small sample sizes for some or all of the years shown in the figure, American Indians/Alaska Natives and Asians/Pacific Islanders who are not Hispanic are included in the totals but not shown separately. The Two or more races (non-Hispanic) category is also included in the total in 2003 through 2008 but not shown separately due to small sample sizes. The variability of Hispanic status rates reflects, in part, small Hispanic sample sizes in earlier years of the Current Population Survey (CPS). Beginning with 1987, estimates reflect new editing procedures for cases with missing data on school enrollment items. Estimates beginning with 1992 reflect new wording of the educational attainment item. Estimates beginning with 1994 reflect changes due to newly instituted computer-assisted interviewing. For details about changes in the CPS over time, please see Kaufman, P., Alt, M.N., and Chapman, C. (2004). Dropout Rates in the United States: 2001 (NCES 2005-046). National Center for Education Statistics, Institute of Education Sciences, U.S. Department of Education. Washington, DC. SOURCE: U.S. Department of Commerce, Census Bureau, Current Population Survey (CPS), October 1972–2008. 23 �Figures Figure 3.—Status dropout rates of 16- through 24-year-olds, by race/ethnicity and sex: October 2008 Percent 40 35 30 25 19.9 16.7 20 15 10 8.5 7.5 5 8.7 18.6 11.6 11.1 5.4 4.2 3.9 4.9 3.6 ! 4.8! 0 Total White, Black, non-Hispanic non-Hispanic Hispanic Asian/ Pacific Islander, non-Hispanic Race/ethnicity Male American Two or Indian/ more races, Alaska non-Hispanic Native, non-Hispanic Female ! Interpret data with caution. Due to relatively large standard errors, estimates are unstable. NOTE: The status dropout rate indicates the percentage of 16- through 24-year-olds who are not enrolled in high school and who lack a high school credential. High school credentials include high school diplomas and equivalent credentials, such as a General Educational Development (GED) certificate. Respondents were able to identify themselves as being two or more races. The White (non-Hispanic), Black (non-Hispanic), Asian/Pacific Islander (non-Hispanic), and American Indian/Alaska Native (non-Hispanic) categories consist of individuals who considered themselves to be one race and who did not identify as Hispanic. Non-Hispanics who identified themselves as multiracial are included in the Two or more races (non-Hispanic) category. The Hispanic category consists of Hispanics of all races and racial combinations. SOURCE: U.S. Department of Commerce, Census Bureau, Current Population Survey (CPS), October 2008. 24 �Figures Figure 4.—Status completion rates of 18- through 24-year-olds not currently enrolled in high school or Figure 4.—below, by race/ethnicity: October 1972 through October 2008 Percent 100 100 White, non-Hispanic 80 Total 80 Black, non-Hispanic 60 60 Hispanic 40 40 20 20 0 1972 1975 1978 1980 1981 1984 1985 1987 1990 1993 1995 1996 1999 2000 2002 2005 0 2008 Year NOTE: Status completion rates measure the percentage of 18- through 24-year-olds who are not enrolled in high school and who also hold a high school diploma or equivalent credential, such as a General Educational Development (GED) certificate. Those still enrolled in high school are excluded from the analysis. Beginning in 2003, respondents were able to identify themselves as being two or more races. The 2003 through 2008 categories for White (non-Hispanic) and Black (non-Hispanic) contain only respondents who indicated just one race. The Hispanic category includes Hispanics of all races and racial combinations. Due to small sample sizes for some or all of the years shown in the figure, American Indians/Alaska Natives and Asians/Pacific Islanders who are not Hispanic are included in the totals but not shown separately. The Two or more races (non-Hispanic) category is also included in the total in 2003 through 2008 but not shown separately due to small sample sizes. The variability of Hispanic status rates reflects, in part, small sample size of Hispanics in earlier years of the Current Population Survey (CPS). Beginning with 1987, estimates reflect new editing procedures for cases missing school enrollment item data. Estimates beginning with 1992 reflect new wording of the educational attainment item. Estimates beginning with 1994 reflect changes due to newly instituted computer-assisted interviewing. For details about changes in the CPS over time, please see Kaufman, P., Alt, M.N., and Chapman, C. (2004). Dropout Rates in the United States: 2001 (NCES 2005-046). National Center for Education Statistics, Institute of Education Sciences, U.S. Department of Education. Washington, DC. SOURCE: U.S. Department of Commerce, Census Bureau, Current Population Survey (CPS), October 1972–2008. 25 �Figures Figure 5.—Status completion rates of 18- through 24-year-olds not currently enrolled in high school or Figure 5.—below, by race/ethnicity and sex: October 2008 Percent 100 89.3 90.5 93.6 94.9 89.1 95.1 95.8 85.0 80 73.2 77.9 88.2 95.2 93.1 74.7 60 40 20 0 Total White, Black, non-Hispanic non-Hispanic Hispanic Race/ethnicity Male Asian/ Pacific Islander, non-Hispanic American Two or Indian/ more races, Alaska non-Hispanic Native, non-Hispanic Female NOTE: Status completion rates measure the percentage of 18- through 24-year-olds who are not enrolled in high school and who also hold a high school diploma or equivalent credential, such as a General Educational Development (GED) certificate. Those still enrolled in high school are excluded from the analysis. Respondents were able to identify themselves as being two or more races. The White (non-Hispanic), Black (non-Hispanic), Asian/Pacific Islander (non-Hispanic), and American Indian/ Alaska Native (non-Hispanic) categories consist of individuals who considered themselves to be one race and who did not identify as Hispanic. Non-Hispanics who identified themselves as multiracial are included in the Two or more races (non-Hispanic) category. The Hispanic category consists of Hispanics of all races and racial combinations. SOURCE: U.S. Department of Commerce, Census Bureau, Current Population Survey (CPS), October 2008. 26 �Figures Figure 6.—Averaged freshman graduation rates of public high school students, by state: School year 2007–08 — Not available. NOTE: The averaged freshman graduation rate (AFGR) is an estimate of the percentage of an entering freshman class graduating in 4 years. For 2007–08, it equals the total number of diploma recipients in 2007–08 divided by the average membership of the 8th-grade class in 2003–04, the 9th-grade class in 2004–05, and the 10th-grade class in 2005–06. See table 13 in this report for more information about these state rates. SOURCE: Stillwell, R. (2010). Public School Graduates and Dropouts From the Common Core of Data: School Year 2007–08 (NCES 2010-341), table 5. 27 ��Tables 29 �Tables Table 1.—Event dropout rates and number and distribution of 15- through 24-year-olds who dropped out Table 1.—of grades 10–12, by selected characteristics: October 2008 Event dropout rate (percent) Number of event dropouts (thousands) Population enrolled1 (thousands) Percent of all dropouts Percent of population enrolled Total 3.5 390 11,058 100.0 100.0 Sex Male Female 3.1 4.0 174 216 5,625 5,433 44.6 55.4 50.9 49.1 2.3 6.4 5.3 156 106 101 6,721 1,651 1,898 40.0 27.1 25.9 60.8 14.9 17.2 Characteristic Race/ethnicity2 White, non-Hispanic Black, non-Hispanic Hispanic Asian/Pacific Islander, non-Hispanic 4.0 ! Family income3 Low income Middle income High income 8.7 3.0 2.0 132 196 61 1,527 6,468 3,063 34.0 50.3 15.7 13.8 58.5 27.7 2.4 3.1 3.6 4.9 14.9 74 118 106 40 51 3,133 3,806 2,959 815 345 19.0 30.4 27.2 10.3 13.1 28.3 34.4 26.8 7.4 3.1 8.1 4.6 35 19 434 418 9.0 4.9 3.9 3.8 3.7 1.4 ! 31 11 ! 842 780 8.0 2.7 ! 7.6 7.1 Age4 15–16 17 18 19 20–24 Recency of immigration Born outside the 50 states and District of Columbia Hispanic Non-Hispanic First generation5 Hispanic Non-Hispanic Second generation or higher5 Hispanic Non-Hispanic 5.5 3.3 17 ! 35 259 See notes at end of table. 30 426 622 7,962 4.3 ! 8.9 66.5 3.9 5.6 72.0 �Tables Table 1.—Event dropout rates and number and distribution of 15- through 24-year-olds who dropped out Table 1.—of grades 10–12, by selected characteristics: October 2008—Continued Characteristic Region Northeast Midwest South West Event dropout rate (percent) Number of event dropouts (thousands) Population enrolled1 (thousands) Percent of all dropouts Percent of population enrolled 2.3 2.7 4.3 4.1 46 71 167 106 1,998 2,640 3,847 2,574 11.8 18.1 42.8 27.3 18.1 23.9 34.8 23.3 ! Interpret data with caution. Estimate is unstable because the standard error represents more than 33 percent of the estimate. This is an estimate of the population of 15- through 24-year-olds enrolled during the previous year in high school based on the number of students still enrolled in the current year and the number of students who either graduated or dropped out the previous year. 2 Respondents were able to identify themselves as being two or more races. The White (non-Hispanic), Black (non-Hispanic), and Asian/Pacific Islander (non-Hispanic) categories consist of individuals who considered themselves to be one race and who did not identify as Hispanic. The Hispanic category consists of Hispanics of all races and racial combinations. Due to small sample size, the American Indians/Alaska Natives and those who identified themselves as being two or more races, but not Hispanic are included in the total but are not shown separately. 3 Low income is defined as the bottom 20 percent of all family incomes for 2008; middle income is between 20 and 80 percent of all family incomes; and high income is the top 20 percent of all family incomes. 4 Age when a person dropped out may be 1 year younger, because the dropout event could occur at any time over a 12-month period. 5 Individuals defined as “first generation” were born in the 50 states or the District of Columbia, and one or both of their parents were born outside the 50 states or the District of Columbia. Individuals defined as “second generation or higher” were born in the 50 states or the District of Columbia, as were both of their parents. NOTE: The event dropout rate indicates the percentage of youth ages 15 through 24 who dropped out of grades 10–12 between one October and the next (e.g., October 2007 to October 2008). Dropping out is defined as leaving school without a high school diploma or equivalent credential, such as a General Educational Development (GED) certificate. Detail may not sum to totals because of rounding. SOURCE: U.S. Department of Commerce, Census Bureau, Current Population Survey (CPS), October 2008. 1 31 �Tables Table 2. —Event dropout rates of 15- through 24-year-olds who dropped out of grades 10–12, and number of Table 2.—dropouts and population of 15- through 24-year-olds who were enrolled: October 1972 through Table 2.—October 2008 Year2 Event dropout rate (percent) Number of event dropouts (thousands) Population enrolled1 (thousands) 1972 1973 1974 1975 1976 6.1 6.3 6.7 5.8 5.9 647 674 735 631 641 10,550 10,736 10,894 10,875 10,844 1977 1978 1979 1980 1981 6.5 6.7 6.7 6.1 5.9 729 739 745 655 636 11,178 11,012 11,044 10,758 10,746 1982 1983 1984 1985 1986 5.5 5.2 5.1 5.2 4.7 573 531 504 502 462 10,435 10,146 9,828 9,597 9,828 1987 1988 1989 1990 1991 4.1 4.8 4.5 4.0 4.0 405 460 403 347 348 9,819 9,613 9,001 8,675 8,700 1992 1993 1994 1995 1996 4.4 4.5 5.3 5.7 5.0 383 381 497 544 485 8,716 8,549 9,374 9,509 9,612 1997 1998 1999 2000 2001 4.6 4.8 5.0 4.8 5.0 454 479 519 488 505 9,984 10,079 10,464 10,126 10,187 2002 2003 2004 2005 2006 3.6 4.0 4.7 3.8 3.8 367 429 486 414 407 10,254 10,698 10,385 10,870 10,849 See notes at end of table. 32 �Tables Table 2. —Event dropout rates of 15- through 24-year-olds who dropped out of grades 10–12, and number of Table 2.—dropouts and population of 15- through 24-year-olds who were enrolled: October 1972 through Table 2.—October 2008—Continued Year2 Event dropout rate (percent) Number of event dropouts (thousands) Population enrolled1 (thousands) 2007 2008 3.5 3.5 383 390 10,967 11,058 1 This is an estimate of the population of 15- through 24-year-olds enrolled during the previous year in high school based on the number of students still enrolled in the current year and the number of students who either graduated or dropped out the previous year. 2 Estimates beginning in 1987 reflect new editing procedures for cases with missing data on school enrollment items. Estimates beginning in 1992 reflect new wording of the educational attainment item. Estimates beginning in 1994 reflect changes due to newly instituted computer-assisted interviewing. For details about changes in the Current Population Survey (CPS) over time, please see Kaufman, P., Alt, M.N., and Chapman, C. (2004). Dropout Rates in the United States: 2001 (NCES 2005-046). National Center for Education Statistics, Institute of Education Sciences, U.S. Department of Education. Washington, DC. NOTE: The event dropout rate indicates the percentage of youth ages 15 through 24 who dropped out of grades 10–12 between one October and the next (e.g., October 2007 to October 2008). Dropping out is defined as leaving school without a high school diploma or equivalent credential, such as a General Educational Development (GED) certificate. SOURCE: U.S. Department of Commerce, Census Bureau, Current Population Survey (CPS), October 1972–2008. 33 �Tables Table 3. —Event dropout rates of 15- through 24-year-olds who dropped out of grades 10–12, by sex and Table 3.—race/ethnicity: October 1972 through October 2008 Sex (percent) Race/ethnicity (percent)1 White, nonBlack, nonHispanic Hispanic Hispanic Year2 Total (percent) Male Female 1972 1973 1974 1975 1976 6.1 6.3 6.7 5.8 5.9 5.9 6.8 7.4 5.4 6.6 6.3 5.7 6.0 6.1 5.2 5.3 5.5 5.8 5.0 5.6 9.5 9.9 11.6 8.7 7.4 11.2 10.0 9.9 10.9 7.3 1977 1978 1979 1980 1981 6.5 6.7 6.7 6.1 5.9 6.9 7.5 6.8 6.7 6.0 6.1 5.9 6.7 5.5 5.8 6.1 5.8 6.0 5.2 4.8 8.6 10.2 9.9 8.2 9.7 7.8 12.3 9.8 11.7 10.7 1982 1983 1984 1985 1986 5.5 5.2 5.1 5.2 4.7 5.8 5.8 5.4 5.4 4.7 5.1 4.7 4.8 5.0 4.7 4.7 4.4 4.4 4.3 3.7 7.8 7.0 5.7 7.8 5.4 9.2 10.1 11.1 9.8 11.9 1987 1988 1989 1990 1991 4.1 4.8 4.5 4.0 4.0 4.3 5.1 4.5 4.0 3.8 3.8 4.4 4.5 3.9 4.2 3.5 4.2 3.5 3.3 3.2 6.4 5.9 7.8 5.0 6.0 5.4 ! 10.4 7.8 ! 7.9 7.3 1992 1993 1994 1995 1996 4.4 4.5 5.3 5.7 5.0 3.9 4.6 5.2 6.2 5.0 4.9 4.3 5.4 5.3 5.1 3.7 3.9 4.2 4.5 4.1 5.0 5.8 6.6 6.4 6.7 8.2 6.7 10.0 12.4 9.0 1997 1998 1999 2000 2001 4.6 4.8 5.0 4.8 5.0 5.0 4.6 4.6 5.5 5.6 4.1 4.9 5.4 4.1 4.3 3.6 3.9 4.0 4.1 4.1 5.0 5.2 6.5 6.1 6.3 9.5 9.4 7.8 7.4 8.8 2002 2003 2004 2005 2006 3.6 4.0 4.7 3.8 3.8 3.7 4.2 5.1 4.2 4.1 3.4 3.8 4.3 3.4 3.4 2.6 3.2 3.7 2.8 2.9 4.9 4.8 5.7 7.3 3.8 5.8 7.1 8.9 5.0 7.0 See notes at end of table. 34 �Tables Table 3.—Event dropout rates of 15- through 24-year-olds who dropped out of grades 10–12, by sex and Table 3.—race/ethnicity: October 1972 through October 2008—Continued Sex (percent) Year2 Total (percent) Male Female 2007 2008 3.5 3.5 3.7 3.1 3.3 4.0 Race/ethnicity (percent)1 White, nonBlack, nonHispanic Hispanic Hispanic 2.2 2.3 4.5 6.4 6.0 5.3 ! Interpret data with caution. Estimate is unstable because the standard error represents more than 33 percent of the estimate. Beginning in 2003, respondents were able to identify themselves as being “more than one race.” The 2003 through 2008 White, non-Hispanic and Black, non-Hispanic categories consist of individuals who considered themselves to be one race and who did not identify as Hispanic. The Hispanic category includes Hispanics of all races and racial combinations. Due to small sample sizes for some or all of the years shown in the table, American Indians/Alaska Natives and Asians/Pacific Islanders are included in the totals but not shown separately. The “more than one race” category is also included in the total in 2003 through 2008 but not shown separately due to small sample size. 2 Estimates beginning in 1987 reflect new editing procedures for cases with missing data on school enrollment items. Estimates beginning in 1992 reflect new wording of the educational attainment item. Estimates beginning in 1994 reflect changes due to newly instituted computer-assisted interviewing. For details about changes in the Current Population Survey (CPS) over time, please see Kaufman, P., Alt, M.N., and Chapman, C. (2004). Dropout Rates in the United States: 2001 (NCES 2005-046). National Center for Education Statistics, Institute of Education Sciences, U.S. Department of Education. Washington, DC. NOTE: The event dropout rate indicates the percentage of youth ages 15 through 24 who dropped out of grades 10–12 between one October and the next (e.g., October 2007 to October 2008). Dropping out is defined as leaving school without a high school diploma or equivalent credential, such as a General Educational Development (GED) certificate. SOURCE: U.S. Department of Commerce, Census Bureau, Current Population Survey (CPS), October 1972–2008. 1 35 �Tables Table 4.—Event dropout rates of 15- through 24-year-olds who dropped out of grades 10–12, by family Table 4.—income: October 1972 through October 2008 Family income (percent)1 Middle income Year2 Total (percent) Low income 1972 1973 1974 1975 1976 6.1 6.3 6.7 5.8 5.9 14.1 17.3 — 15.7 15.4 6.7 7.0 — 6.0 6.8 2.5 1.8 — 2.6 2.1 1977 1978 1979 1980 1981 6.5 6.7 6.7 6.1 5.9 15.5 17.4 17.1 15.8 14.4 7.6 7.3 6.9 6.4 6.2 2.2 3.0 3.6 2.5 2.8 1982 1983 1984 1985 1986 5.5 5.2 5.1 5.2 4.7 15.2 10.4 13.9 14.2 10.9 5.6 6.0 5.1 5.2 5.1 1.8 2.2 1.8 2.1 1.6 1987 1988 1989 1990 1991 4.1 4.8 4.5 4.0 4.0 10.3 13.7 10.0 9.5 10.6 4.7 4.7 5.0 4.3 4.0 1.0 1.3 1.1 1.1 1.0 1992 1993 1994 1995 1996 4.4 4.5 5.3 5.7 5.0 10.9 12.3 13.0 13.3 11.1 4.4 4.3 5.2 5.7 5.1 1.3 1.3 2.1 2.0 2.1 1997 1998 1999 2000 2001 4.6 4.8 5.0 4.8 5.0 12.3 12.7 11.0 10.0 10.7 4.1 3.8 5.0 5.2 5.4 1.8 2.7 2.1 1.6 1.7 2002 2003 2004 2005 2006 3.6 4.0 4.7 3.8 3.8 7.7 7.5 10.4 8.9 9.0 3.6 4.6 4.6 3.8 3.5 1.7 1.4 2.5 1.5 2.0 See notes at end of table. 36 High income �Tables Table 4. —Event dropout rates of 15- through 24-year-olds who dropped out of grades 10–12, by family Table 4.—income: October 1972 through October 2008—Continued Year2 Total (percent) Low income 2007 2008 3.5 3.5 8.8 8.7 Family income (percent)1 Middle income 3.5 3.0 High income 0.9 2.0 — Not available. Low income is defined as the bottom 20 percent of all family incomes for the year; middle income is between 20 and 80 percent of all family incomes; and high income is the top 20 percent of all family incomes. 2 Estimates beginning in 1987 reflect new editing procedures for cases with missing data on school enrollment items. Estimates beginning in 1992 reflect new wording of the educational attainment item. Estimates beginning in 1994 reflect changes due to newly instituted computer-assisted interviewing. For details about changes in the Current Population Survey (CPS) over time, please see Kaufman, P., Alt, M.N., and Chapman, C. (2004). Dropout Rates in the United States: 2001 (NCES 2005-046). National Center for Education Statistics, Institute of Education Sciences, U.S. Department of Education. Washington, DC. NOTE: The event dropout rate indicates the percentage of youth ages 15 through 24 who dropped out of grades 10–12 between one October and the next (e.g., October 2007 to October 2008). Dropping out is defined as leaving school without a high school diploma or equivalent credential, such as a General Educational Development (GED) certificate. SOURCE: U.S. Department of Commerce, Census Bureau, Current Population Survey (CPS), October 1972–2008. 1 37 �Tables Table 5.—Event dropout rates for public school students in grades 9–12, by state: School years 1993–94 Table 5.—through 2007–08 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 –94 –95 –96 –97 –98 –99 –2000 –01 –02 –03 –04 –05 –06 –07 –08 State Reporting states1 2 Alabama Alaska3 Arizona2 Arkansas California — 5.8 — 13.7 5.3 — — — — — — — — — 3.9 4.1 3.9 3.9 4.4 4.1 6.2 5.6 5.3 — 5.6 4.9 9.6 10.2 10.0 4.9 4.1 5.0 — — — 4.8 4.6 9.4 5.4 — 4.4 5.3 8.4 6.0 — 4.5 4.1 3.7 5.5 8.2 8.1 — 10.9 10.5 5.7 5.3 5.3 — — — 3.5 7.6 8.5 4.6 3.2 3.3 7.0 6.7 4.7 3.3 2.8 8.2 6.2 4.3 3.1 2.5 8.0 7.6 3.1 3.7 2.3 7.3 7.6 4.6 5.5 2.2 7.3 6.7 4.7 5.0 Colorado Connecticut Delaware District of Columbia Florida2 — — 4.8 4.9 4.6 4.6 9.5 10.6 — — — 4.8 4.5 — — — — 3.9 3.5 4.5 4.7 — 12.8 — — — 3.3 4.1 8.2 — — 3.1 4.1 7.2 — — 3.0 4.2 — 4.4 — 2.6 6.2 — 3.7 3.5 2.1 5.5 — 3.4 5.4 ‡ 6.1 — 3.4 7.8 ‡ 5.3 — 3.5 7.8 2.0 5.5 ‡ 4.1 6.9 2.1 5.5 7.1 3.8 6.4 2.8 6.0 5.5 3.3 Georgia Hawaii3 Idaho3 Illinois2 Indiana 8.7 — 8.5 6.8 — 9.0 — 9.2 6.6 — 8.5 — 8.0 6.4 — 8.2 — 7.2 6.6 — 7.4 5.3 6.9 6.5 — 7.2 5.3 — 6.2 — 7.2 5.7 5.6 6.0 — 6.5 5.1 3.9 6.4 2.3 5.8 4.7 3.9 5.7 2.2 5.4 4.8 3.1 5.3 2.5 5.6 4.7 3.0 4.5 2.5 5.2 4.7 2.7 4.0 2.9 4.6 5.4 2.6 4.0 2.7 4.3 5.4 2.0 5.2 1.7 Iowa Kansas Kentucky Louisiana4 Maine 3.2 — — 4.7 3.1 3.5 3.1 2.9 2.9 2.5 — — — — — — — — 5.2 4.9 3.5 11.6 11.6 11.4 10.0 3.4 3.1 3.2 3.2 3.3 2.5 — 5.0 9.2 3.3 2.7 3.2 4.6 8.3 3.1 2.4 3.1 4.0 7.0 2.8 1.9 2.4 3.3 7.5 2.8 ‡ 2.2 3.3 7.9 2.7 2.2 2.1 3.5 7.5 2.8 2.2 2.4 3.3 8.4 5.4 2.3 2.7 3.0 7.4 5.3 2.9 2.5 2.8 7.5 4.4 Maryland2 Massachusetts Michigan Minnesota Mississippi 5.2 3.7 — 5.1 6.1 5.2 3.6 — 5.2 6.4 Missouri Montana Nebraska Nevada New Hampshire New Jersey2 New Mexico New York3 North Carolina North Dakota 4.3 3.2 — 4.9 5.8 4.4 3.6 — 4.5 5.0 4.1 3.5 — 4.3 4.9 4.1 3.4 — 4.0 4.6 3.9 — — 3.8 3.9 3.6 3.3 4.5 3.8 3.7 4.1 3.7 4.6 ‡ 2.9 3.9 3.8 3.9 ‡ 2.8 3.9 3.4 3.5 3.1 3.0 3.8 3.8 7.4 3.0 4.3 3.6 3.4 6.2 2.8 4.6 7.0 7.0 — — 4.6 4.5 9.8 10.3 — — 6.5 5.8 5.2 5.6 5.1 4.4 4.5 4.3 4.4 9.6 10.2 10.1 — — — 4.8 4.5 4.2 7.9 — 4.4 4.2 4.0 6.2 — 4.2 4.2 4.0 5.2 5.4 3.6 3.9 4.2 6.4 4.0 3.3 3.6 3.1 6.1 3.8 3.3 3.4 2.8 6.0 3.8 3.7 3.4 2.7 5.8 3.5 4.1 3.7 2.8 7.7 3.2 3.7 3.7 2.8 4.5 3.2 4.9 5.2 2.5 5.1 3.0 4.3 8.1 — — 2.7 4.1 8.3 — — 2.5 3.1 6.7 4.0 — 2.4 3.1 6.0 4.1 — 2.7 2.8 5.3 3.8 6.3 2.2 2.5 5.2 7.1 5.7 2.0 1.8 4.7 5.5 5.2 2.2 ‡ 5.2 5.6 5.2 2.0 ‡ 4.2 5.7 5.2 1.9 1.7 5.5 4.4 ‡ 2.1 2.0 6.1 5.3 5.7 2.3 1.7 5.2 3.9 5.2 2.4 4.0 8.5 — — 2.5 4.8 3.4 — 5.2 6.2 4.9 3.4 — 5.5 6.0 7.3 5.2 6.7 6.9 — 3.7 7.5 — — 2.7 3.5 7.1 3.2 — 2.8 See notes at end of table. 38 �Tables Table 5.—Event dropout rates for public school students in grades 9–12, by state: School years 1993–94 Table 5.—through 2007–08—Continued State 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 –94 –95 –96 –97 –98 –99 –2000 –01 –02 –03 –04 –05 –06 –07 –08 Ohio3 Oklahoma3 Oregon Pennsylvania Rhode Island — 4.6 7.3 3.8 4.9 — 5.8 7.1 4.1 4.6 — 5.7 7.0 4.0 4.6 — 5.9 — 3.9 4.7 — 5.8 6.8 3.9 4.9 — 5.2 6.3 3.7 4.5 — 5.4 6.2 4.0 4.8 — 5.2 5.3 3.6 5.0 3.1 4.4 4.9 3.3 4.3 3.0 4.0 4.4 3.2 4.0 3.3 3.9 — 2.9 3.4 3.5 3.5 — 2.9 4.1 4.1 3.6 4.6 2.8 4.1 4.5 3.5 4.6 — 5.8 4.3 3.1 3.8 2.6 5.3 South Carolina South Dakota3 Tennessee2 Texas Utah — 5.3 4.8 — 3.1 — 5.3 5.0 — 3.5 — 5.7 4.9 — 4.4 — 4.5 5.1 — 4.5 — 3.1 5.0 — 5.2 — 4.5 4.6 — 4.7 — 3.5 4.2 5.0 4.1 3.3 3.9 4.3 4.2 3.7 3.3 2.8 3.8 3.8 3.7 3.2 3.3 3.2 3.6 3.9 3.4 4.2 3.3 3.6 3.8 3.3 4.4 2.7 3.6 3.7 — 4.4 2.8 4.3 3.3 3.9 3.9 3.1 4.0 3.1 3.9 2.3 3.9 4.0 4.2 Vermont2 Virginia3 Washington West Virginia Wisconsin3 Wyoming3 4.8 4.8 — 3.8 3.1 6.5 4.7 5.2 — 4.2 2.7 6.7 5.3 4.7 — 3.8 2.4 5.7 5.0 4.6 — 4.1 2.7 6.2 5.2 4.8 — 4.1 2.8 6.4 4.6 4.5 — 4.9 1.8 5.1 4.7 3.9 — 4.2 2.6 5.7 4.7 3.5 — 4.2 2.3 6.4 4.0 2.9 7.1 3.7 1.9 5.8 3.5 3.0 6.2 3.7 2.0 4.5 2.8 2.8 6.5 4.3 ‡ 4.6 2.6 2.5 4.5 4.1 2.4 4.8 ‡ 2.7 5.6 3.9 2.2 5.7 — 2.6 5.1 4.0 2.2 5.1 — 2.7 5.7 4.4 2.3 5.0 — Not available. These states do not report dropouts that are consistent with the NCES definition. ‡ Reporting standards not met. (Too few cases for a reliable estimate.) 1 Average event dropout rate for all reporting states. Prior to 2002–03, too few states reported to calculate a reporting states total. 2 These states used an alternative calendar for each year shown, reporting students who drop out between one July and the next. The rates from both calendar approaches are comparable (see Winglee et al. 2000). 3 The following states reported data using the alternative calendar of one July to the next in the years indicated: Alaska (1995–96 and 1999–2000 through 2001–02); Hawaii (2000–01); Idaho (1993–94 through 1998–99); New York (1998–99 and 2000–01 through 2003–04); Ohio (1993–94); Oklahoma (1993–94 through 2000–01); South Dakota (1993–94 through 1998–99); Virginia (1993–94 through 1999–2000); Wisconsin (1993–94 through 1996–97 and 1998–99); and Wyoming (1993–94). 4 Effective in the 1995–96 school year, Louisiana changed its dropout data collection from school-level aggregate counts reported to districts to an individual student-record system. The apparent increase in the dropout rate is partly due to the resulting increased ability to track students. NOTE: These event dropout rates measure the percentage of public school students in grades 9–12 who dropped out of school between one October and the next (e.g., October 2007 to October 2008). Data are reported by states to the U.S. Department of Education, National Center for Education Statistics. The Common Core of Data (CCD) includes public school students only. Some estimates differ from those in previously published reports because of updates to the estimates. SOURCE: U.S. Department of Education, National Center for Education Statistics. (n.d.) Documentation to the NCES Common Core of Data Local Education Agency Universe Dropout and Completion Data File: School Years 1991–92 Through 1996–97 , tables 2a, 2b, 2c, and 2d; Sable, J., and Naum, J. (2004a), Documentation to the NCES Common Core of Data Local Education Agency Universe Survey Dropout and Completion Data File: School Year 1997–98 (NCES 2001-302R), table E-1; Sable, J., and Naum, J. (2004b). Documentation to the NCES Common Core of Data Local Education Agency Universe Survey Dropout and Completion Data File: School Year 1998–99 (NCES 2002-310R), table E-3; Sable, J., and Naum, J. (2004c). Documentation to the NCES Common Core of Data Local Education Agency Universe Survey Dropout and Completion Data File: School Year 1999–2000 (NCES 2002-384R), table E-3; Sable, J., and Naum, J. (2004d). Documentation to the NCES Common Core of Data Local Education Agency Universe Survey Dropout and Completion Data File: School Year 2000–01 (NCES 2002-315R), table E-3; Sable, J., Naum, J., and Thomas, J.M. (2004). Documentation to the NCES Common Core of Data Local Education Agency Universe Survey Dropout and Completion Data File: School Year 2001–02 (NCES 2005-349), table E-2; Chapman, C., and Hoffman, L. (2007). Event Dropout Rates for Public School Students in Grades 9–12: 2002–03 and 2003–04 (NCES 2007-026), table 1; Stillwell, R. and Hoffman, L. (2009). Public School Graduates and Dropouts From the Common Core of Data: School Year 2005–06 (NCES 2008-353rev), table 7; Stillwell, R. (2009). Public School Graduates and Dropouts From the Common Core of Data: School Year 2006–07 (NCES 2010-313), table 4; Stillwell, R. (2010). Public School Graduates and Dropouts From the Common Core of Data: School Year 2007–08 (NCES 2010-341), table 7. 39 �Tables Table 6.—Status dropout rates and number and distribution of dropouts of 16- through 24-year-olds, by Table 6.—selected characteristics: October 2008 Status dropout rate (percent) Number of status dropouts (thousands) Population (thousands) Percent of all dropouts Percent of population Total 8.0 3,010 37,569 100.0 100.0 Sex Male Female 8.5 7.5 1,606 1,403 18,948 18,621 53.4 46.6 50.4 49.6 4.8 9.9 18.3 1,103 535 1,232 22,956 5,387 6,721 36.7 17.8 40.9 61.1 14.3 17.9 4.4 67 1,504 2.2 4.0 14.6 43 294 1.4 0.8 4.2 30 706 1.0 1.9 2.2 5.0 7.8 9.9 9.5 93 216 337 413 1,951 4,269 4,349 4,332 4,160 20,459 3.1 7.2 11.2 13.7 64.8 11.4 11.6 11.5 11.1 54.5 32.8 5.5 766 104 2,334 1,908 25.4 3.5 6.2 5.1 10.5 3.1 254 72 2,419 2,326 8.4 2.4 6.4 6.2 10.8 6.0 213 1,602 1,968 26,615 7.1 53.2 5.2 70.8 Characteristic Race/ethnicity1 White, non-Hispanic Black, non-Hispanic Hispanic Asian/Pacific Islander, non-Hispanic American Indian/Alaska Native, non-Hispanic Two or more races, non-Hispanic Age 16 17 18 19 20–24 Recency of immigration Born outside the 50 states and District of Columbia Hispanic Non-Hispanic First generation2 Hispanic Non-Hispanic Second generation or higher2 Hispanic Non-Hispanic See notes at end of table. 40 �Tables Table 6.—Status dropout rates and number and distribution of dropouts of 16- through 24-year-olds, by Table 6.—selected characteristics: October 2008—Continued Characteristic Region Northeast Midwest South West Status dropout rate (percent) Number of status dropouts (thousands) Population (thousands) Percent of all dropouts Percent of population 5.6 7.5 8.8 9.1 377 631 1,191 811 6,708 8,414 13,496 8,949 12.5 21.0 39.6 27.0 17.9 22.4 35.9 23.8 1 Respondents were able to identify themselves as being two or more races. The White (non-Hispanic), Black (non-Hispanic), Asian/Pacific Islander (non-Hispanic), and American Indian/Alaska Native (non-Hispanic) categories consist of individuals who considered themselves to be one race and who did not identify as Hispanic. Non-Hispanics who identified themselves as multiracial are included in the Two or more races (non-Hispanic) category. The Hispanic category consists of Hispanics of all races and racial combinations. 2 Individuals defined as “first generation” were born in the 50 states or the District of Columbia, and one or both of their parents were born outside the 50 states or the District of Columbia. Individuals defined as “second generation or higher” were born in the 50 states or the District of Columbia, as were both of their parents. NOTE: The status dropout rate indicates the percentage of 16- through 24-year-olds who are not enrolled in high school and who lack a high school credential. High school credentials include high school diplomas and equivalent credentials, such as a General Educational Development (GED) certificate. Detail may not sum to totals because of rounding. SOURCE: U.S. Department of Commerce, Census Bureau, Current Population Survey (CPS), October 2008. 41 �Tables Table 7.—Status dropout rates, number of status dropouts, and population of 16- through 24-year-olds: Table 7.—October 1972 through October 2008 Year1 Status dropout rate (percent) Number of status dropouts (thousands) Population (thousands) 1972 1973 1974 1975 1976 14.6 14.1 14.3 13.9 14.1 4,769 4,717 4,847 4,823 4,980 32,643 33,430 33,968 34,700 35,222 1977 1978 1979 1980 1981 14.1 14.2 14.6 14.1 13.9 5,031 5,113 5,264 5,085 5,143 35,658 35,931 36,131 36,143 36,945 1982 1983 1984 1985 1986 13.9 13.7 13.1 12.6 12.2 5,056 4,905 4,626 4,325 4,141 36,452 35,884 35,204 34,382 33,945 1987 1988 1989 1990 1991 12.7 12.9 12.6 12.1 12.5 4,252 4,230 4,038 3,797 3,881 33,452 32,893 32,007 31,443 31,171 1992 1993 1994 1995 1996 11.0 11.0 11.5 12.0 11.1 3,410 3,396 3,727 3,876 3,611 30,944 30,845 32,560 32,379 32,452 1997 1998 1999 2000 2001 11.0 11.8 11.2 10.9 10.7 3,624 3,942 3,829 3,776 3,774 32,960 33,445 34,173 34,568 35,195 2002 2003 2004 2005 2006 10.5 9.9 10.3 9.4 9.3 3,721 3,552 3,766 3,458 3,462 35,495 36,017 36,504 36,761 37,047 See notes at end of table. 42 �Tables Table 7.—Status dropout rates, number of status dropouts, and population of 16- through 24-year-olds: Table 7.—October 1972 through October 2008—Continued Year1 Status dropout rate (percent) Number of status dropouts (thousands) Population (thousands) 2007 2008 8.7 8.0 3,278 3,010 37,480 37,569 1 Estimates beginning in 1987 reflect new editing procedures for cases with missing data on school enrollment items. Estimates beginning in 1992 reflect new wording of the educational attainment item. Estimates beginning in 1994 reflect changes due to newly instituted computer-assisted interviewing. For details about changes in the Current Population Survey (CPS) over time, please see Kaufman, P., Alt, M.N., and Chapman, C. (2004). Dropout Rates in the United States: 2001 (NCES 2005-046). National Center for Education Statistics, Institute of Education Sciences, U.S. Department of Education. Washington, DC. NOTE: The status dropout rate indicates the percentage of 16- through 24-year-olds who are not enrolled in high school and who lack a high school credential. High school credentials include high school diplomas and equivalent credentials, such as a General Educational Development (GED) certificate. SOURCE: U.S. Department of Commerce, Census Bureau, Current Population Survey (CPS), October 1972–2008. 43 �Tables Table 8. —Status dropout rates of 16- through 24-year-olds, by sex and race/ethnicity: October 1972 Table 8.—through October 2008 Sex (percent) Race/ethnicity (percent)1 White, nonBlack, nonHispanic Hispanic Hispanic Total (percent) Male Female 1972 1973 1974 1975 1976 14.6 14.1 14.3 13.9 14.1 14.1 13.7 14.2 13.3 14.1 15.1 14.5 14.4 14.5 14.2 12.3 11.6 11.9 11.4 12.0 21.3 22.2 21.2 22.9 20.5 34.3 33.5 33.0 29.2 31.4 1977 1978 1979 1980 1981 14.1 14.2 14.6 14.1 13.9 14.5 14.6 15.0 15.1 15.1 13.8 13.9 14.2 13.1 12.8 11.9 11.9 12.0 11.4 11.4 19.8 20.2 21.1 19.1 18.4 33.0 33.3 33.8 35.2 33.2 1982 1983 1984 1985 1986 13.9 13.7 13.1 12.6 12.2 14.5 14.9 14.0 13.4 13.1 13.3 12.5 12.3 11.8 11.4 11.4 11.2 11.0 10.4 9.7 18.4 18.0 15.5 15.2 14.2 31.7 31.6 29.8 27.6 30.1 1987 1988 1989 1990 1991 12.7 12.9 12.6 12.1 12.5 13.3 13.5 13.6 12.3 13.0 12.2 12.2 11.7 11.8 11.9 10.4 9.6 9.4 9.0 8.9 14.1 14.5 13.9 13.2 13.6 28.6 35.8 33.0 32.4 35.3 1992 1993 1994 1995 1996 11.0 11.0 11.5 12.0 11.1 11.3 11.2 12.3 12.2 11.4 10.7 10.9 10.6 11.7 10.9 7.7 7.9 7.7 8.6 7.3 13.7 13.6 12.6 12.1 13.0 29.4 27.5 30.0 30.0 29.4 1997 1998 1999 2000 2001 11.0 11.8 11.2 10.9 10.7 11.9 13.3 11.9 12.0 12.2 10.1 10.3 10.5 9.9 9.3 7.6 7.7 7.3 6.9 7.3 13.4 13.8 12.6 13.1 10.9 25.3 29.5 28.6 27.8 27.0 2002 2003 2004 2005 2006 10.5 9.9 10.3 9.4 9.3 11.8 11.3 11.6 10.8 10.3 9.2 8.4 9.0 8.0 8.3 6.5 6.3 6.8 6.0 5.8 11.3 10.9 11.8 10.4 10.7 25.7 23.5 23.8 22.4 22.1 Year 2 See notes at end of table. 44 �Tables Table 8. —Status dropout rates of 16- through 24-year-olds, by sex and race/ethnicity: October 1972 Table 8.—through October 2008—Continued Sex (percent) Year 2 2007 2008 Total (percent) Male Female 8.7 8.0 9.8 8.5 7.7 7.5 1 Race/ethnicity (percent)1 White, nonBlack, nonHispanic Hispanic Hispanic 5.3 4.8 8.4 9.9 21.4 18.3 Beginning in 2003, respondents were able to identify themselves as being “more than one race.” The 2003 through 2008 White, non-Hispanic and Black, non-Hispanic categories consist of individuals who considered themselves to be one race and who did not identify as Hispanic. The Hispanic category includes Hispanics of all races and racial combinations. Due to small sample sizes for some or all of the years shown in the table, American Indians/Alaska Natives and Asians/Pacific Islanders are included in the totals but not shown separately. The “more than one race” category is also included in the total in 2003 through 2008 but not shown separately due to small sample size. 2 Estimates beginning in 1987 reflect new editing procedures for cases with missing data on school enrollment items. Estimates beginning in 1992 reflect new wording of the educational attainment item. Estimates beginning in 1994 reflect changes due to newly instituted computer-assisted interviewing. For details about changes in the Current Population Survey (CPS) over time, please see Kaufman, P., Alt, M.N., and Chapman, C. (2004). Dropout Rates in the United States: 2001 (NCES 2005-046). National Center for Education Statistics, Institute of Education Sciences, U.S. Department of Education. Washington, DC. NOTE: The status dropout rate indicates the percentage of 16- through 24-year-olds who are not enrolled in high school and who lack a high school credential. High school credentials include high school diplomas and equivalent credentials, such as a General Educational Development (GED) certificate. SOURCE: U.S. Department of Commerce, Census Bureau, Current Population Survey (CPS), October 1972–2008. 45 �Tables Table 9.—Status completion rates, and number and distribution of completers ages 18–24 not currently Table 9.