Civic Mathematics: Fundamentals in the Context of Social Issues

CIVICCMATHEATICSICS

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CIVICCMATHEMATICSS Fundamentals in the Context of Social Issues

Terry Vatter

TEACHER IDEAS PRESS

Libraries Unlimited A Division of Greenwood Publishing Group, Inc. Englewood, Colorado 1996

Dedicated to my father, who has always been my favorite teacher.

Copyright © 1996 Terry Vatter All Rights Reserved Printed in the United States of America No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission of the publisher. An exception is made for individual library media specialists and teachers, who may make copies of activity sheets for classroom use in a single school. Other portions of the book (up to 15 pages) may be copied for in-service programs or other educational programs in a single school. TEACHER IDEAS PRESS Libraries Unlimited A Division of Greenwood Publishing Group, Inc. P.O. Box 6633 Englewood, CO 80155-6633 1-800-237-6124 www.lu.com/tip Production Editor: Jason Cook Copy Editor: Ramona Gault Design and Layout::Pamela J. Getchelll Library of Congress Cataloging-in-Publication Data Civic mathematics : fundamentals in the context of social issues / Terry Vatter. xvi, 169 p. 22x28 cm. Includes bibliographical references (p. 165) and index. ISBN 1-56308-435-X 1. Mathematics. 2. Social sciences-Mathematics. I. Title. QA39.2.V38 513\l-dc20

1996

96-3617 CIP

Contents S Preface Acknowledgments Introduction

xi xiii xv

Issues

Firstt Quarterterr of Race andd Gnderrr

UNIT 1 Introduction Social-Context Topics Covered Mathematical Skills Covered Discussion Lesson 1.1: Rounding Unit 1, Lesson 1.1 Homework Lesson 1.2: Estimating Lesson 1.3: Adding and Subtracting Decimals Lesson 1.4: Multiplying Decimals Unit 1, Lesson 1.4 Homework Lesson 1.5: Dividing Decimals Lesson 1.6: Multiplying and Dividing by Powers of 10 Unit 1 Library Research Activity Research Questions Assessment Unit 1 Library Research Guide Research Question

3 3 3 3 3 4 6 7 10 11 12 13 15 17 17 17 18 18

UNIT 2 Introduction Social-Context Topics Covered Mathematical Skills Covered Discussion Lesson 2.1: Making Fractions Unit 2, Lesson 2.1 Homework Lesson 2.2: Equivalent Fractions Unit 2, Lesson 2.2 Homework Lesson 2.3: Simplifying Fractions Unit 2, Lesson 2.3 Homework Unit 2 Library Research Activity Research Questions Assessment Unit 2 Library Research Guide Research Question

20 20 20 20 20 21 25 26 28 29 31 32 32 32 33 33

V

vi / CONTENTS

Secondd Qarterrterr Poverty andd Wthth UNIT 3 Introduction Social-Context Topics Covered Mathematical Skills Covered Discussion Lesson 3.1: Rates Lesson 3.2: Ratios Unit 3, Lesson 3.2 Homework Lesson 3.3: Proportions Unit 3 Library Research Activity Research Questions Assessment Unit 3 Library Research Guide Research Question

37 37 37 37 37 38 40 42 43 46 46 46 47 47

UNIT 4 Introduction Social-Context Topics Covered Mathematical Skills Covered Discussion Lesson 4.1: Fractions, Decimals, Percentages Lesson 4.2: Comparing Fractions Lesson 4.3: Adding and Subtracting Fractions Unit 4, Lesson 4.3 Homework Lesson 4.4: Multiplying Fractions Unit 4 Library Research Activity Research Questions Assessment Unit 4 Library Research Guide Research Question

48 48 48 48 48 49 52 54 56 57 60 60 60 61 61

UNIT 5 Introduction Social-Context Topics Covered Mathematical Skills Covered Discussion Lesson 5.1: Expressions and Sentences Lesson 5.2: Formulas Lesson 5.3: Equations Unit 5 Library Research Activity Research Questions Assessment Unit 5 Library Research Guide Research Question

63 63 63 63 63 64 66 68 70 70 70 71 71

CONTENTS / vii UNIT 6 Introduction Social-Context Topics Covered Mathematical Skills Covered Discussion Lesson 6.1: Finding the Percentage of a Number Lesson 6.2: Finding W h a t Percentage One Number Is of Another Lesson 6.3: Finding a N u m b e r When Percentage of It Is Known Lesson 6.4: Interest Unit 6 Library Research Activity Research Questions Assessment Unit 6 Library Research Guide Research Question

72 72 72 72 72 73 75 77 79 82 82 82 83 83

Thirdd QQuarterr Thee Ennvironmenntt UNIT 7 Introduction Social-Context Topics Covered Mathematical Skills Covered Discussion Lesson 7.1: P e r i m e t e r and Circumference Lesson 7.2: Areas of Polygons Unit 7, Lesson 7.2 Homework Lesson 7.3: Scale Unit 7 Library Research Activity Research Questions Assessment Unit 7 Library Research Guide Body of W a t e r

87 87 87 87 87 88 90 92 93 94 94 94 95 95

UNIT 8 Introduction Social-Context Topics Covered Mathematical Skills Covered Discussion Lesson 8.1: Volume of Rectangular Solids Lesson 8.2: Volume of Cylinder Unit 8 Library Research Activity Research Question Assessment Unit 8 Library Research Guide

96 96 96 96 96 97 99 102 102 102 103

viii / CONTENTS UNIT 9 Introduction Social-Context Topics Covered Mathematical Skills Covered Discussion Lesson 9.1: Tables Lesson 9.2: Bar Graphs Unit 9, Lesson 9.2 Homework Lesson 9.3: Line Graphs Unit 9, Lesson 9.3 Homework Lesson 9.4: Circle Graphs Unit 9 Library Research Activity Research Questions Assessment Unit 9 Library Research Guide Research Question

Fourth Teen

105 105 105 105 105 106 108 110 Ill 113 114 117 117 117 118 118

Quarter Issues

UNIT 10 Introduction Social-Context Topics Covered Mathematical Skills Covered Discussion Lesson 10.1: Mean, Median, Mode, Range Lesson 10.2: Percent Increase or Decrease Unit 10, Lesson 10.2 Homework Unit 10 Library Research Activity Research Questions Assessment Unit 10 Library Research Guide Research Question

121 121 121 121 121 122 124 126 127 127 127 128 128

UNIT 11 Introduction Social-Context Topics Covered Mathematical Skills Covered Discussion Lesson 11.1: Probability Lesson 11.2: Odds, Multiplying Probabilities, Adding Probabilities Unit 11 Library Research Activity Research Questions Assessment Unit 11 Library Research Guide Research Question

129 129 129 129 129 130 133 135 135 135 136 136

CONTENTS / ix UNIT 12 Introduction Social-Context Topics Covered Mathematical Skills Covered Discussion Lesson 12.1: Negative Numbers Unit 12, Lesson 12.1 Homework Lesson 12.2: Coordinate Geometry and Graphing Equations Unit 12 Library Research Activity Research Topics Assessment Unit 12 Library Research Guide Research Topic

138 138 138 138 138 139 141 142 144 144 144 145 145

Appendix

147

Bibliography

165

Index

167

About the Author

169

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Prefacee The idea of the mathematics of social issues grew out of an urgent need to motivate students. Teaching at-risk youth, I found myself daily in a room full of kids who cared little for school, knew little of their role in a larger society, had poor academic skills, didn't know how to function in a cooperative setting, and certainly saw no use for mathematics. The only time it was easy to get their full attention was when we strayed into a class discussion spurred by some crisis in their lives: mistreatment because of race or gender, hassles with a bureaucracy, fights, pregnancy. An idea was born. Right now, educators, politicians, school boards, parents, and students are calling for improvements in education. We want relevance, effectiveness, and, most of all, motivated students who will stay in school and grow into responsible and productive citizens of a democratic society. Civic Mathematicssallows students to see mathematics as a powerful toolll for understanding the world, their world. It demonstrates that mathematics is not an isolated subject, not always abstract. It lends itself to working as part of a team and to interdisciplinary approaches to learning. It fosters reaching outside of the classroom for information, using the library and many resource materials. Students doing Civic Mathematics are aware that they are doing valuable work and dealing with significant problems. They do not ask, "What has this got to do with my life?" This book offers middle school teachers a way to teach mathematics that motivates, is relevant, and works.

xi

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A ckno wledgments I am grateful to my co-workers and principal for making TST Community School a place where creativity can flourish. I also want to thank my family for their support in writing this book, especially my husband, Bill, whose critical reading and rereading always improve my work.

• • •

XIII

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Introductionon Civic Mathematicssis divided into quarters, providing the four social-context umbrellaa issues for the work: race and gender, poverty and wealth, the environment, and teen issues. Each quarter is divided into units specific to the mathematical skills worked with. Each unit is further divided into lessons and finishes with a library activity. The actual teaching of mathematical skills should occur before you turn to Civic Mathematics; these lessons can be viewed as applications of the skills to relevant data. Use whatever method you prefer to introduce the skills, then familiarize yourself with what is offered for those skills here. Each unit can stand alone, as can each library activity. You may therefore choose to incorporate Civic Mathematics into your curriculum in a variety of ways: use all the lessons as the structure for a complete course choose individual lessons or units based on personal preference, class interest, or skills that need a fresh approach use only the library activities to enhance the course or as an assessment tool use any combination of units, lessons, and activities for students who need an extra challenge Keep in mind that applying skills to data is itself an acquired skill. When you begin to use the Civic Mathematics materials, students will need guidance until they gain facility with the kinds of numbers presented. This book contains many tables of data. I tried to keep them in a form that will enable you to put them on the blackboard or the overhead projector or read them aloud. Reproducible sheets—homework projects and library research guides—are marked as such. An early arrival in the classroom might enjoy putting the data on the blackboard, even while you are introducing the topic. It might be useful at this point to "walk" through a typical unit. Discussions at the beginning of each unit and brief remarks at the beginning of each lesson are designed to help you introduce the topics. Each lesson first states what mathematical skills are required to do the work, then the social context activities begin. I also provide the estimated time each lesson will require. Activities can be done individually, aloud as a whole class, or in groups. Sometimes I suggest a procedure, but generally this is up to you, depending on the personality of a particular class, materials available, and so on. Discussion activities are designed for the entire class, and your input will sometimes be needed. Discussion forms the cornerstone of Civic Mathematics, generating interest and giving students an opportunity to examine their own ideas in public. For these reasons, discussions should not be rushed. As students become better at formulating and more comfortable expressing their ideas, the discussions will magnetize students to your class. Nearly always, discussions include a question that requires students to reflect on the mathematical tools being used, a valuable aspect of learning mathematics. Always go over homework activities briefly before class ends, because they vary from unit to unit and differ greatly from traditional homework assignments. The library research activity is an exercise in which students work as a team to explore a real question, using mathematics as a tool. This is what doing research and being an informed citizen are all about. The questions offered are suggestions; you or they may come up with others, depending on student interest and available resources. Again, these activities will impel students to reflect on the mathematics of their work. In addition, this kind of team effort to examine a question builds skills required in life and work. XV

xvi / INTRODUCTION Before students undertake a library research activity, discuss with your school librarian the resources you will need. The librarian should at least have the following on hand. Most of these are standard school library resources. Books Statistical Abstract of the United States (three copies). Washington, D.C.: U.S. Department of Commerce World Almanac & Book of Facts. Mahwah, N.J.: Funk & Wagnalls Periodicals Current Health 2 Scholastic magazines, including Junior Scholastic Scholastic Action Scholastic Choices Scholastic Math Scholastic Scope Scholastic Update Scholastic World Newspapers The New York Times your local newspaper Once you have used any of these activities, you will see the beauty of mathematics in the context of social issues. Bring to these activities your own knowledge of the world and of teaching children to think critically, your own classroom style, and your own enthusiasm, and your students will grow as citizens and as mathematicians.

First Quarter

Issues of Race and Gender Skills Covered: Rounding decimals Estimating Operations with decimals Powers of 10 Making fractions Equivalent fractions Simplifying fractions

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UNIT 1 INTRODUCTION Social-Contextextopicspicsoverederedd Racial breakdown of U.S. population Gender breakdown of U.S. population Numbers of immigrants since 1820 Nationalities of immigrants for 1981-1991 High school dropouts, by race Professional occupations, by gender Rapes, by city Bias crimes Wages, by race and gender Household earnings by race College population, by race and gender

Mathematicalcalkillskillsoverederedd Rounding decimals Estimating Decimal addition, subtraction, multiplication, and division Multiplying and dividing by powers of 10 Discussionon The social-context issues in unit 1 are designed to introduce students to some aspects of our lives that can be related to ethnicity and gender. The issues are not presented in an order intended to lead students to any particular conclusion, but rather to offer a sampling of correlated factors. Indeed, it would be good to explain to students, now and throughout their work, using raw data, the distinction between correlation and causeand-effect. As with all the units, this one provides numbers that can anchor students' divergent views on these issues to hard data. It will allow them to make informed judgments. This should be explained to students at the beginning of the unit. Numbers worked with here are usually from the Statistical Abstract of the United States, 1994. In some lessons the skill being practiced is actually useful in analyzing the data, and in others the data are useful in practicing the math skill. Often data and math skills serve each other.