—enrolled in high school or below, by selected characteristics: October 2008 Completion rate (percent) Number of completers (thousands) Population (thousands) Percent of all completers Percent of population Total 89.9 24,518 27,270 100.0 100.0 Sex Male Female 89.3 90.5 12,169 12,349 13,626 13,644 49.6 50.4 50.0 50.0 94.2 86.9 75.5 16,018 3,254 3,606 16,998 3,744 4,773 65.3 13.3 14.7 62.3 13.7 17.5 95.5 1,045 1,094 4.3 4.0 Characteristic Race/ethnicity1 White, non-Hispanic Black, non-Hispanic Hispanic Asian/Pacific Islander, non-Hispanic American Indian/Alaska Native, non-Hispanic Two or more races, non-Hispanic 82.5 177 215 0.7 0.8 94.2 419 445 1.7 1.6 Age 18–19 20–21 22–24 89.0 91.0 89.7 6,237 7,235 11,047 7,010 7,951 12,308 25.4 29.5 45.1 25.7 29.2 45.1 59.8 93.7 1,104 1,442 1,846 1,539 4.5 5.9 6.8 5.6 85.1 96.2 1,349 1,579 1,584 1,642 5.5 6.4 5.8 6.0 85.8 92.6 1,153 17,892 1,343 19,315 4.7 73.0 4.9 70.8 Recency of immigration Born outside the 50 states and District of Columbia Hispanic Non-Hispanic First generation2 Hispanic Non-Hispanic Second generation or higher2 Hispanic Non-Hispanic See notes at end of table. 46 �Tables Table 9.—Status completion rates, and number and distribution of completers ages 18–24 not currently Table 9.—enrolled in high school or below, by selected characteristics: October 2008—Continued Characteristic Region Northeast Midwest South West Completion rate (percent) Number of completers (thousands) Population (thousands) Percent of all completers Percent of population 92.7 90.3 89.1 88.7 4,530 5,396 8,737 5,854 4,888 5,977 9,804 6,601 18.5 22.0 35.6 23.9 17.9 21.9 36.0 24.2 1 Respondents were able to identify themselves as being two or more races. The White (non-Hispanic), Black (non-Hispanic), Asian/Pacific Islander (non-Hispanic), and American Indian/Alaska Native (non-Hispanic) categories consist of individuals who considered themselves to be one race and who did not identify as Hispanic. Non-Hispanics who identified themselves as multiracial are included in the Two or more races (non-Hispanic) category. The Hispanic category consists of Hispanics of all races and racial combinations. 2 Individuals defined as “first generation” were born in the 50 states or the District of Columbia, and one or both of their parents were born outside the 50 states or the District of Columbia. Individuals defined as “second generation or higher” were born in the 50 states or the District of Columbia, as were both of their parents. NOTE: Status completion rates measure the percentage of 18- through 24-year-olds who are not enrolled in high school and who also hold a high school diploma or equivalent credential, such as a General Educational Development (GED) certificate. Those still enrolled in high school are excluded from the analysis. Detail may not sum to totals because of rounding. SOURCE: U.S. Department of Commerce, Census Bureau, Current Population Survey (CPS), October 2008. 47 �Tables Table 10.—Status completion rates, number of completers, and population of 18- through 24-year-olds: Table 10.—October 1972 through October 2008 Year1 Completion rate (percent) Number of completers (thousands) Population (thousands) 1972 1973 1974 1975 1976 82.8 83.7 83.6 83.8 83.5 19,623 20,377 20,724 21,326 21,677 23,688 24,349 24,794 25,436 25,953 1977 1978 1979 1980 1981 83.6 83.6 83.1 83.9 83.8 22,008 22,308 22,421 22,746 23,342 26,321 26,697 26,982 27,122 27,863 1982 1983 1984 1985 1986 83.8 83.9 84.7 85.4 85.5 23,290 22,988 22,871 22,349 21,766 27,790 27,399 27,014 26,168 25,453 1987 1988 1989 1990 1991 84.7 84.5 84.7 85.6 84.9 21,071 20,838 20,420 20,269 19,831 24,869 24,650 24,102 23,689 23,369 1992 1993 1994 1995 1996 86.4 86.2 85.8 85.3 86.2 19,874 19,682 20,538 20,102 20,074 23,004 22,842 23,946 23,571 23,277 1997 1998 1999 2000 2001 85.9 84.8 85.9 86.5 86.5 20,241 20,451 21,091 21,743 22,084 23,569 24,113 24,540 25,138 25,543 2002 2003 2004 2005 2006 86.6 87.1 86.8 87.6 87.8 22,249 22,508 22,991 23,010 23,331 25,697 25,831 26,476 26,270 26,568 See notes at end of table. 48 �Tables Table 10.—Status completion rates, number of completers, and population of 18- through 24-year-olds: Table 10.—October 1972 through October 2008—Continued Year1 Completion rate (percent) Number of completers (thousands) Population (thousands) 2007 2008 89.0 89.9 24,100 24,518 27,086 27,270 1 Estimates beginning in 1987 reflect new editing procedures for cases with missing data on school enrollment items. Estimates beginning in 1992 reflect new wording of the educational attainment item. Estimates beginning in 1994 reflect changes due to newly instituted computer-assisted interviewing. For details about changes in the Current Population Survey (CPS) over time, please see Kaufman, P., Alt, M.N., and Chapman, C. (2004). Dropout Rates in the United States: 2001 (NCES 2005-046). National Center for Education Statistics, Institute of Education Sciences, U.S. Department of Education. Washington, DC. NOTE: Status completion rates measure the percentage of 18- through 24-year-olds who are not enrolled in high school and who also hold a high school diploma or equivalent credential, such as a General Educational Development (GED) certificate. Those still enrolled in high school are excluded from the analysis. SOURCE: U.S. Department of Commerce, Census Bureau, Current Population Survey (CPS), October 1972–2008. 49 �Tables Table 11.—Status completion rates of 18- through 24-year-olds not currently enrolled in high school or Table 11.—below, by sex and race/ethnicity: October 1972 through October 2008 Sex (percent) Race/ethnicity (percent)1 White, nonBlack, nonHispanic Hispanic Hispanic Year2 Total (percent) Male Female 1972 1973 1974 1975 1976 82.8 83.7 83.6 83.8 83.5 83.0 84.0 83.4 84.1 83.0 82.7 83.4 83.8 83.6 84.0 86.0 87.0 86.7 87.2 86.4 72.1 71.6 73.0 70.2 73.5 56.2 58.7 60.1 62.2 60.3 1977 1978 1979 1980 1981 83.6 83.6 83.1 83.9 83.8 82.8 82.8 82.1 82.3 82.0 84.4 84.2 84.0 85.3 85.4 86.7 86.9 86.6 87.5 87.1 73.9 73.4 72.6 75.2 76.7 58.6 58.8 58.5 57.1 59.1 1982 1983 1984 1985 1986 83.8 83.9 84.7 85.4 85.5 82.7 82.1 83.3 84.0 84.2 84.9 85.6 85.9 86.7 86.7 87.0 87.4 87.5 88.2 88.8 76.4 76.8 80.3 81.0 81.8 60.9 59.4 63.7 66.6 63.5 1987 1988 1989 1990 1991 84.7 84.5 84.7 85.6 84.9 84.0 83.2 83.2 85.1 83.8 85.8 85.8 86.2 86.0 85.9 87.7 88.7 89.0 89.6 89.4 81.9 80.9 81.9 83.2 82.5 65.1 58.2 59.4 59.1 56.5 1992 1993 1994 1995 1996 86.4 86.2 85.8 85.3 86.2 85.3 85.4 84.5 84.3 85.7 87.4 86.9 87.0 85.7 86.8 90.7 90.1 90.7 89.8 91.5 82.0 81.9 83.3 84.5 83.0 62.1 64.4 61.8 62.8 61.9 1997 1998 1999 2000 2001 85.9 84.8 85.9 86.5 86.5 84.6 82.6 84.8 84.9 84.6 87.2 87.0 87.1 88.1 88.3 90.5 90.2 91.2 91.8 91.0 82.0 81.4 83.5 83.7 85.6 66.7 62.8 63.4 64.1 65.7 2002 2003 2004 2005 2006 86.6 87.1 86.8 87.6 87.8 84.8 85.1 84.9 85.4 86.5 88.4 89.2 88.8 89.8 89.1 91.8 91.9 91.7 92.3 92.6 84.7 85.0 83.4 85.9 84.8 67.3 69.2 69.8 70.2 70.8 See notes at end of table. 50 �Tables Table 11.—Status completion rates of 18- through 24-year-olds not currently enrolled in high school or Table 11.—below, by sex and race/ethnicity: October 1972 through October 2008—Continued Sex (percent) Year2 Total (percent) Male Female 2007 2008 89.0 89.9 87.4 89.3 90.6 90.5 1 Race/ethnicity (percent)1 White, nonBlack, nonHispanic Hispanic Hispanic 93.5 94.2 88.8 86.9 72.7 75.5 Beginning in 2003, respondents were able to identify themselves as being “more than one race.” The 2003 through 2008 White, non-Hispanic and Black, non-Hispanic categories consist of individuals who considered themselves to be one race and who did not identify themselves as Hispanic. The Hispanic category includes Hispanics of all races and racial combinations. Due to small sample sizes for some or all of the years shown in the table, American Indians/Alaska Natives and Asians/Pacific Islanders are included in the totals but not shown separately. The “more than one race” category is also included in the total in 2003 through 2008 but not shown separately due to small sample size. 2 Estimates beginning in 1987 reflect new editing procedures for cases with missing data on school enrollment items. Estimates beginning in 1992 reflect new wording of the educational attainment item. Estimates beginning in 1994 reflect changes due to newly instituted computer-assisted interviewing. For details about changes in the Current Population Survey (CPS) over time, please see Kaufman, P., Alt, M.N., and Chapman, C. (2004). Dropout Rates in the United States: 2001 (NCES 2005-046). National Center for Education Statistics, Institute of Education Sciences, U.S. Department of Education. Washington, DC. NOTE: Status completion rates measure the percentage of 18- through 24-year-olds who are not enrolled in high school and who also hold a high school diploma or equivalent credential, such as a General Educational Development (GED) certificate. Those still enrolled in high school are excluded from the analysis. SOURCE: U.S. Department of Commerce, Census Bureau, Current Population Survey (CPS), October 1972–2008. 51 �Tables Table 12.—Averaged freshman graduation rate of public high school students, by state: School year 2007–08 Averaged freshman graduation rate (percent) Regular diplomas, school year 2007–08 74.9 2,964,371 3,958,987 3,841,810 4,247,085 3,788,070 Alabama Alaska Arizona Arkansas California 69.0 69.1 70.7 76.4 71.2 41,346 7,855 61,667 28,725 374,561 59,954 11,370 87,280 37,612 526,251 55,630 11,035 92,763 37,390 519,879 64,569 11,934 92,275 38,359 554,174 59,663 11,140 76,801 37,087 504,701 Colorado Connecticut Delaware District of Columbia Florida 75.4 82.2 72.1 56.0 66.9 46,082 38,419 7,388 3,352 149,046 61,102 46,766 10,250 5,986 222,755 59,962 45,266 9,279 5,775 212,560 64,446 49,177 11,249 6,700 250,263 58,897 45,854 10,222 5,484 205,443 Georgia Hawaii Idaho Illinois Indiana 65.4 76.0 80.1 80.4 74.1 83,505 11,613 16,567 135,143 61,901 127,610 15,278 20,681 168,121 83,516 120,058 14,292 20,609 165,513 81,090 142,079 16,991 21,344 178,280 87,829 120,694 14,549 20,091 160,570 81,629 Iowa Kansas Kentucky Louisiana Maine3 86.4 79.1 74.4 63.5 79.1 34,573 30,737 39,339 34,401 14,350 40,022 38,863 52,910 54,162 16,672 40,151 38,252 50,700 43,292 15,926 41,196 40,557 57,419 59,182 16,766 38,719 37,781 50,611 60,013 17,323 Maryland Massachusetts Michigan Minnesota Mississippi 80.4 81.5 76.3 86.4 63.9 59,171 65,197 115,183 60,409 24,795 73,556 79,984 150,960 69,904 38,812 70,031 76,688 146,291 71,051 35,868 81,270 84,628 163,124 70,751 41,261 69,368 78,635 143,465 67,909 39,306 Missouri Montana Nebraska Nevada New Hampshire 82.4 82.0 83.8 51.3 83.4 61,717 10,396 20,035 17,149 14,982 74,922 12,673 23,906 33,403 17,974 73,142 12,344 23,713 32,665 17,529 78,748 13,238 25,214 36,105 18,644 72,876 12,438 22,792 31,440 17,750 New Jersey New Mexico New York North Carolina North Dakota 84.6 66.8 70.8 72.8 83.8 94,994 18,264 176,310 83,307 6,999 112,326 27,355 248,854 114,447 8,351 111,155 26,075 243,322 108,210 8,261 116,702 30,134 273,438 126,414 8,547 109,120 25,857 229,801 108,717 8,245 State Reporting states2, 3 Estimated first-time Grade 10 Grade 9 Grade 8 9th-graders, membership, membership, membership, school year school year school year school year 2004–051 2005–06 2004–05 2003–04 See notes at end of table. 52 �Tables Table 12.—Averaged freshman graduation rate of public high school students, by state: School year 2007–08 Table 13.——Continued Averaged freshman graduation rate (percent) Regular diplomas, school year 2007–08 Ohio Oklahoma Oregon Pennsylvania Rhode Island 79.0 78.0 76.7 82.7 76.4 120,758 37,630 34,949 130,298 10,347 152,906 48,270 45,549 157,530 13,539 145,999 46,834 44,921 157,058 13,007 165,656 50,404 46,785 164,389 14,591 147,064 47,572 44,941 151,144 13,018 South Carolina South Dakota Tennessee Texas Utah — 84.4 74.9 73.1 74.3 — 8,582 57,486 252,121 28,167 56,742 10,168 76,789 344,696 37,894 51,277 10,046 74,717 323,524 38,319 65,564 10,377 82,168 386,182 38,069 53,384 10,082 73,481 324,381 37,295 Vermont Virginia Washington West Virginia Wisconsin Wyoming 89.3 77.0 71.9 77.3 89.6 76.0 7,392 77,369 61,625 17,489 65,183 5,494 8,275 100,512 85,674 22,623 72,748 7,226 8,152 96,546 84,945 21,415 73,409 7,150 8,552 109,375 89,802 24,199 76,173 7,355 8,121 95,615 82,274 22,256 68,663 7,173 State Estimated first-time Grade 10 Grade 9 Grade 8 9th-graders, membership, membership, membership, school year school year school year school year 2004–051 2005–06 2004–05 2003–04 — Not available. 1 First-time 9th-graders were estimated as the average of student membership in grades 8, 9, and 10 in 3 consecutive years. U.S. totals include any of the 50 states and the District of Columbia that reported all data elements. 3 Maine reported 1,161 diplomas that were awarded to students attending private high schools that received a majority of their funding from public sources. These 1,161 diplomas were included in Maine and the reporting states counts but were not included in the averaged freshman graduation rate (AFGR) calculations for the state and for the reporting states totals. The diploma counts used to calculate the AFGR for Maine and for the United States were 13,189 and 2,964,125, respectively. NOTE: The averaged freshman graduation rate (AFGR) is an estimate of the percentage of an entering freshman class graduating in 4 years. For 2007–08, it equals the total number of diploma recipients in 2007–08 divided by the average membership of the 8th-grade class in 2003–04, the 9th-grade class in 2004–05, and the 10th-grade class in 2005–06. Ungraded students were allocated to individual grades proportionally to the reported enrollments by grade. The sum of the estimated first-time 9th-graders is not equal to the total because the sum of averages is not equal to the average of sums. SOURCE: Stillwell, R. (2010). Public School Graduates and Dropouts From the Common Core of Data: School Year 2007–08 (NCES 2010-341), table 1. 2 53 �Tables Table 13.—Averaged freshman graduation rates of public high school students and change in rates, by state: Table 13.—School years 2001–02 through 2007–08 State Change in rates Averaged freshman graduation rate (percent) from 2006–07 2001–02 2002–03 2003–04 2004–05 2005–06 2006–07 2007–08 to 2007–08 Reporting states1 72.6 73.9 75.0 2 74.7 73.2 Alabama Alaska Arizona Arkansas California 62.1 65.9 74.7 74.8 72.7 64.7 68.0 75.9 76.6 74.1 65.0 67.2 66.8 76.8 73.9 65.9 64.1 84.7 75.7 74.6 Colorado Connecticut Delaware District of Columbia Florida 74.7 79.7 69.5 68.4 63.4 76.4 80.9 73.0 59.6 66.7 78.7 80.7 72.9 68.2 66.4 Georgia Hawaii Idaho Illinois Indiana 61.1 72.1 79.3 77.1 73.1 60.8 71.3 81.4 75.9 75.5 Iowa Kansas Kentucky Louisiana Maine 84.1 77.1 69.8 64.4 75.6 Maryland Massachusetts Michigan Minnesota Mississippi 3 4 73.9 74.9 66.2 66.5 70.5 80.4 69.2 67.1 69.1 69.6 74.4 70.7 69.0 69.1 70.7 76.4 71.2 1.9 0.0 1.1 2.0 0.5 76.7 80.9 73.1 68.8 64.6 75.5 80.9 76.3 ‡ 63.6 76.6 81.8 71.9 54.9 65.0 75.4 82.2 72.1 56.0 66.9 -1.2 0.4 0.2 1.1 1.9 61.2 72.6 81.5 80.3 73.5 61.7 75.1 81.0 79.4 73.2 62.4 75.5 80.5 79.7 73.3 64.1 75.4 80.4 79.5 73.9 65.4 76.0 80.1 80.4 74.1 1.3 0.6 -0.3 0.9 0.2 85.3 76.9 71.7 64.1 76.3 85.8 77.9 73.0 69.4 77.6 86.6 79.2 75.9 63.9 78.6 86.9 77.6 77.2 59.5 76.3 86.5 78.9 76.4 61.3 78.5 86.4 79.1 74.4 63.5 79.1 -0.1 0.2 -2.0 2.2 0.6 79.7 77.6 72.9 83.9 61.2 79.2 75.7 74.0 84.8 62.7 79.5 79.3 72.5 84.7 62.7 79.3 78.7 73.0 85.9 63.3 79.9 79.5 72.2 86.2 63.5 80.0 80.8 77.0 86.5 63.6 80.4 81.5 76.3 86.4 63.9 0.4 0.7 -0.7 -0.1 0.3 Missouri Montana Nebraska Nevada New Hampshire5 76.8 79.8 83.9 71.9 77.8 78.3 81.0 85.2 72.3 78.2 80.4 80.4 87.6 57.4 78.7 80.6 81.5 87.8 55.8 80.1 81.0 81.9 87.0 55.8 81.1 81.9 81.5 86.3 52.0 81.7 82.4 82.0 83.8 51.3 83.4 0.5 0.5 -2.5 -0.7 1.7 New Jersey New Mexico New York North Carolina North Dakota 85.8 67.4 60.5 68.2 85.0 87.0 63.1 60.9 70.1 86.4 86.3 67.0 — 71.4 86.1 85.1 65.4 65.3 72.6 86.3 84.8 67.3 67.4 71.8 82.1 84.4 59.1 68.8 68.6 83.1 84.6 66.8 70.8 72.8 83.8 0.2 7.7 2.0 4.2 0.7 See notes at end of table. 54 4 1.0 �Tables Table 13.—Averaged freshman graduation rates of public high school students and change in rates, by state: Table 13.—School years 2001–02 through 2007–08—Continued State Change in rates Averaged freshman graduation rate (percent) from 2006–07 2001–02 2002–03 2003–04 2004–05 2005–06 2006–07 2007–08 to 2007–08 Ohio Oklahoma Oregon Pennsylvania Rhode Island 77.5 76.0 71.0 80.2 75.7 79.0 76.0 73.7 81.7 77.7 81.3 77.0 74.2 82.2 75.9 80.2 76.9 74.2 82.5 78.4 79.2 77.8 73.0 — 77.8 78.7 77.8 73.8 83.0 78.4 79.0 78.0 76.7 82.7 76.4 0.3 0.2 2.9 -0.3 -2.0 South Carolina South Dakota Tennessee Texas Utah 57.9 79.0 59.6 73.5 80.5 59.7 83.0 63.4 75.5 80.2 60.6 83.7 66.1 76.7 83.0 60.1 82.3 68.5 74.0 84.4 — 84.5 70.6 72.5 78.6 58.9 82.5 72.6 71.9 76.6 — 84.4 74.9 73.1 74.3 — 1.9 2.3 1.2 -2.3 Vermont Virginia Washington West Virginia Wisconsin Wyoming 82.0 76.7 72.2 74.2 84.8 74.4 83.6 80.6 74.2 75.7 85.8 73.9 85.4 79.3 74.6 76.9 — 76.0 86.5 79.6 75.0 77.3 86.7 76.7 82.3 74.5 72.9 76.9 87.5 76.1 88.6 75.5 74.8 78.2 88.5 75.8 89.3 77.0 71.9 77.3 89.6 76.0 0.7 1.5 -2.9 -0.9 1.1 0.2 — Not available. ‡ Reporting standards not met. (Too few cases for a reliable estimate.) 1 Reporting states totals include any of the 50 states and the District of Columbia that reported all data elements. 2 The national estimate of 75.0 percent for 2003–04 does not include data from two states with missing diploma counts: New York and Wisconsin. 3 The national estimate of 73.2 percent for 2005–06 does not include data from two states, Pennsylvania and South Carolina, which did not report data, and the District of Columbia, for which reporting standards were not met. This is an important consideration when comparing the 2005–06 and 2006–07 national rates. Removing these states and the District of Columbia from the 2006–07 national counts results in a national rate of 73.7 percent, while prorating the 2006–07 rates to estimate the District of Columbia, Pennsylvania, and South Carolina data results in a 2005–06 rate of 73.4 percent. 4 In 2007–08, Maine reported 1,161 diplomas that were awarded to students attending private high schools that received a majority of their funding from public sources. These 1,161 diplomas were included in Maine and the reporting states counts but were not included in the averaged freshman graduation rate (AFGR) calculations for the state and for the reporting states totals. The diploma counts used to calculate the AFGR for Maine and for the reporting states were 13,189 and 2,964,125, respectively. 5 New Hampshire included homeschooled students in reported membership in 2000–01. This could inflate the denominator for the AFGR in 2002–03, 2003–04, and 2004–05 slightly. NOTE: The averaged freshman graduation rate (AFGR) is an estimate of the percentage of an entering freshman class graduating in 4 years. For 2007–08, it equals the total number of diploma recipients in 2007–08 divided by the average membership of the 8th-grade class in 2003–04, the 9th-grade class in 2004–05, and the 10th-grade class in 2005–06. Ungraded students were allocated to individual grades proportionally to the reported enrollments by grade. SOURCE: Seastrom, M., Hoffman, L., Chapman, C., and Stillwell, R. (2005). The Averaged Freshman Graduation Rate for Public High Schools From the Common Core of Data: School Years 2001–02 and 2002–03 (NCES 2006-601), table 1; Seastrom, M., Hoffman, L., Chapman, C., and Stillwell, R. (2007). The Averaged Freshman Graduation Rate for Public High Schools From the Common Core of Data: School Years 2002–03 and 2003–04 (NCES 2006-606rev), table 1; Sable, J., and Garofano, A. (2007). Public Elementary and Secondary School Student Enrollment, High School Completions, and Staff From the Common Core of Data: School Year 2005–06 (NCES 2007-352), table 4; Stillwell, R. and Hoffman, L. (2009). Public School Graduates and Dropouts From the Common Core of Data : School Year 2005–06 (NCES 2008-353rev), table 1; Stillwell, R. (2009). Public School Graduates and Dropouts From the Common Core of Data : School Year 2006–07 (NCES 2010-313), table 1. Stillwell, R. (2010). Public School Graduates and Dropouts From the Common Core of Data: School Year 2007–08 (NCES 2010-341), table 1. 55 ��Appendix A—Technical Notes Common Core of Data The Common Core of Data (CCD), administered by the National Center for Education Statistics (NCES), is an annual survey of the state-level education agencies in the 50 states, the District of Columbia, and 7 other jurisdictions.1 Through the CCD, statistical information is collected on all public school districts and their schools, staff, students, and finances. Information is not collected on private schools and their students, homeschoolers, individuals who never attended school in the United States, or those who have been out of a public school system for more than a year. Data from the CCD are used to calculate event dropout rates and averaged freshman graduation rates (AFGR) for public high school students. The dropout data collection was initiated with a set of instructions to state CCD coordinators in the summer of 1991. Those instructions specified the details of dropout data to be collected during the 1991–92 school year. Dropouts are reported for the preceding school year. Thus, the 1991–92 data were submitted to NCES as a component of the 1992–93 CCD data collection. Most recently, the 2007–08 dropout data were submitted as a component of the 2008–09 CCD data collection. Dropout counts from Vermont were suppressed due to a high frequency of missing data. Rates are presented for the District of Columbia and 49 states that submitted data that could be reported for the 2007–08 school year; a “reporting states” rate was calculated based on data from the reporting states (table 5). Data needed to estimate the AFGR, specifically data on diploma awards and enrollment by grade, have traditionally been part of the CCD data collection. Like dropout data, diploma recipient reports are lagged a year (e.g., 2006–07 diploma counts are in the 2007–08 data files). Defining and Calculating Event Dropout Rates Using the CCD The definition of “event dropout rates” that was agreed upon by NCES and the states was the following: 1 Dropout and averaged freshman graduation rate (AFGR) data presented in this report are based on the following CCD data files: “Local Education Agency Universe Survey Dropout and Completion Data File: School Years 1991–92 through 1996–97” (Version 1a); and “Local Education Agency Universe Survey Dropout and Completion Data File,” School Years 1997–98, 1998– 99, 1999–2000, 2000–01 (Versions 1b), and 2001–02 (Version 0d); and “State Nonfiscal Data File,” School Years, 1997–98 (Version 1b), 1998–99 (Version 1c), 1999–2000 (Version 1c), 2000–01 (Version 1b), 2001–02 (Version 1b), 2002–03 (Version 1b), 2003–04 (Version 0c), 2004–05 (Version 0c), 2005–06 (Version 1a), 2006–07 (Version 1a), and 2007–08 (Version 1a). The seven other jurisdictions include Department of Defense dependents schools (domestic and overseas); Bureau of Indian Education; Puerto Rico; American Samoa; Commonwealth of the Northern Mariana Islands; Guam; and the U.S. Virgin Islands. A-1 �Appendix A—Technical Notes The denominator of the rate is the current October 1st membership count for the state for the grades for which the dropout rate is being calculated. For example, the dropout rate for grades 9–12 would use a denominator that equals the October 1st enrollment count for grades 9–12.2 The numerator (dropouts) is all individuals who • were enrolled in school at some time during the previous school year; • were not enrolled at the beginning of the current school year; • have not graduated from high school or completed a state- or district-approved education program; and • do not meet any of the following exclusionary conditions: transferred to another public school district, private school, or state- or district-approved education program; temporary absence due to suspension or school-approved education program; or death. For the purpose of this definition, the following statements apply: • The school year is the 12-month period of time from the first day of school (operationally set as October 1), with dropouts from the previous summer reported for the year and grade in which they fail to enroll. Some states report using an alternative 12-month period from one July to the next, but the different periodicity does not affect the comparability of the estimates (Winglee et al. 2000); • Individuals who are not accounted for on October 1 are considered dropouts; and • A high school completer is an individual who has graduated from high school or completed a state- or district-approved education program upon receipt of formal recognition from school authorities. A state- or district-approved education program may consist of special education and district- or state-sponsored General Educational Development (GED) preparation. 2 Ungraded students are prorated across grades in the denominator proportional to known graded enrollment rates, and ungraded dropouts are included in the numerator. A-2 �Appendix A—Technical Notes Defining the Averaged Freshman Graduation Rate for Public School Students Using the CCD Data from the CCD state nonfiscal files are used to calculate AFGRs in this report. In the AFGR, graduates include only diploma recipients. Other high school completers, such as those who earn a certificate of attendance, and those awarded high school equivalency credentials such as GEDs, are not considered graduates. The purpose of these exclusions is to make the AFGR as similar as possible conceptually to Adequate Yearly Progress provisions in the Elementary and Secondary Education Act (ESEA) of 2001 (P.L. 107-110). These provisions require measurement of on-time graduation from public high schools and explicitly exclude GEDs and other types of nonregular diplomas. Another reason for the exclusion of equivalency credentials in the AFGR is that not all states report giving equivalency credentials, so comparable estimates across states would not be possible. Diploma Recipients. These are individuals who are awarded, in a given year, a high school diploma or a diploma that recognizes some higher level of academic achievement. They can be thought of as students who meet or exceed the coursework and performance standards for high school completion established by the state or other relevant authorities. State and local policies and data collection administration can have profound effects on the numbers of diploma recipients reported by a state. There are differences in what a high school diploma represents in different states. Some states award regular diplomas to all students who meet completion requirements, regardless of the extent to which these requirements address state or district academic standards. Other states award some form of alternative credential to students who meet some, but not all, requirements. Exclusion of Other High School Completers. Other high school completers were excluded from the calculation of the AFGR. These individuals receive a certificate of attendance or some other credential in lieu of a diploma. One example of such a credential is a certificate of attendance for special education students who do not follow a regular academic curriculum. Students awarded this credential typically meet requirements that differ from those for a high school diploma. Some states do not issue an “other high school completion” type of certificate, but award all students who complete school a diploma regardless of what academic requirements the students have met. Exclusion of High School Equivalency Recipients. High school equivalency recipients are awarded a credential certifying that they have met state or district requirements for high school completion by passing an examination or completing some other performance requirement. High school equivalency credentials, such as those earned by passing the GED test, are generally A-3 �Appendix A—Technical Notes considered valid completion credentials, but recipients of such credentials are excluded from the AFGR because the ESEA calls for only regular diploma recipients to be counted (table A-1). Incorporation of equivalency credentials into high school outcome measures would be further complicated by variation in how different states treat GED programs and recipients. Some states incorporate GED programs into their high school education systems and continue to follow the progress of individuals in these programs as part of their overall high school student population. These states count at least some GED recipients as equivalency credential holders in their high school data systems. Some states incorporate GED programs into adult social service programs or other programs outside of secondary education and do not track GED program participants or GED recipients as part of their high school student population. Averaged Freshman Graduation Rate. The AFGR provides an estimate of the percentage of high school students who graduate on time. The rate uses aggregate student enrollment data to estimate the size of an incoming freshman class and aggregate counts of the number of regular diplomas awarded 4 years later. The incoming freshman class size is estimated by summing the enrollment in 8th grade for one year, 9th grade for the next year, and 10th grade for the year after and then dividing by 3. The averaging is intended to account for higher grade retentions in the 9th grade in order to estimate how many of them were first-time 9th-graders. Although not as accurate as an on-time graduation rate computed from a cohort of students using student record data, this estimate of an on-time graduation rate can be computed with currently available data. The AFGR was selected from a number of alternative estimates that can be calculated using cross-sectional data based on a technical review and analysis of a set of alternative estimates (Seastrom et al. 2006a, 2006b). The rate for the class of 2007–08 was calculated in the following manner: High School Diplomas Awarded at End of 2007–08 School Year Enrollment in (Grade 8 in fall 2003 + Grade 9 in fall 2004 + Grade 10 in fall 2005)/3 Although enrollments are reported by grade, some states report ungraded students3 in addition to graded students. To adjust for this, an allocation procedure used in the CCD “Local Education Agency Universe Survey Dropout and Completion Data File” was applied. Through this process, the data for ungraded enrollment counts were redistributed across grades in proportion to the graded enrollment of the state, and the resulting estimates for grades 8, 9, and 10 were added to the reported enrollment counts for those grades. The AFGR for public school students in the United States for 2007–08 is based on data from 4 years. The numerator is the 3 Ungraded students are those who are assigned to a class or program that does not have standard grade designations. A-4 �Appendix A—Technical Notes 2,965,286 diploma recipients reported for school year 2007–08. The denominator is the average of the estimated 3,788,070 students in 8th grade in October 2003, the estimated 4,247,085 students in 9th grade in October 2004, and the estimated 3,841,810 students in 10th grade in October 2005. The 2,965,286 public school diploma recipients divided by the 3,958,987 averaged number of public school freshmen, multiplied by 100, results in a 2007–08 public school graduation rate for the United States of 74.9 percent. The same formula is applied to compute the 2001–02, 2002–03, 2003–04, 2004–05, 2005–06, and 2006–07 AFGRs for public school students in the country and in each state. Note that the AFGR is not the same as a true cohort graduation rate that shows the percentage of actual first-time 9th-grade students who graduated within 4 years of starting 9th grade. A true cohort rate requires data that track a given set of students over time. The CCD data used for the AFGR are collected using repeating cross-sectional surveys. Individual students are not followed from year to year. Although the AFGR was selected as the best of the available alternatives, there are several factors that make it fall short of a true on-time graduation rate. First, the averaged freshman class is, at best, an approximation of the actual number of first-time freshmen. To the extent that the averaging differs from actual net transfers into and out of a class, and to the extent that it does not accurately capture grade retention and dropout rates across all 4 years of a given freshman class’s expected high school stay, the estimate will be less accurate. Second, by including all graduates in a specific year, the graduates may include students who repeated a grade in high school or completed high school early and, thus, are not on-time graduates in that year. Taking these factors one at a time, it is possible that more high school students will move out of a given jurisdiction than move into it during the 4 years between the beginning of 9th grade and the expected graduation date. The averaged freshman count would overestimate the size of the actual cohort and thus underestimate the graduation rate. On the other hand, if more high school students moved into a jurisdiction than moved out during this 4-year period, the averaged freshman count would underestimate the size of the cohort and thus overestimate the graduation rate. Similarly, the use of 8th-, 9th-, and 10th-grade enrollment counts to estimate a first-time freshman class may not work as intended in many situations. Using 8th- and 9th-grade enrollment counts can be inaccurate to the extent that they do not adequately account for grade retention at 9th grade. Retention rates at 9th grade tend to be relatively large. While adding 8thgrade enrollments to the average may help diminish this problem, it is likely that in many cases it will not wholly adjust for actual 9th-grade retention rates, thus overestimating the first-time freshman count and underestimating the graduation rate. Using 9th- and 10th-grade enrollment numbers can be inaccurate to the extent that the 10th-grade counts exclude 9th-graders who A-5 �Appendix A—Technical Notes Table A-1.—Summary table of high school dropout, completion, and graduation rates Current statistic (year) Age group/ Grades Event dropout rate 3.5 percent (2008) 15–24 Percentage of Indicator of the high school annual rate at students who which U.S. high have dropped school students out of grades are leaving school 10–12 in the with an unsucpast year cessful outcome Students who get an equivalency certificate do not count as dropouts. Event dropout rate (public school students) 4.1 percent (2007–08) Grades 9–12 Percentage of State-level public high indicator of the school students annual rate at who have which public high dropped out of school students grades 9–12 in are leaving school a given year with an unsuccessful outcome Students who get a staterecognized equivalency certificate do not count as dropouts. Status dropout rate 8.0 percent (2008) 16–24 Percentage of people who are not enrolled in high school and who do not have a high school credential Indicator of the percentage of young people who lack a basic high school education Students who have earned an equivalency credential do not count as dropouts. 89.9 percent (2008) 18–24 Percentage of young adults who have left high school and who hold a high school credential Indicator of the percentage of young adults who have a basic high school education People who have earned an equivalency credential count as completers. Rate Status completion rate Description See notes at end of table. A-6 Purpose Equivalency certificate status �Appendix A—Technical Notes Table A-1.