3

4 / UNIT 1

LESSON 1.1: ROUNDING • Review decimal place value • Teach rules of rounding • Social-context activities (about 40 minutes) To begin topics of race and gender, it is important to see how our population breaks down along these lines. 1. Round the decimals in this list to the nearest 10th, making a new column: U.S. Population, in Millions Millions Total

262.754

Male

128.292

Female

134.461

White

217.511

Black

33.147

American Indian Hispanic Asian

Rounded

2.247 26.522 9.849

Data from Statistical Abstract of the United States, 1994. 2. Put the list of racial or origin groups in numerical order, greatest to least. 3. Discussion. Possible questions include the following: Why are whites in the majority? Why are there so few American Indians? Why are there almost as many Hispanics as blacks? If your mother is American Indian and your father Hispanic, and the Census Bureau calls your house to ask you what your race is, how would you answer? When is it important to know what someone's race is?

LESSON 1.1: ROUNDING / 5 4. Round the following list of population figures by gender and age to the nearest 100th: U.S. Population, by Age and Sex, in Millions Millions Males under 5

9.836

Females under 5

9.386

Males 15-19

8.834

Females 15-19

8.371

Males 20-24

9.775

Females 20-24

9.419

Males 40-44

9.258

Females 40-44

9.496

Rounded

Data from Statistical Abstract of the United States, 1994. 5. Discussion. Possible questions include the following: W h a t h a p p e n s to the gender balance as people advance from childhood to middle age to old age? How do you account for this? When do you use the rounding skill in daily life? 6. Assign homework.

6 / UNIT 1

U N I T 1 , LESSON 1.1 HOMEWORK Add another column to the table below, rounding the decimals to the nearest unit: Immigrants to United States, 1820-1991, in Millions Millions 1820-1840

.751

1841-1860

4.311

1861-1880

5.127

1881-1900

8.935

1901-1920

14.531

1921-1940

4.635

1941-1960

3.550

1961-1980

7.815

1981-1991 (10 years)

9.166

Rounded

Data from Statistical Abstract of the United States, 1994. 1. Make two observations about the numbers of U.S. immigrants over the years.

2. Which is more useful to you: the column given, or the rounded column t h a t you made?

3. W h a t is one danger of rounding these data?

From Civic Mathematics. © 1996. Teacher Ideas Press. (800) 237-6124.

LESSON 1.2: ESTIMATING / 7

LESSON 1.2: ESTIMATING • Teach estimating sums and differences • Social-context activities (about 40 minutes) 1. Go over Lesson 1.1 homework. It is important to understand that our nation is made up of people from all around the world. This lesson helps us learn where our new citizens come from. 2. Hand out data, have students estimate sums representing 1981-1991, and get answers from around the class. Immigrants, 1981-1991, in Thousands 1981-90

1991

Cambodia

117

3

India

252

45

Iran

158

20

Israel

36

4

Japan

43

5

Korea

339

27

Lebanon

42

6

Pakistan

61

20

Philippines

495

64

Vietnam

401

54

Mexico

1,653

946

Cuba

159

11

Haiti

140

48

El Salvador

215

47

Nicaragua

44

18

Chile

23

8

Ethiopia

27

8

1981-91

Table continues on page 8.

8 / UNIT 1 1981-90

1991

Nigeria

35

8

South Africa

16

6

France

23

5

Germany

70

7

Italy

33

3

former Soviet Union

84

57

former Yugoslavia

19

3

China

389

33

Thailand

64

7

Canada

119

14

Jamaica

214

24

Costa Rica

14

7

Guatemala

88

26

1981-91

Data from Statistical Abstract of the United States, 1994. 3. Discussion. Possible questions include the following: What countries did your ancestors come from? What groups in the United States did not get here by immigrating, and how did they get here?

LESSON 1.2: ESTIMATING / 9 4. As a whole class, estimate differences from the blackboard: People Who Only Completed Eight Years of School, in Millions 1980

1992

All races

23

15

Whites

19

12

Blacks

4

2

Approximate Difference

Data from Statistical Abstract of the United States, 1994. 5. Discussion. Possible questions include the following: Is the t r e n d from 1980 to 1992 for dropping out before the eighth grade a good or a bad one? Why? Why are estimation skills useful?

10 / UNIT 1

LESSON 1.3: ADDING AND SUBTRACTING DECIMALS • Teach adding and subtracting decimals • Social-context activities (about 30 minutes) Professional occupations such as medicine or law are usually higher paying and more highly respected t h a n most other occupations. Women are entering these professions at a much higher r a t e t h a n they used to. This lesson will let us see how far women have progressed. Employment in Managerial and Professional Occupations, in Millions Men

Women

Executives

8.918

6.458

Architects

.100

.023

Engineers

1.568

.148

Natural scientists

.371

.160

Physicians

.473

.132

Dentists

.136

.016

Teachers

.444

.328

Lawyers

.599

.178

Writers

.059

.080

Difference

Data from Statistical Abstract of the United States, 1994. 1. All students independently add together the numbers of physicians and dentists for men, then for women. Do the same for architects and engineers. For each job, find the difference between men and women, m a k i n g a third column, and put a s t a r next to the greater number in the "Men" or "Women" column. Determine from your new column which profession h a s the least gender discrepancy. Add together the entire "Men" column, t h e n the "Women" column, and find the difference. 2. Discussion. Possible questions include the following: Which careers have more women t h a n men? W h a t does t h a t m e a n for women, for men, and for men's and women's working relationships? Why do you t h i n k this imbalance exists?

LESSON 1.4: MULTIPLYING DECIMALS /11

LESSON 1.4: M U L T I P L Y I N G DECIMALS • Teach multiplying decimal by whole number and decimal by decimal • Social-context activities (about 30 minutes) Women are the primary victims of the crime of rape—because of their gender and the gender of the perpetrators of the crime. This lesson will give students an idea of how many rapes are committed and where they occur. A rate is the number of occurrences for a certain size group. For example, the rape rate in New York City is .382 rapes for every 1,000 people. That means if there are 2,000 people, there are twice as many rapes as the rate for 1,000 people, or .382 x 2 1. Compute a third column, based on the rates given below: Rapes per Year Thousands of People

Rate per Thousand

Number of Rapes

New York, NY

.38

X

8,552

=

San Jose, CA

.55

X

1,189

=

Virginia Beach, VA

.38

X

262

=

Honolulu, HI

.37

X

836

=

1.05

X

358

=

.40

X

152

=

1.05

X

174

=

.78

X

239

=

Buffalo, NY Mesa, AZ Anchorage, AK St. Petersburg, FL

Data from Statistical Abstract of the United States, 1994. 2. Discussion. Possible questions include the following: What is one thing that surprises you from the "rate" column? Do you know of a crime in which mostly men are victims, as women are victims of the crime of rape? 3. Assign homework and explain.

12 / UNIT 1

U N I T 1 , LESSON 1.4 HOMEWORK Another type of crime is a bias crime,,a crime in which the victim is chosen on the basiss of race, religion, or other personal characteristics. Below are some d a t a on bias crimes. There were 6,746 known bias crimes committed in the United States in 1994, which is why t h a t number is constant down the "Hundreds of Bias Crimes" column below. Bias Crime Victims in the United States Actual Number of Bias Crimes

Hundreds of Bias Crimes

Crime

Rate

Anti-black

.36

X

67.46

=

Anti-white

.19

X

67.46

=

Anti-Hispanic

.05

X

67.46

=

Anti-gay

.12

X

67.46

=

Anti-Jewish

.16

X

67.46

=

Anti-other religions

.02

X

67.46

=

Other

.10

X

67.46

=

Data from The New York Times, July 11, 1994. 1. Calculate the actual number of bias crimes for each type by multiplying the r a t e by the h u n d r e d s of crimes committed.

2. W h a t surprises you about the "rate" column?

3. Many states are increasing the penalties for bias crimes. Do you agree with doing t h a t ? Why or why not?

From Civic Mathematics.

© 1996. Teacher Ideas Press. (800) 237-6124.

LESSON 1.5: DIVIDING DECIMALS / 1 3

LESSON 1.5: D I V I D I N G DECIMALS • Teach dividing decimals by whole numbers, decimals by decimals, and whole n u m b e r s by decimals • Social-context activities (about 40 minutes) 1. Go over Lesson 1.4 homework. Women's earnings have been gradually rising over the years, the result of an effort to establish equal pay for equal work. These data will let us see how far women have progressed. Wages Paid per Week, by Race and Gender $ Earned

Hours Worked

Average, all workers

463.25

40

Average, males

514.75

40

Average, females

395.50

40

Average, whites

478.80

40

Average, blacks

370.50

40

Average, Hispanics

335.25

40

Hourly Rate

Data from Statistical Abstract of the United States, 1994. 2. Complete the third column, finding average hourly r a t e s by dividing the "$ earned" by "hours worked." 3. Discussion. A possible question is the following: Rank in order, from highest to lowest, the hourly r a t e s . Don't include "average, all workers." Is the result surprising? Why or why not?

14 / UNIT 1 Weekly Earnings Average U.S. Family Size

Type of Family

Average Income

Black

358.85

3.16

White

622.46

3.16

Asian

733.71

3.16

Per Person in Family

Data from Statistical Abstract of the United States, 1994. 4. Calculate the average amount of income per person in a family per week by dividing income by family size for each group above, and compute the third column. 5. Discussion. Possible questions include the following: When comparing these numbers, what surprises you? The average number of family members, 3.16, is for the nation as a whole. Do you think the average for each ethnic group is the same as the national average? What kinds of budget items have to come out of those dollars per family member? Compare individual earnings (the first table) to household earnings (the second table). Why might there be differences?

LESSON 1.6: MULTIPLYING AND DIVIDING BY POWERS OF 10 / 1 5

LESSON 1.6: MULTIPLYING AND DIVIDING BY POWERS OF 10 • Teach concept of "powers of 10" and multiplying and dividing by powers of 10 • Social-context activities (about 40 minutes) This lesson will give t h r e e glimpses of racial and ethnic differences in our population as seen in immigration during this century and in who goes to college. Immigrants to United States Since 1901, in Thousands Period

Number

1901-1920

14,531

1921-1940

4,635

1941-1960

3,550

1961-1980

7,815

1981-1992(11 years only)

8,312

Actual Number

Data from Statistical Abstract of the United States, 1994. 1. Notice t h a t the title of the table says "in Thousands." T h a t m e a n s every number under the "number" column m u s t be multiplied by 1,000. Do t h a t , and put the actual numbers in the empty column. Resident Population, by Race Whites, in Millions

Year

Blacks, in Millions

1850

3.639000

19.553000

1900

8.834000

66.809000

1920

11.891000

110.287000

1950

15.042000

134.942000

1980

26.683000

194.713000

1995

33.117000

218.334000

Actual Number

Data from Statistical Abstract of the United States, 1994.

Actual Number

16 / UNIT 1 2. Notice that the numbers above are in millions. Figure out how many times you move the decimal point and write the actual numbers, in people. College Population Male

93,604,000

Millions 1,000,000

=

Female

101,982,000

=

White

165,757,000

=

Black

22,614,000

=

Hispanic

15,763,000

=

93.6

Data from Statistical Abstract of the United States, 1994. 3. The numbers above can be changed to say, for example, "93.6 million," by rounding and dividing by 1 million or moving the decimal point over the correct number of spaces for 1 million. Complete the "Millions" column. 4. Discussion. Possible questions include the following: Immigration has gone up and down over the last hundred years. When was it highest and why? What surprises you about the college enrollment data? Do you consider the knowledge of moving the decimal point to multiply or divide by powers of 10 a powerful tool? Why?

UNIT 1 LIBRARY RESEARCH ACTIVITY / 17

UNIT 1 LIBRARY RESEARCH ACTIVITY (ABOUT 80 MINUTES)

Divide into groups of two or three students. Pick one of the research questions below for each group. Use the guide to conduct your research. Reconvene as a whole class and have a spokesperson from each group share your results.

Researchh Questionsns 1. How do males and females compare in dropping out or completing high school?

2. How do blacks, whites, and Hispanics compare in dropping out or completing high school?

3. How do males and females compare on some health characteristic, such as smoking, being overweight, length of life, getting AIDS, and so on?