—Summary table of high school dropout, completion, and graduation rates—Continued Rate Averaged freshman graduation rate (public school students) Current statistic (year) Age group/ Grades 74.9 percent (2007–08) Grades 9–12 Description Purpose Percentage of public high school students who graduate with a regular diploma 4 years after starting 9th grade Indicator of on-time graduation from public schools Equivalency certificate status High school equivalency credentials are not counted as “graduation.” SOURCE: Stillwell, R. (2010). Public School Graduates and Dropouts From the Common Core of Data: School Year 2007–08 (NCES 2010-341), tables 1 and 7. U.S. Department of Commerce, Census Bureau, Current Population Survey . (CPS), October 2008. dropped out from the previous year (effectively underestimating the cohort) or include students retained in 10th grade (effectively overestimating the cohort). The inclusion of graduates who spent more or less than 4 years in high school increases the number of graduates in the numerator and yields a higher estimated rate than would be the case if only on-time graduates were included in the numerator. On the other hand, not recording early graduates with their actual cohort decreases the graduation rate for their original 9th-grade classes. Data Considerations for the CCD As a universe data collection, the CCD does not have sampling errors (the difference between an estimate based on a sample and the estimate based on an entire population). However, there are potential sources for nonsampling errors in universe data collections, including inability to get information about all cases (i.e., nonresponse), definitional difficulties, respondent inability to provide correct information, and errors made in recording, coding, and processing data. For more information about the CCD, go to http://nces.ed.gov/ccd/. Current Population Survey The Current Population Survey (CPS) provides nationally representative data for the civilian, noninstitutionalized population of the United States. The survey is conducted in a sample of 50,000–60,000 households each month. Households are interviewed for four successive A-7 �Appendix A—Technical Notes monthly interviews, are not interviewed for the next 8 months, and then are reinterviewed for the following 4 months. Typically, the first and the fifth interviews are conducted in person, with the remaining conducted via computer-assisted telephone interviewing. The sample frame is a complete list of dwelling-unit addresses at the time of the decennial Census updated by demolitions and new construction listings. The population surveyed excludes members of the armed forces, inmates of correctional institutions, and patients in long-term medical or custodial facilities; it is referred to as the civilian, noninstitutionalized population. The household-level nonresponse rate was 8.3 percent in the 2007 October basic CPS and the person-level nonresponse rate for the school enrollment supplement was an additional 5.3 percent. These rates cannot be combined to derive an overall person-level response rate. For more information, please see Current Population Survey, October 2008: School Enrollment and Internet Use Supplement File (Technical Documentation CPS-08) (U.S. Department of Commerce 2009). An adult member of each household serves as the informant for that household, supplying basic monthly data for each member of the household. In addition, in October of each year, supplementary questions regarding school enrollment are asked about eligible household members ages 3 and older. Data are collected about individuals who attend or attended public schools and private schools, who were homeschooled, or who never attended school in the United States. CPS data on educational attainment and enrollment status in the current year and prior year are used to identify dropouts and completers, and additional items in the CPS data are used to describe some of their basic characteristics. The CPS is the only source of national time series data on dropout and completion rates. However, because the CPS collects no information on school characteristics and experiences, its usefulness in addressing dropout and completion issues is primarily for providing insights on who drops out and who completes. Sample sizes in the CPS collections do not support stable state-level estimates. There are important differences in data collection procedures between the CPS and the CCD. First, the CCD collection includes only data for public schools, whereas the CPS counts include students who were enrolled in either public or private schools and some individuals who were never enrolled in school in the United States. Second, the CCD collects data about students from a given state’s public school system. CPS data are based on where individuals currently reside, so the state of residence may differ from the state or country of earlier school attendance. Third, the CCD collection includes dropouts in grades 7–12, versus grades 10–12 in the CPS (although the CCD event rates are reported for grades 9–12 in this report). Fourth, the CCD collection is based on administrative records rather than individual self-reports based on household surveys as in the CPS. Finally, data in the CCD are collected from the full universe of public schools, whereas data in the CPS are collected from a sample of households, not the full universe of households. As a result, CPS data have sampling errors associated with estimates A-8 �Appendix A—Technical Notes whereas CCD data do not. For more information on CPS sampling errors and how to interpret them, see the section “Statistical Procedures for Analyzing CPS-Based Estimates” later in appendix A. Defining and Calculating Dropout and Completion Rates Using the CPS Event Dropout Rates The October Supplement to the CPS is the only national data source that currently can be used to estimate annual national dropout rates. As a measure of recent dropout experiences, the event dropout rate measures the proportion of students who dropped out over a 1-year interval. The numerator of the event dropout rate for 2008 is the number of persons ages 15–244 surveyed in October 2008 who were enrolled in grades 10–12 in October 2007, who were not enrolled in high school in October 2008, and who also did not complete high school (that is, had not received a high school diploma or an alternative credential such as an equivalency certificate) between October 2007 and October 2008. The denominator of the event dropout rate for 2008 is the sum of the dropouts (that is, the numerator) and all persons ages 15–24 who were attending grades 10–12 in October 2007, who were still enrolled in October 2008, or who graduated or completed high school between October 2007 and October 2008. The dropout interval is defined to include the previous summer (in this case, the summer of 2008) and the previous school year (in this case, the 2007 school year), so that once a grade is completed, the student is then at risk of dropping out of the next grade. Given that the data collection is tied to each person’s enrollment status in October of 2 consecutive years, any student who drops out and returns within the 12-month period is not counted as a dropout. Status Dropout Rates The status dropout rate reflects the percentage of individuals who are dropouts, regardless of when they dropped out. The numerator of the status dropout rate for 2008 is the number of individuals ages 16–245 who, as of October 2008, had not completed high school and were not currently enrolled. The denominator is the total number of 16- through 24-year-olds in October 2008. 4 This age range was chosen in an effort to include as many students in grades 10–12 as possible. Because the rate is based on retrospective data, it is lagged 1 year, meaning that some 15-year-olds have turned age 16 by the time of the interview. 5 Age 16 was chosen as the lower age limit because, in some states, compulsory education is not required after age 16. Age 24 was chosen as the upper limit because it is the age at which free secondary education is no longer available and the age at which the average person who is going to obtain a GED does so. A-9 �Appendix A—Technical Notes Status Completion Rates The numerator of the high school status completion rate is the number of 18- through 24year-olds6 who had received a high school diploma or an alternative credential such as a GED. The denominator is the number of 18- through 24-year-olds who are no longer in elementary or secondary school. GED Credentials and the Status Completion Rate. Prior to 2000, editions of this series of high school completion and dropout reports presented estimates of overall status completion rates and estimates of the method of completion—graduation by diploma or completion through an alternative credential such as the GED—based on data obtained through CPS reporting. Because of changes in CPS introduced in 2000, data on the method of completion were not comparable with prior year CPS estimates and the method of completion data were no longer reported. Please see the discussion of the GED Testing Service data below for further information. Data Considerations for the CPS Over the last several decades, data collection procedures, items, and data preparation processes have changed in the CPS. Some of these changes were introduced to ensure that CPS estimates were comparable to those from decennial Census collections, some were introduced to reflect changes in the concepts under study, some were introduced to improve upon measures, and some were introduced to develop measures for new phenomena. The effects of the various changes have been studied to help ensure they do not disrupt trend data from the CPS. For a summary of the changes and studies of their effects, please see appendix C of Dropout Rates in the United States: 2001 (Kaufman, Alt, and Chapman 2004). CPS data include weights to help make estimates from the data representative of the civilian, noninstitutionalized population in the United States. These weights are based on decennial Census data that are adjusted for births, deaths, immigration, emigration, etc., over time. Imputation for Item Nonresponse in the CPS. For many key items in the October CPS, the U.S. Census Bureau imputes data for cases with missing data due to item nonresponse. However, the U.S. Census Bureau did not impute data regarding the method of high school completion before 1997. Special imputations were conducted for these items using a sequential hot deck procedure implemented through the PROC IMPUTE computer program developed by the 6 Age 18 was chosen as the lower age limit because most diploma holders earn their diploma by this age. Age 24 was chosen as the upper limit because it is the age at which free secondary education is no longer available and the age at which the average person who is going to obtain a GED does so. A-10 �Appendix A—Technical Notes American Institutes for Research. Three categories of age, two categories of race, two categories of sex, and two categories of citizenship were used as imputation cells. Age and Grade Ranges in CPS Estimates. The age and grade ranges used in the CPS measures of dropout rates are constrained by available data. Ideally, the estimates would be able to capture reliable estimates of children in grades as low as grade 9. However, the CPS asks the question about enrollment in the previous October only about individuals ages 15 and older. Many 9th-graders are younger than age 15, so 10th grade was selected as the lower boundary of grade ranges in the event dropout rate. Accuracy of CPS Estimates. CPS estimates in this report are derived from samples and are subject to two broad classes of error—sampling and nonsampling error. Sampling errors occur because the data are collected from a sample of a population rather than from the entire population. Estimates based on a sample will differ to some degree (dependent largely on sample size and coverage) from the values that would have been obtained from a universe survey using the same instruments, instructions, and procedures. Nonsampling errors come from a variety of sources and affect all types of surveys—universe as well as sample surveys. Examples of sources of nonsampling error include design, reporting, and processing errors and errors due to nonresponse. The effects of nonsampling errors are more difficult to evaluate than those that result from sampling variability. As much as possible, procedures are built into surveys in order to minimize nonsampling errors. The standard error is a measure of the variability due to sampling when estimating a parameter. It indicates how much variance there is in the population of possible estimates of a parameter for a given sample size. Standard errors can be used as a measure of the precision expected from a particular sample. The probability that a sample statistic would differ from a population parameter by less than the standard error is about 68 percent. The chances that the difference would be less than 1.65 times the standard error are about 90 out of 100, and the chances that the difference would be less than 1.96 times the standard error are about 95 out of 100. Standard errors for percentages and numbers of persons based on CPS data were calculated using the following formulas: A-11 �Appendix A—Technical Notes Percentage: se = where p N b (b / N )( p )(100 − p ) = the percentage (0 < p < 100), = the population on which the percentage is based, and = the regression parameter, which is based on a generalized variance formula and is associated with the characteristic. For 2008, b is equal to 2,131 for the total or White population, 2,410 for the Black population, 2,744 for the Hispanic population, and 2,410 for the Asian/Pacific Islander population ages 14–24. The b for regional estimates are 1.06 for the Northeast, 1.06 for the Midwest, 1.07 for the South, and 1.02 for the West. CPS documentation explains the purpose and process for the generalized variance parameter: Experience has shown that certain groups of estimates have similar relations between their variances and expected values. Modeling or generalizing may provide more stable variance estimates by taking advantage of these similarities. The generalized variance function is a simple model that expresses the variance as a function of the expected value of a survey estimate. The parameters of the generalized variance function are estimated using direct replicate variances (Cahoon 2005, p. 7). Number of persons: se = (bx )(1 − ( x / T )) where x T b = the number of persons (i.e., dropouts), = population in the category (e.g., Blacks ages 16–24), and = as above. Statistical Procedures for Analyzing CPS-Based Estimates Because CPS data are collected from samples of the population, statistical tests are employed to measure differences between estimates to help ensure they are taking into account possible sampling error. 7 The descriptive comparisons in this report were tested using Student’s t statistic. Differences between estimates are tested against the probability of a type I error,8 or significance level. The significance levels were determined by calculating the Student’s t values for the differences between each pair of means or proportions and comparing these with published tables of significance levels for two-tailed hypothesis testing. 7 The CCD and GEDTS data are universe data collections and therefore do not require statistical testing such as that used for estimates from the CPS sample survey data. 8 A Type I error occurs when one concludes that a difference observed in a sample reflects a true difference in the population from which the sample was drawn, when no such difference is present. It is sometimes referred to as a “false positive.” A-12 �Appendix A—Technical Notes Student’s t values may be computed to test the difference between percentages with the following formula: t= P1 − P2 se12 + se22 where P1 and P2 are the estimates to be compared and se1 and se2 are their corresponding standard errors. Several points should be considered when interpreting t statistics. First, comparisons based on large t statistics may appear to merit special attention. This can be misleading since the magnitude of the t statistic is related not only to the observed differences in means or proportions but also to the number of respondents in the specific categories used for comparison. Hence, a small difference compared across a large number of respondents would produce a large t statistic. Second, there is a possibility that one can report a “false positive” or type I error. In the case of a t statistic, this false positive would result when a difference measured with a particular sample showed a statistically significant difference when there was no difference in the underlying population. Statistical tests are designed to control this type of error. These tests are set to different levels of tolerance or risk known as alphas. The alpha level of .05 selected for findings in this report indicates that a difference of a certain magnitude or larger would be produced no more than 1 time out of 20 when there was no actual difference in the quantities in the underlying population. When p values are smaller than the .05 level, the null hypothesis that there is no difference between the two quantities is rejected. Finding no difference, however, does not necessarily imply that the values are the same or equivalent. Third, the probability of a type I error increases with the number of comparisons being made. Bonferroni adjustments are sometimes used to correct for this problem. Bonferroni adjustments do this by reducing the alpha level for each individual test in proportion to the number of tests being done. However, while Bonferroni adjustments help avoid type I errors, they increase the chance of making type II errors. Type II errors occur when there actually is a difference present in a population, but a statistical test applied to estimates from a sample indicates that no difference exists. Prior to the 2001 report in this series, Bonferroni adjustments were employed. Because of changes in NCES reporting standards, Bonferroni adjustments are not employed in this report. Regression analysis was used to test for trends across age groups and over time. Regression analysis assesses the degree to which one variable (the dependent variable) is related to one or more other variables (the independent variables). The estimation procedure most commonly used in regression analysis is ordinary least squares (OLS). When studying changes in rates over time, A-13 �Appendix A—Technical Notes the rates were used as dependent measures in the regressions, with a variable representing time and a dummy variable controlling for changes in the educational attainment item in 1992 (= 0 for years 1972 to 1991, = 1 after 1992) used as independent variables. When slope coefficients were positive and significant, rates increased over time. When slope coefficients were negative and significant, rates decreased over time. Because of varying sample sizes over time, some of the observations were less reliable than others (i.e., some years’ standard errors were larger than those for other years). In such cases, OLS estimation procedures do not apply, and it is necessary to modify the regression procedures to obtain unbiased regression parameters. This is accomplished by using weighted least squares regressions.9 Each variable in the analysis was transformed by dividing by the standard error of the relevant year’s rate. The new dependent variable was then regressed on the new time variable, a variable for 1 divided by the standard error for the year’s rate, and the new editing-change dummy variable. All statements about trend changes in this report are statistically significant at the .05 level. GED Testing Service The GED Testing Service (GEDTS) collects data on individuals who take the GED exam each year and on individuals who pass the exam each year. These data are collected from test sites both in the United States and internationally. The GEDTS releases the data in aggregate form in annual statistical reports. The reports are organized to allow readers to differentiate between those individuals taking and passing the exam in the United States and those taking and passing the exam outside of the United States. Though GEDTS designs and administers the exam, states and sometimes jurisdictions within a state determine who can take the exam, how much pre-exam preparation is required, what scores are needed to pass the exam, how and when exam can be retaken, how much the exam cost, and the official name of the resulting credential (see http://www2.acenet.edu/gedtest/policy/index.cfm?return=1 for details). Prior to 2000, NCES completion and dropout reports presented estimates of those holding alternative credentials such as GEDs directly from CPS data as part of the status completion rate. Examination of the changes in the CPS alternative credential items in the October 2000 and subsequent surveys has indicated that these estimates may not be reliable estimates of high school equivalency completions.10 Therefore, CPS estimates of the method of high school equivalency completion were not presented in several NCES reports. Because GED recipients do 9 For a general discussion of weighted least squares analysis, please see Gujarati, D., Basic Econometrics 2nd ed. McGraw Hill, Inc., New York: New York, 1998. 10 For a comparison of estimates from the CPS and the GED Testing Service of the number of 18- through 24-year-olds who have received a GED, see table A-1 in Laird, J., DeBell, M., Kienzl, G., and Chapman, C. (2007). Dropout Rates in the United States: 2005 (NCES 2007-059). National Center for Education Statistics, Institute of Education Sciences, U.S. Department of Education. Washington, DC. A-14 �Appendix A—Technical Notes have notably different life experiences than those with no high school credential and those with a regular high school diploma, the loss of information about alternative credential holders was an important measurement problem. In response, NCES developed an approach for using GEDTS to estimate how many young people in the civilian, noninstitutionalized population in a given age range had earned a GED by passing the GED exam. It is important to acknowledge here that Mishel and Roy (2006) simultaneously and independently developed a similar approach for research that they were conducting. Table A-2 provides a summary of the data released by GEDTS on the number of people passing the exam each year and the age distribution of those passing the exam (American Council on Education, GED Testing Service 1991–2002, 2003–06, 2007, 2008, 2009). For the U.S. population, GEDTS indicates that approximately 250,000 persons ages 18–24 passed the GED in 2008. The GED status rate indicates the percentage of individuals in a given age range who passed the GED exam irrespective of when they passed the exam.28 In order to derive the GED status rate, data from several GEDTS reports were combined. For 18- through 24-yearolds, this was done by adding the count of 18- through 24-year-olds who passed the exam in 2008 to counts of people who were ages 18–24 in 2008, but who passed the exam in earlier years. The number of 18- through 24-year-olds who passed the exam in 2008 was added to the number of 17- through 23-year-olds who passed the exam in 2007. That sum was added to the number of 16- through 22-year-olds who passed the exam in 2006, the number of 16- through 21-year-olds who passed the exam in 2005, the number of 16- through 20-year-olds who passed the exam in 2004, the number of 16- through 19-year-olds who passed the exam in 2003, the number of 16- through 18-year-olds who passed the exam in 2002, the number of 16- and 17year-olds who passed the exam in 2001, and the number of 16-year-olds who passed the exam in 2000. Sixteen year-olds in 2000 would have been 24 in 2008. Based on this approach, approximately 1,622,000 persons ages 18 through 24 held a GED in 2008. Because the CPS-based status rates developed for this report focus on individuals in the civilian, noninstitutionalized population, adjustments were made to the GED count estimates. GED count data are reported by year the GED was earned, whereas the status rates reflect the experience of individuals over multiple year periods. As such, individuals might have been part of the civilian, noninstitutionalized population when they earned a GED, and subsequently joined the military or the prison populations. Alternatively, individuals might have been in the military or prison when they earned a GED and subsequently reentered the civilian, noninstitutionalized population. To account for both possibilities, data for current active-duty military personnel for 2008 were obtained from the Defense Manpower Data Center and from the Survey of Inmates in 28 The GED Testing Service reports 20- through 24-year-olds as one age group. Single year of age data for those in the 20–24year-old group was estimated by dividing the group count by 5 in a given year. A-15 �Appendix A—Technical Notes State and Federal Correctional Facilities, 2004 (op. cited). More recent prison data including inmate educational attainment were not available. Rates derived from the 2004 prison data were applied to 2008 prison data that contained prison inmate age distributions (table A-3). Prison data for 2008 were drawn from the Bureau of Justice Statistics’ National Prisoner Statistics 2008 (1b). After these adjustments, the estimated number of 18- through 24-year-old individuals in the civilian, noninstitutionalized population holding a GED in 2008 was approximately 1,500,000. A similar approach was used to estimate the number of 16-24-year-olds in the civilian, noninstitutionalized population holding a GED in 2008. Table A-2. —Percentage distribution of persons who passed the General Educational Development (GED) Table A-2.—exam outside of federal and state contract facilities, by age group: 1998–2008 Year1 Number passed 16 17 18 Age group 19 20–24 25 or older 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 480,947 498,015 486,997 648,022 329,515 387,470 405,724 423,714 398,045 428,840 467,994 2.8 3.3 3.2 2.9 4.4 3.9 4.0 3.9 4.1 4.0 3.6 11.8 12.9 13.0 11.5 15.8 14.6 14.0 13.7 14.4 14.3 13.5 19.1 16.1 16.5 14.7 17.4 16.8 16.8 16.1 16.7 17.0 16.9 12.2 12.3 12.2 11.5 11.6 11.4 11.4 10.9 10.9 10.9 11.1 24.1 24.3 24.9 26.4 24.6 25.9 26.2 25.6 24.9 24.1 24.0 30.0 31.1 30.2 33.0 26.2 27.4 27.6 29.8 29.0 29.7 30.9 1 Prior to 2002, those passing GED exams in federal or state contract facilities were issued GEDs in their state of residence. Contract facilities include military installations and prisons. NOTE: Data apply to the 50 states and the District of Columbia. The numbers and percentage distributions for 1998–2001 were reported in the original source as the number receiving a credential. SOURCE: American Council on Education, GED Testing Service. (1991–2002). Who Took the GED? GED Annual Statistical Report. Washington, DC: Author; American Council on Education, GED Testing Service. (2003–06). Who Passed the GED Tests? Annual Statistical Report. Washington, DC: Author; American Council on Education, GED Testing Service. (2007). 2006 GED Testing Program Statistical Report. Washington, DC: Author; American Council on Education, GED Testing Service. (2008). 2007 GED Testing Program Statistical Report. Washington, DC: Author; and American Council on Education, GED Testing Service. (2009). 2008 GED Testing Program Statistical Report. Washington, DC: Author. A-16 �Appendix A—Technical Notes Table A-3.—Percentage distribution of persons who passed the General Educational Development (GED) Table A-3.—exam at federal or state contract facilities, by age group: 1998–2008 Year1 Number passed 16 17 18 Age group 19 20–24 25 or older 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 † † † † 4,414 6,332 8,644 10,591 10,143 11,741 14,727 † † † † 0.0 0.3 0.4 0.3 0.4 0.3 1.0 † † † † 0.4 1.0 1.0 3.1 3.5 3.0 5.8 † † † † 1.6 1.7 2.0 4.0 5.5 7.5 10.9 † † † † 3.8 2.7 2.9 4.1 6.1 7.1 9.1 † † † † 26.8 27.9 25.4 23.9 23.8 25.0 23.5 † † † † 67.4 66.4 68.3 64.6 60.7 57.1 49.7 † Not applicable. 1 Prior to 2002, people passing exams in federal or state contract facilities were issued GEDs in their state of residence. NOTE: Data apply to the 50 states and the District of Columbia. The numbers and percentage distributions for 1998–2001 were reported in the original source as the number receiving a credential. SOURCE: American Council on Education, GED Testing Service. (1991–2002). Who Took the GED? GED Annual Statistical Report. Washington, DC: Author; American Council on Education, GED Testing Service. (2003–06). Who Passed the GED Tests? Annual Statistical Report. Washington, DC: Author; American Council on Education, GED Testing Service. (2007). 2006 GED Testing Program Statistical Report. Washington, DC: Author; American Council on Education, GED Testing Service. (2008). 2007 GED Testing Program Statistical Report. Washington, DC: Author; and American Council on Education, GED Testing Service. (2009). 2008 GED Testing Program Statistical Report. Washington, DC: Author. A-17 ��Appendix B—Glossary For dropout and completion rate estimates, please see the discussions above and table A-1. Age. Age of the subject at the time of the interview. Family income. In the Current Population Survey (CPS), family income is derived from a single question asked of the household respondent. Income includes money income from all sources including jobs, business, interest, rent, and social security payments. The income of nonrelatives living in the household is excluded, but the income of all family members 14 years old and older, including those temporarily living away, is included. Family income refers to receipts over a 12-month period. There are several issues that affect the interpretation of dropout rates by family income using the CPS. First, it is possible that the family income of the students at the time they dropped out was somewhat different from their family income at the time of the CPS interview. Furthermore, family income is derived from a single question asked of the household respondent in the October CPS. In some cases, there are persons ages 15–24 living in the household who are unrelated to the household respondent, yet whose family income is defined as the income of the family of the household respondent. Therefore, the current family income of the respondent may not accurately reflect that person’s family background. In particular, some of the young adults in the 15- through 24-year age range do not live in a family unit with a parent present. GED, or General Educational Development. General Educational Development (GED) tests are standardized tests designed to measure the skills and knowledge that students normally acquire by the end of high school. The tests are developed by the American Council on Education’s GED Testing Service. People who pass may receive a high school equivalency credential. Geographic regions. There are four Census regions used in this report: Northeast, Midwest, South, and West. The Northeast consists of Maine, New Hampshire, Vermont, Massachusetts, Connecticut, Rhode Island, New York, New Jersey, and Pennsylvania. The Midwest consists of Ohio, Indiana, Illinois, Michigan, Wisconsin, Iowa, Minnesota, Missouri, North Dakota, South Dakota, Nebraska, and Kansas. The South consists of Delaware, Maryland, the District of Columbia, Virginia, West Virginia, North Carolina, South Carolina, Georgia, Florida, Kentucky, Tennessee, B-1 �Appendix B—Glossary Alabama, Mississippi, Arkansas, Louisiana, Oklahoma, and Texas. The West consists of Montana, Idaho, Wyoming, Colorado, New Mexico, Arizona, Utah, Nevada, Washington, Oregon, California, Alaska, and Hawaii. Recency of immigration. Recency of immigration was derived from a set of questions on the CPS survey inquiring about the country of birth of the reference person and his or her mother and father. From these questions, the following three categories were constructed: (1) born outside the 50 states and the District of Columbia, (2) first generation, and (3) second generation or higher. First generation is defined as individuals who were born in one of the 50 states or the District of Columbia, but who had at least one parent who was not. Second generation or higher persons are individuals who themselves, as well as both of their parents, were born in one of the 50 states or the District of Columbia. These three categories were subdivided using the variable for the subject’s race/ethnicity (please see below) so that there were six categories: the three immigration categories plus a Hispanic and non-Hispanic category for each of the three immigration categories. Race/ethnicity. This variable is constructed from two variables in the CPS. One asks about the subject’s ethnic background and the second asks about the subject’s race. Those reported as being of Hispanic background on the ethnic background question are categorized as Hispanic irrespective of race. Non-Hispanics are then categorized by race. Beginning in 2003, respondents were able to indicate two or more races. Those who indicated two or more races and who did not indicate that they were Hispanic are categorized as “Two or more races, non-Hispanic.” Sex. Sex of the subject. B-2 �Appendix C—Standard Error Tables C-1 �Appendix C—Standard Error Tables Table C-1.—Standard errors for table 1: Event dropout rates and number and distribution of 15- through Table C-1.—24-year-olds who dropped out of grades 10–12, by selected characteristics: October 2008 Event dropout rate (percent) Number of event dropouts (thousands) Population enrolled (thousands) Percent of all dropouts Percent of population enrolled Total 0.26 28.3 131.6 † † Sex Male Female 0.34 0.39 19.0 21.0 93.7 92.4 3.68 3.68 0.69 0.69 0.27 0.94 0.85 18.0 15.4 16.2 102.6 53.7 62.4 3.62 3.50 3.67 0.68 0.53 0.59 1.47 6.2 27.6 1.60 0.28 Family income Low income Middle income High income 1.05 0.31 0.37 16.1 20.1 11.3 51.0 100.7 66.6 3.50 3.70 2.69 0.48 0.68 0.62 Age 15–16 17 18 19 20–24 0.40 0.41 0.50 1.11 2.79 12.4 15.6 14.8 9.0 9.6 64.7 31.8 44.7 37.4 26.9 2.90 3.40 3.29 2.25 2.50 0.63 0.66 0.61 0.36 0.24 2.17 1.49 9.4 6.2 31.3 26.6 2.40 1.59 0.31 0.26 1.08 0.60 9.1 4.7 40.2 34.1 2.27 1.20 0.42 0.36 1.52 0.29 9.5 23.1 35.1 111.4 2.38 3.49 0.36 0.62 0.50 0.47 0.50 0.58 10.1 12.5 19.1 14.9 57.4 65.4 80.8 64.3 2.45 2.93 3.78 3.33 0.55 0.61 0.68 0.59 Characteristic Race/ethnicity White, non-Hispanic Black, non-Hispanic Hispanic Asian/Pacific Islander, non-Hispanic Recency of immigration Born outside the 50 states and District of Columbia Hispanic Non-Hispanic First generation Hispanic Non-Hispanic Second generation or higher Hispanic Non-Hispanic Region Northeast Midwest South West † Not applicable. The corresponding statistic refers to the total population, which is, by definition, 100 percent of the distribution. SOURCE: U.S. Department of Commerce, Census Bureau, Current Population Survey (CPS), October 2008. C-2 �Appendix C—Standard Error Tables Table C-2. —Standard errors for table 2: Event dropout rates of 15- through 24-year-olds who dropped out Table C-2.—of grades 10–12, and number of dropouts and population of 15- through 24-year-olds who were Table C-2.—enrolled: October 1972 through October 2008 Year Event dropout rate (percent) Number of event dropouts (thousands) Population enrolled (thousands) 1972 1973 1974 1975 1976 0.33 0.33 0.34 0.32 0.32 34.3 35.2 36.6 34.4 34.7 125.7 127.0 128.1 128.3 128.6 1977 1978 1979 1980 1981 0.34 0.34 0.34 0.33 0.33 37.1 37.2 37.2 35.0 34.5 130.0 129.7 129.3 128.7 128.7 1982 1983 1984 1985 1986 0.34 0.33 0.33 0.34 0.32 34.6 33.1 32.4 32.3 31.1 126.8 125.7 123.9 122.8 123.7 1987 1988 1989 1990 1991 0.30 0.36 0.36 0.34 0.34 29.9 34.6 32.4 29.1 29.1 123.1 122.0 119.5 118.9 119.3 1992 1993 1994 1995 1996 0.35 0.36 0.34 0.35 0.34 30.5 30.4 34.5 36.0 34.1 120.1 119.5 123.6 124.3 124.8 1997 1998 1999 2000 2001 0.32 0.33 0.33 0.33 0.33 32.0 32.9 34.2 33.2 33.7 126.7 132.0 134.1 126.7 133.7 2002 2003 2004 2005 2006 0.27 0.28 0.30 0.27 0.27 27.5 29.6 31.4 29.1 28.9 127.2 129.3 128.4 130.5 130.6 See notes at end of table. C-3 �Appendix C—Standard Error Tables Table C-2. —Standard errors for table 2: Event dropout rates of 15- through 24-year-olds who dropped out Table C-2.—of grades 10–12, and number of dropouts and population of 15- through 24-year-olds who were Table C-2.—enrolled: October 1972 through October 2008—Continued Year Event dropout rate (percent) Number of event dropouts (thousands) Population enrolled (thousands) 2007 2008 0.26 0.26 28.1 28.3 131.2 131.6 NOTE: Some of the standard error estimates in this table may differ from those previously published due to changes in the generalized variance parameters developed by the U.S. Census Bureau. SOURCE: U.S. Department of Commerce, Census Bureau, Current Population Survey (CPS), October 1972–2008. C-4 �Appendix C—Standard Error Tables Table C-3.—Standard errors for table 3: Event dropout rates of 15- through 24-year-olds who dropped out Table C-3.—of grades 10–12, by sex and race/ethnicity: October 1972 through October 2008 Sex (percent) Race/ethnicity (percent) White nonBlack nonHispanic Hispanic Hispanic Year Total (percent) Male Female 1972 1973 1974 1975 1976 0.33 0.33 0.34 0.32 0.32 0.46 0.49 0.51 0.44 0.48 0.48 0.45 0.46 0.46 0.43 0.34 0.35 0.35 0.33 0.35 1.32 1.35 1.41 1.25 1.15 2.81 2.65 2.52 2.50 2.05 1977 1978 1979 1980 1981 0.34 0.34 0.34 0.33 0.33 0.49 0.51 0.49 0.49 0.47 0.46 0.46 0.48 0.45 0.46 0.37 0.36 0.37 0.35 0.34 1.20 1.31 1.32 1.21 1.29 2.13 2.75 2.43 2.56 2.28 1982 1983 1984 1985 1986 0.34 0.33 0.33 0.34 0.32 0.49 0.50 0.49 0.50 0.46 0.46 0.45 0.46 0.48 0.45 0.36 0.35 0.36 0.36 0.34 1.21 1.17 1.06 1.26 1.05 2.31 2.44 2.51 2.55 2.69 1987 1988 1989 1990 1991 0.30 0.36 0.36 0.34 0.34 0.44 0.52 0.51 0.48 0.46 0.41 0.50 0.51 0.47 0.49 0.33 0.39 0.37 0.36 0.36 1.14 1.20 1.39 1.15 1.20 1.89 3.09 2.65 2.29 2.17 1992 1993 1994 1995 1996 0.35 0.36 0.34 0.35 0.34 0.46 0.51 0.48 0.51 0.49 0.53 0.50 0.49 0.48 0.51 0.38 0.40 0.37 0.38 0.38 1.09 1.20 1.03 1.00 1.05 2.23 2.03 1.52 1.61 1.50 1997 1998 1999 2000 2001 0.32 0.33 0.33 0.33 0.33 0.47 0.45 0.44 0.49 0.49 0.43 0.47 0.49 0.43 0.44 0.35 0.36 0.36 0.37 0.37 0.92 0.91 1.00 1.01 1.01 1.45 1.48 1.28 1.24 1.38 2002 2003 2004 2005 2006 0.27 0.28 0.30 0.27 0.27 0.39 0.40 0.44 0.40 0.39 0.37 0.38 0.41 0.36 0.36 0.28 0.31 0.34 0.29 0.30 0.87 0.85 0.94 1.03 0.77 1.01 1.06 1.20 0.87 1.01 See notes at end of table. C-5 �Appendix C—Standard Error Tables Table C-3.—Standard errors for table 3: Event dropout rates of 15- through 24-year-olds who dropped out Table C-3.—of grades 10–12, by sex and race/ethnicity: October 1972 through October 2008—Continued Sex (percent) Year Total (percent) Male Female 2007 2008 0.26 0.26 0.37 0.34 0.35 0.39 Race/ethnicity (percent) White nonBlack nonHispanic Hispanic Hispanic 0.26 0.27 0.80 0.94 NOTE: Some of the standard error estimates in this table may differ from those previously published due to changes in the generalized variance parameters developed by the U.S. Census Bureau. SOURCE: U.S. Department of Commerce, Census Bureau, Current Population Survey (CPS), October 1972–2008. C-6 0.98 0.85 �Appendix C—Standard Error Tables Table C-4.—Standard errors for table 4: Event dropout rates of 15- through 24-year-olds who dropped out Table C-4.—of grades 10–12, by family income: October 1972 through October 2008 Year Total (percent) Low income 1972 1973 1974 1975 1976 0.33 0.33 0.34 0.32 0.32 1.55 1.65 † 1.57 1.61 0.45 0.46 † 0.43 0.46 0.39 0.32 † 0.38 0.34 1977 1978 1979 1980 1981 0.34 0.34 0.34 0.33 0.33 1.57 1.69 1.62 1.51 1.50 0.48 0.48 0.47 0.46 0.45 0.35 0.40 0.44 0.38 0.41 1982 1983 1984 1985 1986 0.34 0.33 0.33 0.34 0.32 1.52 1.35 1.49 1.53 1.33 0.46 0.48 0.45 0.47 0.45 0.36 0.39 0.37 0.39 0.34 1987 1988 1989 1990 1991 0.30 0.36 0.36 0.34 0.34 1.29 1.59 1.43 1.39 1.43 0.45 0.48 0.50 0.45 0.44 0.27 0.35 0.33 0.33 0.31 1992 1993 1994 1995 1996 0.35 0.36 0.34 0.35 0.34 1.42 1.57 1.44 1.36 1.34 0.46 0.46 0.44 0.47 0.46 0.36 0.35 0.41 0.39 0.41 1997 1998 1999 2000 2001 0.32 0.33 0.33 0.33 0.33 1.36 1.34 1.26 1.23 1.36 0.41 0.39 0.44 0.45 0.45 0.37 0.46 0.40 0.35 0.37 2002 2003 2004 2005 2006 0.27 0.28 0.30 0.27 0.27 1.05 1.04 1.24 1.06 1.12 0.36 0.39 0.39 0.36 0.34 0.34 0.30 0.41 0.30 0.36 See notes at end of table. C-7 Family income (percent) Middle income High income �Appendix C—Standard Error Tables Table C-4.—Standard errors for table 4: Event dropout rates of 15- through 24-year-olds who dropped out Table C-4.—of grades 10–12, by family income: October 1972 through October 2008—Continued Year Total (percent) Low income 2007 2008 0.26 0.26 1.07 1.05 Family income (percent) Middle income High income 0.34 0.31 † Not applicable. Data for family income are not available for 1974. NOTE: Some of the standard error estimates in this table may differ from those previously published due to changes in the generalized variance parameters developed by the U.S. Census Bureau. SOURCE: U.S. Department of Commerce, Census Bureau, Current Population Survey (CPS), October 1972–2008. C-8 0.25 0.37 �Appendix C—Standard Error Tables Table C-5.—Standard errors for table 6: Status dropout rates and number and distribution of dropouts of Table C-5.—16- through 24-year-olds, by selected characteristics: October 2008 Status dropout rate (percent) Number of status dropouts (thousands) Population (thousands) Percent of all dropouts Percent of population Total 0.20 76.8 — † † Sex Male Female 0.30 0.28 56.0 52.6 — — 1.33 1.33 0.38 0.38 0.21 0.63 0.78 47.3 34.1 52.5 — — — 1.28 1.08 1.48 0.37 0.28 0.33 0.82 12.4 — 0.42 0.16 Characteristic Race/ethnicity White, non-Hispanic Black, non-Hispanic Hispanic Asian/Pacific Islander, non-Hispanic American Indian/Alaska Native, non-Hispanic Two or more races, non-Hispanic 3.20 9.4 — 0.34 0.07 1.17 8.3 — 0.28 0.11 Age 16 17 18 19 20–24 0.33 0.48 0.59 0.68 0.30 13.9 20.9 25.7 28.2 61.3 — — — — — 0.46 0.69 0.84 0.92 1.27 0.24 0.24 0.24 0.24 0.38 1.61 0.76 37.6 14.5 — — 1.31 0.49 0.21 0.17 1.03 0.53 25.0 12.2 — — 0.84 0.41 0.21 0.18 1.16 0.21 22.8 56.6 — — 0.77 1.33 0.19 0.34 0.42 0.43 0.37 0.45 28.3 36.3 49.8 40.0 — — — — 0.91 1.12 1.35 1.19 0.30 0.32 0.37 0.32 Recency of immigration Born outside the 50 states and District of Columbia Hispanic Non-Hispanic First generation Hispanic Non-Hispanic Second generation or higher Hispanic Non-Hispanic Region Northeast Midwest South West — Not available. † Not applicable. The corresponding statistic refers to the total population, which is, by definition, 100 percent of the distribution. SOURCE: U.S. Department of Commerce, Census Bureau, Current Population Survey (CPS), October 2008. C-9 �Appendix C—Standard Error Tables Table C-6.—Standard errors for table 7: Status dropout rates, number of status dropouts, and population Table C-6.—of 16- through 24-year-olds: October 1972 through October 2008 Year Status dropout rate (percent) Number of status dropouts (thousands) Population (thousands) 1972 1973 1974 1975 1976 0.28 0.27 0.27 0.27 0.26 91.1 90.9 92.0 92.0 93.3 — — — — — 1977 1978 1979 1980 1981 0.27 0.27 0.27 0.26 0.26 94.9 95.6 96.8 95.4 96.1 — — — — — 1982 1983 1984 1985 1986 0.27 0.27 0.27 0.27 0.27 100.0 98.6 96.1 93.2 91.4 — — — — — 1987 1988 1989 1990 1991 0.28 0.30 0.31 0.29 0.30 92.3 100.2 98.0 92.0 92.8 — — — — — 1992 1993 1994 1995 1996 0.28 0.28 0.26 0.27 0.27 87.7 87.5 91.4 92.9 90.1 — — — — — 1997 1998 1999 2000 2001 0.27 0.27 0.26 0.26 0.25 87.4 90.8 89.7 89.3 89.3 — — — — — 2002 2003 2004 2005 2006 0.24 0.23 0.23 0.22 0.22 84.2 82.6 84.8 81.7 81.8 — — — — — See notes at end of table. C-10 �Appendix C—Standard Error Tables Table C-6.—Standard errors for table 7: Status dropout rates, number of status dropouts, and population Table C-6.—of 16- through 24-year-olds: October 1972 through October 2008—Continued Year Status dropout rate (percent) Number of status dropouts (thousands) Population (thousands) 2007 2008 0.21 0.20 79.8 76.8 — — — Not available. NOTE: Some of the standard error estimates in this table may differ from those previously published due to changes in the generalized variance parameters developed by the U.S. Census Bureau. SOURCE: U.S. Department of Commerce, Census Bureau, Current Population Survey (CPS), October 1972–2008. C-11 �Appendix C—Standard Error Tables Table C-7.—Standard errors for table 8: Status dropout rates of 16- through 24-year-olds, by sex and Table C-7.—race/ethnicity: October 1972 through October 2008 Sex (percent) Race/ethnicity (percent) White nonBlack nonHispanic Hispanic Hispanic Year Total (percent) Male Female 1972 1973 1974 1975 1976 0.28 0.27 0.27 0.27 0.26 0.40 0.38 0.39 0.37 0.38 0.39 0.38 0.38 0.38 0.37 0.29 0.28 0.28 0.27 0.28 1.07 1.06 1.05 1.06 1.01 2.22 2.24 2.08 2.02 2.01 1977 1978 1979 1980 1981 0.27 0.27 0.27 0.26 0.26 0.38 0.38 0.39 0.39 0.38 0.37 0.37 0.37 0.36 0.35 0.28 0.28 0.28 0.27 0.27 1.00 1.00 1.01 0.97 0.93 2.02 2.00 1.98 1.89 1.80 1982 1983 1984 1985 1986 0.27 0.27 0.27 0.27 0.27 0.40 0.41 0.40 0.40 0.40 0.38 0.37 0.37 0.37 0.37 0.29 0.29 0.29 0.29 0.28 0.98 0.97 0.92 0.92 0.90 1.93 1.93 1.91 1.93 1.88 1987 1988 1989 1990 1991 0.28 0.30 0.31 0.29 0.30 0.40 0.44 0.45 0.42 0.43 0.38 0.42 0.42 0.41 0.41 0.30 0.32 0.32 0.30 0.31 0.91 1.00 0.98 0.94 0.95 1.84 2.30 2.19 1.91 1.93 1992 1993 1994 1995 1996 0.28 0.28 0.26 0.27 0.27 0.41 0.40 0.38 0.38 0.36 0.39 0.40 0.36 0.37 0.36 0.29 0.29 0.27 0.28 0.26 0.95 0.94 0.75 0.74 0.75 1.86 1.79 1.16 1.15 1.13 1997 1998 1999 2000 2001 0.27 0.27 0.26 0.26 0.25 0.39 0.40 0.38 0.38 0.38 0.36 0.36 0.36 0.35 0.34 0.28 0.28 0.27 0.26 0.26 0.80 0.81 0.77 0.78 0.71 1.11 1.12 1.11 1.08 1.06 2002 2003 2004 2005 2006 0.24 0.23 0.23 0.22 0.22 0.35 0.34 0.34 0.33 0.33 0.32 0.30 0.31 0.29 0.30 0.24 0.24 0.24 0.23 0.23 0.70 0.69 0.70 0.66 0.66 0.93 0.90 0.89 0.87 0.86 See notes at end of table. C-12 �Appendix C—Standard Error Tables Table C-7.—Standard errors for table 8: Status dropout rates of 16- through 24-year-olds, by sex and Table C-7.—race/ethnicity: October 1972 through October 2008—Continued Sex (percent) Year Total (percent) Male Female 2007 2008 0.21 0.20 0.32 0.30 0.29 0.28 Race/ethnicity (percent) White nonBlack nonHispanic Hispanic Hispanic 0.22 0.21 0.59 0.63 NOTE: Some of the standard error estimates in this table may differ from those previously published due to changes in the generalized variance parameters developed by the U.S. Census Bureau. SOURCE: U.S. Department of Commerce, Census Bureau, Current Population Survey (CPS), October 1972–2008. C-13 0.83 0.78 �Appendix C—Standard Error Tables Table C-8. —Standard errors for table 9: Status completion rates, and number and distribution of Table C-8.—completers ages 18–24 not currently enrolled in high school or below, by selected Table C-8.—characteristics: October 2008 Completion rate (percent) Number of completers (thousands) Population (thousands) Percent of all completers Percent of population Total 0.27 72.6 — † † Sex Male Female 0.39 0.37 52.6 50.0 — — 0.47 0.47 0.44 0.44 0.26 0.86 1.03 44.4 32.0 49.2 — — — 0.44 0.34 0.37 0.43 0.32 0.38 0.98 10.7 — 0.20 0.18 Characteristic Race/ethnicity White, non-Hispanic Black, non-Hispanic Hispanic Asian/Pacific Islander, non-Hispanic American Indian/Alaska Native, non-Hispanic Two or more races, non-Hispanic 4.03 8.7 — 0.08 0.08 1.72 7.7 — 0.13 0.12 Age 18–19 20–21 22–24 0.55 0.47 0.40 38.3 37.3 49.1 — — — 0.41 0.43 0.46 0.39 0.40 0.44 1.89 0.91 34.9 14.0 — — 0.22 0.22 0.25 0.20 Recency of immigration Born outside the 50 states and District of Columbia Hispanic Non-Hispanic First generation Hispanic Non-Hispanic Second generation or higher Hispanic Non-Hispanic 1.48 0.69 23.5 11.3 — — 0.24 0.23 0.23 0.21 1.58 0.27 21.2 53.0 — — 0.22 0.41 0.22 0.40 Region Northeast Midwest South West 0.56 0.58 0.47 0.57 27.4 34.4 46.6 37.9 — — — — 0.37 0.40 0.46 0.40 0.35 0.38 0.44 0.38 — Not available. † Not applicable. The corresponding statistic refers to the total population, which is, by definition, 100 percent of the distribution. SOURCE: U.S. Department of Commerce, Census Bureau, Current Population Survey (CPS), October 2008. C-14 �Appendix C—Standard Error Tables Table C-9.—Standard errors for table 10: Status completion rates, number of completers, and population Table C-9.—of 18- through 24-year-olds: October 1972 through October 2008 Year Completion rate (percent) Number of completers (thousands) Population (thousands) 1972 1973 1974 1975 1976 0.32 0.31 0.31 0.30 0.30 82.8 82.3 83.3 83.8 85.3 — — — — — 1977 1978 1979 1980 1981 0.30 0.30 0.30 0.30 0.29 94.5 87.4 88.9 87.5 88.9 — — — — — 1982 1983 1984 1985 1986 0.31 0.31 0.31 0.31 0.31 93.1 92.2 89.8 86.6 85.1 — — — — — 1987 1988 1989 1990 1991 0.32 0.36 0.36 0.34 0.34 86.0 93.7 91.7 86.5 84.4 — — — — — 1992 1993 1994 1995 1996 0.33 0.34 0.34 0.35 0.35 82.3 82.1 79.8 80.3 80.9 — — — — — 1997 1998 1999 2000 2001 0.35 0.36 0.34 0.33 0.33 82.3 85.8 83.8 83.4 83.4 — — — — — 2002 2003 2004 2005 2006 0.31 0.30 0.30 0.30 0.29 79.8 78.6 80.3 78.0 77.8 — — — — — See notes at end of table. C-15 �Appendix C—Standard Error Tables Table C-9.—Standard errors for table 10: Status completion rates, number of completers, and population Table C-9.—of 18- through 24-year-olds: October 1972 through October 2008—Continued Year Completion rate (percent) Number of completers (thousands) Population (thousands) 2007 2008 0.28 0.27 75.2 72.6 — — — Not available. NOTE: Some of the standard error estimates in this table may differ from those previously published due to changes in the generalized variance parameters developed by the U.S. Census Bureau. SOURCE: U.S. Department of Commerce, Census Bureau, Current Population Survey (CPS), October 1972–2008. C-16 �Appendix C—Standard Error Tables Table C-10. —Standard errors for table 11: Status completion rates of 18- through 24-year-olds not currently Table C-10.—enrolled in high school or below, by sex and race/ethnicity: October 1972 through October Table C-10.—2008 Sex (percent) Race/ethnicity (percent) White nonBlack nonHispanic Hispanic Hispanic Year Total (percent) Male Female 1972 1973 1974 1975 1976 0.32 0.31 0.31 0.30 0.30 0.51 0.49 0.49 0.47 0.48 0.48 0.47 0.46 0.46 0.45 0.33 0.31 0.31 0.30 0.31 1.20 1.17 1.17 1.18 1.12 1.83 1.83 1.70 1.72 1.68 1977 1978 1979 1980 1981 0.30 0.30 0.30 0.30 0.29 0.49 0.48 0.49 0.48 0.48 0.45 0.45 0.45 0.43 0.43 0.31 0.31 0.31 0.30 0.30 1.12 1.11 1.11 1.07 1.02 1.66 1.61 1.58 1.51 1.46 1982 1983 1984 1985 1986 0.31 0.31 0.31 0.31 0.31 0.49 0.50 0.49 0.49 0.50 0.45 0.45 0.45 0.44 0.45 0.32 0.32 0.32 0.32 0.32 1.06 1.06 0.99 1.00 0.99 1.57 1.59 1.54 1.58 1.51 1987 1988 1989 1990 1991 0.32 0.36 0.36 0.34 0.34 0.51 0.57 0.57 0.53 0.55 0.47 0.51 0.51 0.50 0.50 0.34 0.36 0.37 0.34 0.35 0.99 1.13 1.11 1.03 1.06 1.47 1.78 1.73 1.54 1.53 1992 1993 1994 1995 1996 0.33 0.34 0.34 0.35 0.35 0.53 0.53 0.49 0.50 0.50 0.49 0.50 0.45 0.47 0.48 0.33 0.35 0.34 0.36 0.34 1.07 1.07 1.02 1.01 1.08 1.53 1.49 1.43 1.40 1.49 1997 1998 1999 2000 2001 0.35 0.36 0.34 0.33 0.33 0.51 0.53 0.50 0.49 0.50 0.47 0.47 0.46 0.44 0.43 0.36 0.36 0.34 0.33 0.34 1.10 1.11 1.04 1.01 0.97 1.42 1.37 1.39 1.36 1.31 2002 2003 2004 2005 2006 0.31 0.30 0.30 0.30 0.29 0.46 0.46 0.46 0.45 0.48 0.41 0.40 0.40 0.38 0.44 0.31 0.31 0.31 0.30 0.36 0.95 0.96 0.98 0.91 1.03 1.15 1.15 1.12 1.12 1.10 See notes at end of table. C-17 �Appendix C—Standard Error Tables Table C-10. —Standard errors for table 11: Status completion rates of 18- through 24-year-olds not currently Table C-10.—enrolled in high school or below, by sex and race/ethnicity: October 1972 through October Table C-10.—2008—Continued Sex (percent) Year Total (percent) Male Female 2007 2008 0.28 0.27 0.42 0.39 0.37 0.37 Race/ethnicity (percent) White nonBlack nonHispanic Hispanic Hispanic 0.28 0.26 0.80 0.86 1.07 1.03 NOTE: Some of the standard error estimates in this table may differ from those previously published due to changes in the generalized variance parameters developed by the U.S. Census Bureau. SOURCE: U.S. Department of Commerce, Census Bureau, Current Population Survey (CPS), October 1972–2008. Table C-11. —Standard errors for figure 3: Status dropout rates of 16- through 24-year-olds, by Table C-12.—race/ethnicity and sex: October 2008 Total Race/ethnicity White, non-Hispanic Black, non-Hispanic Hispanic Asian/Pacific Islander, non-Hispanic American Indian/Alaska Native, non-Hispanic Two or more races, non-Hispanic Male Female 0.30 0.28 0.30 0.85 1.12 1.11 5.32 1.51 0.28 0.93 1.08 1.21 3.86 1.80 SOURCE: U.S. Department of Commerce, Census Bureau, Current Population Survey (CPS), October 2008. Table C-12. —Standard errors for figure 5: Status completion rates of 18- through 24-year-olds not Table C-13.—currently enrolled in high school or below, by race/ethnicity and sex: October 2008 Total Race/ethnicity White, non-Hispanic Black, non-Hispanic Hispanic Asian/Pacific Islander, non-Hispanic American Indian/Alaska Native, non-Hispanic Two or more races, non-Hispanic Male Female 0.39 0.37 0.39 1.15 1.48 1.47 7.04 2.18 0.35 1.25 1.42 1.30 4.51 2.69 SOURCE: U.S. Department of Commerce, Census Bureau, Current Population Survey (CPS), October 2008. C-18 � Dublin Core The Dublin Core metadata element set is common to all Omeka records, including items, files, and collections. For more information see, http://dublincore.org/documents/dces/. Title A name given to the resource GED Resources Text A resource consisting primarily of words for reading. Examples include books, letters, dissertations, poems, newspapers, articles, archives of mailing lists. Note that facsimiles or images of texts are still of the genre Text. Dublin Core The Dublin Core metadata element set is common to all Omeka records, including items, files, and collections. For more information see, http://dublincore.org/documents/dces/. Title A name given to the resource Trends in High School Dropout and Completion Rates in the United States: 1972–2008 Description An account of the resource This report builds upon a series of National Center for Education Statistics (NCES) reports on high school dropout and completion rates that began in 1988. It presents estimates of rates in 2008, provides data about trends in dropout and completion rates over the last three and a half decades (1972–2008), and examines the characteristics of high school dropouts and high school completers in 2008. Creator An entity primarily responsible for making the resource Chris Chapman, Jennifer Laird and Angelina KewalRamani Source A related resource from which the described resource is derived <a href="https://nces.ed.gov/pubs2011/2011012.pdf">https://nces.ed.gov/pubs2011/2011012.pdf</a> Publisher An entity responsible for making the resource available United States Department of Education National Center for Education Statistics Date A point or period of time associated with an event in the lifecycle of the resource Created: 2010 Contributor An entity responsible for making contributions to the resource John Roper Format The file format, physical medium, or dimensions of the resource pdf Language A language of the resource English Type The nature or genre of the resource Text Identifier An unambiguous reference to the resource within a given context GEDdoc006 Getting Started https://lis5472.cci.fsu.edu/sp19/group8/files/original/5369d8d68e115db3f514371d38483d7f.pdf bcc6945547566926b2164f1052fbe106 PDF Text Text �� Dublin Core The Dublin Core metadata element set is common to all Omeka records, including items, files, and collections. For more information see, http://dublincore.org/documents/dces/. Title A name given to the resource GED Resources Text A resource consisting primarily of words for reading. Examples include books, letters, dissertations, poems, newspapers, articles, archives of mailing lists. Note that facsimiles or images of texts are still of the genre Text. Dublin Core The Dublin Core metadata element set is common to all Omeka records, including items, files, and collections. For more information see, http://dublincore.org/documents/dces/. Title A name given to the resource GEN-14-06 Recognized Equivalent of a High School Diploma Description An account of the resource This "Dear Colleague" letter from the U.S. DOE makes clear that GED certifications (or any alternate method a state may use for high school equivavlency) qualifies as a high school diploma for purposes of federal law. The memo also provides specific instructions for GED certificate holders on completing the FAFSA application for higher education financial aid. Creator An entity primarily responsible for making the resource United States Department of Education Publisher An entity responsible for making the resource available United States Department of Education Date A point or period of time associated with an event in the lifecycle of the resource Created: 2014 Contributor An entity responsible for making contributions to the resource John Roper Format The file format, physical medium, or dimensions of the resource pdf Language A language of the resource English Type The nature or genre of the resource Text Identifier An unambiguous reference to the resource within a given context GEDdoc005 Source A related resource from which the described resource is derived <a href="https://ifap.ed.gov/dpcletters/attachments/GEN1406.pdf">https://ifap.ed.gov/dpcletters/attachments/GEN1406.pdf</a> Getting Started Success Stories https://lis5472.cci.fsu.edu/sp19/group8/files/original/ee1ee5f22c9a1622e13d78258ddfd693.mp4 c82892f4967890e690772f3f76e39912 Dublin Core The Dublin Core metadata element set is common to all Omeka records, including items, files, and collections. 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Title A name given to the resource 2017-18 GED Graduation Ceremony keynote address Description An account of the resource AstraZeneca executive Andrea Nance addresses the 2017-18 GED graduates of Williamsburg-James City County Public Shcools in Williamsburg, VA Creator An entity primarily responsible for making the resource Williamsburg-James City County Public Shcools Source A related resource from which the described resource is derived <a href="https://www.youtube.com/watch?v=SvAbViUE7TQ&amp;t=1059s">2017-18 GED Graduation Ceremony, Willamsburg-James City County Public Schools</a> Publisher An entity responsible for making the resource available Williamsburg-James City County Public Shcools Date A point or period of time associated with an event in the lifecycle of the resource Created: 2018-06-14 Contributor An entity responsible for making contributions to the resource John Roper Rights Information about rights held in and over the resource Creative Commons Attribution license Format The file format, physical medium, or dimensions of the resource mp4 Language A language of the resource English Type The nature or genre of the resource MovingImage Identifier An unambiguous reference to the resource within a given context GEDvid002 Coverage The spatial or temporal topic of the resource, the spatial applicability of the resource, or the jurisdiction under which the resource is relevant Virginia Success Stories https://lis5472.cci.fsu.edu/sp19/group8/files/original/c00b52fc2fce98e850df0fe3cb7fabd9.pdf 92121fefb2863a461506165b23fcdaac PDF Text Text South Carolina Computer-Based GED Test Centers as of September 1, 2015 County GED Testing Center Street Address City Zip Phone Abbeville Abbeville County Adult Education Center 400 Greenville Street Abbeville 29620 864-366-4226 Aiken Aiken County Adult Education - Byrd Learning Center 1 Willis Circle Graniteville 29803 803-641-2476 Allendale Allendale-Fairfax Learning Center 1843 Main Street South Allendale 29810 803-584-3107 Anderson Anderson 5 Adult Education Center 2005 North Main Street Anderson 29621 864-260-5075 Anderson Anderson Districts 1 and 2 Adult Education Center 214 Lebby Street Pelzer 29669 864-947-9311 Bamberg No Test Center At This Time Barnwell No Test Center At This Time Beaufort Beaufort County Adult Education Center 1300 King Street Beaufort 29901 843-322-0780 Berkeley Berkeley Educational Center 113 East Main Street Moncks Corner 29461 843-899-8703 Berkeley Fishburne Educational Center 6215 Murray Drive Hanahan 29410 843-820-3742 Calhoun Charleston No Test Center At This Time Charleston County Adult Education at Brentwood Campus 2685 Leeds Avenue N. Charleston 29405 843-529-3142 Cherokee Ola H. Copeland Community Learning Center 243 Allison Drive Gaffney 29341 864-206-6992 Chester No Test Center At This Time Chesterfield Chesterfield County Adult Education Center 116 Edwards Road Chesterfield 29709 843-623-2200 Clarendon F.E. DuBose Career Center-Central Carolina Technical College 3351 Sumter Highway Manning 29102 803-473-2531 Colleton Colleton County Adult Education Center 609 Colleton Loop Walterboro 29488 843-782-0018 Darlington Darlington County Adult Education Center 100 Magnolia Street Darlington 29532 843-398-2856 Dillon Dillon County Adult Education Center 214 West Main Street Dillon 29536 843-774-1218 Dorchester Summerville Adult Learning Center 1325 Boone Hill Road Ste A Summerville 29483 843-873-7372 Edgefield Edgefield County Adult Education Center 117 Cardinal Street Johnston 29832 803-275-4158 Fairfield No Test Center At This Time Florence Florence 1 - Poynor Adult Education Center 301 South Dargan Street Florence 29506 843-664-8152 x 6409 Georgetown Howard Adult Education Center 500 S. Kaminski Street Georgetown 29440 843-546-0219 Greenville Lifelong Learning at Sullivan Center 206 Wilkins Street Greenville 29605 864-355-3433 Greenwood Greenwood County Adult Education Center 400 Glenwood Street Greenwood 29649 864-941-5450 Hampton No Test Center At This Time Horry Conway Adult Education Center 1620 Sherwood Drive Conway 29526 843-488-6200 Horry Myrtle Beach Family Learning Center 3101 Oak Street Myrtle Beach 29577 843-488-6200 Jasper No Test Center At This Time Kershaw Kershaw County Adult Education Center 874 Vocational Lane Camden 29020 803-425-8980 Lancaster Lancaster County Adult Education Center 610 East Meeting Street Lancaster 29720 803-285-7660 Laurens Laurens County Adult Education - Higher Education Center 663 Medical Ridge Road Clinton 29325 864-938-1524 1 - 9/16/2015 �South Carolina Computer-Based GED Test Centers as of September 1, 2015 County GED Testing Center Street Address City Zip Phone Lee Lee County Adult Education Center 123 East College Street Bishopville 29010 803-484-4040 Lexington Adult Education of Lexington-Richland Counties-Irmo 6671 Saint Andrews Road Columbia 29212 803-476-8229 Lexington Lexington 1 Adult Education Center 420 Hendrix Street Lexington 29072 803-821-2950 Lexington Lexington 2 Adult Education-Pair Center 2325 Platt Springs Road West Columbia 29169 803-739-4048 Lexington Lexington District 3 Lifelong Learning Center 101 West Columbia Avenue Batesburg/Leesville 29006 803-532-2141 Lexington Lexington 4 Adult Education Center 135 Lewis Rast Road Swansea 29160 803-399-7979 Marion Marion County Adult Education Center 410 E. Liberty Street Marion 29571 843-423-2591 Marlboro Marlboro County Adult Education Center 215 Broad Street Bennettsville 29512 843-479-5923 McCormick McCormick County Adult Education Center 6981 Highway 28 South McCormick 29835 864-443-0051 Newberry Newberry County Adult Education Center 591 McSwain Street Newberry 29108 803-321-2112 Oconee Oconee County Adult Education Center 315 Holland Avenue Seneca 29678 864-886-4429 Orangeburg Orangeburg-Calhoun Technical College 3250 Saint Matthews Road Orangeburg 29118 803-268-2539 Pickens Pickens County Adult Learning Center 106 Glazner Street Easley 29640 864-397-3825 Richland Richland One Adult Education Center 2612 Covenant Road Columbia 29204 803-251-4512 Richland W R Rogers Adult, Continuing, and Technology Education Center 750 Old Clemson Road Columbia 29229 803-736-8787 Richland Virginia College 7201 Two Notch Road Columbia 29223 803-509-7100 Richland Adult Education of Lexington-Richland Counties-Irmo 6671 Saint Andrews Road Columbia 29212 803-476-8229 Saluda Saluda County Adult Education Center 403B North Calhoun Street Saluda 29138 864-445-3346 Spartanburg Spartanburg County Adult Education- Z L Madden Learning Center 459 West Centennial Street Spartanburg 29303 Sumter Sumter County Adult Education Center 905 North Main Street Sumter 29150 864-594-4428 803-778-6432 Union Union County Adult Education Center 517 East Main Street Union 29379 864-429-1770 Williamsburg Williamsburg County Adult Education Center-Kingstree 500 North Academy Street Kingstree 29556 843-355-6887 Williamsburg Williamsburg County Adult Education Center-Hemingway 2811 SC Highway, 41/51 South Hemingway 29554 843-355-6887 York Rock Hill Flexible Learning Center 1234 Flint Street Extension Rock Hill 29730 803-981-1375 2 - 9/16/2015 � Dublin Core The Dublin Core metadata element set is common to all Omeka records, including items, files, and collections. For more information see, http://dublincore.org/documents/dces/. Title A name given to the resource GED Resources Text A resource consisting primarily of words for reading. Examples include books, letters, dissertations, poems, newspapers, articles, archives of mailing lists. Note that facsimiles or images of texts are still of the genre Text. Dublin Core The Dublin Core metadata element set is common to all Omeka records, including items, files, and collections. For more information see, http://dublincore.org/documents/dces/. Title A name given to the resource South Carolina Computer-Based GED Test Centers Description An account of the resource A listing of all GED test centers and addresses in South Carolina as of September 2015 Creator An entity primarily responsible for making the resource South Carolina Department of Education Source A related resource from which the described resource is derived <a href="https://ed.sc.gov/scdoe/assets/File/instruction/adult-education/GED%20Testing%20Sites%20September%202015.pdf">https://ed.sc.gov/scdoe/assets/File/instruction/adult-education/GED%20Testing%20Sites%20September%202015.pdf</a> Publisher An entity responsible for making the resource available South Carolina Department of Education Date A point or period of time associated with an event in the lifecycle of the resource Created: 2015-09-16 Contributor An entity responsible for making contributions to the resource John Roper Format The file format, physical medium, or dimensions of the resource pdf Language A language of the resource English Type The nature or genre of the resource Text Identifier An unambiguous reference to the resource within a given context GEDdoc004 Coverage The spatial or temporal topic of the resource, the spatial applicability of the resource, or the jurisdiction under which the resource is relevant South Carolina Getting Started Test Preparation https://lis5472.cci.fsu.edu/sp19/group8/files/original/0dbf3bccfeae5bcc1bbcc3bbcfa360dc.pdf 8ab3e62b947f6f83edd5d2fd7ddf21c0 PDF Text Text �·TESTING BUREAU TEMPLE UNIVERSITY Commonwealth of Pennsylvania DEPARTMENT OF PUBLIC EDUCATION Harrisburg, Pa. 17126 APPLICATION PROCEDURES FOR THE COMMONWEALTH SECONDARY $CHOOL DIPLOMA OR GRADE EQUIVALENT CERTIFICATE The General Educational Development Testing Program (G.E.D.) was adopted by the State Council of Education in August, 1963, to enable Pennsylvania residents, who are not High School graduates, to earn a Commonwealth Secondary School Diploma. The G.E.D. Program was initiated by the Department of Public Education and implimented by the Division of Testing to replace the procedure of accumulating sufficient subject credits in order to qualify for the Secondary School Diploma. Since its inception in 1963, over 20,000 Pennsylvania residents have successfully completed the G.E.D. Test and have been awarded a Secondary School Diploma. More than 9,500,.:applicants were tested during 1967. At the present time, the Bureau of Guidance receives more than 1,000 applications per month. The G.E.D. Test has been constructed somewhat differently from the usual school achievement tests. In a formal secondary setting, there is likely to be a more complete and detailed coverage of specific facts learned through the use of reference books, textbooks, and planned lesson presentations. The G.E.D, Test is designed to permit the individual to take advantage of knowledge acquired as a result of first-hand observation, direct experience, self-directed reading and study, conversations and informal group discussions , and other experiences with problems, ideas, and people. WHO IS ELIGIBLE? Any resident (living in Pennsylvania at least three months prior to making application to the test), not currently enrolled in an approved secondary school program. eighteen years of age or older, or whose original class has graduated, is eligible to take the G.E.D. Test. No previous school attendance is required if the applicant meets these requirements . A transcript of grades previously earned is not required. Non-residents may take the G.E.D. Test but they will be issued a Certificate of Completion and not a Commonwealth Diploma. HeM TO APPLY Applicants should secure a G.E.D. application from the local high school principal Test Center Director or write to Division of Testing, Box 911. Harrisburg, Pennsylvania. �2 Please print all information sections using a ballpoint pen or pencil and use sufficient pressure to permit the markings to show on all three copies. All items must be completed if the application is to be processed for approval. Please complete the home address section at the bottom of the application and the identification section (Social Security I·iumber and :•:arne) in the upper right portion of the application. Do not write in the Test Center Information section. Do not sign your name in the blocks numbered 8 or 9. Report to the Testing Bureau one half-hour before testing time with your completed application for registration and application approval. Testing times are listed on the enclosed sheet. Applicat i ons may be approved during this time only . Applicants are required to show a piece of acceptable identification which includes their signature and/or photograph (i.e., driver's license, draft card, etc.). The fee for testing i s $10.00 and mus_t be paid in full at time of registration. Checks should be made payable to Temple University. TEST CO;ITE '·.JT The G.E.D. Test cons i ~+. s of five seperate tests and measures the candidate's knowledge and underst anding in the following areas: 1. Correctness and Effectiveness of Expression (spelling and English grammar) *2. Reading and Interpretation of Materials in Social Studies *3. Reading and Interpretation of Materials in Natural Sciences *4. Reading and Interpretation of Materials in Literary Materials *These three tests are designed to determine the applicant's ability to interpret and to evaluate a number of reading selections. Factual recall is not of prime importance in this type of test • 5. General Mathematical Ability (problem solving, use of tables and graphs, units of measurement, algebraic and geometric concepts) EIGHTH AI'ID TENTH GRADE CERTIFI CATES Residents in need of ~ certificate for job or professional licensing can obtain an Eighth Grade Equivalent Certificate or Tenth Grade Equivalent Certificate thr~ the G.E.D. Testing Program. The official Test Centers administer this program and applicants for the Tenth Grade Certificate should follow the procedure outlined above. MILTIARY PERS O~!NEL Residents who have completed the G.E.D. Test while a member of the Armed Forces may be eligibl e to receive the Secondary School Diploma. �3 I~ he is currently serving on active duty, the applicant should contact his Unit Education Of~icer ~or application procedures. 