4. How do various racial or ethnic groups compare on some health characteristic, such as smoking, being overweight, length of life, getting AIDS, and so on?

Assessmentnt For this activity, you will be assessed on the following: seriousness in approach to library work (5%) quality (clarity and value) of statements based on data (20%) quality of application of math skills to statements (30%) quality of revised statements (20%) quality of final organization and presentation (20%) insight of concluding observation (5%)

From Civic Mathematics. © 1996. Teacher Ideas Press. (800) 237-6124.

18 / UNIT 1

UNIT 1 LIBRARY RESEARCH GUIDE Researchh Questionon 1. Locate a source that contains information on your question. Write down the title, author, publisher, and date of publication.

2. Write down, in complete sentences, 5 to 10 statements of fact based on the data. For example: "In 1980, there were 5,212,000 dropouts aged 16 to 17 in the United States."

3. Perform at least five of the following math skills on the statements above: rounding estimating adding decimals subtracting decimals multiplying decimals dividing decimals multiplying by powers of 10 dividing by powers of 10 For example, given the statement above, you might say, "Around 5 million dropouts . . ."

4. Organize your new statements into an orderly, logical, interesting whole, so that they make sense for presenting to the class.

From Civic Mathematics. © 1996. Teacher Ideas Press. (800) 237-6124.

UNIT 1 LIBRARY RESEARCH GUIDE /19 5. Make at least one concluding observation, either factual or reflecting an opinion shared by the whole group, based on your data. This concluding observation should relate to an issue covered during this unit, from the following list: immigration earnings careers education crime 6. State which of the math skills you worked with in this unit was the most useful in the library research activity and why.

From Civic Mathematics. © 1996. Teacher Ideas Press. (800) 237-6124.

Unit 2 INTRODUCTION Social-Contextxtopics

Coverededd

Population breakdown by race and gender Wages earned Hispanic law enforcement officials Professional occupations College enrollment Death and infant mortality Personal health practices

Mathematical

Skills

Covered

Making fractions Equivalent fractions Simplifying fractions

Discussionnn The social-context issues of unit 2 are designed to provide a broader view of ethnic and gender differences. Some of the topics are revisited from unit 1, with new topics related to health comparisons. Students also will work with data relevant to a democratic society—representation in government. The mathematics in this unit really serve the data, and students should be made aware that they can now begin to interpret and analyze data in a way that makes them more meaningful to themselves and others.

20

LESSON 2.1: MAKING FRACTIONS / 21

LESSON 2 . 1 : MAKING FRACTIONS • Teach least common multiple (LCM) and greatest common factor (GCF) • Review meaning of fraction (part/whole) • Social-context activities (about 40 minutes) Fractions are a powerful tool in analyzing data. In this lesson, we will apply this tool to some of the data we encountered in previous units. 1. With the data below, make a fraction for each segment of the U.S. population. The first one is done already. U.S. Population, in Millions Fraction Total

263

—

Male

128

128

Female

134

White

218

Black

33

American Indian

Hispanic

/263

2

27

Data from Statistical Abstract of the United States, 1994.

22 / UNIT 2 2. Make fractions of the following data, using "average all workers" for the denominator: Average Wages Paid per Week, by Race and Gender $ Earned

Fraction

All workers

463

—

Males

515

Females

396

Whites

479

Blacks

371

Hispanics

335

Data from Statistical Abstract of the United States, 1994. 3. Discussion. Possible questions include the following: W h a t do you notice about your fractions for "males" and "whites"? When you see a fraction like V5 in m a t h , w h a t does it mean? What does it m e a n for the d a t a above? Does anything surprise you about the d a t a on the breakdown of our population? Who h a s the highest average wage, and who the lowest?

LESSON 2.1: MAKING FRACTIONS / 23 4. For the d a t a below, m a k e fractions for each region. You will need to total all regions first in order to determine w h a t to use for a denominator. Number of Hispanic Elected Officials in Judicial and Law Enforcement Region

Fraction

Northeast

14

Midwest

7

South

392

West

210

Data from Statistical Abstract of the United States, 1994.

Figure 2.1. 5. Discussion. Possible questions include the following: Why might the n u m b e r of Hispanic public officials be comparatively high in the South? W h a t is one problem with the fractions we have been m a k i n g in this lesson?

24 / UNIT 2 6. Out of a total of 435 members of the U.S. Congress, m a k e the fractions for the d a t a below. Members of Congress Year

Black or Hispanic Fraction

Women

1981

24

19

1983

29

21

1985

30

22

1987

34

24

1989

36

25

1991

38

26

1993

55

48

Fraction

Data from Statistical Abstract of the United States, 1994. 7. Discussion. Possible questions include the following: Are these the fractions you would have expected? Why or why not? Why is it i m p o r t a n t to have minorities and women in Congress? When you t u r n 18, do you plan to vote? 8. H a n d out and explain homework.

UNIT 2, LESSON 2.1 HOMEWORK / 25

U N I T 2 , LESSON 2.1 HOMEWORK Managerial and Professional Occupations, in Thousands Black

Hispan.

1,567

3

2

352

3

2

511

3

5

123

2

1

Total

Male

Female

White

Architects

103

90

13

99

Engineers

1,572

1,566

6

Natural scientists

357

336

Physicians

519

503

16

119

Dentists Lawyers

612

597

15

608

3

1

Writers

62

15

47

59

2

1

Data from Statistical Abstract of the United States, 1994. 1. W h a t fraction of physicians is female? 2. What fraction of writers is female? 3. W h a t fraction of lawyers is Hispanic? 4. W h a t fraction of engineers is white? Some information is missing from this table. Fill it in, based on the following s t a t e m e n t s : 5. The fraction of women dentists is 7 /i26 • 6. Of the total n u m b e r of architects in the United States, 2,000 are black and 2,000 are Hispanic. 7. How m a n y n a t u r a l scientists are female? Fill it in on the table. 8. W h a t ethnic groups are left out of this tally?

From Civic Mathematics.

© 1996. Teacher Ideas Press. (800) 237-6124.

26 / UNIT 2

LESSON 2.2: EQUIVALENT FRACTIONS • Teach finding equivalent fractions by multiplying or dividing • Social-context activities (about 40 minutes) Fractions are really most useful when put into low terms that we can relate to. Have students use rounding skills, along with their knowledge of factors, to restate facts such as "15/62 of writers are male" to "about V4 of writers are male." We will practice doing that in this lesson. 1. Go over Lesson 2.1 homework. 2. Complete the "Total" figure first, then fill in the missing information in the columns of the table below. College Population Millions Male

Fraction of Total

Equivalent Fraction

—

—

94

Female

102

White

156

Black

20

Hispanic

15

Total

Rounded to Tens

196

Data from Statistical Abstract of the United States, 1994. Compare "equivalent fraction" results among students.

LESSON 2.2: EQUIVALENT FRACTIONS / 27 3. Discussion. Possible questions include the following: What do you think about combining your math skills like this to interpret data? What happens to the figures for black and Hispanic when you round? Do you think it is more useful to raise fractions to higher terms or reduce them to lower terms in interpreting data? What surprises you about these numbers? 4. Remember the "rate," for example, the "rape rate." That was the number of rapes per 1,000 people in a city. A rate is really a fraction. If the rape rate in Buffalo is one rape per 1,000 people, what fraction of the population are the victims of rape? From the data below on death, find equivalent fractions, rounded and in lower terms: Death Rates in the United States, per 1,000

White male

9.3

White female

8.5

Black male

Black female

Rounded to Units

Rate as Fraction

Equivalent Fraction

9

Hooo

Vioo

10.0

7.4

Data from Statistical Abstract of the United States, 1994. 5. Discussion. Possible questions include the following: What happens to the difference between white males and females when you round? Who has the best (lowest) death rate and who has the worst? What factors do you think influence a population's death rate? Why do you think men's death rates are higher than women's? 6. Hand out and explain homework.

28 / UNIT 2

UNIT 2, LESSON 2.2 HOMEWORK Below is a table containing data on infant deaths. Statistics on infant deaths are often used to illustrate the relative health of a given population. They are especially used when comparing living conditions among countries. Complete the missing columns in the table and answer the questions below. U.S. Infant Mortality Rates per 1,000 Births

Rate

Fraction

White infants, 1970

18

18

Black infants, 1970

33

White infants, 1991

7

Black infants, 1991

18

Equivalent Lower Fraction

/1,000

Data from Statistical Abstract of the United States, 1994. 1. Make an observation comparing infant mortality r a t e s from 1970 to 1991. 2. Make an observation comparing infant mortality rates between blacks and whites.

From Civic Mathematics.

© 1996. Teacher Ideas Press. (800) 237-6124.

LESSON 2.3: SIMPLIFYING FRACTIONS / 29

LESSON 2.3: SIMPLIFYING FRACTIONS • Teach simplifying fractions • Social-context activities (about 40 minutes) 1. Go over Lesson 2.2 homework. Students have been reducing fractions from "rates." In this lesson, we will apply the same skills, but to raw d a t a — t h e actual numbers of people—and further explore health factors regarding gender and race. 2. From the table below, do the following: round each figure to the nearest thousand find a total, male + female, for each cause of death m a k e a fraction for each gender, for each cause of death, including "all causes" simplify each fraction as far as possible Causes of Death for People Aged 15-24, by Gender Male

Female

All causes

27

549

Accidents

11,534

3,744

Homicide

6,923

1,236

Suicide

4,073

678

Data from Statistical Abstract of the United States, 1994. 3. Discussion. Possible questions include the following: Why would so m a n y more males t h a n females in this age bracket die of all the listed causes? Do you t h i n k this would r e m a i n t r u e in all age brackets? (This may be answered with certainty during the library research activity!) 4. From the table below, perform the following: round each figure to the nearest thousand find the total, black + white m a k e a fraction for each cause of death for each race, including "all causes" simplify each fraction as far as possible

30 / UNIT 2 Causes of Death in United States, by Race Black

White

All causes

269,500

1,868,900

Accidents

12,500

74,400

Homicide

13,000

12,800

2,100

28,000

Suicide

Data from Statistical Abstract of the United States, 1994. 5. Discussion. Possible questions include the following: Given that our population is composed of many more whites than blacks, do the figures for "deaths by all causes" make sense? What about comparing the "homicide" fractions? How do you explain that? What social problems might influence these numbers? 6. Hand out and explain homework.

UNIT 2, LESSON 2.3 HOMEWORK / 31

U N I T 2 , LESSON 2.3 HOMEWORK Personal h e a l t h practices can influence how long we live. The table below contains information on personal health related to race and gender. Be sure to round and reduce! Personal Health Practices of Persons 18 and Over Total Persons

Eat Breakfast

Exercise Regularly

Smoke

Overweight

M

86,278,000

47,107,778

37,962,320

24,502,952

25,538,288

F

95,169,000

55,198,020

35,878,713

21,698,532

24,363,264

Bl

20,248,000

9,496,312

6,945,064

5,304,976

7,694,240

W

155,301,000

89,763,978

64,449,915

39,757,056

41,465,367

Hs

14,314,000

7,514,850

4,995,586

3,292,220

3,950,664

Data from Statistical Abstract of the United States, 1994. 1. W h a t fractions of whites, blacks, and Hispanics eat breakfast regularly?

2. Using the fraction, what group exercises the least? The most?

3. W h a t surprises you about the fractions for smoking?

4. Using the fraction, show which group h a s a greater problem of being overweight— males or females.

5. Where do you stand regarding these health factors?

From Civic Mathematics.

© 1996. Teacher Ideas Press. (800) 237-6124.

32 / UNIT 2

U N I T 2 LIBRARY RESEARCH A C T I V I T Y (ABOUT 80 MINUTES)

Divide into groups of two or three students. Pick one of the research questions below for each group. Use the guide to conduct your research. Reconvene as a whole class and have a spokesperson from each group share results. Research

Questions

1. How has the U.S. population changed since the earliest records were kept (about 1790) regarding the size of various ethnic groups? 2. How do races or genders compare on the numbers of AIDS cases? 3. How does the death rate in the United States compare with that in specific other countries? 4. How do races and genders compare in number of years of education?

Assessmentnttt For this activity, you will be assessed on the following: seriousness in approach to library work (5%) quality of statements based on data (20%) quality of application of math skills to statements (30%) quality of revised statements (20%) quality of final organization and presentation (20%) quality of final completion of math statement (5%)

From Civic Mathematics.

© 1996. Teacher Ideas Press. (800) 237-6124.

UNIT 2 LIBRARY RESEARCH GUIDE / 33

UNIT 2 LIBRARY RESEARCH GUIDE Researchh Questionnn 1. Locate a source that contains information on your question. Write down the title, author, publisher, and date of publication.

2. Write down, in complete sentences, 5 to 10 statements of fact based on the data. For example, "24,502,952 of the total 86,278,000 males in the United States smoke cigarettes."

3. Perform at least one of each of the following math skills on the statements above: making a fraction making an equivalent fraction simplifying a fraction For example, given the statement above, you might say, "Around 2/9 of males smoke."

4. Organize your new statements into an orderly, logical, interesting whole, so that they make sense for presenting to the class.

From Civic Mathematics. © 1996. Teacher Ideas Press. (800) 237-6124.

34 / UNIT 2 5. Make at least one concluding observation, either factual or reflecting an opinion shared by the whole group, based on your data. This concluding observation should relate to an issue covered during the unit, from the following list: population breakdown wages public officials professional occupations college enrollment or college education death rates or infant mortality causes of death personal health practices representation in government

6. Complete one of the following statements: It is good to round raw data because . . . It is bad to round raw data because . . . It is good to be able to turn raw data into a simplified fraction because Rates are really just fractions because . . .

From Civic Mathematics.

© 1996. Teacher Ideas Press. (800) 237-6124.

Second Quarter

Poverty and Wealth Skills Covered: Rates Ratios Proportions Fractions (multiplying, adding, subtracting) Mixed numbers Comparing fractions Interchanging fractions, decimals, and percents Algebra Formulas Finding percent of a number Finding what percent one number is of another Interest

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UNIT 3 INTRODUCTION Social-Contextext TopicspicsCovedredd Earnings, by occupation Federal taxes paid, by income level Earnings, by educational attainment Unemployment, by educational attainment Educational spending disparity International comparisons of level of living Mathematicalcal Skillsillsoverederedd Rates Ratios Proportions

Discussiononn Unit 3's social-context topics begin the quarter devoted to poverty and wealth. Students get an idea of the range in standards of living in the United States and around the world. The focus is on the advantages of staying in school—the clearest across-theboard correlation to income level. In addition, I hope students will gain some appreciation of the relatively high standard of living enjoyed in the United States, but this is not intended to diminish the urgent problems of the poor in this country. Those problems will be explored in subsequent units. The mathematics in this unit pulls together students' skills in rounding, making and simplifying fractions, and making sense of raw data. It lays the groundwork for concepts in algebra.

37

38 / UNIT 3

LESSON 3 . 1 : RATES • Review equivalent fractions (simplifying) • Social-context activities (about 30 minutes) The best way to begin studying poverty and wealth is to look at pay rates—for the richest, the poorest, and everyone in between. You remember t h a t a r a t e is a fraction. If you are babysitting, you might earn $3 an hour: dollars hour

=

3.00 1

1. Set up some r a t e fractions for the 40-hour earnings below. T h a t is, you are given the 40-hour earnings. Simplify the fractions so you know what the r a t e is for 1 hour by getting a 1 in the denominator (divide top and bottom by the denominator). Median Weekly Earnings Occupation

Weekly

Electricians

$550

Plumbers

518

Carpenters

425

Roofers

416

Secretaries

373

Dental assistants

332

Cosmetologists

260

Kitchen workers

236

Teachers

674

Physicians

Fraction 550

/40

Hourly 13.7^

2,476

Data from Career World, January 1995, and Statistical Abstract of the United States, 1994.

LESSON 3.1: RATES / 39 2. If you know how much someone earns in a 40-hour week, then you can compute hourly rate by dividing by 40. If you know how much someone earns in a day, how do you calculate the hourly rate? Assume an 8-hour day. Let's look at a really rich person. The last I heard, Mr. E. Horrigan, a vice president of RJR Nabisco, the cigarette manufacturer, was earning $21,700,000 per year. Let's say he works 52 weeks, 6 days a week, 10 hours a day (he's rich, but a hard worker). How much does he earn per hour? 3. People at different income levels pay taxes at different rates. For the income breakdown below, figure out how much each salary earner would pay in federal taxes: Tax Rates, by Income Level Income Level

Tax Rate

$20,000

$2/$1,000

$30,000

$9/$1,000

$50,000

$10/$1,000

$70,000

$15/$1,000

Tax Paid

Data from Statistical Abstract of the United States, 1994. 4. Discussion. Possible questions include the following: Do you think everyone should have the same income? What factors should influence how much a person makes? Do you think in our society we will always have rich and poor? Why or why not? Do you think it's fair that the higher the income, the higher the tax rate? What are any rates that you are aware of, stated in words (e.g., inches of snow falling per hour)?

40 / UNIT 3

LESSON 3.2: RATIOS • Teach meaning of ratio • Social-context activities (about 40 minutes) A ratio is most useful in the form of a fraction, rather than using "to" or ":". In this lesson you will practice using data on education, earnings, and unemployment to make ratios. 1. In the United States, schools in poor areas have less money to spend on each student than schools in wealthy areas because school funding is based partly on property values. From the data below, make ratios, rounded to the nearest thousand, of highest spending per pupil lowest spending per pupil ^blic School District Spending, per Pupil State

Highest

Lowest

Arkansas

$7,795

$2,986

California

20,000

2,808

Florida

5,943

3,868

Illinois

12,198

2,423

9,571

3,441

Kansas

11,308

2,984

Massachusetts

21,000

2,846

Minnesota

17,845

2,810

New York

32,792

5,066

Oregon

18,750

2,222

Pennsylvania

10,046

3,799

Texas

40,505

2,570

Wisconsin

10,214

3,693

Iowa

Data from Rethinking Schools, summer 1995.

Ratio in Thousands

8/3

LESSON 3.2: RATIOS / 41 2. Discussion. Possible questions include the following: Do you t h i n k our system of funding education works out okay? Why or why not? How much do you think is spent per pupil in your school? You can ask your principal. How should education be paid for? Do you think more money spent per pupil means better education? Why or why not? 3. Answer the questions based on the following data: Unemployment Rates by Level of Education, per Hundred Less than high school diploma

11

High school diploma, no college

6

Less than 4-year degree

5

College graduate

3

Data from Statistical Abstract of the United States, 1994.

W h a t is the ratio of high school dropout unemployed to college g r a d u a t e unemployed? What is the ratio of high school graduate unemployed to college graduate unemployed? W h a t is the ratio of high school dropout unemployed to high school g r a d u a t e unemployed? What level of educational a t t a i n m e n t h a s the biggest impact on unemployment? 4. Discussion. A possible question is the following: For this table you made ratios out of rates, per hundred. Explain what the number 11 m e a n s for the "less t h a n high school" group. 5. H a n d out and explain homework.

42 / UNIT 3

UNIT 3, LESSON 3.2 HOMEWORK Average Monthly Income, by Educational Level Monthly Income

Education Not a high school graduate

Rounded to Hundreds

$856

High school graduate only

1,357

Some college, no degree

1,545

Vocational training

1,568

2-year degree

1,879

4-year degree

2,489

M.S. degree

3,211

Professional degree

5,554

Ph.D. degree

4,545

Data from Statistical Abstract of the United States, 1994. 1. Make a third column, rounding the dollar figures to h u n d r e d s .

2. Make up six interesting s t a t e m e n t s involving ratios, using complete sentences. For example: The ratio of monthly income of a person with vocational t r a i n i n g to a person with j u s t a high school diploma is 1600 1400

From Civic Mathematics. © 1996. Teacher Ideas Press. (800) 237-6124.

LESSON 3.3: PROPORTIONS / 43

LESSON 3.3: PROPORTIONS • Teach proportions and checking with cross-products • Social-context activities (about 40 minutes) 1. Go over Lesson 3.2 homework. Though the United States h a s too many people who are poor, it is sometimes useful to put our s t a n d a r d of living in a global perspective before we focus on poverty in America. This lesson will help you to do t h a t . 2. Round each U.S. and Russian figure to the nearest 5, filling in the missing columns in the table below. Comparison of Time Required to Earn Enough to Buy Certain Items Item

as.

Rounded

Russia

Rounded

1 pound sugar

3 minutes

5

13 minutes

15

1 pound bread

5 minutes

3 minutes

1

10 minutes

19 minutes

1 pound sausage

16 minutes

54 minutes

1 gal. gasoline

10 minutes

49 minutes

1 television

6 days

54 days

/2 gal. milk

Data from The New York Times, October 16, 1994. 3. Set up the following ratios, then make proportions with 1 in the numerator, checking each by finding the cross-product. U.S. sugar time Russian sugar time U.S. milk time Russian milk time U.S. gasoline time Russian gasoline time

44 / UNIT 3 U.S. TV time Russian TV time U.S. bread time Russian bread time U.S. sausage time Russian sausage time 4. Discussion. Possible questions include the following: Where is it cheaper to live, based on these items—the United States or Russia? How do you measure wealth—by how much money you have or by what you can buy? Could you be happy with no TV? Could you be happy with no car? What do you consider to be absolute necessities of life? Be specific; don't just say food—which foods? 5. Complete the rounding and ratio columns in the table below. Rate (per $100 worth of goods) of Spending on Food Country United States

$ 7

Canada

11

Germany

20

India

51

Philippines

53

Great Britain

11

Round to 5s

Rate as Ratio

5

5/100

Data from Statistical Abstract of the United States, 1994. 6. Make proportions of each ratio, with 1 in the numerator. For example, for the United States: 5 100

==

1 20

LESSON 3.3: PROPORTIONS / 45 7. State what each final ratio means. For example, for every $20 spent for private consumption in the United States, $1 must go to food. 8. Discussion. Possible questions include the following: Based on these data, in which countries does the highest portion of a person's money go to food? That portion is about half. Can you think for a moment about a life in which half of your income must go to food? Do you think it is like that for any people in the United States?

46 / UNIT 3

UNIT 3 LIBRARY RESEARCH ACTIVITY (ABOUT 80 MINUTES)

Divide into groups of two or three students. Pick one of the research questions below for each group. Use the guide to conduct your research. Reconvene as a whole class and have a spokesperson from each group share results.

Research

Questions

1. What are some factors that seem to affect earnings besides educational attainment?

2. What are some factors that seem to affect unemployment besides educational attainment?

3. How have earnings changed over the years?

4. How has unemployment changed over the years?

Assessmenttt For this activity, you will be assessed on the following: seriousness in approach to library work (10%) quality of statements based on data (50%) quality of final organization and presentation (30%) insight of concluding observation (10%)

From Civic Mathematics. © 1996. Teacher Ideas Press. (800) 237-6124.

UNIT 3 LIBRARY RESEARCH GUIDE / 47

UNIT 3 LIBRARY RESEARCH GUIDE Researchh Qestionion 1. Locate a source that contains information on your question. Write down the title, author, publisher, date of publication.

2. Write down in complete sentences 5 to 10 statements of fact based on the data. For example: "In 1993 the ratio of unemployment rates for blacks to whites was 4 /3." Each statement must contain evidence that you are familiar with one or more of the following math concepts: rate ratio proportion

3. Organize your statements into an orderly, logical, interesting whole, so that they make sense for presenting to the class.

4. Make at least one concluding observation, either factual or reflecting an opinion shared by the group, based on your data. The concluding observation should relate to an issue covered during this unit, from the following list: earnings unemployment education taxes international standard of living comparisons

5. State which math skill you employed that was most useful and why.

From Civic Mathematics. © 1996. Teacher Ideas Press. (800) 237-6124.

UNIT 4 INTRODUCTION Social-Contextext TpicsicsCoveredredd Minimum wage earners Income brackets in the United States Middle-class family finances People in the United States below poverty level. Federally funded preschool programs Mathematicalcal Skillsoveredoveredd. Interchanging fractions, decimals, and percentages Fraction and mixed number addition, subtraction, and multiplication Comparing fractions

Discussionon In this unit, students will scrutinize poverty in the United States, exploring factors that are correlated with poverty and working with some real families' household budgets to get a feel for how financial decisions are made, based on income. The data are ideally suited to the math skills used here, revealing to students the many ways math gives us to present facts.

48

LESSON 4.1: FRACTIONS, DECIMALS, PERCENTAGES / 49

LESSON 4 . 1 : FRACTIONS, DECIMALS, PERCENTAGES • Teach interchanging fractions, decimals, and percentages • Social-context activities (about 40 minutes) To continue our study of poverty and wealth, we will now focus on people living in the middle in the United States: earning the average wage or less—the m i n i m u m wage. 1. Complete t h e missing columns in the table below, changing the percentage to a decimal, t h e n a fraction, t h e n a simplified fraction. Workers Earning Minimum Wage Type of Worker

Percentage Earning Minimum

Decimal

Fraction

Reduced

Age 16-24

10

.10

10

Vio

Age 16-19

19

25 and older

2

Male

3

Female

5

White

4

Black

5

Hispanic

7

Full-time

2

Part-time

10

/100

Data from Statistical Abstract of the United States, 1994. 2. Discussion. Possible questions include the following: W h a t inequalities do you notice about the data? How might they be explained? Do you t h i n k we should continue to have a federal m i n i m u m wage? Why or why not?