'I'he applicant should also request a Diploma or Certificate from Credentials Evaluation, Department of Public Education, Box 911, Harrisburg, Pennsylvania, 17126. If an applicant has concluded his active military service, he should write to USAFI Headquarters, Madison, Wisconsin, and request that o~ice to send a transcript of his test results to Credentials Evaluation in Harrisburg. The applicant should also request a Diploma or Certi~icate from the Credentials Evaluation Division. RETESTING An applicant who has not successfully completed the G.E.D. Test may take a retest following a waiting period of twelve (12) months. This waiting period can be reduced if the applicant receives twenty-five (25) hours o~ private tutoring or completes twenty-five (25) hours of work in a Standard Evening School Program or an Adult Education Program. The Philadelphia Board of Education can supply information concerning tutoring. An applicant does not have to retake the entire test. He may chose to take one or more test areas in order to acquire the score necessary to qualify for the Diploma or Certificate. The testing procedure for retesting is identical to the process stated above. See section entitled "How to Apply.'' SINGLE SUBJECT TESTING Some residents will have a need to earn individual subject credit to qualify for entrance into college. The of~icial Testing Centers have available single subject tests and will administer these tests to qualified applicants possessing a regular High School Diploma or Commonwealth Secondary Diploma. A full range of Academic and General Secondary Subject tests are available. Interested applicants should consult with the Testing Center. REGULATIONS CONCERNING REQUIRED SCORES, AGE, AND GRADE COMPLETION Total Score Required Average Scores Required Lowest Passing Score on Subtests Minimum Age for Issuance of Credential Original Class Must Have Completed Grade Waiting Period for Retests (Months) Secondary Diploma Tenth Grade Certificate 225 195 39 45 35 18 12 12 31 17 10 6 �PROCEDURES AND TEST SCHEDULE FOR THE GENERAL EDUCATIONAL DEVELOPMENT (GED) PROGRAM April 1, 1971 to August 29, 1971 TESTING BUREAU- TEMPLE UNIVERSITY (215) 787-8615 1. GED tests are taken in order to obtain a Commonwea lth Secondary School Diploma or Grade Equivalent Certificate for grades eight and t en. Also, GED tests are taken for enlistment in the Armed Forces, or for special training programs requiring results of the five GED tests. 2. Tests will be given every Thursday and Friday f ro m 12: 30 Noon to 4:30P.M. and every Saturday from 9:30A.M . to 1:30 P.M., except on t hose days when the University is closed (holidays). Approximately ten hours are requ ired to complete the GED battery of five tests. A test may not be started with less than two hours remaining in the test period. Every test must be finished on the day it Is started. 3. The fee for the GED Test Battery (f ive test s) for th e high school equivalent diploma or for the 10th grade certificate is $10, payable in full on the first day of testing. The fee for the 8th grade equivalent test is $6. 4. No appointment is necessary for the regul ar testing dates. Candidates taking the GED Testing Program must register at the Testing Bureau, Room 300 Sull ivan Hall, Park Avenue & Berks Street, Philadelphia, Pa. Applicants are required to show a piece of acceptable identification which includes their signature and/ or photograph . Registration on test days is between 12:00 and 12:30 o'clock on Thursdays and Fri days, and between 9:00A.M. and 9 :30A.M. on Saturdays. Late arrivals wil l be registered, but w ill probabl y be able to take only one test on that day. The registration procedure is presented in Section Five. 5. Registration procedures involve: A. Candidates for the Commonwealth Secondary School Diploma must report to the Testing Bureau , Room 300 Sullivan Hall, located at Park Avenue and Berks Street, Philadelphia, Pa. on the fi rst day of t esting. 6. B. Fees will be paid at the Comptrollers Office, fi rst floor of Conwell Hall, Broad Street and Montgomery Avenue. C. Testing is conducted in Room 10 Curtis Hall , located at Montgomery and Park Avenues. Upon completion of the examinations (GED or Equ ivalent) the Testing Bureau will forward the results to the Department of Public Education, or to any authorized college, industrial or Armed Forces recruiting center. Diploma candidates will receive notification of passing or failing from the Department of Publ ic Educat ion, Harrisburg, approximately six weeks after completion of testing. The Commonwealth Secondary School Diploma will be issued approximately eight weeks after testing, for those who have successfully met the standards. Harold C. Reppert, Ph.D. Director, Testing Bureau � Dublin Core The Dublin Core metadata element set is common to all Omeka records, including items, files, and collections. For more information see, http://dublincore.org/documents/dces/. Title A name given to the resource GED Resources Text A resource consisting primarily of words for reading. Examples include books, letters, dissertations, poems, newspapers, articles, archives of mailing lists. Note that facsimiles or images of texts are still of the genre Text. Dublin Core The Dublin Core metadata element set is common to all Omeka records, including items, files, and collections. For more information see, http://dublincore.org/documents/dces/. Contributor An entity responsible for making contributions to the resource John Roper Title A name given to the resource GED Diploma with Instructions-Pennsylvania 1972 Description An account of the resource Application procedures for a high school equivalency diploma in Pennsylvania in 1972, including an embedded image of an actual high school equivalency diploma issues by the Commonwealth of Pennsylvania. Creator An entity primarily responsible for making the resource Commonwealth of Pennsylvania Department of Public Education Source A related resource from which the described resource is derived <a href="https://commons.wikimedia.org/wiki/File:GED-Diploma-with-Instructions-Pennsylvania-1972.pdf">Wikimedia Commons</a> Publisher An entity responsible for making the resource available Commonwealth of Pennsylvania and Temple University Date A point or period of time associated with an event in the lifecycle of the resource Created: 1972 Rights Information about rights held in and over the resource Public Domain Format The file format, physical medium, or dimensions of the resource pdf Language A language of the resource English Type The nature or genre of the resource Text Identifier An unambiguous reference to the resource within a given context GEDdoc003 Coverage The spatial or temporal topic of the resource, the spatial applicability of the resource, or the jurisdiction under which the resource is relevant Pennsylvania Getting Started Success Stories Dublin Core The Dublin Core metadata element set is common to all Omeka records, including items, files, and collections. For more information see, http://dublincore.org/documents/dces/. Title A name given to the resource GED Resources Hyperlink A link, or reference, to another resource on the Internet. URL http://www.aceleon.org/career-pathways Dublin Core The Dublin Core metadata element set is common to all Omeka records, including items, files, and collections. For more information see, http://dublincore.org/documents/dces/. Title A name given to the resource Career Pathways Description An account of the resource The career pathways approach is a framework for weaving together adult education, training and post-secondary programs, and connecting those services to the workforce needs of employers. Source A related resource from which the described resource is derived <a href="http://www.aceleon.org/career-pathways">http://www.aceleon.org/career-pathways</a> Publisher An entity responsible for making the resource available Leon County Schools Adult & Education (ACE) Creator An entity primarily responsible for making the resource Leon County Schools Adult & Education (ACE) Contributor An entity responsible for making contributions to the resource Cristina Carter Language A language of the resource English Type The nature or genre of the resource InteractiveResource Identifier An unambiguous reference to the resource within a given context GEDurl001 Coverage The spatial or temporal topic of the resource, the spatial applicability of the resource, or the jurisdiction under which the resource is relevant Florida Getting Started Dublin Core The Dublin Core metadata element set is common to all Omeka records, including items, files, and collections. For more information see, http://dublincore.org/documents/dces/. Title A name given to the resource GED Resources Hyperlink A link, or reference, to another resource on the Internet. Dublin Core The Dublin Core metadata element set is common to all Omeka records, including items, files, and collections. For more information see, http://dublincore.org/documents/dces/. Title A name given to the resource Our Great Start to a Better Future Description An account of the resource This video tells the story of five students and how earning a high school diploma by passing the GED test was a great option for them! Creator An entity primarily responsible for making the resource Leon County Schools Adult & Community Education (ACE) Source A related resource from which the described resource is derived <a href="https://vimeo.com/102942071">https://vimeo.com/102942071</a> Publisher An entity responsible for making the resource available <span>Leon County Schools</span> Contributor An entity responsible for making contributions to the resource Cristina Carter Language A language of the resource English Type The nature or genre of the resource MovingImage Identifier An unambiguous reference to the resource within a given context GEDvid003 Coverage The spatial or temporal topic of the resource, the spatial applicability of the resource, or the jurisdiction under which the resource is relevant Florida Success Stories https://lis5472.cci.fsu.edu/sp19/group8/files/original/fde7579d45fb99e3584d7108b7a10037.pdf 008d5ef7559f4c835b5a10ed6cd161ea PDF Text Text ADULT LITERACY FUNDAMENTAL MATHEMATICS ��Adult Literacy Fundamental Mathematics Book 1 Prepared by Wendy Tagami Based on the work of Leslie Tenta (1993) and Marjorie E. Enns (1983) Steve Ballantyne, Lynne Cannon, James Hooten, Kate Nonesuch (1994) �Canadian Cataloguing in Publication Data Downloading Information http://urls.bccampus.ca/abefundmath1 ISBN 978-0-7726-6302-3 Adult Literacy Fundamental Mathematics Book 1 ISBN 978-0-7726-6303-0 Adult Literacy Fundamental Mathematics Book 2 ISBN 978-0-7726-6304-7 Adult Literacy Fundamental Mathematics Book 3 ISBN 978-0-7726-6305-4 Adult Literacy Fundamental Mathematics Book 4 ISBN 978-0-7726-6306-1 Adult Literacy Fundamental Mathematics Book 5 ISBN 978-0-7726-6307-8 Adult Literacy Fundamental Mathematics Book 6 ISBN 978-0-7726-6347-4 Adult Literacy Fundamental Mathematics, Instructor’s Manual and Test-Bank �Copyright © 2010 Province of British Columbia Ministry of Advanced Education and Labour Market Development Unless otherwise noted, this book is released under a Creative Commons Attribution 4.0 Unported License also known as a CC-BY license. This means you are free to copy, redistribute, modify, or adapt this book. Under this license, anyone who redistributes or modifies this textbook, in whole or in part, can do so for free providing they properly attribute the book as follows: Adult Literacy Fundamental Mathematics: Book 1 by Wendy Tagami and Liz Girard is used under a CC-BY 4.0 international license. For questions regarding this licensing, please contact opentext@bccampus.ca. To learn more about BCcampus Open Textbook project, visit http://open.bccampus.ca �Acknowledgments Curriculum Writers: Liz Girard, North Island College Wendy Tagami, Selkirk College Advisory Committee members: Jill Auchinachie, Camosun College Leanne Caillier-Smith, College of the Rockies Mercedes de la Nuez, Northwest Community College Barbara Stirsky, University of the Fraser Valley Jan Weiten, Vancouver Community College The Deans and Directors of Developmental Education: Stephanie Jewell, Vancouver Community College Vivian Hermansen, North Island College Lyle Olsen, Selkirk College Allison Alder, Selkirk College The Adult Literacy Fundamental Working Group Cheryl Porter, North Island College Stephen & Jennifer Marks, Layout editors ��Table of Contents – Book 1 Unit 1: Number Sense Topic A: Emotions and Learning ......................................................................................... 2 Math Anxiety ................................................................................................................... 3 How to Deal with Math Anxiety ..................................................................................... 4 Topic B: Counting .................................................................................................................. 5 Topic B: Self-Test ........................................................................................................ 12 Topic C: Place Value ........................................................................................................... 14 Reading and Writing Numerals ..................................................................................... 27 Topic C: Self-Test ........................................................................................................ 36 Topic D: Ordering Numerals .............................................................................................. 38 Greater Than, Less Than, Equals .................................................................................. 42 Topic D: Self-Test ........................................................................................................ 43 Topic E: Rounding Numbers .............................................................................................. 44 Rounding to the Nearest Ten ......................................................................................... 45 Topic F: More Counting...................................................................................................... 55 Topic F: Self-Test ......................................................................................................... 63 Unit 1 Review - Number Sense ............................................................................................ 66 i �Unit 2: Addition Topic A: Addition ................................................................................................................ 76 Adding Across ............................................................................................................... 99 Word Problems ............................................................................................................ 103 Topic A: Self-Test ...................................................................................................... 106 Topic B: Addition of Three or More Numbers ............................................................... 109 Perimeter...................................................................................................................... 121 Topic B: Self-Test ...................................................................................................... 124 Topic C: Addition of Larger Numbers ............................................................................ 127 Topic C: Self-Test ...................................................................................................... 138 Unit 2 Review - Addition .................................................................................................... 141 Unit 3: Subtraction Topic A: Subtraction ......................................................................................................... 150 Subtracting Across ...................................................................................................... 174 Word Problems ............................................................................................................ 178 Topic A: Self-Test ...................................................................................................... 181 Topic B: Subtraction of Larger Numbers ....................................................................... 184 Topic B: Self-Test ...................................................................................................... 196 Unit 3 Review - Subtraction ............................................................................................... 199 ii �Unit 4: Estimating, Time & Shapes Topic A: Estimating ........................................................................................................... 206 Topic B: Time ..................................................................................................................... 214 A.M. and P.M .............................................................................................................. 217 Rounding Time ............................................................................................................ 219 Topic C: Shapes.................................................................................................................. 221 Unit 4 Review – Estimating, Time, Shapes ....................................................................... 228 Book 1 Review ..................................................................................................................... 237 Glossary................................................................................................................................ 254 ii �4 �To the Learner: Welcome to Fundamental Mathematics Book One. Adult Math Learners You have the skills you need to be a strong student in this class. Adult math learners have many skills. They have a lot of life experience. They also use math in their everyday lives. This means that adult math learners may already know some of what is being taught in this book. Use what you already know with confidence! Grades Record You have also been given a sheet to write down your grades. After each test, you can write in the mark. This way you can keep track of your grades as you go through the course. This is a good idea to use in all your courses. You can find this grade sheet at the end of the book. How to Use this Book This textbook has:  A Table of Contents listing the units, the major topics and subtopics.  A Glossary giving definitions for mathematical vocabulary used in the course.  A grades record to keep track of your marks. The textbook has many exercises; some are quite short, but others have a great number of questions. You do not have to do every single question! Do as many questions as you feel are necessary for you to be confident in your skill. It is best to do all the word problems. If you leave out some questions, try doing every second or every third question. Always do some questions from the end of each exercise because the questions usually get harder at the end. You might use the skipped questions for review before a test. If you are working on a difficult skill or concept, do half the exercise one day and finish the exercise the next day. That is a much better way to learn. 5 �Self-tests at the end of most topics have an Aim at the top. If you do not meet the aim, talk to your instructor, find what is causing the trouble, and do some more review before you go on. A Review and Extra Practice section is at the end of each unit. If there is an area of the unit that you need extra practice in, you can use this. Or, if you want, you can use the section for more review. A Practice Test is available for each unit. You may: Write the practice test after you have studied the unit as a practice for the end-of-chapter test, OR You might want to write it before you start the unit to find what you already know and which areas you need to work on. Unit tests are written after each unit. Again, you must reach the Aim before you begin the next unit. If you do not reach the aim, the instructor will assist you in finding and practising the difficult areas. When you are ready, you can write a B test to show that you have mastered the skills. A Final Test is to be written when you have finished the book. This final test will assess your skills from the whole book. You have mastered the skills in each unit and then kept using many of them throughout the course. The test reviews all those skills. 6 �Grades Record Book 1 Unit Practice Test Example √ Date of Test A Test A 25 33 Sept. 4, 2011 1 2 3 4 Final Test vii Date of Test B Sept. 7, 2011 Test B 28 33 �viii �Unit 1 Number Sense Fundamental Mathematics 1 �Topic A: Emotions and Learning Emotions, or what we feel about something, play a big part in how we learn. If we are calm, we learn well. If we are afraid or stressed, we do not learn as well. Many people are afraid of math. They fear making a mistake. “Math anxiety” is the fear of math. People who suffer from math anxiety may get headaches, sick stomachs, cold hands or they may just sweat a lot or just feel scared. Do you suffer from math anxiety? Read the list below and put a check mark (√) beside the ones you feel. Are your palms moist? Is your stomach fluttering? Do you feel like you can’t think clearly? Do you feel like you would rather do anything else than learning math? Are you breathing faster than normal? Is your heart pounding? Do you feel cold? Add any other things you are feeling. 2 Book 1 �Math Anxiety “Math anxiety” or the fear of math is a learned habit. If it is learned, it can be unlearned. Most math anxiety comes from bad memories while learning math. It may be from doing badly on a test or asking a question then being made fun of. These bad memories can make learning math hard. Everyone can learn math. There is no special talent for math. There are some people who are better at math than others, but even these people had to learn to be good at math. Fundamental Mathematics 3 �How to Deal with Math Anxiety Anyone can feel anxiety that will slow down learning. The key to learning is to be the “boss” of your anxiety. One way to be the “boss” is to relax. Try this breathing exercise. Start by breathing in slowly to the count of four. It may help to close your eyes and count. Now hold your breath for four counts and then let your breath out slowly to the count of four. The counting is silent and should follow this pattern: “breathe in, two, three four; hold, two, three, four; breathe out, two, three, four; wait, two, three four.” With practice, the number of counts can be increased. This is an easy and good way to relax. Now try this exercise quietly and repeat it five times slowly. Each time you feel anxious about learning, use the breathing exercise to help calm yourself. Ask yourself if what you tried worked. Do you feel calmer? Remember learning to deal with your math anxiety may take some time. It took you a long time to learn “math anxiety”, so it will take some time to overcome it. 4 Book 1 �Topic B: Counting To learn to read, you first need to learn the letters of the alphabet. Once you know the alphabet, you put the letters together to make words, then sentences, then paragraphs and then stories. Those letters become the “tools” used to write everything. The same is true for math. In math we use digits. The digits are: 0 1 2 3 4 5 6 7 8 9 Digits are named after our fingers. Our fingers are also called digits. The mathematics term comes from the days of counting on our fingers. We have ten fingers and there are ten digits. We use the letters of the alphabet to make up words, and we use digits to make up numbers. There are two ways to write numbers. You can write them as numerals. You can write them using word names. Numeral 0 1 2 3 4 5 6 7 8 9 Word Name zero one two three four five six seven eight nine Counting is matching the number name to the things being counted. You see a bowl of apples on the table. You want to know how many apples are in the bowl. You answer that question by saying “There are one, two, three, four apples.” You are giving the number names “one”, “two”, “three,” and “four” to the apples. The last number you say is the total number of apples. Fundamental Mathematics 5 �Exercise One Count the number of shapes in each picture. Then write the numeral and the word name. Check your work using the answer key at the end of the exercise. Example: 3 Word name: three a) b) Numeral: Word Name: Numeral: Word Name: c) d) Numeral: Word Name Numeral: Word Name: 6 Book 1 �e) f) Numeral: Numeral: Word Name: Word Name: g) h) Numeral: Word Name: Numeral: Word Name: i) Numeral: Word Name: Exercise One – Answer Key a) 2, two d) 9, nine g) 7, seven Fundamental Mathematics b) 6, six e) 1, one h) 4, four c) f) i) 8, eight 5, five 0, zero 7 �Need More Practice? Ask your instructor for the dominoes to do this page. Take the dominoes zero-zero to fivefive. Flip them over so you cannot see the dots. Pick a domino and flip it over. Draw the number of dots then count the number of dots. Write the numeral and word name. Have your instructor check these for you. Example: ●● ●● ● ● Numeral: 6 Word Name: six a) b) Numeral: Numeral: Word Name: Word Name: c) d) Numeral: Numeral: Word Name: Word Name: e) 8 f) Numeral: Numeral: Word Name: Word Name: Book 1 �Exercise Two Here are the numerals from one to ten. 1 2 3 4 5 6 7 8 9 10 Practice writing them below. Now practice writing the numerals from one to ten in the following. Try to do them without looking. Check your work using the answer key at the end of the exercise. a) 1 3 5 7 9 b) 2 4 6 8 10 c) 1 4 7 d) 3 Fundamental Mathematics 6 9 9 �e) 1 4 7 f) 1 5 9 g) 1 6 h) 5 i) 10 Book 1 �Answers to Exercise Two a) 2 4 6 8 10 b) 1 3 5 3 5 7 9 c) 2 6 8 9 10 d) 1 2 4 5 7 8 10 e) 2 3 2 3 4 2 3 4 1 2 3 4 1 2 3 4 f) 5 6 6 8 9 10 7 8 10 7 8 9 10 6 7 8 9 10 6 7 8 9 10 g) h) 5 i) Fundamental Mathematics 5 11 �Topic B: Self-Test Mark /18 Aim 15/18 A. Count the number of things in each picture, then write the numeral and the word name. a) c) b) Numeral: Numeral: Word Name: Word Name: ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● d) ● ● ● Numeral: Numeral: Word Name: Word Name: B. Write the numerals from one to 10. 12 ● ● 8 marks 10 marks Book 1 �Topic B: Self-Test – Answer Key A: a) 0, zero b) 6, six c) 8, eight d) 9, nine B: 1 2 3 4 5 6 7 8 9 10 Emotions Check How are you feeling? Are your palms moist? How is your breathing? Take control. Be the boss. If you are feeling anxious, practice your breathing exercise. Remember: breathe in slowly to the count of four, hold it for the count of four and breathe out slowly to the count of four. Fundamental Mathematics 13 �Topic C: Place Value As you know, we count much higher than ten in our world. Each place in a number has a value. The ones place tells how many ones there are. 3 means 3 ones 0 means 0 ones 9 means 9 ones 9 is the largest amount that we can express (write or say) with one digit. The tens place shows how many tens there are. The ones place must have a digit in it before there can be a digit in the tens place. Every ten is ten ones. = 43 means 4 tens and 3 ones 20 means 2 tens and 0 ones. The zero holds the ones place. 14 Book 1 �99 means 9 tens and 9 ones. 99 is the largest amount that we can express (write or say) using only two digits. Exercise One Example: 49 means Fill in the blanks to make each sentence true. Draw a picture for questions c, f, h and j like the examples. Check your work using the answer key at the end of the exercise. Ask your instructor to check your sketches. 4 tens and 9 ones a) 37 means tens and ones. b) 65 means tens and ones. Fundamental Mathematics 15 �c) 56 means tens and ones. (Draw your picture below.) d) 87 means tens and ones. e) 33 means tens and ones. f) 60 means tens and ones. (Draw your picture below.) 16 Book 1 �g) 70 means tens and ones. h) 44 means tens and ones. (Draw your picture below.) i) 98 means tens and ones. j) 75 means tens and ones. (Draw your picture below.) Fundamental Mathematics 17 �Exercise One – Answer Key a) b) 6 tens, 5 ones c) 5 tens, 6 ones d) 8 tens, 7 ones e) 3 tens, 3 ones f) 6 tens, 0 ones g) 7 tens, 0 ones h) 4 tens, 4 ones i) 9 tens, 8 ones j) 18 3 tens, 7 ones 7 tens, 5 ones Book 1 �The place to the left of the tens place is the hundreds place. It shows how many hundreds there are. A number written using three whole digits has a hundreds place, a tens place, and a ones place. Every hundred is ten tens – every hundred is the same as one hundred ones. 100 100 100 425 means 4 hundreds, 2 tens, and 5 ones. 354 means 3 hundreds, 5 tens, and 4 ones. Fundamental Mathematics 19 �Exercise Two a) 190 = Fill in the blanks to make each sentence true. Draw a picture for questions c, e, and h, like the examples. Check your work using the answer key at the end of the exercise. Ask your instructor to check your sketches. 1 hundreds, 9 tens, 0 ones b) 555 = hundreds, tens, ones c) 309 = hundreds, tens, ones tens, ones (Draw your picture below.) d) 499 = 20 hundreds, Book 1 �e) 480 = hundreds, tens, ones (Draw your picture below.) f) 999 = hundreds, tens, ones g) 657 = hundreds, tens, ones h) 125 = hundreds, tens, ones (Draw your picture below.) Fundamental Mathematics 21 �i) 212 = hundreds, tens, ones Answers to Exercise Two b) 5 hundreds, 5 tens, 5 ones c) 3 hundreds, 0 tens, 9 ones d) 4 hundreds, 9 tens, 9 ones e) 4 hundreds, 8 tens, 0 ones f) g) 6 hundreds, 5 tens, 7 ones i) 2 hundreds, 1 ten, 2 ones 9 hundreds, 9 tens, 9 ones h) 1 hundred, 2 tens, 5 ones Exercise Three Count the hundreds, tens, and ones shown in the drawings. The pictures will help you understand the quantity of a number. Then write the numeral. The first one is done for you. Check your work using the answer key at the end of the exercise. a) 2 hundreds 0 tens 3 ones = 203 b) hundreds 22 tens ones = Book 1 �c) hundreds tens ones = hundreds tens ones = hundreds tens d) e) ones = Answers to Exercise Three b) 4 hundreds, 3 tens, 1 one, 431 c) 1 hundred, 8 tens, 0 ones, 180 d) 3 hundreds, 1 ten, 6 ones, 316 e) 2 hundreds, 0 tens, 3 ones, 203 Fundamental Mathematics 23 �Need more practice? Ask your instructor for some play money. Using the one, ten and hundred dollar bills practice trading ten of one type of bill for one of the next value. Example: 24 ABE Bucks $1 One ABE Bucks $1 One ABE Bucks $1 One ABE Bucks $1 One ABE Bucks $1 One ABE Bucks $1 One ABE Bucks $1 One ABE Bucks $1 One ABE Bucks $1 One ABE Bucks $1 One equals ABE Bucks $10 Ten Book 1 �Exercise Four a) 622 Write the place value name (ones, tens, hundreds) for each underlined digit. Check your work using the answer key at the end of the exercise. hundreds b) 468 c) 920 d) 920 e) 648 f) 426 g) 534 h) 555 i) 451 j) 901 k) 226 l) 486 tens Answers to Exercise Four c) ones d) hundreds e) f) ones g) hundreds h) tens i) tens j) k) hundreds l) ones Exercise Five ones tens Underline the digit for the place value named. Check your work using the answer key at the end of the exercise. a) hundreds 416 b) tens 368 c) tens 364 d) hundreds 456 e) ones 206 f) ones 634 Fundamental Mathematics 25 �g) hundreds 742 h) hundred 543 i) tens 221 j) ones 100 k) ones 169 l) tens 684 Answers to Exercise Five a) 4 b) 6 c) 6 d) 4 e) 6 f) 4 g) 7 h) 5 i) 2 j) 0 k) 9 l) 8 Emotions Check How are you feeling? Are your palms moist? How is your breathing? Take control. Be the boss. If you are feeling anxious, practice your breathing exercise. Remember: breathe in slowly to the count of four, hold it for the count of four and breathe out slowly to the count of four. 26 Book 1 �Reading and Writing Numerals You know that the digits are 0 1 2 3 4 5 6 7 8 9 and that digits are arranged in different places so we can count larger amounts than our ten fingers! When we use digits we call what we write the numeral. 328 is a numeral 46 is a numeral 3 is a numeral We use numerals to represent numbers. If we think about language instead of mathematics it will be clearer. Letters are used to make words. We respond to the meaning of words. Digits are the “letters” of math. Numerals are the “words” of math. Numbers are the “meaning” of math. Now you know the place value of digits up to three places. Next you will learn to read and write numerals and number words. Some of the words to read and spell may be new to you. The numerals from 1 to 12 have special words. These are 0 1 2 3 4 5 6 zero one two three four five six Fundamental Mathematics 7 8 9 10 11 12 seven eight nine ten eleven twelve 27 �The number names for numerals from 13 to 19 are made up of two parts. The first part tells us how many units. The second part (“teen”) tells us there is also 1 ten. 13 14 15 16 17 18 19 Exercise Six 28 thirteen fourteen fifteen sixteen seventeen eighteen nineteen three units and 1 ten four units and 1 ten five units and 1 ten six units and 1 ten seven units and 1 ten eight units and 1 ten nine units and 1 ten Write the word name for each number. Try not to look at the list. Check your work using the answer key at the end of the exercise. a) 8 b) 16 c) 7 d) 15 e) 5 f) 11 g) 9 h) 18 i) 6 j) 17 k) 4 l) 14 m) 12 n) 13 o) 19 p) 3 Book 1 �Answers to Exercise Six a) eight b) sixteen c) seven d) fifteen e) f) eleven g) nine h) eighteen i) six j) seventeen k) four l) fourteen m) twelve n) thirteen o) nineteen five p) three The word names for the numbers 20 to 90 are also made up of two parts. The first part tells us how many groups of tens. The second part (“ty”) tells us we are counting groups of tens and not something else. The “-ty” may have come from a shortening of the word “ten”. 20 30 40 50 60 70 80 90 twenty thirty forty fifty sixty seventy eighty ninety two tens three tens four tens five tens six tens seven tens eight tens nine tens The names for the numbers between groups of tens also follow a pattern. The first number tells us how many tens. The second number tells us how many ones. Tens Ones Tens Ones Tens Ones 20 twenty 30 thirty 40 forty 21 twenty-one 31 thirty-one 41 forty-one 22 twenty-two 32 thirty-two 42 forty-two 23 twenty-three 33 thirty-three 43 forty-three 24 twenty-four 34 thirty-four 44 forty-four 25 twenty-five 35 thirty-five 45 forty-five 26 twenty-six 36 thirty-six 46 forty-six 27 twenty-seven 37 thirty-seven 47 forty-seven 28 twenty-eight 38 thirty-eight 48 forty-eight 29 twenty-nine 39 thirty-nine 49 forty-nine Fundamental Mathematics 29 �The written names for numbers that have tens and ones are written with a hyphen (-) between them. This pattern with the hyphen continues up to ninety-nine (99). Exercise Seven a) 24 Write the word names for these numbers. Check your work using the answer key at the end of the exercise. twenty-four b) 35 c) 83 d) 46 e) 59 f) 20 g) 71 h) 94 i) 62 j) 53 thirty-five Answers to Exercise Seven c) eighty-three d) forty-six e) fifty-nine f) twenty g) seventy-one h) ninety-four i) sixty-two j) fifty-three Exercise Eight a) 44 30 forty-four Without looking back, write the word names for these numbers.Check your work using the answer key at the end of the exercise. b) 97 c) 71 d) 86 e) 53 f) 25 g) 15 h) 38 Book 1 �Answers to Exercise Eight b) ninety-seven c) seventy-one d) eighty-six e) fifty-three f) twenty-five g) fifteen h) thirty-eight Exercise Nine a) ninety-nine Write the numerals for these word names. Check your work using the answer key at the end of the exercise. 99 b) sixty-seven c) eighty-one d) eighteen e) twenty-six f) thirteen g) thirty h) forty-three i) sixteen j) twenty 67 Answers to Exercise Nine c) 81 d) 18 e) 26 f) 13 g) 30 h) 43 i)16 j) 20 When we write hundreds in words, we need two words. The first word tells us how many hundreds. The second word tells us we are counting hundreds. 200 two hundred You now know how to write numbers in words up to 999. Fundamental Mathematics 31 �367 is made of 3 hundreds 6 tens 7 ones Each is written: three hundred sixty seven Put the parts together: three hundred sixty-seven Remember: hyphen (-) between the tens and units no hyphen anywhere else no “s” on the hundred no „and” between the hundreds place and the tens place Here is another example. Watch out for the empty space! 504 is made of 5 hundreds 0 tens Each is written: five hundred Put the parts together: five hundred four 4 ones four Here is another example. Watch out for the empty space! 890 is made of 8 hundreds 9 tens Each is written: eight hundred ninety Put the parts together: eight hundred ninety 0 ones Here is another example. Watch out for the empty spaces! 100 is made of 1 hundreds Each is written: one hundred Put the parts together: one hundred 0 tens 0 ones Remember: empty spaces are not written in words. 