50 / UNIT 4 Do you t h i n k it should apply to all jobs, or exclude some, such as babysitting, as it does now? Do you t h i n k there should be a minimum wage even if it m e a n s a small business h a s to go under? 3. Complete the decimal and percentage columns in the table below. Household Income Household Type

Fraction

Earning under $10,000

3

$10,000-$14,999

1

$15,000-$24,999

17

$25,000-$34,999

3

$35,000-$49,999

17

/100

$50,000-$74,999

16

/100

$75,000 and over

V10

Decimal

Percentage

/20 /10 /100

/20

Data from Statistical Abstract of the United States, 1994. 4. Discussion. Possible questions include the following: If you combine the percentages for $15,000-$49,999, w h a t do you get? Do you consider t h a t to be middle class? If not, w h a t then? If you earn the current minimum wage ($4.35 in 1995) and multiply it by 2,000 hours (the s t a n d a r d way to figure a n n u a l pay), w h a t bracket do you fall into? Does t h a t surprise you? Why or why not?

LESSON 4.1: FRACTIONS, DECIMALS, PERCENTAGES / 51 5. Complete the missing columns in the table below. Average Weekly Food Costs, Family of 4, Both Parents Working, as Percentage of Income Year

Percentage of Budget

1980

17%

1985

16%

1990

15%

1993

14%

Decimal

Reduced Fraction

Data from Statistical Abstract of the United States, 1993 and 1994. 6. Discussion. Possible questions include the following: Describe the t r e n d over the years in amount of budgets allocated to food. Is it a positive or negative trend? Does it surprise you? Would you prefer to be told this information in percentage, decimal, or fraction?

52 / UNIT 4

LESSON 4 . 2 : COMPARING FRACTIONS • Teach finding common denominators • Social-context activities (about 30 minutes) The Matthews family, living in New York City, is a family of six: Gilbert, Debra, and their four children. Gilbert takes home $2,200 per month, and his pay is budgeted as follows: rent phone

2

/5

V10

car

3

food

1

savings

1

miscellaneous

1

/8 /5 /20 /10

Data from The New York Times, October 5, 1989. 1. Find a common denominator, and determine which is the largest budget item, the next largest, and so on. 2. Discussion. Possible questions include the following: If the Matthewses fell on hard times, what budget items could they change, and how? The average fraction of income budgeted for food in the United States is V50 . How does that compare with the Matthewses' budget? The poverty level, as defined by the U.S. government, is based on income and consumer prices. It is adjusted every year. In 1992, for example, it was $14,335 for a family of four. That's roughly equivalent to one person earning $7.17 an hour and supporting a spouse and two children, or a single parent supporting three children.

LESSON 4.2: COMPARING FRACTIONS / 53 3. Find a common denominator in order to determine in which years the poverty level was highest, next highest, and so on, from the table below. People Below Poverty Level, as a Fraction of the Total Population 1960

1

1965

3

/l6

1970

2

/l6

1975

v8

1980

V8

1992

3

/4

/l6

Data from Statistical Abstract of the United States, 1994. 4. Discussion. Possible questions include the following: How would you describe the trend in the poverty level since 1960? What factors do you think determine the rise and fall of the poverty level? Do you think the government (i.e., the taxpayers) should assist the poor? Why or why not? Is it easier to compare fractions or percentages?

54 / UNIT 4

LESSON 4.3: ADDING AND SUBTRACTING FRACTIONS • Teach adding and subtracting fractions and mixed numbers • Social-context activities (about 40 minutes) Let's introduce another middle-class family from New York City: H a r r y and Arlene Biolsi and their four children. H a r r y is a truck driver and takes home about $1,800 a month. Arlene stays home with their two-year-old twins. Here is what their budget looks like: food

V3

rent

v6 ?

1 savings loans

4

telephone

1

miscellaneous

7

/30 /15

/30

Data from The New York Times, October 3, 1989. 1. Find a common denominator for the data above, add together the budget items you have, and see what fraction is left for savings by subtracting your total from 1. Persons Living Below Poverty Level, by Age Under 18

7

18-24

V9

25-34

1

35-44

V9

45-54

1

55-64

1

65 and older

v9

/l8

/6

/18 /18

Data from Statistical Abstract of the United States, 1994.

LESSON 4.3: ADDING AND SUBTRACTING FRACTIONS / 55 2. Reduce the d a t a above to a simpler table with broader age categories by adding age groups together, below. Persons Living Below Poverty Level, by Age Under 18 18-34 35-54 55 and older

3. For each year shown in the table below, figure out the fraction of children who were living below the poverty level. Children in the United States Year

Above Poverty

1970

17

/20

1975

S3

/100

1980

41

1985

4

1990

%

1991

Z9

1992

79

Below Poverty

/ 50

/5

/100 /ioo

Data from Statistical Abstract of the United States, 1994. 4. Discussion. Possible questions include the following: Comparing the fractions you got on age groups, does anything surprise you? Why? Do you think our society feels it is acceptable for children to be poor? If not, w h a t would you like to see done about it? If you were 18 and a registered voter, would you want poverty to be a high-profile issue in the next presidential race? 5. Explain and h a n d out homework.

56 / UNIT 4

UNIT 4, LESSON 4.3 HOMEWORK Children Living in Poverty, Selected Industrialized Nations Nation

Difference

Amount Less Than United States

United States

V5

—

—

former West Germany

3

/l00

1

17

Netherlands

1

/25

France

1

United Kingdom

2

/25

Australia

9

/ioo

Canada

9

/ioo

Sweden

1

/5- 3 /|00

/100

/20

/50

Data from Education Week, September 29, 1993. 1. By subtracting, find out how much smaller is the fraction of children in poverty in each country t h a n in the United States.

2. Change all the resulting fractions to h u n d r e d t h s in order to compare.

3. What do you learn by this international comparison?

From Civic Mathematics. © 1996. Teacher Ideas Press. (800) 237-6124.

LESSON 4.4: MULTIPLYING FRACTIONS / 57

LESSON 4.4: M U L T I P L Y I N G FRACTIONS • Teach multiplying and dividing fractions and mixed n u m b e r s • Social-context activities (about 40 minutes) 1. Go over Lesson 4.3 homework. When you use fractions and multiplication, you can find meaningful data. S t a t e m e n t s like "one-fourth of children are . . ." become "23,542 children are . . ." 2. Complete the table below by multiplying the number of people times the fraction of t h e m in poverty to learn the number in poverty. Persons 65 and Older Living in Poverty Year

Number of People (thousands)

Fraction in Poverty

1970

19,973

V4

1980

22,250

3

1990

31,078

3

1992

32,284

13

Number in Poverty

/20

/25 /100

Data from Statistical Abstract of the United States, 1994. 3. Discussion. Possible questions include the following: Do you t h i n k it is acceptable to have elderly people in our society living in poverty? Do you t h i n k our government (taxpayers) h a s an obligation to m a k e sure the elderly are cared for?

58 / UNIT 4 4. Back to the Biolsis—the middle-class family of six from New York City. Their monthly budget is $1,800, and they allocate their money as follows: food

V3

rent

V6

savings

1

loans

4

telephone

1

miscellaneous

7

/15

/30 /15 /30

Data from The New York Times, October 3, 1989. Calculate how many dollars they spend on each item. 5. A study was done in Michigan to determine whether federally funded preschool programs are worthwhile. They studied 122 three- and four-year-olds, half of whom had a preschool program and half of whom did not, and followed up on t h e m at age 27. Here is w h a t the researchers discovered: Results of Michigan Preschool Study with Poor Children

Receiving welfare Had been arrested 5 or more times Had out-of-wedlock births Earned more than $2,000 per month Had graduated from high school Owned their own home

61 in Program

61 Not in Program

Fraction

Fraction

Number

3

4

2

V3

/5

/25

3

/5

3

/l0

7

/io

%

/5

% 2

/25

V2 3

/25

Data adapted from The New York Times, December 30, 1994.

Number

LESSON 4.4: MULTIPLYING FRACTIONS / 59 Complete the "number" columns by multiplying the fractions by the total number of people (61). 6. Discussion. Possible questions include the following: Based on this study, would you be in favor of a government- (taxpayer-) funded preschool for children below the poverty level? Why or why not?

60 / UNIT 4

U N I T 4 LIBRARY RESEARCH A C T I V I T Y (ABOUT 80 MINUTES)

Divide into groups of two or three students. Pick one of the research questions below for each group. Use the guide to conduct your research. Reconvene the whole class and have a spokesperson from each group share results.

Researchh Questionnss 1. What is the relationship between poverty and gender?

2. What is the relationship between poverty and race?

3. What are some of the factors relating to wealth: How many people are wealthy, whom do they tend to be, what do they do, and so on?

4. What is the relationship between poverty and where you live in this country—city, state, region?

Assessmentnt For this activity, you will be assessed on the following: seriousness in approach to library work (5%) quality of statements based on data (20%) quality of application of math skills (30%) quality of revised statements (20%) quality of final organization and presentation (20%) insight of concluding observation (5%)

From Civic Mathematics.

© 1996. Teacher Ideas Press. (800) 237-6124.

UNIT 4 LIBRARY RESEARCH GUIDE / 61

U N I T 4 LIBRARY RESEARCH GUIDE Researchch Qestionionn 1. Locate a source t h a t contains information on your question. Write down the title, author, publisher, date of publication.

2. Write down, in complete sentences, five to 10 s t a t e m e n t s of fact based on the data. For example: "In Alabama, 20 percent of people were living below the poverty level in 1990."

3. Perform at least one of the following m a t h skills on each statement: changing fractions to percentages changing percentages to fractions changing fractions to decimals changing decimals to fractions changing decimals to percentages changing percentages to decimals comparing fractions adding fractions subtracting fractions multiplying fractions For example, g i v e n t h e s t a t e m e n t above, you might say, "In Alabama in 1990 about V5 of the people lived below the poverty level."

From Civic Mathematics. © 1996. Teacher Ideas Press. (800) 237-6124.

62 / UNIT 4 4. Organize your new statements into an orderly, logical, and interesting whole, so that they make sense for presenting to the class.

5. Make at least one concluding observation, either factual or reflecting an opinion shared by the whole group, based on your data. This concluding observation should relate to an issue covered during this unit, from the following list: minimum wage earners income brackets in the United States food as percentage of expenditures in American family middle-class family finances poverty levels in United States children in poverty federally funded preschool programs for poor children

From Civic Mathematics.

© 1996. Teacher Ideas Press. (800) 237-6124.

UNIT 5 INTRODUCTION Social-Context Topics Covered Budgeting for groceries on food stamps Working while on public assistance

Mathematicalal SSkillssCoveredede Expressions and sentences Formulas Equations

Discussion n This unit explores the life of a fictitious person on social services (AFDC): both the problems and relative advantages. Students are urged to think about these social programs critically and ponder solutions to program shortfalls after first getting the numbers clearly laid out. The next unit explores how these programs are paid for. The algebra skills used here are typically covered late in a standard course, but they become such useful tools in this context that students find it easier to learn them. They are further employed in unit 6.

63

64 / UNIT 5

LESSON 5 . 1 : EXPRESSIONS AND SENTENCES • Teach expressions and sentences • Social-context activities (about 40 minutes) Meet Sonja. She has two children, ages four and six. The father of Sonja's children is absent, so that makes her a single parent. Sonja stays home with her children—she doesn't have a job—and they are supported by AFDC (Aid to Families with Dependent Children), a federally (taxpayer) funded program. Her monthly income consists of cash ($700) and food stamps ($200). 1. Sonja has to buy the following food items for this week and wants to figure out ahead of time how much it will cost. For each item, make up an algebraic expression and then evaluate it to find the cost. Sonja's Food Shopping Food Item

Unit Cost

Amount Needed

Algebraic Expression

Total Cost

Flour

$1.89 per 5 lb. bag

2 bags

2x

$3.78

Bread

$1.09 per loaf

3 loaves

Butter

$.80 per stick

4 sticks

Tuna

$1.15 per can

6 cans

Sugar

$.41 per pound

3 lbs.

Hamburger

$1.50 per pound

5 lbs.