32 Book 1 �Exercise Ten Write the word names for these numerals. Check your work using the answer key at the end of the exercise. a) 623 is made of Each is written: Put the parts together: b) 364 is made of Each is written: Put the parts together: c) 213 is made of Each is written: Put the parts together: d) 405 is made of Each is written: Put the parts together: e) 820 is made of Each is written: Put the parts together: Fundamental Mathematics 33 �f) 704 g) 470 h) 993 i) 100 j) 972 34 Book 1 �Answers to Exercise Ten a) 623 is made of 6 hundreds 2 tens 3 ones Each is written: six hundred twenty three Put the parts together: six hundred twenty-three b) 364 is made of 3 hundreds 6 tens 4 ones Each is written: three hundred sixty four Put the parts together: three hundred sixty-four c) 213 is made of 2 hundreds 1 ten Each is written: two hundred thirteen Put the parts together: two hundred thirteen 3 ones d) 405 is made of 4 hundreds Each is written: four hundred Put the parts together: four hundred five 0 tens 5 ones five e) f) 820 is made of 8 hundreds 2 tens Each is written: eight hundred twenty Put the parts together: eight hundred twenty seven hundred four h) nine hundred ninety-three j) g) four hundred seventy i) one hundred 0 ones nine hundred seventy-two Fundamental Mathematics 35 �Topic C: Self-Test Mark A. Write the place value for the underlined digit. a) 765 b) 903 c) 479 d) 185 e) 732 f) 397 B. Write the word names for these numerals. /17 Aim 14/17 6 marks 6 marks a) 79 b) 492 c) 378 d) 820 e) 405 f) 583 C. Write the numerals for these word names. 5 marks a) five hundred forty-seven b) three hundred eighty c) two hundred seventy-five d) four hundred sixteen e) nine hundred twenty-three 36 Book 1 �Answers to Topic C Self-test A. a) tens b) tens c) hundreds d) ones e) ones f) hundreds B. a) seventy-nine b) four hundred ninety-two c) three hundred seventy-eight d) eight hundred twenty e) four hundred five f) five hundred eighty-three C. a) 547 b) 380 d) 416 e) 923 Fundamental Mathematics c) 275 37 �Topic D: Ordering Numerals We arrange numerals in order from smallest to largest. Sorting numbered papers such as order forms, arranging items by the date and comparing prices are some of the ways you use this skill. Look at two numerals and tell which one is larger. How do you do this? Exercise One Draw a box around the larger numeral in each pair. a) 43 48 b) 27 21 c) 64 63 d) 24 35 e) 92 89 f) 72 81 Answers to Exercise One b) 27 c) 64 d) 35 e) 92 f) 81 To compare numerals, look at the place with the largest value. Example A: Compare 63 and 59 Look at the tens place. 63 has a 6 in the tens place. 59 has a 5 in the tens place. 63 is larger than 59. Example B: Compare 496 and 476. Look at the hundreds – both have 4’s. Look at the tens place. 496 has a 9 in the tens place. 476 has a 7 in the tens place. 496 is larger than 476. 38 Book 1 �Note: Numerals with one digit are always less than numerals with two digits. Numerals with two digits are always less than numerals with three digits, and so on. 9 is less than 15 87 is less than 107 999 is less than 1 001 Exercise Two Draw a box around the larger numeral in each pair. Check your work using the answer key at the end of the exercise. a) 36 46 b) 580 59 c) 87 67 d) 716 116 e) 429 449 f) 289 283 g) 229 329 h) 230 210 i) 51 159 j) 836 935 k) 36 37 l) 461 468 Answers to Exercise Two b) 580 c) 87 d) 716 e) 449 f) 289 j) 935 g) 329 k) 37 h) 230 l) 468 i) 159 Fundamental Mathematics 39 �Exercise Three Draw a box around the larger numeral in each pair. Check your work using the answer key at the end of the exercise. a) 148 151 b) 129 132 c) 34 37 d) 325 236 e) 118 13 f) 489 423 g) 471 422 h) 316 322 i) 876 319 Exercise Three – Answer Key b) 132 f) 489 c) 37 g) 471 d) 325 h) 322 e) 118 i) 876 Now use the same ideas to arrange more than two numerals in order. For example, to arrange 6, 616, 1, 66, 666, 61, and 16 in order from smallest to largest, use the following method: First, sort the numerals with the same number of digits into groups. 6, 1 66, 16, 61 and 616, 666 The group of one digit numerals contains 6 and 1. As 1 is smaller than 6, the list starts with 1, then 6. The group of two-digit numerals contains 66, 61, and 16. Use your skills in ordering numerals to see that 16 is smallest, then 61, and 66 is the largest of this group. The list now reads, 1, 6, 16, 61, 66. Finally, look at the three-digit numerals, 616 and 666. As 616 is smaller than 666, it will come first. The list now reads: 1, 6, 16, 61, 66, 616, 666. 40 Book 1 �40 Book 1 �Exercise Four Arrange these numbers in order from smallest to largest. Check your work using the answer key at the end of the exercise. a) 323 32 332 33 3 322 2 b) 44 7 474 47 744 74 77 c) 123 135 152 125 d) 472 427 452 475 Answers to Exercise Four a) c) 2, 3, 32, 33, 322, 323, 332 123, 125, 135, 152 Fundamental Mathematics b) d) 7, 44, 47, 74, 77, 474, 744 427, 452, 472, 475 41 �Greater Than, Less Than, Equals The sign < means “is less than” (smaller than). The sign > means “is greater than” (bigger than). The greater than and less than signs always point to the smaller number. That is, the point or the tip of the sign is close to the small number. 5 < 12 6>3 means 5 is less than 12 means 6 is greater than 3 The sign = means “equals” and is used when two amounts are the same. Exercise Five a) 3 c) Write <, >, or = in each blank as needed. Check your work using the answer key at the end of the exercise. < > 5 b) 8 12 9 d) 28 28 e) 48 84 f) 376 376 g) 520 530 h) 582 521 i) 674 296 j) 214 251 k) 879 900 l) 784 784 7 Answers to Exercise Five 42 c) > g) < d) = h) > k) < l) = e) < i) > f) = j) < Book 1 �Topic D: Self-Test Mark /12 Aim 10/12 A. Box the larger number of each pair. 6 marks a) 978 789 b) 566 556 c) 120 142 d) 701 710 e) 430 403 f) 879 987 B. Arrange these numerals in order from smallest to largest. a) 75 754 b) 18 237 475 429 47 824 747 37 2 marks 574 775 994 112 C. Write >, <. or = in each blank to make a true statement. 4 marks a) 678 768 b) 102 100 c) 463 846 d) 101 101 Answers to Topic D Self-Test A. a) 978 b) 566 c) 142 d) 710 e) 430 f) 987 b) > c) < B. a) < d) = C. a) 47, 75, 475, 574, 747, 754, 775 b) 18, 37, 112, 237, 429, 824, 994 Fundamental Mathematics 43 �Topic E: Rounding Numbers We use numbers a lot in our everyday lives. List some of the ways you use numbers. You may have written money, shopping, time, and counting as part of your answer. Think about time. Let’s say it takes eight minutes to walk to the bus. If someone asks you how long it takes, you will probably say, “About ten minutes.” If you buy a sweater that cost $29, you may say, “Oh, it was around thirty dollars.” How far is it from Vancouver to Prince George? The map says 796 km, but we would probably say, “About 800 kilometres.” You have just read examples of rounding numbers. We round numbers for many reasons: We may not know the exact number. The exact number may not be important for what we are doing. We may need a quick way to figure something out. When you are rounding numbers, use zeros to hold the places at the end of the number. Work through the following examples and exercises carefully. Rounding is an important skill. 44 Book 1 �Rounding to the Nearest Ten A number rounded to the nearest ten will have a zero in the ones place. The number will end with 0, 10, 20, 30, 40, 50, 60, 70, 80, or 90. When rounding to the nearest 10, we are looking for the closest group of 10. Example: 20 20, 23 and 30. 23 30 Is 23 closer to 20 or 30? It is closest to 20. Which gives a better estimate of 23…..2 tens or 3 tens. 2 tens If we round 23 to the nearest ten, the result would be 20. Remember: The rounded number has a zero in the ones place. Example: 40 40, 46 and 50 46 50 Is 46 closer to 40 or 50? it is closest to 50. Which gives a better estimate of 46……4 tens or 5 tens? 5 tens If we round 46 to the nearest ten, the result would be 50. Fundamental Mathematics 45 �Example: 60, 65 and 70 60 65 70 Is 65 closer to 60 or 70? It is closer to 70. Which gives a better estimate of 65…… 6 tens or 7 tens? 7 tens When we have a number which ends in 5, we always round up to the next ten. If we round 65 to the nearest 10, the result would be 70. Example: Round 32 to the nearest 10. 32 is between 3 tens and 4 tens. 32 is closest to 3 tens. Rounded number is 30 . Exercise One a) Round each number to the nearest 10. Check your work using the answer key at the end of the exercise. 47 is between tens and 47 is closest to tens. Rounded number is b) c) tens and 81 is closest to tens. tens. . 14 is between tens and 14 is closest to tens. Rounded number is 46 . 81 is between Rounded number is tens. tens. . Book 1 �d) 26 is between 26 is closest to tens and tens. Rounded number is e) . 98 is between tens and 98 is closest to tens. Rounded number is f) 57 is between tens and 57 is closest to tens. 73 is between tens and 73 is closest to tens. i) tens and 2 is closest to tens. j) tens and 39 is closest to tens. 65 is between tens and 65 is closest to tens. tens and 18 is closest to tens. Fundamental Mathematics tens. . 18 is between Rounded number is tens. . Rounded number is k) tens. . 39 is between Rounded number is tens. . 2 is between Rounded number is tens. . Rounded number is h) tens. . Rounded number is g) tens. tens. . 47 �Answers to Exercise One a) b) 8 tens, 9 tens 8 tens 80 c) 1 ten, 2 tens 1 ten 10 d) 2 tens, 3 tens 3 tens 30 e) f) 5 tens, 6 tens 6 tens 60 g) 7 tens, 8 tens 7 tens 70 h) 0 tens, 1 ten 0 tens 0 j) k) 1 ten, 2 tens 2 tens 20 48 4 tens, 5 tens 5 ten 50 6 tens, 7 tens 7 tens 70 9 tens, 10 tens 10 tens 100 i) 3 tens, 4 tens 4 tens 40 Book 1 �Now look at a shorter method to round to the nearest ten. When rounding to the nearest ten, do this: Step 1: Underline the tens digit. 83 Step 2: Look at the digit following in the ones place. 83 Step 3: If the digit in the ones place is less than 5, write a 0 in the ones place. leave the tens digit as it is. 42 rounds to 40 (42 is nearer to 40 than to 50) 14 rounds to 10 83 rounds to 80 Step 4: If the digit in the ones place is 5 or more, write a 0 in the ones place. add one more ten to the tens place. 36 rounds to 40 (36 is nearer to 40 than to 30) 25 rounds to 30 98 rounds to 100 (one more ten than nine tens is ten tens) Note: If you are rounding to the nearest ten, single digits are rounded like this: 0, 1, 2, 3, 4 all round to 0. 5, 6, 7, 8, 9 all round to 10. When you round a number, use the sign that means “approximately equal” Fundamental Mathematics 49 �Exercise Two a) 22 Round each number to the nearest ten. Check your work using the answer key at the end of the exercise. 20 b) 86 90 c) 31 d) 96 e) 84 f) 55 g) 8 h) 2 i) 63 j) 49 k) 25 l) 71 m) 38 n) 51 o) 88 Answers to Exercise Two c) 30 d) 100 e) 80 f) 60 g) 10 h) 0 i) 60 j) 50 k) 30 l) 70 m) 40 n) 50 o) 90 Numbers of any size can be rounded to the nearest ten using the method you have just learned. 238 50 240 883 880 297 300 Book 1 �Exercise Three Round each number to the nearest ten. Check your work using the answer key at the end of the exercise. a) 424 b) 867 c) 499 d) 132 e) 278 f) 617 g) 208 h) 851 i) 124 j) 576 k) 315 l) 742 m) 397 n) 952 o) 639 Answers to Exercise Three a) 420 b) 870 c) 500 d) 130 e) 280 f) 620 g) 210 h) 850 i) 120 j) 580 k) 320 l) 740 m) 400 n) 950 o) 640 Fundamental Mathematics 51 �Exercise Four For each problem, round the numbers to the nearest ten. Check your work using the answer key at the end of the exercise. Example: Mei Ling has just moved into a new apartment. She bought the following items. Round each amount to the nearest ten. Item Cost Rounded to nearest ten Towels Dishes Saucepan Microwave Carving Knife $14 $32 $43 $109 $18 $10 $30 $40 $110 $20 a) Akkul walked 12 kilometres on Monday, 26 kilometres on Tuesday and 6 kilometres on Wednesday. Round each number to the nearest ten. Day Monday Number 12 Tuesday 26 Wednesday 6 Rounded Number b) Werner is a keen bird watcher. On Monday, he saw 57 birds, on Tuesday he saw 124 birds, on Wednesday he saw 31 birds and on Thursday he saw 75 birds. Round each number to the nearest ten. Day Number Rounded Number Monday Tuesday Wednesday Thursday 52 Book 1 �c) Jamir drove 678 kilometres. 493 kilometres, 387 kilometres and 914 kilometres in one week. Round each mileage to the nearest ten. Day Kilometres Rounded Number #1 #2 #3 #4 d) Koho Industries canned 281 cans of salmon last week and 392 cans of salmon this week. They plan to can 438 cans of salmon next. Round each number of cans to the nearest ten. Week Cans Rounded Number Last week This week Next week e) During one week at the movie theatre there were 423 people on Monday, 328 people of Tuesday, 148 people on Wednesday and 523 people on Thursday. Round each number to the nearest ten. Day People Rounded Number Monday Tuesday Wednesday Thursday Answers to Exercise Four a) 10, 30, 10 b) 60, 120, 30, 80 d) 280, 390, 440 e) Fundamental Mathematics c) 680, 490, 390, 910 420, 330, 150, 520 53 �Topic E: Self-Test Mark /12 A. Round your answer to the nearest ten. Aim 10/12 8 marks a) 47 b) 123 c) 4 d) 945 e) 329 f) 481 g) 865 h) 916 B. Round each number to the nearest ten. 4 marks a) Mary scored 78, 91, 79, 67 and 102 on her arithmetic test. Round her scores to the nearest ten. Score Rounded Score Answers to Topic E Self-Test A. a) 50 b) 120 c) 0 d) 950 e) f) 480 g) 870 h) 920 330 B. a) 80, 90, 80, 70, 100 54 Book 1 �Topic F: More Counting Practice your counting by filling in the counting chart. Have your instructor check your chart when you are done. 0 1 2 3 4 5 6 7 8 9 10 If you had a pile of pennies or loonies, you would count by ones in order to find out how much money you have. Fundamental Mathematics 55 �Use your counting chart and start at 1. Write down every second number. 0 1 3 5 The numbers above are called odd numbers. Use your counting chart and starting at 0. Write down every second number. 0 56 2 4 6 Book 1 �The numbers above are called the even numbers. If you had a pile of toonies, you could count by two’s to find out how much money you have. Use your counting chart and start at 0. Count five and write down that number. 0 5 10 If you had a pile of nickels or five dollar bills and wanted to know how much money you have, you would count be 5’s. Use your counting chart and starting at 0. Count ten and write down that number. 0 10 20 If you had a pile of dimes or ten dollar bills and wanted to know how much money you have, you would count by 10’s. Fundamental Mathematics 57 �Exercise One Count how much money you have. Check your work using the answer key at the end of the exercise. Example: 5 How many nickels? 10 15 3 How much money do you have? 15 cents a) How many twonies do you have? How much money do you have? dollars b) How many dimes do you have? How much money do you have? 58 cents Book 1 �c) How many nickels to you have? How much money do you have? cents d) How many dimes do you have? How much money do you have? cents e) How many nickels to you have? How much money do you have? Fundamental Mathematics cents 59 �f) How many twonies do you have? How much money do you have? dollars g) How much money do you have? 60 cents Book 1 �h) How much money do you have? dollars i) How much money do you have? Fundamental Mathematics cents 61 �Answers to Exercise One a) 4 twonies, $8 b) 7 dimes, 70 cents c) 9 nickels, 45 cents d) 4 dimes, 40 cents e) 10 nickels, 50 cents f) 3 twonies, $26 g) 90 cents h) $36 i) 70 cents 62 Book 1 �Topic F: Self-Test Mark A. Write the first 10 odd numbers starting with 1. /16 Aim 13/16 5 marks B. Write the first 10 even numbers starting at 2. C. How much money do you have? 5 marks 6 marks (2 marks each) i) How much money do you have? Fundamental Mathematics cents 63 �ii) How much money do you have? 64 dollars Book 1 �iii) How much money do you have? cents Answers to Topic F Self-Test A. 1, 3, 5, 7, 9, 11, 13, 15, 17, 19 B. 2,4,6,8,10,12,14,16,18, 20 C. i) 75 cents ii) 38 dollars iii) 80 cents Emotions Check How are you feeling? Are your palms moist? How is your breathing? Take control. Be the boss. If you are feeling anxious, practice your breathing exercise. Remember: breathe in slowly to the count of four, hold it for the count of four and breathe out slowly to the count of four. Fundamental Mathematics 65 �Unit 1 Review - Number Sense You will now practice all the skills you learned in Unit 1. Check your work using the answer key at the end of the review. A. Count the number of things in each picture. Write the number and word name. a) Numeral: Word Name: b) c) Numeral: Numeral: Word Name: Word Name: 66 Book 1 �d) e) Numeral: Numeral: Word Name: Word Name: B. Fill in the blanks to make each sentence true. Draw a picture for questions b and e. a) 46 means tens and ones. b) 25 means tens and ones. Draw your picture below. c) means Fundamental Mathematics tens and ones 67 �d) 138 = hundreds, tens, ones. e) 231 = hundreds, tens, ones. Draw your picture below. f) hundreds C. 68 tens ones = Write the place value name (ones, tens, hundreds) for each underlined digit. a) 821 b) 294 c) 638 d) 417 e) 346 f) 573 Book 1 �D. E. F. G. Underline the digit for the place value named. a) hundreds 164 b) tens 892 c) tens 250 d) hundreds 371 e) ones 485 f) ones 743 Write the word names for the numbers. a) 73 b) 14 c) 5 d) 39 e) 52 f) 496 g) 803 h) 640 Write the numerals for these word names. a) forty-seven b) nineteen c) sixty-five d) thirty-eight e) twenty-four f) five hundred thirty-five g) three hundred sixty h) two hundred four Arrange these numbers in order from smallest to largest. a) 258 Fundamental Mathematics 32 23 282 345 534 69 �b) H. I. J. 155 27 635 208 452 335 Write <, >, or = in each blank as needed. a) 37 52 b) 4 0 c) 349 394 d) 67 67 e) 86 68 f) 732 751 Round each number to the nearest ten. a) 37 b) 344 c) 68 d) 25 e) 51 f) 876 How much money do you have? a) How much money do you have? 70 cents Book 1 �b) How much money do you have? dollars c) How much money do you have? Fundamental Mathematics cents 71 �K. Word Problems a) Hussein’s fruit stand sold 114 watermelons, 287 honeydew melons and 345 cantaloupes. Round each number to the nearest ten. Melon Number Rounded Number Watermelons Honeydew Melons Cantaloupes b) Yi-Min drove her delivery van 106 kilometres on Saturday, 187 kilometres on Sunday and 285 kilometres on Monday. Round each number to the nearest ten. Kilometres Number Rounded Number Saturday Sunday Monday 72 Book 1 �Answers to Unit 1 Review A. a) 9, nine b) 7, seven c) 6, six d) 8, eight e) 5, five B. a) 4 tens, 6 ones b) 2 tens, 5 ones c) 63, 6 tens, 3 ones d) 1 hundred, 3 tens, 8 ones e) 2 hundreds, 3 tens, 1 one f) 3 hundreds, 2 tens 5 ones, 325 C. a) hundreds e) tens D. a) 164 b) tens f) ones b) 892 c) 250 E. a) seventy-three b) fourteen e) fifty-two F. a) 47 g) 360 b) 19 h) 204 c) ones d) 371 e) 485 c) five f) four hundred ninety-six c) 65 d) 38 G. a) 23, 32, 258, 282, 345, 534 d) hundreds f) 743 d) thirty-nine g) six hundred forty e) 24 f) 535 b) 27, 155, 208, 335, 452, 635 H. a) < b) > c) < d) = e) > f) < I. a) 40 b) 340 c) 70 d) 30 e) 50 f) 880 J. a) 70 cents b) 26 dollars c) 90 cents K. a) b) Melon Number Rounded Number Watermelons 114 110 Honeydew Melons 287 Cantaloupes 345 Fundamental Mathematics Kilometres Rounded Number Saturday 106 110 290 Sunday 187 190 350 Monday 285 290 Day 73 �CONGRATULATIONS!! Now you have finished Unit 1. TEST TIME! Ask your instructor for the Practice Test for this unit. Once you’ve done the practice test, you need to do the unit 1 test. Again, ask your instructor for this. Good luck! 74 Book 1 �Unit 2 Addition Fundamental Mathematics 75 �Topic A: Addition Addition puts amounts together. The answer of addition is called the sum or the total. The plus sign + means to add. 3 + + 2 = = 5 says “three plus two equals five” or “three and two is five” The sum is 5. You can count on your fingers to get the answers to addition questions, but counting takes too long. Addition facts are a tool that you use to do adding questions. Exercise One a) e) 76 Check out your addition facts by doing this exercise as quickly as possible without counting on your fingers. The highest total or sum (what the numbers add up to) for these number facts is 9. Check your work using the answer key at the end of the exercise. Then, make a list of any addition facts you do not know or which are slow – practice them. 2 +4 6 b) 3 +1 4 c) 1 +2 d) 7 +0 0 +4 f) 1 +4 g) 5 +2 h) 3 +3 Book 1 �i) 2 +0 j) 6 +3 k) 4 +4 l) 3 +0 m) 5 +3 n) 1 +6 o) 0 +5 p) 8 +1 q) 2 +6 r) 1 +0 s) 1 +5 t) 2 +2 u) 3 +2 v) 2 +1 w) 5 +4 x) 1 +7 y) 9 +0 z) 5 +1 aa) 0 +3 bb) 4 +1 Answers to Exercise One a) 6 b) 4 c) 3 d) 7 e) 4 f) 5 g) 7 h) 6 i) j) 9 k) 8 l) 3 m) 8 n) 7 o) 5 p) 9 q) 8 r) 1 s) 6 t) u) 5 v) 3 w) 9 x) 8 y) 9 z) 6 aa) 3 2 Fundamental Mathematics 4 bb) 5 77 �Exercise Two a) 4 +5 9 Check out your addition facts by doing this exercise as quickly as possible without counting on your fingers. The highest total or sum (what the numbers add up to) for these number facts is 9. Check your work using the answer key at the end of the exercise. Then, make a list of any addition facts you do not know or which are slow – practice them. b) 1 +8 9 c) 8 +0 d) 4 +3 e) 0 +0 f) 2 +3 g) 7 +1 h) 0 +9 i) 4 +2 j) 0 +2 k) 0 +7 l) 1 +1 m) 2 +7 n) 0 +1 o) 6 +2 p) 0 +6 q) 1 +3 r) 3 +5 s) 2 +5 t) 0 +8 78 Book 1 �u) 3 +4 v) 4 +0 w) 3 +6 x) 5 +0 y) 6 +1 z) 6 +0 aa) 7 +2 bb) 0 +3 Answers to Exercise Two a) 9 b) 9 c) 8 d) 7 e) 0 f) 5 g) 8 h) 9 i) 6 j) 2 k) 7 l) 2 m) 9 n) 1 o) 8 p) 6 q) 4 v) 4 w) 9 x) 5 r) 8 y) 7 s) 7 z) 6 t) 8 aa) 9 u) 7 bb) 3 Exercise Three Check out your addition facts by doing this exercise as quickly as possible without counting on your fingers. The highest total or sum (what the numbers add up to) for these number facts is 9. Check your work using the answer key at the end of the exercise. Then, make a list of any addition facts you do not know or which are slow – practice them. a) 3 +6 9 b) 4 +5 9 c) 4 +1 d) 9 +0 e) 2 +2 f) 3 +4 g) 0 +6 h) 5 +2 Fundamental Mathematics 79 �i) 4 +0 j) 1 +8 k) 2 +3 l) 0 +5 m) 0 +0 n) 1 +2 o) 4 +3 p) 6 +1 q) 6 +2 r) 3 +2 s) 2 +7 t) 0 +7 u) 5 +4 v) 1 +7 w) 5 +3 x) 3 +3 y) 1 +4 z) 2 +4 aa) 0 +4 bb) 1 +3 cc) 1 +6 dd) 0 +8 ee) 8 +1 ff) 3 +5 80 Book 1 �gg) 3 +0 hh) 6 +3 ii) 3 +1 jj) 7 +1 kk) 2 +6 ll) 4 +4 mm) 2 +5 nn) 3 +4 Answers to Exercise Three a) 9 b) 9 c) 5 d) 9 e) 4 f) 7 g) 6 h) 7 i) 4 j) 9 k) 5 l) 5 m) 0 n) 3 o) 7 p) 7 q) 8 r) 5 s) 9 t) u) 9 v) 5 z) 7 8 w) 8 x) 6 y) 6 aa) 4 bb) 4 cc) 7 dd) 8 ee) 9 ff) 8 gg) 3 hh) 9 ii) jj) 8 kk) 8 ll) 8 mm) 7 nn) 7 Exercise Four a) 6 +5 11 Fundamental Mathematics 4 Check out your addition facts by doing this exercise as quickly as possible without counting on your fingers. The highest total or sum (what the numbers add up to) for these number facts is 12. Check your work using the answer key at the end of the exercise. Then, make a list of any addition facts you do not know or which are slow – practice them. b) 8 +2 10 c) 5 +3 d) 5 +7 81 �e) 3 +4 f) 2 +6 g) 7 +3 h) 3 +9 i) 9 +3 j) 8 +1 k) 4 +5 l) 1 +9 m) 2 +7 n) 3 +5 o) 6 +6 p) 5 +6 q) 4 +6 r) 5 +8 s) 8 +4 t) 5 +2 u) 3 +7 v) 2 +8 w) 2 +9 x) 7 +1 Answers to Exercise Four a) 11 b) 10 c) 8 d) 12 e) 7 f) 8 g) 10 h) 12 i) 12 j) 9 k) 9 l) 10 m) 9 n) 8 o) 12 p) 11 q) 10 r) 11 s) 12 t) u) 10 v) 10 w) 11 x) 8 82 7 Book 1 �Exercise Five Check out your addition facts by doing this exercise as quickly as possible without counting. The highest total or sum (what the numbers add up to) for these number facts is 12. Check your work using the answer key at the end of the exercise. Then, make a list of any addition facts you do not know or which are slow – practice them. a) 9 +2 b) 6 +4 c) 4 +7 d) 2 +5 e) 8 +3 f) 7 +4 g) 6 +3 h) 5 +5 i) 9 +1 j) 7 +5 k) 4 +8 l) 6 +2 m) 7 +2 n) 1 +7 o) 3 +6 p) 5 +4 q) 4 +7 r) 7 +6 s) 9 +2 t) 4 +8 Fundamental Mathematics 83 �u) 6 +6 v) 3 +6 w) 8 +2 x) 4 +5 Answers to Exercise Five a) 11 b) 10 c) 11 d) 7 e) 11 f) h) 10 i) 10 j) 12 k) 12 l) 8 o) p) 9 q) 11 r) 13 s) 11 w) 10 x) 9 9 v) 9 Exercise Six 11 g) 9 m) 9 n) 8 t) u) 12 12 Check out your addition facts by doing this exercise as quickly as possible without counting. The highest total or sum (what the numbers add up to) for these number facts is 12. Check your work using the answer key at the end of the exercise. Then, make a list of any addition facts you do not know or which are slow – practice them. a) 3 +9 b) 5 +3 c) 4 +6 d) 4 +3 e) 6 +5 f) 2 +8 g) 9 +1 h) 7 +5 84 Book 1 �i) 3 +8 j) 5 +2 k) 6 +6 l) 2 +9 m) 4 +6 n) 3 +9 o) 3 +7 p) 5 +7 q) 8 +3 r) 8 +4 s) 1 +9 t) 6 +2 u) 2 +9 v) 5 +6 w) 9 +3 x) 2 +6 y) 3 +5 z) 6 +4 aa) 6 +5 bb) 7 +3 cc) 3 +4 dd) 6 +3 ee) 7 +4 ff) 5 +5 Fundamental Mathematics 85 �Answers to Exercise Six a) 12 b) 8 c) 10 d) 7 e) 11 f) 10 g) 10 h) 12 i) 11 j) 7 k) 12 l) 11 m) 10 n) 12 o) 10 p) 12 q) 11 w) 12 dd) 9 x) 8 ee) 11 r) 12 y) 8 ff) 10 s) 10 z) 10 t) 8 aa) 11 u) 11 bb) 10 v) 11 cc) 7 Need more practice? Practice your addition facts using a set of dice. Roll the dice and add the amounts on the dice. Exercise Seven Check out your addition facts by doing this exercise as quickly as possible without counting. The highest total or sum (what the numbers add up to) for these number facts is 20. Check your work using the answer key at the end of the exercise. Then, make a list of any addition facts you do not know or which are slow – practice them. a) 7 +6 13 b) 5 +9 14 c) 10 +3 d) 5 +7 e) 7 +9 f) 10 +9 g) 8 +7 h) 6 +4 i) 5 + 10 j) 8 +9 k) 8 +2 l) 10 +6 86 Book 1 �m) 7 +4 n) 6 + 10 o) 6 +7 p) 10 +4 q) 9 +8 r) 2 + 10 s) 9 +7 t) 5 +8 u) 10 +2 v) 5 +6 w) 8 +5 x) 4 + 10 y) 9 +6 z) 8 +4 aa) 9 + 10 bb) 9 +4 Answers to Exercise Seven a) 13 b) 14 c) 13 d) 12 e) 16 f) 19 g) 15 h) 10 i) 15 j) 17 k) 10 l) 16 m) 11 n) 16 o) 13 p) 14 q) 17 v) 11 w) 13 x) 14 r) 12 y) 15 s) 16 z) 12 t) 13 aa) 19 u) 12 bb) 13 Fundamental Mathematics 87 �Exercise Eight Check out your addition facts by doing this exercise as quickly as possible without counting. The highest total or sum (what the numbers add up to) for these number facts is 20. The highest total or sum (what the numbers add up to) for these number facts is 20. Then, make a list of any addition facts you do not know or which are slow – practice them. a) 10 +1 b) 7 +7 c) 10 +8 d) 7 +8 e) 4 +6 f) 1 + 10 g) 4 +7 h) 3 + 10 i) 0 +7 j) 3 +9 k) 10 +7 l) 6 +4 m) 0 + 10 n) 6 +9 o) 9 +9 p) 10 +5 88 Book 1 �q) 4 +8 r) 2 +9 s) 10 + 10 t) 6 +6 u) 9 +3 v) 7 +4 w) 9 +1 x) 8 +8 y) 7 + 10 a) 9 +2 aa) 8 +6 bb) 9 +5 Answers to Exercise Eight a) 11 b) 14 c) 18 d) 15 e) 10 f) 11 g) 11 h) 13 i) 7 f) 12 k) 17 l) 10 m) 10 n) 15 o) 18 p) 15 q) 12 r) 11 s) 20 t) u) v) 11 w) 10 x) 16 y) 17 z) 11 aa) 14 Fundamental Mathematics 12 12 bb) 14 89 �Exercise Nine Check out your addition facts by doing this exercise as quickly as possible without counting. The highest total or sum (what the numbers add up to) for these number facts is 20. Then, make a list of any addition facts you do not know or which are slow – practice them. a) 4 +9 b) 7 +2 c) 5 +5 d) 3 +6 e) 6 + 10 f) 8 +5 g) 6 +9 h) 6 +6 i) 3 +7 j) 9 +3 k) 2 +8 l) 5 +10 m) 5 +5 n) 10 +3 o) 8 +8 p) 2 + 10 q) 7 +9 r) 10 +8 s) 5 +8 t) 1 + 10 90 Book 1 �u) 7 +6 v) 10 + 10 w) 7 +7 x) 6 +5 y) 5 +7 z) 9 +9 aa) 10 +0 bb) 8 +2 Answers to Exercise Nine a) 13 b) 9 c) 10 d) 9 e) 16 f) 13 g) 15 h) 12 i) j) k) 10 l) 15 m) 10 n) 13 o) 16 p) 12 q) 16 r) 18 s) 13 t) u) 13 v) 20 w) 14 x) 11 y) 12 z) 18 10 12 Exercise Ten 11 aa) 10 bb) 10 Check out your addition facts by doing this exercise as quickly as possible without counting. The highest total or sum (what the numbers add up to) for these number facts is 20. Then, make a list of any addition facts you do not know or which are slow – practice them. a) 7 + 10 b) 10 +4 c) 8 +7 d) 2 +9 e) 4 +6 f) 3 + 10 g) 7 +4 h) 3 +8 Fundamental Mathematics 91 �i) 8 +3 j) 7 +8 k) 5 +9 l) 9 +5 m) 8 +6 n) 10 +9 o) 4 +7 o) 8 +9 q) 7 +5 r) 9 + 10 s) 1 +9 t) 6 +7 u) 9 +4 v) 6 +1 w) 6 +0 x) 7 +2 y) 3 +4 z) 0 +8 aa) 6 +4 bb) 5 +8 cc) 2 +5 dd) 7 +6 ee) 0 +3 ff) 9 +7 92 Book 1 �Answers to Exercise Ten a) 17 h) 11 b) 14 c) 15 d) 11 e) 10 f) 13 g) 11 i) j) k) 14 l) 14 m) 14 n) 19 o) 11 p) 17 q) 12 r) 19 s) 10 t) u) 13 v) 7 w) 6 x) 9 y) 7 z) 8 aa) 10 dd) 13 ee) 3 ff) 16 cc) 7 11 15 Exercise Eleven 13 bb) 13 Check out your addition facts by doing this exercise as quickly as possible without counting. The highest total or sum (what the numbers add up to) for these number facts is 20. Check your work using the answer key at the end of the exercise. Then, make a list of any addition facts you do not know or which are slow – practice them. a) 7 +2 b) 4 +4 c) 3 +5 d) 4 +6 e) 8 +1 f) 9 +6 g) 1 +3 h) 0 +2 i) 4 +9 j) 9 +2 k) 4 +1 l) 8 +8 Fundamental Mathematics 93 �m) 1 +5 n) 7 +3 o) 2 +2 p) 9 +5 q) 6 +1 r) 6 +0 s) 3 +2 t) 4 +8 u) 5 +5 v) 3 +6 w) 9 +8 x) 3 +9 y) 2 +3 z) 1 +9 aa) 2 +8 bb) 6 +6 cc) 5 +4 dd) 6 +8 ee) 4 +5 ff) 1 +7 gg) 5 +6 hh) 4 +0 ii) 3 +5 jj) 7 +2 94 Book 1 �Answers to Exercise Eleven a) 9 b) 8 c) 8 h) 2 i) j) 11 o) 4 p) 14 q) 7 v) 9 w) 17 x) 12 y) cc) 9 dd) 14 ee) 9 ff) 8 13 d) 10 e) 9 f) k) 5 l) 16 r) 6 s) 5 5 z) 10 aa) 10 bb) 12 hh) 4 ii) gg) 11 15 g) 4 m) 6 n) 10 t) u) 10 12 8 jj) 9 Need some extra practice? Find a partner and play the following card game. You will use a regular deck of cards Take out the jacks, queens and kings. Shuffle the cards and deal them out. Do not look at your cards. Leave them in a pile in from of you. Each player flips over a card. Take turns adding the numbers on the cards. If the person whose turn it is gets the right answer that person gets to keep the cards. If the person whose turn it is gets the wrong answer the other player gets the cards. The person who collects all the cards is the winner. You could also set a time limit and the person with the most cards when time is up is the winner. Fundamental Mathematics 95 �Exercise Twelve Here are some extra questions if you need more practice. The highest total or sum (what the numbers add up to) for these number facts is 20. Check your work using the answer key at the end of the exercise. a) 6 +7 13 b) 8 +3 11 c) 4 +2 d) 8 +7 e) 1 +2 f) 6 +4 g) 5 +8 h) 2 +5 i) 7 +6 j) 0 +3 k) 9 +7 l) 7 +2 m) 4 +4 n) 3 +5 o) 4 +6 p) 8 +1 q) 9 +6 r) 1 +3 s) 0 +2 t) 4 +9 96 Book 1 �u) 9 +2 v) 4 +1 w) 8 +8 x) 1 +5 y) 7 +3 z) 2 +2 aa) 9 +5 bb) 6 +1 cc) 6 +0 dd) 3 +2 ee) 4 +8 ff) 5 +5 gg) 3 +6 hh) 9 +8 ii) 3 +9 jj) 2 +3 kk) 1 +9 ll) 2 +8 mm) 6 +6 nn) 5 +4 oo) 6 +8 pp) 4 +5 qq) 1 +7 rr) 5 +6 Fundamental Mathematics 97 �Answers to Exercise Twelve a) 13 b) 11 c) 6 d) 15 e) 3 f) 10 g) 13 8 11 h) 7 o) 10 i) p) 13 9 j) 3 q) 15 k) 16 r) 4 l) s) 9 2 m) 8 t) 13 n) u) v) 5 cc) 6 w) 16 dd) 5 x) 6 ee) 12 y) 10 ff) 10 z) 4 gg) 9 aa) 14 hh) 17 bb) 7 ii) 12 jj) 5 qq) 8 kk) 10 rr) 11 ll) 10 mm) 12 nn) 9 oo) 14 pp) 9 98 Book 1 �Adding Across So far you have only been adding numbers when they are up and down or vertical. Example: 4 +5 9 Another way to add numbers is across or horizontally. Example: 4 + 5 = 9 In math, sometimes you will need to work from left to right. Exercise Thirteen Practice adding across or horizontally. The highest total or sum (what the numbers add up to) for these number facts is 20. Check your work using the answer key at the end of the exercise. a) 10 + 0 = b) 2 + 2 = c) 5 + 3 = d) 1 + 1 = e) 8 + 4 = f) 7 + 1 = g) 0 + 4 = h) 6 + 3 = i) 3 + 2 = j) 1 + 10 = k) 9 + 3 = l) 4 + 9 = m) 3 + 7 = n) 4 + 8 = Fundamental Mathematics 99 �o) 8 + 0 = p) 6 + 4 = q) 4 + 1 = r) 7 + 2 = s) 10 + 10 = t) 6 + 5 = Answers to Exercise Thirteen a) 10 b) 4 c) 8 d) 2 e) 12 f) h) o) k) 12 r) 9 l) s) 13 20 m) 10 t) 11 9 8 i) 5 p) 10 j) 11 q) 5 Exercise Fourteen g) 4 n) 12 Practice adding across or horizontally. The highest total or sum (what the numbers add up to) for these number facts is 20. Check your work using the answer key at the end of the exercise. a) 5 + 10 = b) 0 + 0 = c) 3 + 8 = d) 8 + 3 = e) 9 + 5 = f) 6 + 2 = g) 9 + 0 = h) 2 + 9 = i) 4 + 7 = j) 8 + 2 = 100 8 Book 1 �k) 3 + 6 = l) 9 + 4 = m) 0 + 2 = n) 5 + 2 = o) 1 + 3 = p) 4 + 2 = q) 10 + 3 = r) 5 + 4 = s) 8 + 5 = t) 6 + 6 = Answers to Exercise Fourteen a) h) o) 15 11 4 b) 0 i) 11 p) 6 Exercise Fifteen c) 11 j) 10 q) 13 d) 11 k) 9 r) 9 e) l) s) 14 13 13 g) n) 9 7 Practice adding across or horizontally. The highest total or sum (what the numbers add up to) for these number facts is 20. Check your work using the answer key at the end of the exercise. a) 9 + 6 = b) 8 + 9 = c) 9 + 9 = d) 2 + 3 = e) 7 + 3 = f) 10 + 8 = Fundamental Mathematics f) 8 m) 2 t) 12 101 �g) 9 + 7 = h) 8 + 8 = i) 8 + 10 = j) 3 + 9 = k) 9 + 2 = l) 4 + 4 = m) 6 + 8 = n) 2 + 7 = o) 5 + 7 = p) 3 + 3 = q) 7 + 0 = r) 5 + 8 = s) 10 + 8 = t) 9 + 8 = Answers to Exercise Fifteen a) b) 17 c) 18 d) 5 e) 10 f) 18 g) 16 h) 16 i) j) k) 11 l) 8 m) 14 n) 9 o) p) 6 r) s) 18 t) 102 15 12 18 12 q) 7 13 17 Book 1 �Word Problems Learning addition facts is very important. Once you know them all, you can use them to solve word problems. Words such as more than, plus, added to, sum, total, have altogether and in all tell you to add the numbers together. Look for these words when reading word problems and underline them before trying to solve a problem. Circle the information that is given. Example: Before lunch Jane read 2 pages. After lunch she read 9 pages. How many pages did she read in all? Before lunch Jane read read in all? 2 pages. After lunch she read 9 pages. How many pages did she You have circled 2 pages and 9 pages. This is the information you will use to find the answer. You have underlined “in all”. These words tell you to add. 2 pages + 9 pages 11 pages Jane read 11 pages in all. Exercise One Solve each of the following word problems. Be sure to underline the words that tell you to add. Circle the information that is given. Have your instructor check your underlining and circling. a) Sven bought 7 cans of juice on Monday. He bought 9 cans of juice on Wednesday. How many cans of juice did he buy altogether? Fundamental Mathematics 103 �Fundamental Mathematics 103 �b) During the hockey game, Ewan took 8 shots from the blue line and 4 shots from in front of the net. How many shots did he take in all? c) Marlene noticed that there were 4 people in her math class. The next day 6 more people were in her math class. What is the total number of people in Marlene’s math class? d) The Blue Jays played two baseball games in a row. They got 10 runs in the first game and 7 runs in the second game. How many runs did they score altogether? e) Jaswinder had 9 apples in her grocery cart. She added 5 more different apples. How many apples did she have in total? 104 Book 1 �f) Enlai and his dad were fishing. Enlai caught 3 fish. His father caught 5 fish. How many fish did they have in total? Answers to Exercise One a) 16 cans b) 12 shots c) 10 people d) 17 runs f) 8 fish e) 14 apples Fundamental Mathematics 105 �Topic A: Self-Test A. B. 106 Mark /22 Find the sums. Be sure to check your answers. Aim 19/22 12 marks a) 9 +6 b) 5 +8 c) 4 +2 d) 7 +6 e) 3 +5 f) 1 +9 g) 2 +3 h) 6 +4 i) 8 +1 j) 9 +8 k) 7 +4 l) 5 +6 Find the sums. Be sure to check your answers. a) 6 + 7 = b) 3 + 8 = c) 4 + 6 = d) 8 + 5 = 4 marks Book 1 �C. Solve each of the following word problems. Be sure to include the unit of measure in your answer. Be sure to circle 6 marks (2 marks each) information and underline what is being asked. a) Paco worked 5 hours on Monday and 9 hours on Tuesday. Paco work in total? How many hours did b) In the park, Ming-Mai counted 6 robins in the morning. In the afternoon, she counted 8 more robins. How many robins in all did Ming-Mai count? c) Omari bought 3 bananas on Monday. He bought 5 bananas on Tuesday. How many bananas did he buy altogether? Fundamental Mathematics 107 �Answers to Topic A Self-Test A. a) 15 b) 13 c) 6 d) 13 e) 8 h) 10 i) 9 j) 17 k) 11 l) 11 c) 10 d) 13 f) 10 g) 5 B. a) 13 C. a) 14 hours 108 b) 11 b) 14 robins c) 8 bananas Book 1 �Topic B: Addition of Three or More Numbers To add three or more numbers together, use the following steps. Step 1: Add the first two numbers together. Step 2: Add that sum to the next number. Step 3: Add that sum to the next number (if needed). Example A: 6 1 +3 Step 1: Add the first two numbers together. 6 +1 7 Step 2: Add that sum to the next number. 7 +3 10 The sum of Fundamental Mathematics 6 1 +3 10 109 �Example B: 4 5 +7 Step 1: Add the first two numbers together. 4 +5 9 Step 2: Add that sum to the third number. 9 +7 16 The sum of Example C: 4 5 +7 16 1 3 4 +5 Step 1: Add the first two numbers together. 1 +3 4 Step 2: Add that sum to the third number. 4 +4 8 110 Book 1 �Step 3: Add that sum to the fourth number. 