Eggs

$.93 per dozen

3 dozen

Milk

$1.39 per half-gallon

4 gallons

Cheese

$3.40 per pound

2 pounds

Apples

$.76 per pound

10 pounds

Peanut butter

$1.88 per pound

2 pounds

Corn

$.50 per can

6 cans

Potatoes

$.31 per pound

5 pounds

Green beans

$.50 per can

6 cans Total:

LESSON 5.1: EXPRESSIONS AND SENTENCES / 65 2. Sonja wonders if this is good long-term budgeting: about $65 per week. Each week she has to spend an additional $7 or so on food not on her list (lettuce, oil, and so on), which comes to $28 per month. So for a month (four weeks), if we let x = her grocery bill per week, she can expect to spend 4x + 28. How much is that at $65 per week? Remember, her food stamp budget is $200. Is she overspending? Calculate food budgets for the following weekly amounts: Sonja's Monthly Grocery Bill Weekly Bill (x)

Monthly Bill (4x + 28)

57 55 53 51 49 47 45 43 41

How much can she spend a week? 3. Discussion. Possible questions include the following: What is the purpose of giving someone food stamps instead of just that much more cash? There are certain grocery items you can't buy with food stamps. What purchases do you think should not be allowed with food stamps? Why? 4. Sonja needs to eliminate $22 from her week's shopping list. Come up with a new shopping list within her food stamp budget, causing as little hardship as possible on herself and her children. 5. Discussion. A possible question is the following: Algebra really is useful in these situations. Does it make sense to you? Why or why not?

66 / UNIT 5

LESSON 5.2: FORMULAS • Teach formulas • Social-context activities (about 30 minutes) • Sonja's food stamp allotment might have been figured as follows: lx adult food cost + 2x child food cost = food stamps or l a + 2c = FS or a + 2c = FS with a = $75 and c = $62.50. An adult gets about $75 worth of food a month, and a child gets about $62.50 worth. 1. Using the formula a + c = FS, and a = $75 and c = $62.50, calculate the food stamp budgets for the following families: Family

Formula

Food Stamps

mother, father, 1 child

2a + c = FS

$212.50

father, 3 children mother, father, 2 children mother, father, 7 children mother, 5 children

2. Sonja wants to bake a turkey, figuring it is relatively inexpensive and she can use the leftovers in various dishes. The formula for baking a turkey is t = 15w + 10 where t = time and w = weight. This means the baking time is 15 minutes for each pound, plus 10 minutes. She is at the store and will be home by 1:00 P.M. She wants the turkey done by 6:00 P.M.—that's 300 minutes of baking time.

LESSON 5.2: FORMULAS / 67 Calculate the missing column and help Sonja pick out the biggest turkey she h a s time to bake. Turkey Baking Times Weight of Turkey

Minutes Required to Bake

10 pounds 11 pounds 12 pounds 13 pounds 14 pounds 15 pounds 16 pounds 17 pounds 18 pounds 19 pounds 20 pounds

3. Discussion. Possible questions include the following: If someone asked you how to calculate how much a family gets in food stamps, how would you explain it? For the 10-pound turkey, did you calculate "15w" in your head using your powers of 10 skills?

68 / UNIT 5

LESSON 5.3: EQUATIONS • Teach solving equations • Social-context activities (about 30 minutes) You could use equation-solving skills to calculate what Sonja can spend per month on food and the weight of the turkey she can buy. In this lesson you will continue to work with the kinds of problems Sonja faces, as well as solve equations. 1. Now that you know how to solve equations, let's revisit Sonja's food allowance. She can only spend $200 a month, so 4x + 28 = 200 First, let's say she eliminates the $7 a week for incidentals, to save money. The equation becomes 4x = 200 Solve for x and you have her weekly budget! Now find the weekly budgets for all these other families, using the rules of algebra. Be sure to round! Family

Equation

Solution

Mother, father, 1 child

4x = 212.50

$

Father, 3 children

4x = 262.50

$

Mother, father, 2 children

4x = 275

$

Mother, father, 7 children

4x = 587.50

$

Mother, 5 children

4x = 387.50

$

2. For cooking the turkey, you just added 10 minutes onto what you calculated, so let's use t = 15w She has 300 minutes, so 300 = 15w Solve for w, and you know what weight turkey she can get.

LESSON 5.3: EQUATIONS / 69 Calculate some maximum weights of meat, given cooking time, using the rules of algebra.

Food

Minutes per Pound

Maximum Cooking Time

Formula

Beef

35

120 minutes

35x = 120

Pork

30

90 minutes

Chicken

15

60 minutes

Ham

20

180 minutes

Lamb

18

90 minutes

Maximum Weight

3. If Sonja gets a part-time job working at home, she must report her earnings and thus receive that much less per month in her cash allowance. Remember, she gets $700 per month total. cash + earnings = $700 Her job pays varying amounts each month. Complete this table, using the rules of algebra to calculate what she will get in cash each month (x). Earnings

Formula

Solution (cash)

$100

x + 1 0 0 = 700

$600

$87 $125

$98 $55 $136

4. Discussion. Possible questions include the following: Did Sonja raise her income by working part-time at home? Why would she want to work? How would you design an AFDC program that encourages people to work?

70 / UNIT 5

U N I T 5 LIBRARY RESEARCH A C T I V I T Y (ABOUT 80 MINUTES)

Divide into groups of two or three students. Pick one of the research questions below for each group. Use the guide to conduct your research. Reconvene the whole class and have a spokesperson from each group share results.

Researchh Questionsns 1. How many people have gotten AFDC over the years?

2. What kinds of family groups get AFDC in what proportions?

3. What other kinds of public assistance do people below the poverty level get? How much do they get?

4. Have any programs been created to help people get off public assistance? How do they work?

Assessmenttnt For this activity, you will be assessed on the following: seriousness in approach to library work (5%) quality of statements based on data (20%) quality of use of algebra (40%) quality of presentation (30%) insight of concluding observation (5%)

From Civic Mathematics.

© 1996. Teacher Ideas Press. (800) 237-6124.

UNIT 5 LIBRARY RESEARCH GUIDE / 71

U N I T 5 LIBRARY RESEARCH GUIDE Researchh Qestionion 1. Locate a source that contains information on your question. Write down the title, author, publisher, date of publication.

2. Write down 5 to 10 statements of fact based on the data. For example: "A woman in Chicago got a job earning $12,480 per year and stopped getting public assistance, but she is still $3,000 below the poverty level."

3. Find one statement or group of statements to which you can apply algebra, expressions, or formulas; define a variable; write an equation; and explain the equation. For example: earnings + cash deficit = poverty level $12,480 + x = $15,480 where x = cash deficit. Explain how to solve the equation.

4. Make at least one concluding observation, either factual or reflecting an opinion shared by the whole group, based on your data. This concluding observation should relate to an issue covered during this unit: living on food stamps working while on public assistance

From Civic Mathematics. © 1996. Teacher Ideas Press. (800) 237-6124.

UNIT 6 INTRODUCTION Social-Contextxtopics

Coverededd

Government outlays for public aid and other budget items Where government money comes from Public aid programs as budget items Percentage of income going to taxes, by level and by family unit State taxes Home mortgage, car, credit card debt National debt

Mathematicalal SSkillss Coveeredd Finding percent of number Finding what percent one number is of another Finding number when percent of it is known Interest

Discussion n This unit is devoted to funding of public assistance programs. It will explore what levels of government finance the programs (federal, state, local), where the tax dollars come from, and the cost of the programs relative to other government expenditures. Students will learn the numbers behind the arguments of this much-talked-about social issue. The math for unit 6 is extremely useful in analyzing data and probably easier to grasp than that of unit 5. It uses algebra skills, sometimes so stated and sometimes not.

72

LESSON 6.1: FINDING THE PERCENTAGE OF A NUMBER / 73

LESSON 6 . 1 : FINDING THE PERCENTAGE OF A NUMBER • Teach finding percentage of a number using r x b = p (rate x base = percent) • Social-context activities (about 40 minutes) In this lesson you will see how federal, state, and local budgets are spent, specifically, how much of these budgets is devoted to public assistance programs. 1. Complete the table below to see how much of the federal budget h a s been devoted to public aid, which includes AFDC, food stamps, and other public assistance. Federal Expenditures on Public Aid Year

Total Budget (millions)

Percentage on Public Aid

1980

$ 590,947

8%

1990

$1,252,705

7%

1991

$1,323,793

9%

$ on Public Aid (millions)

Data from Statistical Abstract of the United States, 1994. 2. Complete a similar table below to see how much of state and local budgets h a s been devoted to public aid. State and Local Expenditures on Public Aid Year

Total Budget (millions)

Percentage on Public Aid

1980

$ 451,537

5%

1990

$1,032,115

5%

1991

$1,080,262

6%

$ on Public Aid (millions)

Data from Statistical Abstract of the United States, 1994. 3. Discussion. Possible questions include the following: W h a t did you learn from the data t h a t you did not know before? When you have heard people arguing about how to cut the budget by reducing money for public aid, did you know they were talking about 5 percent to 9 percent of the budget?

74 / UNIT 6 4. Let's compare public aid spending to some other federal budget items. Compute below the amount of money spent on each item. Total Federal Budget: $1,323,793 million Budget Item

Percentage

Defense

21%

Interest on debt

23%

Social Security

20%

NASA

$ Million

1%

Data from Statistical Abstract of the United States, 1994.

5. Discussion. Possible questions include the following: Is there anything surprising to you about the budget items? Which budget expense do you consider the most urgent to reduce, if you believe in reducing federal expenditures? 6. You have just been given control over a new country on an isolated island in the Pacific Ocean. You have $900,000 million (that's actually $900 billion!) to allocate the first year. You're lucky—you have no national debt. Decide how you would divide it. Be sure to check your totals at the end of your work. Budget Item

Percentage of Budget

$ Million

100%

$900,000 million

Judicial (including prisons) National defense International affairs Public aid Social Security Education Natural resources Energy Agriculture Science (including space research)

7. Compare priorities throughout the class.

LESSON 6.2: FINDING WHAT PERCENTAGE ONE NUMBER IS OF ANOTHER / 75

LESSON 6.2: FINDING WHAT PERCENTAGE ONE NUMBER IS OF ANOTHER • Teach finding w h a t percentage one number is of another • Social-context activities (about 40 minutes) Where does the money for the government's many programs come from? This lesson will help you answer t h a t question. 1. Make a third column in the table below, computing w h a t percentage each source is out of the total revenues of $1,259,393 million (more t h a n a trillion dollars). Partial List of Federal Receipts Source

$ Millions

Individual income taxes

$476,465

Corporation income taxes

Percentage of Total

100,270 10,397

Interest earnings Insurance trust revenue (Social Security) Postal Service

404,562 45,158

Data from Statistical Abstract of the United States, 1994. 2. Make a third column in the table below, calculating w h a t percentage each source is of the total s t a t e and local revenues of $1,185,191 million. Partial List of State and Local Receipts Source

$ Million

Federal government aid

$179,184

Individual income taxes

115,170

Property taxes

178,536

Corporation income taxes Sales taxes

Percentage of Total

23,595 196,112

Data from Statistical Abstract of the United States, 1994. 3. Combine individual income taxes and property taxes, and determine w h a t percentage t h a t is of the total.

76 / UNIT 6 4. Discussion. Possible questions include the following: Do you think ordinary taxpayers' share of the state, local, and federal government budgets is too large, too small, or j u s t right? Why? Do you t h i n k corporations' share is too large, too small, or j u s t right? Why? 5. Finally, let's see how the government money spent on low-income persons breaks down, out of a total of $289,880 million in benefits granted to low-income persons through various programs. Complete the third column. Partial List of Public Aid Expenses Expense

$ Million

Medical care

$134,032

AFDC

24,293

Foster care

4,170

Food stamps

24,918

School lunch program

3,895

Nutrition for elderly

659

Housing

20,535

Education

16,037

Preschool programs

2,753

Jobs and training

5,500

Percentage of Total

Data from Statistical Abstract of the United States, 1994. 6. Discussion. Possible questions include the following: Are you surprised t h a t medical care is such a huge chunk of public aid? W h a t else is surprising about this list? If you could reallocate this money, in w h a t order would you put this list, from most i m p o r t a n t to least important? If you had to eliminate two items, which would you eliminate?

LESSON 6.3: FINDING A NUMBER WHEN PERCENTAGE OF IT IS KNOWN / 77

LESSON 6.3: FINDING A NUMBER WHEN PERCENTAGE OF IT IS KNOWN • Teach finding number when percentage of it is known • Social-context activities (about 40 minutes) Let's see in this lesson how the income tax burden is shared. 1. Calculate the third column in the table below, the "adjusted gross income" of taxpayers paying the given amount at the given percentage rate. Amount of Federal Income Tax Paid Amount of Tax

Percentage of Gross

$ 1,000

7.1%

$ 2,000

8.7%

$ 2,600

9.4%

$ 3,700

10.6%

$ 7,700

12.8%

$13,200

15.4%

$68,500

23.6%

$641,300

26.3%

Adjusted Gross Income

Data from Statistical Abstract of the United States, 1994. 2. Discussion. A possible question is the following: Do the data seem fair to you—that the higher the income, the higher percentage paid in taxes? If not, how do you think it should be set up?

78 / UNIT 6 3. Compute the last column in the table below—each family type's average income. Portion of Annual Income Going to Taxes Type of Family

$ Going to Taxes

Percentage

Husband and wife only

$3,997

12%

With oldest child under 6

$4,176

11%

With oldest child 6-17

$5,214

12%

With oldest child 18 or over

$4,887

11%

Single parent, at least 1 child under 18

$724

Total Income

3%

Data from Statistical Abstract of the United States, 1994. 4. Discussion. Possible questions include the following: Does it seem fair to you, the way taxes break down when looking at family units? Of the t h r e e kinds of percentage problems—find a percentage of a number, find w h a t percentage one number is of another, and find a number when a percentage of it is known—which is the most useful? Why? 5. Remember, states devote some of their budgets to public aid. Let's t a k e a look at the tax revenues of some richer states and some poorer states. State Tax Collections State

Percentage from Income Tax

Amount from Income Tax (millions)

Alabama

29%

$1,234

Arkansas

31%

$850

Mississippi

18%

$440

California

37%

$17,030

New York

50%

$14,913

Pennsylvania

29%

$4,689

Total Tax Revenues (millions)

Data from Statistical Abstract of the United States, 1994. 6. Discussion. A possible question is the following: Why would the wealthier states collect higher percentages of their revenues from individual income taxes?

LESSON 6.4: INTEREST / 79

LESSON 6.4: INTEREST • Teach interest (i = prt) • Social-context activities (about 40 minutes) When people do not have enough cash for what they want or need, it is time for credit: credit cards, personal loans, home mortgage loans. Remember Sonja? She now has a job that is secure enough that she could qualify for a home mortgage loan. She needs to decide whether it will save her money to stop renting and buy a home. 1. Sonja pays $600 a month rent. How much will that add up to in 30 years? 2. The average price of a single-family house in the United States is $106,800. The current home mortgage interest rate is 7.36 percent. If Sonja got a loan for that amount for 30 years, how much would she end up paying back (interest plus principal)? Based on comparing those figures, should Sonja buy a house? 3. Discussion. Possible questions include the following: What other factors should Sonja consider? What are other costs involved in owning a home, besides the mortgage payments? 4. The cost of borrowing money to buy a car has changed over the years. Complete the last columns to compare. New Car Rates Year

Cost of Car

Rate

Time

1980

$ 7,500

14.82%

3 years

1985

$ 9,000

11.98%

3 years

1990

$13,300

12.54%

3 years

1993

$16,500

9.48%

3 years

Data from Statistical Abstract of the United States, 1994.

$ Interest

Total Cost

80 / UNIT 6 New Car Rates Year

Cost of Car

Rate

Time

1980

$ 7,500

14.82%

54 months

1985

$ 9,000

11.98%

54 months

1990

$13,300

12.54%

54 months

1993

$16,500

9.48%

54 months

$ Interest

Total Cost

$ Interest

Total Cost

Data from Statistical Abstract of the United States, 1994. Used Car Rates Year

Cost of Car

Rate

Time

1980

$2,500

19.10%

2 years

1985

$3,000

17.59%

18 months

1990

$4,300

15.99%

30 months

1993

$6,000

12.79%

3 years

Data from Statistical Abstract of the United States, 1994. 5. Sonja j u s t got a credit card. Credit card companies give you their r a t e s either by the month or by the year. You can compare either by multiplying or by dividing by 12. For the purposes of figuring out Sonja's credit expenses for a year, we are going to look at her charges each month. Complete the table below, given t h a t her credit card company charges 16.8 percent per year. Sonja's Charges for One Year Month

Charges

Rate

January

$58.95

1.4%

February

$65.19

1.4%

March

$15.00

1.4%

April

$123.48

1.4%

May

$35.15

1.4%

June

$28.00

1.4%

July

$257.90

1.4%

$0

1.4%

$465.20

1.4%

October

$21.65

1.4%

November

$37.50

1.4%

December

$357.00

1.4%

August September

Interest If She Pays Late

Total:

LESSON 6.4: INTEREST / 81 6. The national debt is a hot topic among politicians. Try to get a feel for the size of it by computing just the interest on the debt at a rate of 8 percent. Interest on National Debt Year

Debt

Rate

1990

$3,226 billion

8%

1991

$3,683 billion

8%

1992

$4,083 billion

8%

1993

$4,351 billion

8%

1994

$4,676 billion

8%

Time

$ Interest

Data from Statistical Abstract of the United States, 1994. 7. How much would you have to earn each year if you worked 40 years to earn as much as the interest on the 1994 national debt? What is that per month? Per week? Per day? 8. Discussion. Possible questions include the following: What do you think about people getting mortgage loans? Car loans? Credit card debts? What do you think about the national debt? It has increased steadily—in 1945 it was $260,123 million.

82 / UNIT 6

U N I T 6 LIBRARY RESEARCH A C T I V I T Y (ABOUT 80 MINUTES)

Divide into groups of two or three students. Each group should pick one of the research questions below. Use the guide to conduct your research. Reconvene the whole class and have a spokesperson from each group share results.

Researchh Questionsns 1. How do other countries compare with the United States in their systems of public assistance?

2. Does any of the revenue from lottery tickets fund public assistance? If so, how much?

3. What kinds of loans do individuals in the United States have? How much money is tied up in loans?

4. How is federal money for job training programs allocated—how much for what kinds of programs?

Assessmenntt For this activity, you will be assessed on the following: seriousness in approach to library work (5%) quality of statements based on data (20%) quality of application of math skills to statements (30%) quality of revised statements (20%) quality of final organization and presentation (20%) insight of concluding observation (5%)

From Civic Mathematics.cs© 1996. Teacher Ideas Press. (800) 237-6124...

UNIT 6 LIBRARY RESEARCH GUIDE / 83

U N I T 6 LIBRARY RESEARCH GUIDE Researchh Questionon 1. Write down, in complete sentences, 5 to 10 statements of fact based on the data. For example: "In 1992, of the 2,166,667 people getting job training, there were 65,000 people in the Job Corps."

2. Perform at least one of each of the following math skills on each of the above statements: finding the percentage of a number finding what percentage one number is of another finding the number when a percentage of it is known the interest formula For example, given the statement above, you might say, "In 1992, Job Corps trainees made up 3 percent of people getting job training from federal public assistance."

3. Organize your new statements into an orderly, logical, interesting whole, so that they make sense for presenting to the class.

From Civic Mathematics. © 1996. Teacher Ideas Press. (800) 237-6124.

84 / UNIT 6 Make at least one concluding observation, either factual or reflecting an opinion nn shared by the group, based on your data. This concluding observation should relate to an issue covered during this unit, from the following list: government expenditures for public aid government sources of revenue public aid programs income taxes loans the national debt

5. State which of the math skills you worked with in this unit was the most useful in the library research activity and why.

From Civic Mathematics. © 1996. Teacher Ideas Press. (800) 237-6124.

Third Quarter

The Environment Skills Covered: • Parallel and perpendicular lines • Perimeter • Scale • Area • Circumference • Volume of rectangular solids • Volume of cylinders • Making bar graphs • Making line graphs • Making circle graphs • Making tables

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UNIT 7 INTRODUCTION Social-ContextxtTopics

Coveredd

Rain forests Acid rain Population density Farming chemicals The death of the Aral Sea

Mathematicalal SSkillssCovereded Perimeter and circumference Area Scale Conversion of units

Discussionnn To introduce the quarter on the environment, basic plane geometry comes into play, applied in several practical and informative ways. Students will begin with gaining an understanding of how much rain forest there is in the world and how much it has been depleted, then move on to other problems with land and water use and misuse.

87

88 / UNIT 7

LESSON 7 . 1 : PERIMETER AND CIRCUMFERENCE • Teach finding perimeters of polygons and circumference • Social-context activities (about 30 minutes) There is much attention paid to the rain forests these days—saving the rain forests m e a n s saving a magnificent ecosystem rich in plant and animal diversity. Logging—for wood or to clear land to raise animals for meat—has led to the destruction of the rain forest at a n alarming r a t e . This lesson will give students an idea of the scale of t h a t depletion, using perimeter and circumference to do so. 1. Figure out w h a t the dimensions of the rain forest areas would be, if they were collected into a n approximate square of the perimeters given for 1975 and projected for the year 2000. Rain Forest Land Region West Africa

Perimeter 1975

Square Dimensions

Perimeter 2000

930 mi.

658 mi.

Central Africa

3,241 mi.

3,202 mi.

Eastern Islands

3,260 mi.

3,034 mi.

Asian continent

2,711 mi.

2,410 mi.

South America

5,700 mi.

5,371 mi.

Central America

2,498 mi.

2,397 mi.

Square Dimensions

Total

Data from An Introduction to Tropical Rain Forests, 1990. 2. To give you a n idea of these relative sizes, here are the square dimensions of some regions you are more familiar with. Calculate their perimeters. Sizes of Familiar Regions Region

Side, If Square

United States

1,732 mi.

Canada

1,875 mi.

Texas

517 mi.

Alaska

784 mi.

Perimeter

Data from Statistical Abstract of the United States, 1994.

LESSON 7.1: PERIMETER AND CIRCUMFERENCE / 89 3. Using C = n d, calculate the diameters of the sections of rain forest if they were gathered into a round area, for 1975 and 2000. Rain Forest Land Region West Africa

Circumference 1975

Diameter

Circumference 2000

823 mi.

583 mi.

Central Africa

2,871 mi.

2,839 mi.

Eastern Islands

2,888 mi.

2,688 mi.

Asian Continent

2,402 mi.

2,135 mi.

South America

5,051 mi.

4,759 mi.

Central America

2,213 mi.

2,124 mi.

Diameter

4. Discussion. Possible questions include the following: Do you know what you can do to avoid contributing to the destruction of the rain forest? Notice that the perimeter of a square rain forest area is different from the circumference of the same rain forest—how? Do you know why? (You will learn more about this when you study area.)

90 / UNIT 7

LESSON 7.2: AREAS OF POLYGONS • Teach formulas for area of rectangles and circles • Social-context activities (about 40 minutes) In this lesson we will explore acid rain and its effect on our inland waters, as well as the effects of population density and farming chemicals on waters. 1. A major cause of acid rain is sulfur dioxide emissions, which come primarily from fuel combustion. According to The New York Times (March 22, 1993), a 1990 governm e n t study found high acidity levels in 4.2 percent of lakes and 3 percent of s t r e a m s in the United States. Calculate the areas and dimensions of affected water, given the dimensions below. Dimensions given are approximately what they would be if all the water were gathered into a rectangle. You will need to do the same for a square and a circle.

Body of Water Dimensions Lakes

150 mi. x 372 mi.

Streams

150 mi. x 80 mi.

Area

Area Affected

Square Dimension

Diameter If Round

Data from Statistical Abstract of the United States, 1994. 2. Overpopulation creates problems for many reasons: shortages of n a t u r a l resources, more waste produced, more water and air pollution. This exercise will give you a feel for population density. The population divided by the n u m b e r of square miles available will give the number of people per square mile. Calculate the missing columns below. Region

Rectangular Dimensions

Population

United States

3,000 mi. x 1,244 mi.

257,908,000

New York

200 mi. x 270 mi.

18,197,000

Iowa

200 mi. x 280 mi.

2,814,000

Texas

500 mi. x 535 mi.

18,031,000

Area (square miles)

People per Square Mile

Data from Statistical Abstract of the United States, 1994. 3. Chemicals used in farming—fertilizer, herbicides, and pesticides—sometimes m a k e their way into our food and waterways. Some of these have been shown to cause cancer. A farmer in Iowa applies an average of 1 pound of herbicides and pesticides per 1,556 square feet of field. Complete the table below, figuring out about how much each field on this farm in Iowa will require.

LESSON 7.2: AREAS OF POLYGONS / 91

Field

Dimensions

North field

300 ft. x 250 ft.

South field

600 ft. x 400 ft.

East field

200 ft. x 700 ft.

West field

350 ft. x 500 ft.

Area

Chemicals Needed (divide by 1,556)

4. You have decided to eat only food that contains no chemicals from herbicides or pesticides, and the best way to do that is to grow your own garden. You also want a pond nearby, and you're going to put them both in your backyard, which measures 75 feet x 200 feet. In groups of two or three students, draw your backyard with a rectangular garden and a circular pond, calculating all areas and labeling all dimensions. 5. Discussion. Possible questions include the following: Does anything surprise you about how much of the United States is covered by water? Explain the difference between area and perimeter. Are you surprised at the results of the acid rain study done by the government? Why? What do you think are some of the problems caused by a growing population? Are you concerned about herbicide and pesticide residues in your food? 6. Hand out and explain homework.

92 / UNIT 7

U N I T 7, LESSON 7.2 HOMEWORK Land area is usually measured in acres. 1 square mile = 640 acres So, to go from acres to square miles, divide by 640. To go from square miles to acres, multiply by 640. 1. Calculate t h e following: Area in Sq. Mi.