8 +5 13 The sum of Exercise One 1 3 4 +5 13 Find the sums. Check your work using the answer key at the end of the exercise. a) 1 2 +5 b) 6 3 +2 c) 7 1 +6 d) 3 6 +5 e) 8 1 +4 f) 5 4 +8 g) 1 5 +7 h) 7 2 +5 i) 1 8 +3 j) 4 5 +9 k) 2 2 +8 l) 6 3 +5 Fundamental Mathematics 111 �m) 7 2 +5 n) 3 2 +5 o) 6 2 +5 p) 4 4 +5 q) 3 3 +9 r) 7 1 +9 s) 1 7 +5 t) 2 4 +5 u) 7 2 +8 v) 3 5 +7 w) 1 4 +8 x) 5 3 +8 Answers to Exercise One a) b) 11 h) 14 i) 12 o) 13 p) 13 q) 15 v) 15 w) 13 x) 16 112 8 c) 14 j) 18 d) 14 e) 13 f) 17 g) 13 k) 12 l) 14 m) 14 n) 10 r) s) 13 t) u) 17 17 11 Book 1 �Exercise Two Find the sums. Check your work using the answer key at the end of the exercise. a) 3 5 +7 b) 2 6 +8 c) 4 1 +9 d) 5 4 +2 e) 3 6 +4 f) 2 5 +4 g) 6 3 +2 h) 3 5 +3 i) 3 4 +7 j) 4 5 +9 k) 6 3 +2 l) 5 2 +9 m) 4 5 +7 n) 5 2 +8 o) 2 3 +8 p) 1 5 +6 q) 4 3 +5 r) 2 6 +5 s) 4 5 +3 t) 5 2 +4 Fundamental Mathematics 113 �u) 3 4 +7 v) 7 1 +5 w) 2 1 +9 x) 3 6 +3 Answers to Exercise Two a) 15 b) 16 h) 11 i) 14 o) 13 p) 12 q) 12 v) 13 w) 12 x) 12 Exercise Three c) 14 j) 18 d) 11 e) 13 f) 11 g) 11 k) 11 l) 16 m) 16 n) 15 r) s) 12 t) u) 14 13 11 Find the sums. Check your work using the answer key at the end of the exercise. a) 3 2 +8 b) 2 1 +4 c) 4 3 +1 d) 1 2 +8 e) 3 2 +2 f) 5 1 +2 g) 7 2 +8 h) 4 2 +6 114 Book 1 �i) 7 2 +7 j) 6 1 +1 k) 2 7 +6 l) 3 4 +2 m) 3 4 +1 n) 7 1 +9 o) 2 6 +4 p) 3 1 +2 q) 5 1 +3 r) 4 2 +6 s) 3 4 +6 t) 8 1 +7 u) 2 5 +8 v) 6 3 +1 w) 2 7 +5 x) 6 3 +4 Answers to Exercise Three a) 13 b) 7 c) 8 d) 11 e) 7 f) 8 g) 17 h) 12 i) j) 8 k) 15 l) 9 m) 8 n) 17 o) 12 p) 6 q) 9 r) s) 13 t) u) 15 v) 10 w) 14 x) 13 16 Fundamental Mathematics 12 16 115 �Exercise Four Find the sums. Check your work using the answer key at the end of the exercise. a) 1 3 4 +5 b) 2 3 4 +6 c) 4 3 2 +8 d) 3 1 5 +6 e) 2 2 3 +2 f) 3 3 1 +2 g) 2 1 2 +4 h) 1 2 4 +6 i) 2 4 1 +6 j) 3 2 3 +3 k) 2 1 4 +0 l) 3 1 4 +1 m) 3 2 3 +2 n) 3 5 1 +6 o) 6 1 2 +9 p) 4 3 2 +1 116 Book 1 �q) 1 4 3 +5 r) 4 2 1 +9 s) 3 4 2 +7 t) 2 4 3 +6 u) 2 3 3 +5 v) 1 3 5 +7 w) 4 4 1 +8 x) 6 2 1 +7 Answers to Exercise Four a) b) 15 c) 17 d) 15 e) 9 f) g) 9 h) 13 13 i) j) 11 k) 7 l) 9 m) 10 n) 15 o) 18 p) 10 q) 13 r) s) 16 t) u) 13 v) 16 w) 17 x) 16 13 Exercise Five a) 1 3 4 +8 Fundamental Mathematics 16 9 15 Find the sums. Check your work using the answer key at the end of the exercise. b) 5 3 1 +4 c) 7 1 1 +9 d) 2 3 4 +9 117 �e) 1 2 6 +9 f) 2 3 2 +3 g) 4 1 4 +6 h) 1 3 5 +8 i) 2 1 5 +7 j) 3 1 2 +9 k) 2 2 5 +8 l) 3 2 4 +7 m) 4 1 1 +2 n) 2 4 3 +6 o) 1 5 2 +1 p) 3 3 1 +2 q) 1 4 3 +6 r) 2 1 5 +3 s) 3 1 6 +5 t) 2 3 4 +6 118 Book 1 �u) 2 1 4 +8 v) 2 3 2 +6 w) 3 1 3 +2 x) 1 0 5 +4 Answers to Exercise Five a) 16 b) 13 c) 18 d) 18 e) 18 f) g) 15 h) 17 i) j) 15 k) 17 l) 16 m) 8 n) 15 o) 9 p) 9 q) 14 r) s) 15 t) u) 15 v) 13 w) 9 x) 10 15 Exercise Six 11 10 15 Find the sums. Check your work using the answer key at the end of the exercise. a) 2 1 5 +0 b) 4 2 2 +5 c) 1 3 4 +3 d) 1 2 6 +4 e) 3 4 2 +6 f) 2 4 4 +5 g) 2 3 5 +1 h) 4 3 1 +5 Fundamental Mathematics 119 �i) 4 1 2 +1 j) 3 2 5 +7 k) 1 3 1 +3 l) 4 2 3 +7 m) 1 3 7 +1 n) 2 1 3 +1 o) 3 2 1 +1 p) 4 1 1 +2 q) 3 0 3 +1 r) 2 1 1 +3 s) 1 0 4 +3 t) 2 3 4 +7 u) 2 1 5 +6 v) 4 3 2 +2 w) 4 1 5 +6 x) 2 4 2 +5 Answers to Exercise Six a) b) 13 h) 13 i) 8 o) 7 p) 8 q) 7 v) 11 w) 16 x) 13 120 8 c) 11 j) 17 d) 13 e) 15 f) 15 g) 11 k) 8 l) 16 m) 12 n) 7 r) s) 8 t) u) 14 7 16 Book 1 �Perimeter Did you spot the fact that each answer in the word problems before had a unit of measure? A unit of measure just tells you what you measured. Units of measure can be pages, fish, cans, kilometres, meters, centimetres, litres, millilitres, grams or kilograms. When you answer a word problem, you must include the unit of measure in your answer. Try the following questions. Be sure to include the unit of measure in your answer. Perimeter means distance around. To find the perimeter of a shape, find the lengths of the sides and add them together. Example: 3 metres 2 metres Vegetable Garden 2 metres 3 metres Rectangle To find the perimeter, add the lengths of the sides of the rectangle. Perimeter = 3 + 2 + 3 + 2 Perimeter = 10 meters Example: 4 centimetres 3 centimetres 5 centimetres Triangle To find the perimeter, add the lengths of the sides of the triangle. Perimeter = 4 + 3 + 5 Perimeter = 12 centimetres Fundamental Mathematics 121 �Exercise One a) Find the perimeter of each figure. Be sure to include the units of measure in your answer. Check your work using the answer key at the end of the exercise. Find the perimeter of the swimming pool. 3 metres 4 metres Pool 4 metres 3 metres Rectangle b) Find the perimeter of the garden. 3 metres 6 metres Garden 4 metres Triangle 122 Book 1 �c) Find the perimeter of the greenhouse. 3 metres Greenhouse 3 metres 3 metres 3 metres Square d) Find the perimeter of the sign. 2 metres Sign 3 metres 3 metres 2 metres Rectangle Answers to Exercise One a) 14 metres b) 13 metres Fundamental Mathematics c) 12 metres d) 10 metres 123 �Topic B: Self-Test A. 124 Mark /18 Aim 15/18 Find the sums. Be sure to check your answers. 12 marks a) 4 6 +2 b) 3 6 +9 c) 7 2 +8 f) 2 1 +4 g) 3 5 +8 h) 4 6 +7 i) 3 1 5 +2 j) 4 2 3 +7 k) 5 3 1 +8 l) 3 5 1 +3 m) 1 5 4 +6 n) 2 1 6 +5 Book 1 �B. Solve each of the following word problems. 6 marks Be sure to include the unit of measure in your answer. (2 marks each) Be sure to circle information and underline what is being asked. a) It took the cleanup crew 4 hours on Monday, 3 hours on Tuesday and 9 hours on Wednesday to clean the factory after each day’s work. How many hours in total did it take to clean the factory? b) Nella wants to put a fence around her garden. The garden measures 5 metres, 3 metres and 1 metre. How much fence does she need? c) Find the perimeter of the garden. 4 metres Garden 2 metres 2 metres 4 4 metres Fundamental Mathematics 125 �Answers to Topic B Self-Test A. a) 12 b) 18 c) 17 d) 7 e) 16 f) 17 g) 11 17 j) k) 16 l) 14 B. a) 16 hours 126 h) 16 i) b) 9 metres c) 12 12 metres Book 1 �Topic C: Addition of Larger Numbers Use these steps to complete each addition question. Step 1: Add the ones to the ones. Step 2: Add the tens to the tens. Step 3: Add the hundreds to the hundreds. Example A: 23 + 56 Step 1: Add the ones to the ones. 3 ones + 6 ones = 9 ones 23 + 56 9 Write the answer in line with the ones in the question. Step 2: Add the tens. 2 tens + 5 tens = 7 tens 23 + 56 79 The sum of 23 + 56 = 79 Example B: 372 + 415 Step 1: Add the ones. 2 ones + 5 ones = 7 ones 372 + 415 7 Fundamental Mathematics 127 �Step 2: Add the tens. 7 tens + 1 ten = 8 tens 372 + 415 87 Step 3: Add the hundreds. 3 hundreds + 4 hundreds = 7 hundreds 372 + 415 787 Exercise One Find the sums. Check your work using the answer key at the end of the exercise. a) 54 + 32 b) 20 + 69 c) 58 + 21 d) 62 + 13 e) 73 + 14 f) 44 + 54 g) 10 + 75 h) 36 + 22 i) 10 + 36 j) 16 + 23 k) 40 + 50 l) 37 + 32 m) 14 + 50 n) 23 + 16 o) 41 + 38 p) 40 + 11 128 Book 1 �q) 28 + 70 r) 21 + 56 s) 72 + 12 t) 31 + 14 u) 47 + 12 v) 34 + 65 w) 63 + 34 x) 31 + 45 Answers to Exercise One a) 86 b) 89 c) 79 d) 75 e) 87 f) 98 g) 85 h) 58 i) j) 39 k) 90 l) 69 m) 64 n) 39 o) 79 p) 51 q) 98 r) s) 84 t) u) 59 v) 99 w) 97 x) 76 46 Exercise Two 77 45 Find the sums. Check your work using the answer key at the end of the exercise. a) 47 + 51 b) 65 + 24 c) 78 + 21 d) 84 + 12 e) 73 + 22 f) 64 + 13 g) 25 + 64 h) 51 + 38 Fundamental Mathematics 129 �i) 26 + 43 j) 40 + 57 k) 76 + 23 l) 86 + 13 m) 28 + 71 n) 35 + 62 o) 27 + 12 p) 19 + 40 q) 41 + 43 r) 53 + 32 s) 61 + 22 t) 52 + 21 u) 23 + 64 v) 32 + 43 w) 13 + 65 x) 46 + 42 Answers to Exercise Two a) 98 b) 89 c) 99 d) 96 e) 95 f) 77 g) 89 h) 89 i) 69 j) k) 99 l) 99 m) 99 n) 97 o) 39 p) 59 q) 84 r) s) 83 t) u) 87 v) 75 w) 78 x) 88 130 97 85 73 Book 1 �Exercise Three Find the sums. Check your work using the answer key at the end of the exercise. a) 32 + 64 b) 23 + 54 c) 61 + 22 d) 83 + 11 e) 32 + 45 f) 63 + 33 g) 75 + 24 h) 46 + 12 i) 44 + 35 j) 25 + 42 k) 41 + 38 l) 54 + 45 m) 25 + 32 n) 35 + 42 o) 32 + 44 p) 22 + 14 q) 57 + 21 r) 42 + 54 s) 34 + 23 t) 25 + 42 u) 13 + 41 v) 60 + 25 w) 34 + 62 x) 77 + 21 Fundamental Mathematics 131 �Answers to Exercise Three a) 96 b) 77 c) 83 d) 94 e) 77 f) 96 g) 99 h) 58 i) 79 j) k) 79 l) 99 m) 57 n) 77 o) 76 p) 36 q) 78 r) s) 57 t) u) 54 v) 85 w) 96 x) 98 Exercise Four 67 96 67 Find the sums. Check your work using the answer key at the end of the exercise. a) 286 + 513 b) 649 + 250 c) 156 + 542 d) 503 + 361 e) 273 + 620 f) 27 + 961 g) 852 + 36 h) 300 + 50 i) 364 + 523 132 Book 1 �j) 568 + 210 k) 432 + 325 l) 621 + 214 m) 312 + 541 n) 135 + 420 o) 231 + 354 p) 532 + 141 q) 537 + 21 r) 145 + 441 s) 235 + 214 t) 723 + 113 u) 521 + 344 v) 624 + 174 w) 524 + 221 x) 463 + 425 Fundamental Mathematics 133 �Answers to Exercise Four a) 799 b) 899 c) 698 d) 864 e) 893 f) 988 g) 888 h) 350 i) 887 j) k) 757 l) 835 m) 853 n) 555 o) 585 p) 673 q) 558 r) s) 449 t) u) 865 v) 798 w) 745 x) 888 Exercise Five 778 586 836 Find the sums. Check your work using the answer key at the end of the exercise. a) 172 + 401 b) 314 + 553 c) 431 + 317 d) 213 + 384 e) 163 + 224 f) 412 + 531 g) 731 + 142 h) 314 + 524 i) 253 + 401 134 Book 1 �j) 243 + 425 k) 653 + 434 l) 576 + 303 m) 732 + 210 n) 251 + 734 o) 605 + 143 p) 715 + 223 q) 254 + 125 r) 351 + 645 s) 754 + 231 t) 425 + 143 u) 465 + 233 v) 501 + 368 w) 335 + 403 x) 561 + 234 Fundamental Mathematics 135 �Answers to Exercise Five a) 573 b) 867 c) 748 d) 597 e) 387 f) 943 g) 873 h) 838 i) 654 j) k) 1087 l) 879 m) 942 n) 985 o) 748 p) 938 q) 379 r) s) 985 t) u) 698 v) 869 w) 738 x) 795 Exercise Six 668 996 568 Find the sums. Check your work using the answer key at the end of the exercise. a) 754 + 231 b) 410 + 257 c) 653 + 142 d) 815 + 170 e) 243 + 146 f) 615 + 303 g) 124 + 762 h) 451 + 206 i) 705 + 261 136 Book 1 �j) 627 + 512 k) 357 + 130 l) 725 + 273 m) 753 + 902 n) 425 + 203 o) 652 + 137 p) 357 + 132 q) 675 + 214 r) 802 + 254 s) 524 + 321 t) 723 + 306 u) 243 +152 v) 145 + 213 w) 262 + 321 x) 545 + 131 Answers to Exercise Six a) 985 b) 667 c) 795 d) 985 e) 389 f) h) 657 i) j) 1 139 k) 487 l) 998 o) 789 p) 489 q) 889 r) s) 845 v) 358 w) 583 x) 676 966 Fundamental Mathematics 1 056 918 g) 886 m) 1 655 n) 628 t) u) 395 1 029 137 �Topic C: Self-Test A. 138 Mark /22 Find the sums. Be sure to check your answers. Aim 19/22 12 marks a) 46 + 23 b) 32 + 13 c) 72 + 25 d) 56 + 21 e) 65 + 34 f) 25 + 51 g) 324 + 263 h) 183 + 514 i) 753 + 145 j) 618 + 120 k) 224 + 465 l) 563 + 216 Book 1 �B. Solve each of the following word problems. 6 marks Be sure to include the unit of measure in your answer. (2 marks each) Be sure to circle information and underline what is being asked. a) Mahala’s dad worked 45 hours one week and 52 hours the next week. How many hours did he work during those two weeks? b) A trucker drove 526 kilometers on the first trip and 341 kilometers on the next. How many kilometers did the trucker drive altogether? c) Find the perimeter of the garden. 12 metres Garden 11 metres 11 metres 12 metres Fundamental Mathematics 139 �Answers to Topic C Self-Test A. a) 69 b) 45 c) 97 d) 77 e) 99 f) 76 g) 587 h) 697 i) 898 j) 738 k) 689 l) 779 b) 867 kilometres c) 46 metres B. a) 97 hours Emotions Check How are you feeling? Are your palms moist? How is your breathing? Take control. Be the boss. If you are feeling anxious, practice your breathing exercise. Remember: breathe in slowly to the count of four, hold it for the count of four, and breathe out slowly to the count of four. 140 Book 1 �Unit 2 Review - Addition You will now practice all the skills you learned in Unit 2. Check your work using the answer key at the end of the review. A. Check out your addition facts. a) 5 +6 b) 8 +2 c) 3 +4 d) 9 +7 e) 7 + 10 f) 6 +8 g) 9 +4 h) 2 +3 i) 8 +4 j) 3 +3 k) 9 +9 l) 5 +4 m) 1 +2 n) 3 +1 o) 6 +9 p) 5 +3 Fundamental Mathematics 141 �B. C. Add across or horizontally. a) 8 + 7 = b) 0 + 3 = c) 8 + 10 = d) 5 + 2 = e) 2 + 2 = f) 7 + 5 = g) 9 + 8 = h) 3 + 6 = i) 9 + 5 = j) 1 + 5 = k) 6 + 10 = l) 4 + 1 = m) 7 + 3 = n) 5 +8 = o) 2 + 6 = p) 8 + 3 = Find the sums. a) 6 2 +4 b) 5 2 +1 c) 4 4 +8 d) 3 4 +5 e) 2 3 +4 f) 6 4 +7 142 Book 1 �g) D. 3 4 +6 h) 7 2 +4 i) 3 6 +8 Find the sums. a) 26 + 30 b) 42 + 57 c) 44 + 32 d) 32 + 81 e) 83 + 13 f) 76 + 12 g) 34 + 51 h) 54 + 22 i) 52 + 43 j) 25 + 42 k) 72 + 35 l) 66 + 12 Fundamental Mathematics 143 �E. Find the sums. a) 342 + 523 b) 725 + 142 c) 362 + 417 d) 425 + 172 e) 284 + 314 f) 315 + 132 g) 363 + 415 h) 741 + 225 i) 403 + 445 j) 654 + 215 k) 234 + 352 l) 525 + 431 144 Book 1 �F. Word Problems. a) Find the perimeter of the shape. Be sure to put the unit of measure in your answer. Write the name of the shape below the picture. 3 metres 1 metre 1 metre 3 metres b) 5 metres 5 metres 5 metres 5 metres c) The CN Tower in Toronto is 554 metres high. On top of the tower is a TV mast that is 122 metres high. What is the total height of the tower and TV mast? Fundamental Mathematics 145 �d) Seung weighs 36 kilograms. His father weighs 62 kilograms. How much do they weigh altogether? Answers to Unit 2 Review A. a) f) 11 14 b) g) 10 13 c) h) 7 5 d) 16 i) 12 e) 17 j) 6 k) p) 18 8 l) 9 m) 3 n) 4 o) 15 B. a) f) 15 12 b) g) 3 17 c) h) 18 9 d) 7 i) 14 e) 4 j) 6 k) p) 16 11 l) 5 m) 10 n) 13 o) 8 C. a) f) 12 17 b) g) 8 13 c) h) 16 13 d) 12 i) 17 e) 9 D. a) f) 56 88 b) g) 99 85 c) h) 76 76 d) 113 i) 95 e) 96 j) 67 k) 107 l) 78 E. a) 865 b) 867 c) 779 d) 597 e) 598 f) k) 447 586 g) l) 778 956 h) 966 i) j) F. a) 8 metres, rectangle 146 b) 20 metres, square c) 676 metres 848 d) 869 98 kilograms Book 1 �CONGRATULATIONS!! Now you have finished Unit 2. TEST TIME! Ask your instructor for the Practice Test for this unit. Once you’ve done the practice test, you need to do the unit 2 test. Again, ask your instructor for this. Good luck! Fundamental Mathematics 147 �148 Book 1 �Unit 3 Subtraction Fundamental Mathematics 149 �Topic A: Subtraction Subtraction takes an amount away from another amount. The result of subtraction is called the difference. The minus sign ─ means to subtract. says nine minus three equals six or nine take away three is six The difference between 9 and 3 is 6. Subtraction is the opposite of addition. Look at the examples: 5+4=9 4+5=9 9–4=5 9–5=4 8 +3 11 11 ─3 8 3 +8 11 11 ─8 3 Subtraction facts are a tool that you will use to do subtraction questions. Exercise One Check out your subtraction facts by doing this exercise as quickly as you can. Use your addition facts to help find the subtraction facts. Check your work using the answer key at the end of the exercise. Then, make a list of any subtraction facts you do not know or which are slow for you and practice them. a) b) 150 5 ─4 3 ─2 c) 7 ─7 d) 1 ─0 Book 1 �e) 8 ─ 2 f) 9 ─7 g) 4 ─3 h) 6 ─1 i) 7 ─2 j) 2 ─2 k) 7 ─6 l) 8 ─7 m) 0 ─0 n) 7 ─1 o) 3 ─0 p) 6 ─6 q) 4 ─2 r) 6 ─2 s) 9 ─5 t) 8 ─6 u) 5 ─3 v) 8 ─1 w) 1 ─1 x) 7 ─0 y) 9 ─9 z) 3 ─1 aa) 2 ─1 bb) 7 ─4 Fundamental Mathematics 151 �Answers to Exercise One 1 b) 1 c) 0 d) 1 e) 6 f) 2 g) 1 h) 5 a) i) 5 j) k) 1 l) 1 m) 0 n) 6 o) 3 p) 0 q) 2 r) 4 s) 4 t) u) 2 v) 7 w) 0 x) 7 y) 0 z) 2 aa) 1 0 2 bb) 3 Exercise Two Check out your subtraction facts by doing this exercise as quickly as you can. Use your addition facts to help find the subtraction facts. Check your work using the answer key at the end of the exercise. Then, make a list of any subtraction facts you do not know or which are slow for you and practice them. a) 8 ─4 b) 9 ─1 c) 7 ─5 d) 6 ─4 e) 9 ─4 f) 5 ─2 g) 2 ─0 h) 6 ─3 i) 8 ─3 j) 6 ─5 k) 4 ─4 l) 9 ─0 m) 7 ─3 n) 5 ─5 o) 9 ─8 p) 3 ─3 152 Book 1 �q) 5 ─0 r) 9 ─2 s) 4 ─1 t) 8 ─5 u) 5 ─1 v) 9 ─3 w) 6 ─0 x) 8 ─8 y) 9 ─6 z) 4 ─0 aa) 8 ─0 bb) 7 ─4 Answers to Exercise Two a) 4 b) 8 c) 2 h) 3 i) j) 1 o) 1 p) 0 v) 6 w) 5 6 d) 2 e) 5 f) 3 k) 0 l) 9 m) 4 n) 0 q) 5 r) 7 s) t) u) 4 x) 0 y) 3 z) 4 3 g) 2 3 aa) 8 bb) 3 Exercise Three Check out your subtraction facts by doing this exercise as quickly as you can. Use your addition facts to help find the subtraction facts. Check your work using the answer key at the end of the exercise. Then, make a list of any subtraction facts you do not know or which are slow for you – practice the. a) b) 8 ─4 Fundamental Mathematics 5 ─5 c) 2 ─1 d) 4 ─3 153 �e) 3 ─3 f) 6 ─3 g) 7 ─6 h) 9 ─2 i) 9 ─0 j) 5 ─4 k) 8 ─8 l) 4 ─2 m) 7 ─7 n) 2 ─0 o) 6 ─1 p) 9 ─8 q) 6 ─4 r) 3 ─1 s) 9 ─9 t) 8 ─7 u) 3 ─2 v) 7 ─5 w) 8 ─3 x) 9 ─5 y) 8 ─6 z) 5 ─3 aa) 7 ─1 bb) 6 ─5 154 Book 1 �cc) 4 ─1 dd) 1 ─1 ee) 0 ─0 ff) 8 ─0 gg) 9 ─7 hh) 6 ─6 ii) 9 ─6 jj) 7 ─4 kk) 9 ─3 ll) 8 ─5 mm) 7 ─2 nn) 5 ─1 Answers to Exercise Three a) 4 b) 0 c) 1 d) 1 e) 0 f) 3 g) 1 h) 7 i) 9 j) 1 k) 0 l) 2 m) 0 n) 2 o) 5 p) 1 q) 2 r) 2 s) 0 t) u) 1 v) 2 z) 1 2 w) 5 x) 4 y) 2 aa) 6 bb) 1 cc) 3 dd) 0 ee) 0 ff) 8 gg) 2 hh) 0 ii) jj) 3 kk) 6 ll) 3 mm) 5 nn) 4 Fundamental Mathematics 3 155 �Exercise Four Check out your subtraction facts by doing this exercise as quickly as you can. Use your addition facts to help find the subtraction facts. Check your work using the answer key at the end of the exercise. Then, make a list of any subtraction facts you do not know or which are slow for you and practice them. a) 11 ─7 b) 10 ─4 c) 12 ─7 d) 8 ─6 e) 10 ─8 f) 7 ─4 g) 9 ─3 h) 9 ─5 i) 7 ─3 j) 10 ─9 k) 12 ─8 l) 10 ─7 m) 8 ─3 n) 11 ─4 o) 10 ─6 p) 12 ─5 q) 10 ─4 r) 12 ─9 s) 8 ─5 t) 11 ─2 156 Book 1 �u) 11 ─8 v) 12 ─6 w) 10 ─2 x) 11 ─6 Answers to Exercise Four a) 4 b) 6 c) 5 h) 4 i) j) 1 o) 4 p) 7 q) 6 v) 6 w) 8 x) 5 4 d) 2 e) 2 f) 3 g) 6 k) 4 l) 3 m) 5 n) 7 r) s) 3 t) u) 3 3 9 Exercise Five Check out your subtraction facts by doing this exercise as quickly as you can. Use your addition facts to help find the subtraction facts. Check your work using the answer key at the end of the exercise. Then, make a list of any subtraction facts you do not know or which are slow for you and practice them. a) 12 ─3 b) 9 ─6 c) 11 ─9 d) 10 ─5 e) 8 ─8 f) 10 ─3 g) 12 ─4 h) 7 ─6 Fundamental Mathematics 157 �i) 9 ─8 j) 11 ─5 k) 9 ─7 l) 11 ─3 m) 10 ─2 n) 9 ─9 o) 12 ─6 p) 11 ─2 q) 12 ─9 r) 11 ─6 s) 10 ─4 t) 8 ─4 u) 9 ─4 v) 11 ─8 w) 12 ─2 x) 8 ─5 Answers to Exercise Five a) 9 b) 3 c) 2 d) 5 e) 0 f) 7 g) 8 h) 1 i) 1 j) k) 2 l) 8 m) 8 n) 0 o) 6 p) 9 q) 3 r) s) 6 t) u) 5 v) 3 w) 10 x) 3 158 6 5 4 Book 1 �Exercise Six Check out your subtraction facts by doing this exercise as quickly as you can. Use your addition facts to help find the subtraction facts. Check your work using the answer key at the end of the exercise. Then, make a list of any subtraction facts you do not know or which are slow for you and practice them. a) 11 ─7 b) 12 ─6 c) 10 ─9 d) 8 ─3 e) 12 ─5 f) 10 ─4 g) 9 ─7 h) 7 ─3 i) 8 ─4 j) 11 ─9 k) 6 ─5 l) 7 ─2 m) 10 ─7 n) 9 ─6 o) 12 ─8 p) 9 ─2 q) 11 ─4 r) 10 ─2 s) 12 ─7 t) 7 ─5 Fundamental Mathematics 159 �u) 11 ─6 v) 12 ─9 w) 10 ─3 x) 7 ─6 y) 10 ─6 z) 8 ─2 aa) 11 ─5 bb) 9 ─1 cc) 10 ─5 dd) 12 ─3 ee) 9 ─4 ff) 11 ─3 Answers to Exercise Six 4 b) 6 c) 1 d) 5 e) 7 f) 6 g) 2 h) 4 a) i) 4 j) 2 k) 1 l) 5 m) 3 n) 3 o) 4 p) 7 q) 7 r) 8 s) 5 t) u) 5 v) 3 w) 7 x) 1 y) 4 z) 6 cc) 5 dd) 9 ee) 5 ff) 8 2 aa) 6 bb) 8 Need more practice? Practice your subtraction facts using dominoes. Place all the dominoes face down. Flip over two dominoes and subtract. 160 Book 1 �Exercise Seven Check out your subtraction facts by doing this exercise as quickly as you can. Use your addition facts to help find the subtraction facts. Check your work using the answer key at the end of the exercise. Then, make a list of any subtraction facts you do not know or which are slow for you and practice them. a) 13 ─5 b) 10 ─1 c) 9 ─4 d) 5 ─4 e) 9 ─9 f) 16 ─8 g) 11 ─7 h) 6 ─3 i) 18 ─9 j) 7 ─2 k) 13 ─7 l) 8 ─6 m) 4 ─3 n) 14 ─5 o) 2 ─0 p) 17 ─8 q) 14 ─6 r) 16 ─7 s) 12 ─4 t) 3 ─0 Fundamental Mathematics 161 �u) 5 ─2 v) 13 ─6 w) 10 ─7 x) 8 ─8 y) 13 ─9 z) 7 ─5 aa) 15 ─7 bb) 12 ─9 Answers to Exercise Seven a) 8 b) 9 c) 5 d) 1 e) 0 f) 8 g) 4 h) 3 i) 9 j) k) 6 l) 2 m) 1 n) 9 o) 2 p) 9 q) 8 r) 9 s) 8 t) u) 3 v) 7 w) 3 x) 0 y) 4 z) 2 aa) 8 5 3 bb) 3 Exercise Eight Check out your subtraction facts by doing this exercise as quickly as you can. Use your addition facts to help find the subtraction facts. Check your work using the answer key at the end of the exercise. Then, make a list of any subtraction facts you do not know or which are slow for you and practice them. a) b) 162 12 ─3 6 ─2 c) 10 ─4 d) 11 ─9 Book 1 �e) 1 ─0 f) 8 ─1 g) 12 ─5 h) 11 ─2 i) 3 ─2 j) 11 ─8 k) 14 ─7 l) 8 ─3 m) 15 ─9 n) 9 ─7 o) 7 ─1 p) 11 ─5 q) 12 ─7 r) 10 ─8 s) 8 ─7 t) 6 ─5 u) 9 ─6 v) 7 ─3 w) 10 ─0 x) 9 ─1 y) 16 ─7 z) 9 ─2 aa) 9 ─0 bb) 8 ─4 Fundamental Mathematics 163 �Answers to Exercise Eight a) 9 b) 4 c) 6 h) 9 i) 1 o) 6 p) 6 q) 5 v) 4 w) 10 x) 8 y) j) 3 d) 2 e) 1 f) 7 g) 7 k) 7 l) 5 m) 6 n) 2 r) 2 s) 1 t) u) 3 9 z) 7 aa) 9 1 bb) 4 Exercise Nine Check out your subtraction facts by doing this exercise as quickly as you can. Use your addition facts to help find the subtraction facts. Check your work using the answer key at the end of the exercise. Then, make a list of any subtraction facts you do not know or which are slow for you and practice them. a) 1 ─1 b) 7 ─6 c) 12 ─3 d) 5 ─0 e) 11 ─3 f) 4 ─1 g) 8 ─0 h) 14 ─9 i) 6 ─6 j) 12 ─8 k) 9 ─3 l) 2 ─1 164 Book 1 �m) 17 ─9 n) 6 ─0 o) 13 ─4 p) 4 ─2 q) 2 ─2 r) 10 ─3 s) 7 ─7 t) 5 ─1 u) 15 ─8 v) 3 ─1 w) 16 ─9 x) 9 ─5 y) 13 ─8 z) 7 ─4 aa) 12 ─6 bb) 4 ─0 Answers to Exercise Nine a) 0 b) 1 c) 9 d) 5 e) 8 f) 3 g) 8 h) 5 i) j) 4 k) 6 l) 1 m) 8 n) 6 o) 9 p) 2 q) 0 r) 7 s) 0 t) u) 7 v) 2 w) 7 x) 4 y) 5 z) 3 aa) 6 0 Fundamental Mathematics 4 bb) 4 165 �Exercise Ten Check out your subtraction facts by doing this exercise as quickly as you can. Use your addition facts to help find the subtraction facts. Check your work using the answer key at the end of the exercise. Then, make a list of any subtraction facts you do not know or which are slow for you and practice them. a) 15 ─6 b) 3 ─3 c) 6 ─4 d) 11 ─4 e) 5 ─5 f) 10 ─2 g) 6 ─1 h) 14 ─8 i) 12 ─3 j) 8 ─2 k) 4 ─4 l) 7 ─0 m) 11 ─6 n) 5 ─3 o) 8 ─5 p) 10 ─9 q) 16 ─7 r) 9 ─8 s) 7 ─2 t) 4 ─3 166 Book 1 �u) 13 ─6 v) 2 ─2 w) 9 ─2 x) 17 ─8 y) 14 ─5 z) 1 ─0 aa) 12 ─8 bb) 3 ─1 cc) 8 ─6 dd) 10 ─6 ee) 13 ─4 ff) 7 ─4 Answers to Exercise Ten a) 9 b) 0 c) 2 d) 7 e) 0 f) 8 g) 5 h) 6 i) 9 j) 6 k) 0 l) 7 m) 5 n) 2 o) 3 p) 1 q) 9 r) 1 s) 5 t) u) 7 v) 0 w) 7 x) 9 y) 9 z) 1 aa) 4 cc) 2 dd) 4 ee) 9 ff) 3 Fundamental Mathematics 1 bb) 2 167 �Exercise Eleven Check out your subtraction facts by doing this exercise as quickly as you can. Use your addition facts to help find the subtraction facts. Check your work using the answer key at the end of the exercise. Then, make a list of any subtraction facts you do not know or which are slow for you and practice them. a) 18 ─9 b) 1 ─1 c) 3 ─0 d) 14 ─7 e) 8 ─3 f) 12 ─5 g) 6 ─4 h) 15 ─7 i) 11 ─3 j) 5 ─1 k) 6 ─0 l) 10 ─9 m) 5 ─3 n) 11 ─7 o) 4 ─0 p) 15 ─9 q) 16 ─8 r) 7 ─5 s) 10 ─2 t) 6 ─3 168 Book 1 �u) 13 ─8 v) 9 ─4 w) 2 ─0 x) 8 ─5 y) 10 ─1 z) 5 ─5 aa) 11 ─5 bb) 12 ─6 cc) 8 ─2 dd) 7 ─1 ee) 11 ─2 ff) 9 ─6 gg) 12 ─3 hh) 8 ─0 ii) 10 ─7 jj) 6 ─6 kk) 14 ─9 ll) 10 ─3 mm) 8 ─7 nn) 7 ─0 Fundamental Mathematics 169 �Answers to Exercise Eleven a) 9 b) 0 c) 3 d) 7 e) 5 f) 7 g) 2 h) 8 i) 8 j) 4 k) 6 l) 1 m) 2 n) 4 o) 4 p) 6 q) 8 r) 2 s) 8 t) u) 5 v) 5 w) 2 x) 3 y) 9 z) 0 aa) 6 bb) 6 cc) 6 dd) 6 ee) 9 ff) 3 gg) 9 hh) 8 ii) 3 jj) 0 kk) 5 ll) 7 mm) 1 nn) 7 3 Need some extra practice? Find a partner and play this card game. Using a regular deck of cards, a jack will be eleven, a queen will be twelve and a king will be thirteen. Shuffle the cards and deal them out. Keep your cards in a pile in front of you. Each player flips over a card. Take turns subtracting the numbers on the cards. If the person gets the right answer that person gets to keep the cards. If the person gets the wrong answer the other player gets the cards. The person who collects all the cards is the winner. You could also set a time limit and the person with the most cards when time is up is the winner. 170 Book 1 �Exercise Twelve Check out your subtraction facts by doing this exercise as quickly as you can. Use your addition facts to help find the subtraction facts. Check your work using the answer key at the end of the exercise. Then, make a list of any subtraction facts you do not know or which are slow for you and practice them. a) 5 ─2 b) 9 ─1 c) 12 ─4 d) 4 ─2 e) 17 ─9 f) 2 ─1 g) 11 ─9 h) 7 ─7 i) 14 ─6 j) 16 ─9 k) 9 ─3 l) 8 ─1 m) 9 ─0 n) 14 ─8 o) 10 ─5 p) 15 ─8 Fundamental Mathematics 171 �q) 12 ─9 r) 13 ─5 s) 6 ─5 t) 5 ─0 u) 13 ─9 v) 8 ─4 w) 10 ─0 x) 7 ─3 y) 11 ─8 z) 9 ─9 aa) 6 ─1 bb) 4 ─4 cc) 13 ─7 dd) 3 ─2 ee) 11 ─4 ff) 5 ─4 gg) 11 ─6 hh) 9 ─5 ii) 6 ─2 jj) 3 ─3 kk) 4 ─1 ll) 7 ─6 mm) 10 ─4 nn) 12 ─7 172 Book 1 �oo) 15 ─6 pp) 10 ─8 qq) 9 ─7 rr) 8 ─8 Answers to Exercise Twelve a) 3 b) 8 c) 8 d) 2 e) 6 f) 1 g) 2 h) 0 i) 8 j) 7 k) 6 l) 7 m) 9 n) 6 o) 5 p) 7 q) 3 r) 8 s) 1 t) u) 4 v) 4 w) 10 x) 4 y) 3 z) 0 aa) 5 bb) 0 cc) 6 dd) 1 ee) 7 ff) 1 gg) 5 hh) 4 ii) jj) 0 kk) 3 ll) 1 mm) 6 nn) 5 oo) 9 pp) 2 qq) 2 rr) 0 5 4 Emotions Check How are you feeling? Are your palms moist? How is your breathing? Take control. Be the boss. If you are feeling anxious, practice your breathing exercise. Remember: breathe in slowly to the count of four, hold it for the count of four and breathe out slowly to the count of four. Fundamental Mathematics 173 �Subtracting Across So far you have only been subtracting numbers when they are up and down or vertical. Example: 9 ─5 4 Another way to subtract numbers is across or horizontally. Example: 9 ─ 5 = 4 When you subtract numbers across, you work from left to right. Exercise One Practice subtracting across or horizontally. Check your work using the answer key at the end of the exercise. a) 6 ─ 3 = b) 12 ─ 8 = c) 4 ─ 1 = d) 8 ─ 6 = e) 18 ─ 9 = f) 11 ─ 4 = g) 7 ─ 2 = h) 16 ─ 7 = i) 10 ─ 5 = j) 2 ─ 0 = k) 9 ─ 5 = l) 17 ─ 8 = m) 5 ─ 3 = n) 14 ─ 9 = o) 15 ─ 6 = p) 3 ─ 1 = q) 13 ─ 7 = r) 1 ─ 0 = s) 10 ─ 4 = t) 6 ─ 2 = 174 Book 1 �Answers to Exercise One a) 3 b) 4 c) 3 d) 2 e) 9 f) 7 g) 5 h) 9 i) 5 j) 2 k) 4 l) 9 m) 2 n) 5 o) 9 p) 2 r) s) 6 t) Exercise Two q) 6 1 Practice subtracting across or horizontally. Check your work using the answer key at the end of the exercise a) 9 ─ 6 = b) 14 ─ 5 = c) 8 ─ 4 = d) 7 ─ 1 = e) 11 ─ 7 = f) 5 ─ 0 = g) 4 ─ 3 = h) 15 ─ 8 = i) 11 ─ 9 = j) 10 ─ 2 = k) 9 ─ 2 = l) 8 ─ 3 = m) 13 ─ 5 = n) 12 ─ 6 = o) 10 ─ 7 = p) 7 ─ 4 = q) 5 ─ 1 = r) 16 ─ 8 = s) 10 ─ 9 = t) 6 ─ 0 = Fundamental Mathematics 4 175 �Answers to Exercise Two 3 b) 9 c) 4 d) 6 e) 4 f) 5 g) 1 h) 7 a) i) 2 j) k) 7 l) 5 m) 8 n) 6 o) p) 3 r) s) 1 t) 3 Exercise Three 8 q) 4 8 Practice subtracting across or horizontally. Check your work using the answer key at the end of the exercise a) 3 ─ 2 = b) 17 ─ 9 = c) 14 ─ 7 = d) 9 ─ 3 = e) 12 ─ 5 = f) 8 ─ 8 = g) 6 ─ 1 = h) 13 ─ 4 = i) 11 ─ 6 = j) 4 ─ 0 = k) 8 ─ 1 = l) 16 ─ 9 = m) 7 ─ 0 = n) 13 ─ 8 = o) 12 ─ 3 = p) 9 ─ 4 = q) 15 ─ 7 = r) 10 ─ 6 = s) 11 ─ 5 = t) 5 ─ 2 = 176 6 Book 1 �Answers to Exercise Three a) 1 b) 8 c) 7 d) 6 e) 7 f) 0 g) 5 h) 9 i) 5 j) 4 k) 7 l) 7 m) 7 n) 5 o) p) 5 r) s) 6 t) 9 Fundamental Mathematics q) 8 4 3 177 �Word Problems Learning subtraction facts is very important because once you know them all they become a tool to use when solving problems. Words such as less than, minus, subtracted from, how many more, how much more, and difference tell you to subtract the numbers. Look for these words when reading word problems and underline them before trying to solve a problem. Circle the information that is given. Example:There were 14 nails in a box. Lu used 7 of them. How many nails were still in the box? There were box? 14 nails in a box. Lu used 7 of them. How many nails were still in the You have circled 14 nails and 7. This is the information you will use to find the answer. You have underlined “How many”. These words tell you to subtract. 14 nails — 7 nails 7 nails Exercise One a) 178 Solve each of the following word problems. Be sure to underline the words that tell you to subtract. Circle the information that is given. Check your work using the answer key at the end of the exercise. Have your instructor check your underlining and circling. Wolfgang walked 11 blocks. Ingrid walked 6 blocks. Wolfgang walked how much farther than Ingrid? Book 1 �178 Book 1 �b) Mika and her father went fishing. Mika caught 18 fish and her father caught 9 fish. How many more fish did Mika catch? c) Kuan-Lin was making moon cakes for the class party. She needed 15 cakes for the party. On Monday she had made 7 moon cakes. How many moon cakes did she still need to make? d) Malik counted 12 cars in the parking lot where he worked. One hour later, he counted only 4 cars. How many cars left? e) There were 17 chairs in a room. Eight of them were being used. How many chairs were not being used? Fundamental Mathematics 179 �f) Amelie had $12 in her wallet. She bought a latté for $4. Find the difference. Answers to Exercise One a) 5 blocks b) 9 fish c) 8 moon cakes d) 8 cars e) 9 chairs f) $8 180 Book 1 �Topic A: Self-Test A. Mark /21 Find the differences. Be sure to check your answers. 9 marks a) 16 ─8 b) 18 ─9 c) 14 ─8 d) 11 ─4 e) 9 ─3 f) 17 ─9 g) 10 ─6 h) 7 ─5 i) 15 ─6 B. Find the differences. Be sure to check your answers. a) 10 ─ 6 = b) 7 ─ 5= c) 15 ─ 9 = d) 9 ─ 4= e) 11 ─ 3 = f) 10 ─ 7 = Fundamental Mathematics Aim 18/27 6 marks 181 �C. Solve each of the following word problems. 6 marks Be sure to include the unit of measure in your answer. (2 marks each) Be sure to circle information and underline what is being asked. a) Shada caught 17 fish. She gave 8 fish to her grandmother. How many fish did she have left? b) Yuan went to the store with $15 to buy some rice. The rice cost $6. How much did he have left? c) Carlo had 13 metres of fencing. He used 8 metres around his flower garden. How many metres did he have left? 182 Book 1 �Answers to Topic A Self-Test A. a) 8 b) 9 c) 6 g) 4 h) 2 i) B. a) 4 b) c) 6 C. a) 9 fish 2 b) Fundamental Mathematics $9 d) 7 e) 6 f) 8 d) 5 e) 8 f) 3 9 c) 5 metres 183 �Topic B: Subtraction of Larger Numbers You can find the difference between two large numbers using the basic subtraction facts you have been practicing. Always take away or subtract the number after the minus sign. Use these steps to complete each subtraction question. Step 1: Subtract the ones from the ones. Step 2: Subtract the tens from the tens. Step 3: Subtract the hundreds from the hundreds. Example A: 57 - 26 Step 1: Subtract the ones from the ones. 7 ones – 6 ones = 1 one 57 - 26 1 Write the answer in line with the ones in the question. Step 2: Subtract the tens from the tens. 5 tens – 2 tens = 3 tens 57 - 26 31 The difference between 57 and 26 is 31. 184 Book 1 �Example B: 628 ─ 524 Step 1: Subtract the ones from the ones. 8 ones – 4 ones = 4 ones 628 ─ 524 4 Write the answer in line with the ones in the question. Step 2: Subtract the tens. 2 tens – 2 tens = 0 tens 628 ─ 524 04 Write the answer in line with the tens in the question. The 0 must be placed in the answer to hold the tens place. Step 3: Subtract the hundreds. 6 hundreds – 5 hundreds = 1 hundred 628 ─ 524 104 Write the answer in line with the hundreds in the question. The difference between 628 and 524 is 104. Fundamental Mathematics 185 �Exercise One Find the differences. Check your work using the answer key at the end of the exercise. a) 87 ─ 36 b) 29 ─ 21 c) 48 ─ 40 d) 99 ─ 63 e) 75 ─ 45 f) 73 ─ 20 g) 92 ─ 21 h) 58 ─ 27 i) 84 ─ 23 j) 69 ─ 38 k) 45 ─ 23 l) 49 ─ 19 m) 59 ─ 14 n) 87 ─ 63 o) 88 ─ 15 p) 56 ─ 44 q) 96 ─ 75 r) 37 ─ 17 s) 70 ─ 50 t) 38 ─ 24 u) 31 ─ 10 v) 27 ─ 12 w) 74 ─ 53 x) 45 ─ 20 186 Book 1 �Answers to Exercise One a) 51 b) 8 c) 8 d) 36 e) 30 f) 53 g) 71 h) 31 i) j) 31 k) 22 l) 30 m) 45 n) 24 o) 73 p) 12 q) 21 r) s) 20 t) u) 21 v) 15 w) 21 x) 25 61 20 14 Exercise Two Find the differences. Check your work using the answer key at the end of the exercise. a) 46 ─ 23 b) 65 ─ 42 c) 45 ─ 13 d) 53 ─ 20 e) 34 ─ 21 f) 48 ─ 32 g) 56 ─ 13 h) 26 ─ 15 i) 49 ─ 22 j) 58 ─ 27 k) 95 ─ 71 l) 37 ─ 14 m) 69 ─ 19 n) 86 ─ 71 o) 99 ─ 50 p) 89 ─ 55 Fundamental Mathematics 187 �q) 97 ─ 13 r) 87 ─ 25 s) 48 ─ 26 t) 36 ─ 11 u) 46 ─ 12 v) 86 ─ 43 w) 59 ─ 32 x) 84 ─ 14 Answers to Exercise Two a) 23 b) 23 c) 32 d) 33 e) 13 f) 16 g) 43 h) 11 i) 27 j) k) 24 l) 23 m) 50 n) 15 o) 49 p) 34 q) 84 r) s) 22 t) u) 34 v) 43 w) 27 x) 70 31 62 25 Exercise Three Find the differences. Check your work using the answer key at the end of the exercise. a) 23 ─ 11 b) 53 ─ 21 c) 32 ─ 20 d) 77 ─ 32 e) 31 ─ 21 f) 38 ─ 15 g) 33 ─ 13 h) 92 ─ 30 188 Book 1 �i) 94 ─ 23 j) 54 ─ 42 k) 74 ─ 33 l) 88 ─ 72 m) 46 ─ 36 n) 75 ─ 41 o) 85 ─ 12 p) 56 ─ 45 q) 64 ─ 22 r) 27 ─ 15 s) 76 ─ 53 t) 63 ─ 41 u) 52 ─ 41 v) 57 ─ 44 w) 69 ─ 46 x) 77 ─ 42 Answers to Exercise Three a) 12 b) 32 c) 12 d) 45 e) 10 f) 23 g) 20 h) 62 i) j) 12 k) 41 l) 16 m) 10 n) 34 o) 73 p) 11 q) 42 r) s) 23 t) u) 11 v) 13 w) 23 x) 35 71 Fundamental Mathematics 12 22 189 �Exercise Four Find the differences. Check your work using the answer key at the end of the exercise. a) 476 ─ 413 b) 873 ─ 560 c) 589 ─ 384 d) 793 ─ 170 e) 228 ─ 123 f) 995 ─ 452 g) 896 ─ 450 h) 769 ─ 405 i) 788 ─ 435 j) 579 ─ 234 k) 958 ─ 403 l) 696 ─ 251 190 Book 1 �m) 657 ─ 234 n) 745 ─ 412 o) 967 ─ 143 p) 456 ─ 214 q) 627 ─ 512 r) 878 ─ 425 s) 357 ─ 130 t) 725 ─ 214 u) 678 ─ 623 v) 526 ─ 116 w) 724 ─ 221 x) 429 ─ 316 Answers to Exercise Four a) 63 b) 313 c) 205 d) 623 e) 105 f) 543 g) 446 h) 364 i) j) 345 k) 555 l) 445 m) 423 n) 333 o) 824 p) 242 q) 115 r) s) 227 t) u) 55 v) 410 w) 503 x) 113 353 Fundamental Mathematics 453 511 191 �Exercise Five Find the differences. Check your work using the answer key at the end of the exercise. a) 543 ─ 132 b) 752 ─ 150 c) 328 ─ 115 d) 758 ─ 341 e) 587 ─ 425 f) 857 ─ 143 g) 545 ─ 302 h) 466 ─ 115 i) 964 ─ 231 j) 679 ─ 424 k) 757 ─ 136 l) 467 ─ 132 192 Book 1 �m) 536 ─ 325 n) 897 ─ 287 o) 979 ─ 465 p) 907 ─ 605 q) 496 ─ 144 r) 778 ─ 635 s) 573 ─ 232 t) 859 ─ 734 u) 735 ─ 420 v) 912 ─ 811 w) 966 ─ 732 x) 578 ─ 343 Answers to Exercise Five a) 411 b) 602 c) 213 d) 417 e) 162 f) 714 g) 243 h) 351 i) j) 255 k) 621 l) 335 m) 211 n) 610 o) 514 p) 302 q) 352 r) s) 341 t) u) 315 v) 101 w) 234 x) 235 733 Fundamental Mathematics 143 125 193 �Exercise Six Find the differences. Check your work using the answer key at the end of the exercise. a) 353 ─142 b) 896 ─ 675 c) 786 ─ 325 d) 743 ─ 623 e) 548 ─ 336 f) 685 ─ 143 g) 393 ─ 241 h) 965 ─ 130 i) 478 ─ 352 j) 968 ─ 605 k) 435 ─ 234 l) 694 ─ 523 m) 576 ─ 314 n) 946 ─ 615 o) 664 ─ 532 194 Book 1 �p) 824 ─ 513 q) 768 ─ 633 r) 497 ─ 335 s) 985 ─ 843 t) 679 ─ 436 u) 598 ─ 365 v) 984 ─ 672 w) 569 ─ 238 x) 747 ─ 636 Answers to Exercise Six a) 211 b) 221 c) 461 d) 120 e) 212 f) 542 g) 152 h) 835 i) j) 363 k) 201 l) 171 m) 262 n) 331 o) 132 p) 311 q) 135 r) s) 142 t) u) 233 v) 312 w) 331 x) 111 126 Fundamental Mathematics 162 243 195 �Topic B: Self-Test A. B. 196 Mark /27 Find the differences. Be sure to check your answers. Aim 23/27 6 marks a) 59 ─ 33 b) 27 ─ 14 c) 78 ─ 23 d) 93 ─ 81 e) 67 ─ 45 f) 86 ─ 56 Find the differences. Be sure to check your answers. 6 marks a) 896 ─ 422 b) 788 ─ 531 c) 467 ─ 126 d) 549 ─ 318 e) 936 ─ 725 f) 654 ─ 242 Book 1 �C. Solve each of the following word problems. 6 marks Be sure to include the unit of measure in your answer. (2 marks each) Be sure to circle information and underline what is being asked. a) At noon the temperature was 34 degrees Celsius. At nine o’clock in the evening, it was 12 degrees Celsius. How many degrees did the temperature drop? b) Misha’s family is on a 179 kilometer trip. They have already gone 123 kilometers. How much farther to they have to go? c) The Burj Khalifa in Dubai is one of the tallest buildings in the world at 828 metres. The Eiffel Tower in Paris is 324 metres tall. How much taller is the Burj Khalifa than the Eiffel Tower? Fundamental Mathematics 197 �Answers to Topic B Self-Test A. a) 26 b) 13 c) 55 d) 12 e) 22 f) 30 B. a) 474 341 d) 231 e) 211 f) 412 b) 257 C. a) 22 degrees Celsius 198 c) b) 56 kilometres c) 504 metres Book 1 �Unit 3 Review - Subtraction You will now practice all the skills you learned in Unit 3. Check your work using the answer key at the end of the review. A. Check out your subtraction facts. a) 5 ─2 b) 8 ─7 c) 3 ─1 d) 9 ─5 e) 18 ─9 f) 11 ─4 g) 13 ─5 h) 10 ─5 i) 6 ─6 j) 14 ─8 k) 16 ─7 l) 12 ─9 m) 17 ─9 n) 9 ─3 o) 13 ─6 p) 15 ─8 Fundamental Mathematics 199 �B. Subtract across or horizontally. a) 8 ─6 = b) 12 ─ 5 = c) 10 ─ 10 = d) 9 ─ 8= e) 11 ─ 6 = f) 8 ─ 4= g) 7 ─3 = h) 14 ─ 9 = i) 10 ─ 8 = j) 8 ─ 5= k) 13 ─ 4 = l) 15 ─ 7 = m) 14 ─ 7 = n) 7 ─ 1= o) 17 ─ 8 = p) 13 ─ 7 = C. Find the differences. a) 45 ─ 23 b) 78 ─ 15 c) 84 ─ 52 d) 57 ─ 10 e) 78 ─ 21 f) 69 ─ 43 200 Book 1 �g) 96 ─ 45 h) 88 ─ 35 i) 95 ─ 33 j) 45 ─ 15 k) 85 ─ 31 l) 87 ─ 45 D. Find the differences a) 583 ─ 163 b) 799 ─ 265 c) 629 ─ 305 d) 847 ─ 406 e) 978 ─ 252 f) 797 ─ 652 g) 765 ─ 243 h) 854 ─ 344 i) 536 ─ 314 Fundamental Mathematics 201 �j) E. 202 897 ─ 246 k) 669 ─ 238 l) 769 ─ 564 Word Problems a) One week, Tiago changed 258 light bulbs in the building. The next week, Tiago changed 141 light bulbs. How many more bulbs did Tiago change the first week? b) Anoki drove 769 kilometres while his friend Dasan drove 534 kilometres on their trip. How many more kilometres did Anoki drive? Book 1 �Answers to Unit 3 Review A. a) 3 b) 1 c) 2 d) 4 e) 9 f) k) 7 9 g) l) 8 3 h) m) 5 8 i) 0 n) 6 j) 6 o) 7 p) 7 B. a) 2 b) 7 c) 0 d) 1 e) 5 f) k) 4 9 g) l) 4 8 h) m) 5 7 i) 2 n) 6 j) 3 o) 9 p) 6 C. a) 22 b) 63 c) 32 d) 47 e) 57 f) k) 26 54 g) l) 51 42 h) 53 i) j) D. a) f) 420 145 b) g) 534 522 c) h) 324 510 d) 441 i) 222 k) 431 l) 205 E. a) 117 light bulbs 62 30 e) 726 j) 651 b) 235 kilometres Fundamental Mathematics 203 �CONGRATULATIONS!! Now you have finished Unit 3. TEST TIME! Ask your instructor for the Practice Test for this unit. Once you’ve done the practice test, you need to do the unit 3 test. Again, ask your instructor for this. Good luck! 204 Book 1 �Unit 4 Estimating, Time and Shapes Fundamental Mathematics 205 �Topic A: Estimating You use numbers in your everyday life. You often use estimating in your everyday life. You go shopping and you only have twenty dollars, you may need to estimate how much your groceries are going to cost before you go to pay for them. You commute by bus each day to work and it takes thirty-three minutes going to work and thirty-three minutes coming home at the end of the day. You would say that it takes you about one hour on the bus. These are examples of estimating. You have already learned about rounding numbers. You need to be able to round numbers in order to be able to estimate. When you solve math problems, it is a good idea to estimate what the answer may be. Estimating the answer means finding an answer that is close to the real answer. Estimating helps you to see if the real answer is sensible. To estimate an answer, you need to round the numbers then add or subtract the rounded numbers. Remember to round to the nearest ten. 206 Example: 23 + 45 Estimate: 20 + 50 70 Example: 67 ─ 31 Estimate: 70 ─ 30 40 Example: 372 + 416 Estimate: 370 + 420 790 Example: 564 ─ 243 Estimate: 560 ─ 240 320 Book 1 �Exercise One Estimate the following answers. Be sure to round to the nearest 10 before adding. Check your work using the answer key at the end of the exercise. a) 27 + 31 Estimate: b) 42 + 51 Estimate: c) 26 + 32 Estimate: d) 14 + 52 Estimate: e) 44 + 24 Estimate: f) 31 + 27 Estimate: g) 65 + 22 Estimate: h) 46 + 23 Estimate: i) 23 + 72 Estimate: j) 42 + 36 Estimate: k) 64 + 14 Estimate: l) 32 + 20 Estimate: Fundamental Mathematics 207 �m) 423 + 324 Estimate: n) 526 + 345 Estimate: o) 123 + 541 Estimate: p) 752 + 243 Estimate: q) 429 + 316 Estimate: r) 324 + 115 Estimate: s) 162 + 531 Estimate: t) 156 + 322 Estimate: u) 302 + 473 Estimate: v) 326 + 607 Estimate: w) 312 + 148 Estimate: x) 341 + 248 Estimate: Answers to Exercise One a) 60 b) 90 c) 60 d) 60 e) 60 f) h) 70 i) 90 j) k) 70 l) 50 o) 660 p) 990 q) 750 r) s) 690 v) 940 w) 460 x) 590 208 80 440 60 g) 90 m) 740 n) 880 t) u) 770 480 Book 1 �Exercise Two Estimate the following answers. Be sure to round to the nearest 10 before subtracting. Check your work using the answer key at the end of the exercise. a) 35 ─ 16 Estimate: b) 52 ─ 14 Estimate: c) 67 ─ 19 Estimate: d) 51 ─ 23 Estimate: e) 36 ─ 17 Estimate: f) 72 ─ 44 Estimate: g) 38 ─ 19 Estimate: h) 74 ─ 26 Estimate: i) 93 ─ 89 Estimate: j) 82 ─ 57 Estimate: k) 56 ─ 27 Estimate: l) 94 ─ 48 Estimate: Fundamental Mathematics 209 �210 m) 752 ─ 342 Estimate: n) 765 ─ 439 Estimate: o) 673 ─ 424 Estimate: p) 645 ─ 309 Estimate: q) 811 ─ 502 Estimate: r) 591 ─ 57 Estimate: s) 972 ─ 447 Estimate: t) 178 ─ 152 Estimate: u) 471 ─ 146 Estimate: v) 316 ─ 222 Estimate: w) 678 ─ 425 Estimate: x) 486 ─ 211 Estimate: Book 1 �Answers to Exercise Two a) 20 b) 40 c) 50 h) 40 i) j) 20 o) 250 p) 340 q) 310 v) 100 w) 250 x) 280 0 Exercise Three Example: d) 30 e) 20 f) k) 30 l) 40 r) s) 520 540 30 g) 20 m) 410 n) 330 t) u) 320 30 Estimate the following answers. Be sure to round to the nearest ten before adding or subtracting. Remember to circle the information and underline what is being asked. Check your work using the answer key at the end of the exercise. There are 186 people living in my apartment building. If 103 are children, how many are adults? There are 186 people living in my apartment building. If how many are adults? 186 ─ 103 Estimate: 103 are children, 190 ─ 100 90 About 90 people are adults. a) The bus has 84 passenger seats. All the seats are filled and 39 passengers are standing. How many passengers are on the bus? Fundamental Mathematics 211 �Fundamental Mathematics 211 �b) Trisha counted 67 boxes on one shelf. She counted 78 boxes on the next shelf. How many boxes were there altogether? c) The library loaned out 157 books on Monday. It loaned out 118 books on Tuesday. How many book did it loan on both days? d) Ryan worked on the computer for 78 minutes. Helen worked on the computer for 54 minutes. How much longer did Ryan work on the computer? 212 Book 1 �e) The Ludlow factory has 73 people working in the factory. The Watson factory has 48 people working in their factory. How many more people work in the Ludlow factory? f) Mr. Martinez needs 257 metres of fencing. He has 125 metres. How much more fencing does he need to buy? Answers to Exercise Three a) 120 passengers b) 150 boxes c) 280 books d) e) f) 130 meters 30 minutes Fundamental Mathematics 20 people 213 �Topic B: Time The ancient Babylonians used a number system based on 60. We still use their number system when we talk about time. There are 60 minutes in an hour, and there are 60 seconds in a minute. 60 minutes = 1 hour 60 seconds = 1 minute Writing Time in Standard Format Time is written in a standard format. Hours: Minutes: Seconds Example: 12 noon would be written as 12:00:00 or 12:00 (without the seconds) Example: 4 o’clock would be written as 4:00:00 or 4:00 (without the seconds) Example: 8 hours, 47 minutes, 3 seconds would be written as 8:47:03 Note: When there is only one number, put in a zero to hold the tens place. Example: 214 3 hours, 9 minutes, 3 seconds would be written as 3:09:03 Book 1 �Exercise One Example: Write the following times in standard format. Check your work using the answer key at the end of the exercise. 2 hours, 7 minutes, 31 seconds 2:07:31 Note: If there is only one number, remember to put in a zero to hold the tens place. a) 3 hours, 56 minutes, 42 seconds b) 12 hours, 2 minutes, 29 seconds c) 1 hour, 23 minutes, 54 seconds d) 6 hours, 7 minutes, 39 seconds e) 11 hours, 41 minutes Fundamental Mathematics 215 �f) 7 hours, 14 minutes, 59 seconds g) 21 hours, 36 minutes h) 1 hour, 51 minutes, 41 seconds i) 5 hours, 18 minutes, 10 seconds. Answers to Exercise One a) 3:56:42 b) 12:02:29 c) 1:23:54 d) 6:07:39 e) 11:41 f) 7:14:59 g) 21:36 h) 1:51:41 i) 5:18:10 216 Book 1 �A.M. and P.M. You need to go to the dentist at 9:00 a.m. This is in the morning because of the a.m. The abbreviation a.m. means ante meridiem or before noon. We use a.m. for any times between 12 midnight and 12 noon. You are meeting friends for dinner at 6:00 p.m. This is at night because of the p.m. The abbreviation p.m. means post meridiem or after noon. We use p.m. for any times between 12 noon and 12 midnight. Example: You catch the bus at 7 o’clock in the morning. The time would be written as 7:00 a.m. Example: You are meeting friends to go fishing at 6:30 at night. The time would be written as 6:30 p.m. Exercise Two Example: Write the following times using a.m. or p.m. Check your work using the answer key at the end of the exercise. The sun rises at 7:07 in the morning. 7:07 a.m. a) Your shift at work starts at 8:30 in the morning. b) Your class starts at 1:00 in the afternoon. c) Your son has soccer practice at 4:00 in the afternoon. Fundamental Mathematics 217 �d) You catch your bus at 6:15 in the morning. e) You need to go to the doctor at 3:20 in the afternoon. f) You eat dinner at 6:30 in the evening. g) Your children go to bed at 8:45 in the evening. h) Your alarm goes off at 5:50 in the morning. i) Your friend called at 11:25 in the morning. Answers to Exercise Two a) 8:30 a.m. b) 1:00 p.m. c) 4:00 p.m. d) 6:15 a.m. e) 3:20 p.m. f) 6:30 p.m. g) 8:45 p.m. h) 5:50 a.m. i) 11:25 a.m. 218 Book 1 �Rounding Time When you round time, if the minutes are more than thirty, you round up to the next number of hours. If the minutes are less than thirty, you remain at the same number of hours. Example: If it took 45 minutes to drive to school, you would round that to one hour because 45 minutes is greater than 30 minutes. Example: If it took one hour and 15 minutes to get to school by bus, you would round that to one hour because 15 minutes is less than 30 minutes. Example: If it took 8 hours and 37 minutes to complete the painting job, you would round that to 9 hours because 37 minutes is greater than 30 minutes. Exercise Three Example: Round the following times to the nearest hour. Check your work using the answer key at the end of the exercise. The movie lasted 3 hours and 13 minutes. 3 hours a) You needed 2 hours and 15 minutes for grocery shopping. b) It took 1 hour and 50 minutes to cook dinner. c) You drove for 9 hours and 23 minutes. d) Your baby slept for 1 hour and 47 minutes. Fundamental Mathematics 219 �e) You visited with friends for 3 hours and 11 minutes. f) It took 2 hours and 35 minutes to play the hockey game. g) You rode on the bus for 1 hour and 28 minutes. h) You walked to work in 38 minutes. i) How long does it take you to get to school? Answers to Exercise Three a) 2 hours b) 2 hours c) 9 hours d) 2 hours e) 3 hours f) 3 hours g) 1 hour h) 1 hour i) check with your instructor 220 Book 1 �Topic C: Shapes Circle The circle is a shape we all know. These objects suggest the idea of a circle. rim of coffee cups and glasses top of lamp shades top of cans of food compact discs the ends of pipes and hoses (called the cross-section) the coloured part of your eye (the iris) Add some examples of your own. Fundamental Mathematics 221 �Triangle A triangle is a three-sided shape. Triangles have three sides and three angles. Draw some different sized triangles here. Rectangle A rectangle is a four-sided shape. Rectangles have four sides and four right angles (square corners). Can you think of anything that has a rectangle shape? Write it here. 222 Book 1 �Squares A square is a special kind of rectangle. Squares have square corners and four sides are the same length Can you think of anything that has a square shape? Write it here. Exercise One The following things give the idea of a shape. Write the nameof the shape in each blank. Then draw the shape. Example: A cookie is a a) A door is a . b) This page is a . c) A yield sign is a . Fundamental Mathematics circle . 223 �d) A room is usually a . e) A coin is a . f) A ten dollar bill is a . g) The rim of a jar is a . h) This warning sign is a i) A pizza is a . . Answers to Exercise One a) rectangle b) rectangle c) triangle d) rectangle e) f) rectangle g) circle h) triangle i) circle 224 circle Book 1 �Exercise Two Look around the room and find each of the following shapes. Write the name on the line. Have your instructor check your answers. Example: a) A circle b) A rectangle c) A square d) A triangle Exercise Three a) A rectangle door Circle the correct shape in each line. Have your instructor check your answers. A rectangle. Fundamental Mathematics 225 �b) A circle c) A square d) A triangle Exercise Four a) 226 What shape are the following things? Write triangle, square, rectangle or circle on the line. b) Book 1 �c) d) e) f) g) h) Answers to Exercise Four a) circle b) triangle c) rectangle f) circle h) rectangle g) square Fundamental Mathematics d) square e) rectangle or triangle 227 �Unit 4 Review – Estimating, Time, Shapes You will now practice all the skills you learned in Unit 4. Check your work using the answer key at the end of the review. A. B. Estimate the following sums. Be sure to round to the nearest 10 before adding. a) 23 + 32 Estimate: b) 68 + 17 Estimate: c) 34 + 28 Estimate: d) 42 + 53 Estimate: e) 74 + 24 Estimate: f) 33 + 28 Estimate: g) 17 + 42 Estimate: h) 27 + 18 Estimate: Estimate the following sums. Be sure to round to the nearest 10 before adding. a) 625 + 254 228 Estimate: b) 432 + 325 Estimate: Book 1 �C. c) 328 + 163 Estimate: d) 529 + 248 Estimate: e) 536 + 137 Estimate: f) 867 + 215 Estimate: g) 843 + 107 Estimate: h) 435 + 127 Estimate: Estimate the following answers. Be sure to round to the nearest 10 before subtracting. a) 43 ─ 28 Estimate: b) 64 ─ 25 Estimate: c) 73 ─ 47 Estimate: d) 83 ─ 24 Estimate: e) 68 ─ 28 Estimate: f) 54 ─ 22 Estimate: Fundamental Mathematics 229 �g) D. E. 67 ─ 29 Estimate: h) 85 ─ 29 Estimate: Estimate the following answers. Be sure to round to the nearest 10 before subtracting. a) 625 ─ 407 Estimate: b) 908 ─ 413 Estimate: c) 976 ─ 134 Estimate: d) 882 ─ 257 Estimate: e) 572 ─ 154 Estimate: f) 908 ─ 713 Estimate: g) 965 ─ 702 Estimate: h) 988 ─ 254 Estimate: Write the following times in standard format. a) 10 hours, 20 minutes, 12 seconds 230 Book 1 �b) 8 hours,45 minutes, 6 seconds c) 5 hour, 32 minutes, 45 seconds d) 1 hour, 7 minutes, 28 seconds e) 12 hours, 55 minutes f) 6 hours, 5 minutes, 39 seconds F. Write the following times using a.m. or p.m. a) The movie starts at 6:45 in the evening. b) Your friend calls and wakes you up at 3:23 in the morning. c) Your dog barks at the mailman at 2:35 in the afternoon. d) Your morning break is at 10:15. Fundamental Mathematics 231 �G. Round the following times to the nearest hour. a) You took a walk for 47 minutes. b) Your round trip (there and back) to the mall took 2 hours and 12 minutes. H. Circle the correct shape in each line. a) A triangle b) A square I. The following things give the idea of a shape. Write the name of the shape in each blank. a) 232 A window is a . Book 1 �b) A checkerboard is a . c) A watch is a . d) A yield sign is a . J. Word Problems. Estimate the following answers. Be sure to round to the nearest 10 before adding or subtracting. Remember to circle the information and underline what is being asked. a) The Sears Tower is 443 metres tall. It has a 105 metre TV antenna on top. Estimate the height of the building and the antenna. b) A restaurant used 76 kilograms of potatoes and 68 kilograms of meat. Estimate how many kilograms of potatoes and meat the restaurant used altogether. Fundamental Mathematics 233 �c) Paolo’s father weighs 78 kilograms. Paolo weighs 29 kilograms. Estimate how much more Paolo’s father weighs. d) Chi bought 54 litres of gasoline on Tuesday. He bought 38 litres of gasoline on Friday. Estimate how many litres of gas he bought altogether. 234 Book 1 �Answers to Unit 4 Review A. a) 50 b) 90 g) 60 h) 50 a) 880 b) g) 950 h) 570 a) 10 b) g) 40 h) 60 a) 220 b) g) 270 h) 740 c) 60 d) 90 e) 90 f) 60 c) 490 d) 780 e) 680 f) 1 090 c) 20 d) 60 e) 40 f) 30 c) 850 d) 620 e) 420 f) 200 B. 760 C. 30 D. 500 E. a) 10:20:12 b) 8:45:06 c) 5:32:45 d) 1:07:28 e) 12:55 f) 6:05:39 F. a) 6:45 p.m. b) 3:23 a.m. c) 2:35 p.m. d) 10:15 a.m. G. a) 1 hour b) 2 hours H. Have your instructor check these. I. a) rectangle b) square c) circle b) 150 kilograms c) 50 kilograms d) triangle J. a) 550 metres d) 90 litres Fundamental Mathematics 235 �CONGRATULATIONS!! Now you have finished Unit 4. TEST TIME! Ask your instructor for the Practice Test for this unit. Once you’ve done the practice test, you need to do the unit 4 test. Again, ask your instructor for this. Good luck! 236 Book 1 �Book 1 Review You will now practice all the skills you learned in Book 1. Check your work using the answer key at the end of the review. If you can‟t remember how to do a question, go back to the lesson on this topic to refresh your memory. The unit and topic for where each question came from is listed next to the question. Example: 1-B means Unit 1, Topic B 1-B A. Count the number of things in each picture. Write the number and word name. a) b) Numeral: Numeral: Word Name Word Name c) d) ●●● ● ●●● Numeral: Numeral: Word Name: Word Name: 1-C B. Fill the blanks to make each sentence true. Draw a picture for b and d. a) 58 means Fundamental Mathematics tens and ones. 237 �C. 238 b) 18 means tens and Draw your picture below. c) 471 means d) 127 means hundreds, Draw your picture below. ones. hundreds, tens, tens, ones. ones. Write the place value name (ones, tens, hundreds) for each underlined digit. a) 564 b) 239 c) 986 d) 534 Book 1 �D. Name the digit for the place value named from the number below. 5 782 a) E. F. tens b) hundreds Write the word names for the numbers. a) 17 b) 342 c) 625 Write numerals for these word names. a) seventy-five b) nineteen c) seven hundred fifty d) nine hundred five e) eight hundred seventy-three 1-D G. Place a box around the larger number. a) 452 H. 245 b) 678 687 Arrange these numbers in order from smallest to largest. a) 86 668 Fundamental Mathematics 886 686 868 66 866 239 �b) 23 I. 323 223 33 332 322 232 Write <, > or = in each blank as needed. a) 23 34 c) 667 576 b) 118 118 d) 405 450 1-E J. K. Round each number to the nearest 10. a) 52 b) 123 c) 178 d) 89 Word Problems. For each problem, round the numbers to the nearest 10. a) The polar bear can weigh 1 002 kilograms, a koala bear can weigh 14 kilograms, a panda bear can weigh 113 kilograms, a kodiak bear can weigh 679 kilograms and a black bear can weigh 272 kilograms. Round each number to the nearest 10. Bear Number Rounded Number Polar bear Koala bear Panda bear Kodiak bear Black bear 240 Book 1 �L. How much money do you have? a) How much money to you have? cents b) How much money do you have? dollars 2-A M. Check out your addition facts. a) 0 +8 b) 2 +3 c) 8 +2 d) 1 +4 e) 5 +0 f) 9 +5 g) 6 +7 h) 3 +6 Fundamental Mathematics 241 �N. O. P. Add across or horizontally. a) 7 + 4 = b) 3 + 0 = c) 2 + 9 = d) 9 + 8 = e) 6 + 2 = f) 5 + 6 = g) 8 + 9 = h) 4 + 2 = Find the sums. a) 4 5 +3 b) 2 7 +8 c) 4 2 +8 d) 4 6 +7 e) 3 2 +3 f) 6 1 +5 b) 2 3 4 +7 c) 3 0 1 +2 Find the sums. a) 242 5 2 3 +4 Book 1 �d) Q. 2 3 1 +2 e) 5 1 3 +2 f) 4 3 2 +6 Find the perimeter of the shape. Be sure to put the unit of measure in your answer. Write the name of the shape below the picture. a) 3 metres 2 metres b) 5 metres 3 metres 4 metres c) 2 metres Fundamental Mathematics 243 �R. S. Find the sums. a) 46 + 33 b) 35 + 93 c) 82 + 56 d) 91 + 17 e) 740 + 859 f) 638 + 610 g) 521 + 848 h) 970 + 625 Word Problems. a) Seven cars were in the first row. Four cars were in the second row. How many cars are there in the first two rows? b) One bicycle stored ordered 56 bikes. Another store ordered 72 bikes. How many bikes did both stores order? 244 Book 1 �c) A mail carrier walked 51 kilometres in a week. The next week she walked 48 kilometres the next week. How far did she walk in two weeks? 3-A T. U. Check out your subtraction facts. a) 9 −5 b) 6 −3 c) 17 −8 d) 14 −7 e) 14 g) 11 g) 12 h) 9 Subtract across or horizontally. a) 4−1 = b) 8−2 = c) 17 − 8 = d) 11 − 6 = e) 6−4= f) 11 − 3 = g) 10 − 1 = h) 13 − 8 = Fundamental Mathematics 245 �3-B V. W. Find the differences. a) 76 b) 84 c) 95 d) 69 e) 852 f) 789 g) 938 h) 959 Word Problems. Solve each work problem. a) There were 18 roses in a bouquet. Milton gave 9 roses away. How many roses were left? b) A city has 89 mail carriers. One day only 54 were at work. How many were not at work? 246 Book 1 �c) Mariko and Stefan went 5-pin bowling. Mariko scored 274 points while Stefan scored 152. How many more points did Mariko score? 4-A X. Estimate the following answers. Be sure to round to the nearest 10 before adding. a) 81 + 74 Estimate: b) 53 + 39 Estimate: c) 43 + 68 Estimate: d) 733 + 719 Estimate: Estimate f) 623 + 914 Estimate: e) 907 + 448 Y. Estimate the following answers. Be sure to round to the nearest 10 before subtracting. a) 82 Estimate: Fundamental Mathematics b) 67 Estimate: 247 �c) 61 e) 577 Z. Estimate: d) 968 Estimate: Estimate f) 742 Estimate: Word Problems. Estimate the following answers. Be sure to round to the nearest 10 before adding or subtracting. a) Mr. Han worked in his store for 33 years. Before owning a store, he had worked in a bank for 24 years. How many years has Mr. Han worked? b) The longest span of the Lions Gate Bridge in Vancouver is 473 metres. The longest span of the Confederation Bridge in Prince Edward Island is 247 metres. What is the difference? 248 Book 1 �4-B AA. Write the following times in standard format. a) 3 h, 22 min, 51 s b) 8 h, 38 min, 9 s c) 10 h, 18 min, 23 s d) 7 h, 43 min, 34 s BB. Write the following times using a.m. or p.m. a) The movie begins at 8:30 in the evening. b) The coffee shop opens at 5:15 in the morning. c) The shopping mall closes at 10:00 at night. CC. Round the following times to the nearest hour. a) The running time for the movie was 2 hours and 25 minutes. Fundamental Mathematics 249 �b) It took 5 hours and 53 minutes to go the hockey and return home after the game. DD. The following things give the idea of a shape. Write the name of the shape in each blank. j) A Christmas tree is a . k) A swimming pool is a . l) A quarter is a EE. a) 250 . What shape are the following things. Write triangle, square, rectangle or circle on the line. b) Book 1 �Answers to Book 1 Review A. a) 4, four b) 3, three B. a) 5 tens, 8 ones b) 1 ten, 8 ones d) 1 hundred, 2 tens, 7 ones c) 8, eight c) 4 hundreds, 7 tens, 1 one C. a) tens b) ones D. a) 8 b) 7 E. a) seventeen b) three hundred forty-two F. a) b) 19 b) 687 75 G. a) 452 c) c) H. a) 66 86 668 686 866 868 886 d) tens d) c) 750 6, six hundreds six hundred twenty-five d) 905 e) 873 b) 23 33 223 232 322 323 332 I. a) < b) = c) > d) < J. a) 50 b) 120 c) 180 d) 90 K. a) Bear Number Rounded Number Polar bear 1 002 1 000 Koala bear 14 10 Panda bear 113 110 Kodiak bear 679 680 Black bear 272 270 Fundamental Mathematics 251 �L. a) 40 cents b) 12 dollars M. a) 8 b) 5 c) 10 f) 14 g) 13 h) 9 N. a) 11 b) 3 c) 11 f) g) 17 h) 6 11 d) 5 e) 5 d) 17 e) 8 O. a) 12 b) 17 c) 14 d) 17 e) 8 f) 12 P. a) 13 b) 16 c) 6 d) 8 e) 11 f) 15 Q. a) 10 metres, rectangle b) 12 metres, triangle c) R. a) 79 f) 1 248 b) g) 128 1 369 c) h) 138 1 595 S. a) b) 128 bikes c) 99 kilometres T. a) 4 b) 3 c) 9 f) 9 g) 7 h) 6 U. a) 3 b) 6 c) 9 f) g) 9 h) 5 V. a) 51 b) 41 c) 21 f) g) 137 h) 427 252 11 cars 8 139 8 metres, square d) 108 e) 1 799 d) 7 e) 5 d) 5 e) 2 d) 53 e) 531 Book 1 �W. a) 9 roses b) X. a) 80 + 70 = 150 35 mail carriers c) 122 points b) 50 + 40 = 90 e) 910 + 450 = 1 360 c) f) d) b) e) c) f) Z. a) 50 years b) 220 metres d) 730 + 720 = 1 450 Y. a) AA. a) 3:22:51 b) 8:38:09 c) 10:18:23 BB. a) 8:30 p.m. b) 5:15 a.m. c) 10:00 p.m. CC. a) 2 hours b) 6 hours DD. a) triangle b) rectangle c) circle EE. a) rectangle b) square Fundamental Mathematics 40 + 70 = 110 620 + 910 = 1 530 d) 7:43:34 253 �Glossary addends The numbers to be added together in an addition question. In 3 + 5 = 8, the addends are 3 and 5. axis Any straight line used for measuring or as a reference. balance Balance has many meanings. In money matters, the balance is the amount left. It might be the amount left in a bank account (bank balance) or it might be the amount you still must pay on a bill (balance owing). cancelled cheque A cheque that has been cashed. The cheque is stamped, or cancelled, so it is no longer negotiable. circumference The distance around a circle; the perimeter of a circle. commission Salespeople may be paid a percentage of the money made in sales. The commission is part or all their earnings. common fractions eg, , , cross multiply In a proportion, multiply the numerator of the first fraction times the denominator of the second fraction. Then multiply the denominator of the first fraction times the numerator of the second fraction. In a true proportion, the products of the cross multiplication are equal. denominator The bottom number in a common fraction; tells into how many equal parts the whole thing has been divided. diameter The distance across a circle through its centre. difference The result of a subtraction question, the answer. Subtraction gives the difference between two numbers. digit Any of the ten numerals (0 to 9) are digits. This term comes from our ten fingers which are called digits. The numerals came to be called "digits" from the practice of counting on the fingers! discount An amount taken off the regular cost. If something is bought "at a discount" it is bought at less than the regular price. divide To separate into equal parts. dividend The number or quantity to be divided; what you start with before you divide. 254 Book 1 �divisor The number of groups or the quantity into which a number (the dividend) is to be separated. equal = The same as equation A mathematical statement that two quantities are equal. An equation may use numerals with a letter to stand for an unknown quantity. 6 + Y = 9 equivalent Equal in value; equivalent numbers (whole or fractions) can be used interchangeably; that is, they can be used instead of each other. estimate Make an approximate answer. Use the sign to mean approximately equal. factors The numbers or quantities that are multiplied together to form a given product. 5 2 = 10, so 5 and 2 are factors of 10. fraction Part of the whole; a quantity less than one unit. horizontal in a flat position; we are horizontal when we lie in a bed. A horizontal line goes across the page. improper fraction A common fraction with a value equal to or more than one. infinite Without end, without limit. invert To turn upside down. like fractions With the same denominators. lowest terms When the terms of a common fraction or ratio do not have a common factor (except 1), the fraction or ratio are in lowest terms (also called simplest form). minuend The first number in a subtraction question. mixed number A whole number and a common fraction. 1 mixed decimal A whole number and a decimal fraction. 1.75 multiple If a certain number is multiplied by another number, the product is a multiple of the numbers. Think of the multiplication tables. For example, 2, 4, 6, 8, 10, 12, 14. . . are multiples of 2. multiplicand The number to be multiplied. multiplier The number you multiply by. Fundamental Mathematics 255 �negotiable Something which can be cashed, that is, exchanged or traded as money. numbers Numbers represent the amount, the place in a sequence; number is the idea of quantity or order. numerals The digits 1,2,3,4,5,6,7,8,9,0 are also called numerals. These ten digits are combined to make infinite numerals. Digits are like the letters, numerals are like the words and numbers are the meaning. numerator The top number in a common fraction; the numerator tells how many parts of the whole thing are being considered. overdrawn If the value of the cheques or money taken from a bank account is higher than the amount of money in the account, then the account is overdrawn. The account is "in the hole" or "in the red" are expressions sometimes used. parallel Two objects or lines side by side, never crossing and always the same distance from each other. Railway tracks are parallel, the lines on writing paper are parallel. percent % For every one hundred. perimeter The distance around the outside of a shape. place value We understand numbers by the way the digits (numerals) are arranged in relationship to each other and to the decimal point. Each position has a certain value. Our number system is a decimal system. The place value is based on ten. prime number A number that can only be divided evenly by itself and 1. product The result of a multiplying question, the answer. proper fraction A common fraction with a value less than one. proportion Generally, proportion is a way of comparing a part of something to the whole thing. Eg. his feet are small in proportion to his height. In mathematics, proportion is used to describe two or more ratios that are equivalent to each other. quotient The result of a division question; the quotient tells how many times one number is contained in the other. radius The distance from the centre of a circle to the outside of the circle. ratio The relationship between two or more quantities. Eg. the ratio of men to women in the armed forces is 10 to 3 (10:3) 256 Book 1 �reciprocal A number, when multiplied by its reciprocal, equals 1. To find the reciprocal of a common fraction, invert it. =1 reduce Write a common fraction in lowest terms. Divide both terms by same factor. remainder The amount left when a divisor does not divide evenly into the dividend. The remainder must be less than the divisor. sign In mathematics, a symbol that tells what operation is to be performed or what the relationship is between the numbers. + plus, means to add - minus, means to subtract multiplied by, "times" divided by, division = equal, the same quantity as not equal approximately equal < less than > greater than less than or equal to greater than or equal to simplify See reduce. subtrahend The amount that is taken away in a subtraction question. sum The result of an addition question, the answer to an addition question. symbol A written or printed mark, letter, abbreviation etc. that stands for something else. term a) A definite period of time, such as a school term or the term of a loan. b) Conditions of a contract; the terms of the agreement. c) In mathematics, the quantities in a fraction and in a ratio are called the terms of the fraction or the terms of the ratio. In an algebra equation, the quantities connected by a + or - sign are also called terms. total The amount altogether. transaction One piece of business. A transaction often involves money. When you pay a bill, take money from the bank or write a cheque, you have made a transaction. unit Any fixed quantity, amount, distance or measure that is used as a standard. In mathematics, always identify the unit with which you are working. Eg. 3 km, 4 cups, 12 people, $76, 70 books, 545 g. unit price The price for a set amount. Eg. price per litre, price per gram. Fundamental Mathematics 257 �unlike fractions Fractions which have different denominators. vertical in an up and down position; we are vertical when we are standing up. On a page, a vertical line is shown from the top to the bottom of the page. 258 Book 1 � Dublin Core The Dublin Core metadata element set is common to all Omeka records, including items, files, and collections. For more information see, http://dublincore.org/documents/dces/. Title A name given to the resource GED Resources Text A resource consisting primarily of words for reading. Examples include books, letters, dissertations, poems, newspapers, articles, archives of mailing lists. Note that facsimiles or images of texts are still of the genre Text. Dublin Core The Dublin Core metadata element set is common to all Omeka records, including items, files, and collections. For more information see, http://dublincore.org/documents/dces/. Title A name given to the resource Adult Literacy Fundamental Mathematics: Book One Description An account of the resource A Workbook in math fundamentals produced by the Province of British Columbia Ministry of Advanced Education Creator An entity primarily responsible for making the resource Wendy Tagami Publisher An entity responsible for making the resource available Province of British Columbia Ministry of Advanced Education Date A point or period of time associated with an event in the lifecycle of the resource Created: 2010 Rights Information about rights held in and over the resource released under a Creative Commons Attribution 4.0 Unported License Format The file format, physical medium, or dimensions of the resource pdf Language A language of the resource English Type The nature or genre of the resource Text Source A related resource from which the described resource is derived <a href="https://open.bccampus.ca/browse-our-collection/find-open-textbooks/?uuid=1eade072-4b30-4c2e-b3d8-cb2512765e8d&amp;contributor=&amp;keyword=&amp;subject=">BC Campus</a> Contributor An entity responsible for making contributions to the resource John Roper Identifier An unambiguous reference to the resource within a given context GEDdoc002 Test Preparation Dublin Core The Dublin Core metadata element set is common to all Omeka records, including items, files, and collections. For more information see, http://dublincore.org/documents/dces/. Title A name given to the resource GED Resources Hyperlink A link, or reference, to another resource on the Internet. Local URL The URL of the local directory containing all assets of the website www.bestgedclasses.org/ged/practice URL <a href="http://www.bestgedclasses.org/ged/practice" target="_blank" rel="noreferrer noopener">www.bestgedclasses.org/ged/practice</a> Dublin Core The Dublin Core metadata element set is common to all Omeka records, including items, files, and collections. For more information see, http://dublincore.org/documents/dces/. Title A name given to the resource BestGEDclasses.org Practice Exams Creator An entity primarily responsible for making the resource Covcell GED Prep Publisher An entity responsible for making the resource available bestgedclasses.org Contributor An entity responsible for making contributions to the resource Anthony Dixon Description An account of the resource These practice tests provided by Covcell GED Prep are associated with the 4 GED subjects and students can choose from short (10-question quizzes) to long tests (up to 50-question quizzes). There are also tests with a built-in timer, so students can check how they perform under time pressure. Source A related resource from which the described resource is derived <a href="http://www.bestgedclasses.org/ged/practice">www.bestgedclasses.org/ged/practice</a> Language A language of the resource English Type The nature or genre of the resource InteractiveResource Identifier An unambiguous reference to the resource within a given context GEDurl002 Test Preparation Dublin Core The Dublin Core metadata element set is common to all Omeka records, including items, files, and collections. For more information see, http://dublincore.org/documents/dces/. Title A name given to the resource GED Resources Hyperlink A link, or reference, to another resource on the Internet. URL <a href="https://study.com/ged/ged-practice-tests.html" target="_blank" rel="noreferrer noopener">https://study.com/ged/ged-practice-tests.html</a> Local URL The URL of the local directory containing all assets of the website www.study.com/GED/Test_Prep Dublin Core The Dublin Core metadata element set is common to all Omeka records, including items, files, and collections. For more information see, http://dublincore.org/documents/dces/. Title A name given to the resource Study.com GED Practice Tests Description An account of the resource Free timed 15-question GED practice tests. These sample tests are intended to tell students where they stand before they start studying for the GED. Study.com also provides more extensive resources for a fee. Creator An entity primarily responsible for making the resource Study.com Publisher An entity responsible for making the resource available Study.com Contributor An entity responsible for making contributions to the resource Anthony Dixon Source A related resource from which the described resource is derived <a href="https://study.com/ged/ged-practice-tests.html" target="_blank" rel="noreferrer noopener">https://study.com/ged/ged-practice-tests.html</a> Rights Information about rights held in and over the resource © copyright 2003-2019 Study.com Language A language of the resource English Type The nature or genre of the resource InteractiveResource Identifier An unambiguous reference to the resource within a given context GEDurl003 Test Preparation