State New York

Area in Acres

53,989

New Jersey

8,215

Rhode Island

1,231

Iowa

56,276 158,869

California

Data from Statistical Abstract of the United States, 1994. 2. Leech Lake, in Minnesota (a place I know you'd love to go swimming) is about 13 miles X 13 miles. How many acres is t h a t ?

3. Calculate the acreage of the following lakes, given their dimensions: Lake

Dimensions

Great Salt Lake, UT

43 mi. x 43 mi.

Lake Okeechobee, FL

26 mi. x 26 mi.

Lake Tahoe, CA/NV

14 mi. x 14 mi.

Yellowstone Lake, WY

11 mi. x 11 mi.

Area in Sq. Mi.

Acres

Data from Statistical Abstract of the United States, 1994.

From Civic Mathematics. © 1996. Teacher Ideas Press. (800) 237-6124.

LESSON 7.3: SCALE / 93

LESSON 7.3: SCALE • Teach scale • Social-context activities (about 40 minutes) 1. Go over Lesson 7.2 homework. You have decided to simulate the death of a lake, scaled down to a smaller size. The Aral Sea, in the former Soviet Union, has shrunk from 19,300 square miles to 11,580 square miles. This is the result of draining the lake for irrigation of croplands. As the lake disappears, it leaves dry, salt-encrusted wastelands and water of increasing salinity. The fishing industry there is disappearing, and the dust from the drying lake leads to a high rate of throat cancer, among other illnesses, as well as high infant mortality. Winters near the lake are colder and summers hotter than they used to be. (Case study from Environmental Science, 1992.) What would the dimensions of a 19,300-square-mile lake be if it were square? 2. Divide into groups of two or three. Figure a scale of miles to feet, so that you could create this lake on your school grounds. 3. Figure a scale of feet to inches, so you can draw a picture of your plan. 4. Draw the lake before drainage and draw it again, possibly inside the first drawing, after drainage. 5. Discussion. Possible questions include the following: Would you have been able to predict the problems encountered in draining the Aral Sea? If you really wanted to see how such an ecosystem would be affected by drainage, how could you do this project at your school? (Allow plenty of time—years if necessary!) Think of another kind of simulation you could do, relating to the environment and water and using the math skill of scale.

94 / UNIT 7

U N I T 7 LIBRARY RESEARCH A C T I V I T Y (ABOUT 80 MINUTES)

Divide into groups of two or three students. Use the guide to conduct your research and create a report. Reconvene the whole class and have a spokesperson from each group share results.

Research

Questions: See Unit 7 Library Research

Guide on p. 95

Assessmentnt For this activity, you will be assessed on the following: seriousness in approach to library work (5%) thoroughness in gathering information about body of water (20%) quality of math leading to scale drawing (30%) neatness of scale drawing (20%) quality of final statements for presentation (20%) insight of concluding observation (5%)

From Civic Mathematics. © 1996. Teacher Ideas Press. (800) 237-6124.

UNIT 7 LIBRARY RESEARCH GUIDE / 95

U N I T 7 LIBRARY RESEARCH GUIDE Body of

Water

1. Pick a body of water in the United States to research—a river or lake—and write down everything you can find about its dimensionssand any information about itss health—whether polluted and how so, whether overused, and so on.

2. Create a scale drawing of your body of water.

3. Select three to five statements from (1) to present to the whole class along with the

drawing, being sure to use the following math tools at least once:

perimeter/circumference area scale

4. Organize your statements from (1) and (3) into an effective presentation for the class that will describe your body of water and its health.

5. Make at least one concluding observation, either factual or reflecting an opinion shared by the whole group, based on your research and relating to environmental issues.

From Civic Mathematics.cs© 1996. Teacher Ideas Press. (800) 237-61244.

UNIT 8 INTRODUCTION Social-ContextxtTopicscsCovereded Garbage generated Composting Packaging Landfills MathematicalallSkillslsCoverededd Volume of rectangular solids Volume of cylinders

Discussion n The social-context topics in this unit will focus on solid waste—how much we generate and how to deal with it. Volume is the most essential mathematical skill in approaching solid waste management—it would be impossible to understand the solid waste problem without the concept of volume.

96

LESSON 8.1: VOLUME OF RECTANGULAR SOLIDS / 97

LESSON 8 . 1 : VOLUME OF RECTANGULAR SOLIDS • Teach V = lwh • Social-context activities (about 40 minutes) In this lesson we will look closely at our own garbage—how much we generate and where it goes. 1. A typical garbage bag is 3 feet X 2 feet X IV2 feet. What is its volume? The average weight of a bag of household garbage is 18 pounds. How many pounds in each cubic foot? So for each cubic foot, multiply by 2 to get pounds. Or divide weight in pounds by 2 to get cubic feet. Complete the table below, calculating the volume of the garbage generated. Solid Waste Generated in United States Year

Pounds per Person per Day

Volume

1960

2.66

1.33 cubic feet

1970

3.27

1980

3.65

1990

4.30

Data from Statistical Abstract of the United States, 1994. 2. Discussion. Possible questions include the following: What has been the trend in amount of garbage generated? How would you explain the increase? What are some ways to cut down on the amount of garbage we generate? 3. If you generate 4.3 pounds of garbage per day, how much is that per year? What would be its volume? In as close to a cube as possible, what would its dimensions be? Calculate to the nearest whole number. Estimate and calculate the volume of your classroom. How many people would it take to fill the classroom with garbage in a year? Estimate and calculate the volume of your bedroom. How many years would it take for you to fill your bedroom with your own garbage?

98 / UNIT 8 4. If you live in Madison, Wisconsin, you live in a city of 380,000 people. If each person generates 4.3 pounds of garbage per day for a year, what volume of landfill is needed to hold it? Household garbage will compress to about half its volume, so then how much space would you need? Calculate the dimensions, in feet, of the landfill, if it is as close to a cube as possible. Adjust those figures, because you cannot dig the landfill more than 30 feet deep, so one dimension must be 30 feet. 5. Discussion. Possible questions include the following: Roughly describe the size of the landfill needed for the residents of Madison for one year. Do you think you generate 4.3 pounds of garbage each day? What do you throw away? Think about your share of what the family throws away, what the school throws away, what restaurants you go to throw away.

LESSON 8.2: VOLUME OF CYLINDER / 99

LESSON 8.2: VOLUME OF CYLINDER • Teach V = 7rr 2 h • Social-context activities (about 40 minutes) Some of the garbage you generate could be composted—placed in conditions where microbes can break it down to a smaller and more useful (as fertilizer) mass. Much of a city's garbage could be dealt with in the same way, and many cities are attempting to do so. The composition of municipal solid waste (and yours, too) is as follows: Paper

39%

Yard waste

17%

Rubber, textiles, wood

12%

Metal

9%

Glass

8%

Plastic

8%

Food waste

7%

1. You can compost yard waste and food waste. What is the total percentage of those items? If you generate 1,570 pounds of garbage per year, how much is compostable? How many cubic feet of it will you have (i.e., its volume)? What size of cylindrical compost bin will handle your year's worth of garbage if its height is 5 feet? Draw your compost bin, indicating the dimensions (not necessarily to scale). 2. Figure out the diameters of the following cities' compost "bins," if they also compost 24 percent of their solid waste for one day: V = TI r 2 h, h = 5 feet

100 / UNIT 8

City

Population

Pounds of Waste per Day

Madison, Wl

195,000

838,500

New Haven, CT

124,000

Independence, MO

113,000

Abilene, TX

108,000

Washington, DC

585,000

Compostable (24%)

Volume (divide by 2)

r2 (divide by 3.14, then 5) r

d

201,240

100,620

6,409

160

80

Population figures from Statistical Abstract of the United States, 1994. 3. Discussion. Possible questions include the following: Do you t h i n k composting is a good idea for cities? Do you know what can be done with the other 76 percent of solid waste—paper, plastics, glass, metal, rubber, textiles, and wood? Do you think recycling should be m a n d a t e d by law? Do you t h i n k composting should be m a n d a t e d by law? 4. In 1987, a load of garbage was put on a barge in Islip, New York, to go to sea in search of a landfill space along the coast. It went to North Carolina, Alabama, Mississippi, Louisiana, Mexico, and Belize before r e t u r n i n g to New York, undumped. It was a crisis. W h a t was its volume, put in a cylindrical shape, if it was stacked to a height of 100 feet and was 200 feet in diameter? How many pounds did it weigh? (Remember, 1 cubic foot weighs about 2 pounds.) That's about what it was—actually, it weighed 3,200 tons. 5. Figure out w h a t you should buy, if you are trying to generate a m i n i m u m amount of waste—the two small cans or the one large can, in figure 8.1. V = 7tr h

Figure 8.1. First, figure the volumes of all the cans and compare. If you take a p a r t the metal containers for the two small cans and flatten them, you get the pieces shown in figure 8.2.

LESSON 8.2: VOLUME OF CYLINDER / 101

Figure 8.2. Compute t h e total metal area by adding the areas of all the pieces together. Now do the same for the large can in figure 8.3.

Figure 8.3. Considering efficient use of packaging, which should you buy? 6. Discussion. A possible question is the following: Besides buying products in larger packages, in w h a t other ways can you minimize w h a t you throw away?

102 / UNIT 8

UNIT 8 LIBRARY RESEARCH ACTIVITY (ABOUT 80 MINUTES)

Researchch Questionon In this activity, all groups will research how landfills are constructed and draw a scale drawing of a landfill for their selected city, computing all volumes and scales. Divide into groups of two or three students. Use the guide to conduct your research. Assessment ntt For this activity you will be assessed on the following: seriousness in approach to library work (10%) accuracy of mathematical calculations (75%) quality of final drawing (15%)

From Civic Mathematics.

© 1996. Teacher Ideas Press. (800) 237-6124.

UNIT 8 LIBRARY RESEARCH GUIDE / 103

UNIT 8 LIBRARY RESEARCH GUIDE City you will design a landfill for:

Population:

Information needed: One person generates 4.3 lbs. garbage per day. One cubic foot of garbage weighs 2 pounds. V of rectangular solid = lwh V of cylinder = n r h 71 = 3.14 1 year = 365 days A landfill is made up of parallel layers, which are as follows, beginning at the bottom: clay liner, 4 percent of total depth drainage pipe, 4 percent of total depth sand, 4 percent of total depth garbage, 75 percent of total depth gravel, 4 percent of total depth clay cap, 4 percent of total depth topsoil, 5 percent of total depth 1. Calculate the volume of garbage you will get from your city.

2. Notice that the garbage is 75 percent of the landfill, so calculate the total volume the landfill will need to be.

From Civic Mathematics. © 1996. Teacher Ideas Press. (800) 237-6124.

104 / UNIT 8 3. Using this new volume, calculate the volumes of each of the landfill components.

4. Decide on a scale for your drawing.

5. Calculate the dimensions of the layers of the landfill and the dimensions of the layers for your drawing.

6. Draw your landfill, labeling layers and dimensions.

From Civic Mathematics. © 1996. Teacher Ideas Press. (800) 237-6124.

UNIT 9 INTRODUCTION Social-ContextextopicspicsssCoceredvered Water use Land use Water as a resource Energy sources Oil spills World energy use Greenhouse gas emissions Recycling Pollution abatement spending Population growth Motor fuel consumption Costs of cleanup Hazardous waste Endangered species MathematicalcalSkillsillssCoveredered Tables Bar graphs Line graphs Circle graphs Discussiononn In studying these common ways of presenting data, we are free to cover any of the social-context topics related to the environment. This unit takes full advantage of that freedom. It offers a sampling of many aspects of the use of natural resources, population, pollution, and efforts to preserve our natural world. Mathematical skills from earlier in the course are incorporated in working with these graphic skills, especially fractions, decimals, and percents.

105

106 / UNIT 9

LESSON 9 . 1 : TABLES • Social-context activities (about 40 minutes) Students have been using data presented in tables—arrays of rows and columns of information. In this lesson they will learn the logic of tables by making their own—tables are really j u s t the most efficient way of organizing information. 1. Arrange t h e information from the p a r a g r a p h below into a simple table. The rows should be the type of water use and the column should be gallons used. You will need to label all the columns and give the table a title. A typical U.S. family of four uses a total of 356 gallons of water per day: 6 for cooking and drinking, 19 for dishes, 104 for flushing toilets, 83 for bathing, 40 for laundry, and 104 for lawns and outdoor work. 2. Do the same for the following p a r a g r a p h : The water on our planet is in the following forms: 97.6 percent in oceans; 1.9 percent in ice sheets and glaciers; .47 percent in groundwater; .02 percent in rivers, lakes, and inland seas; .01 percent in the atmosphere. (Data fromEnnvirnmentalntall Science, 1992.) 3. Do the same for the following p a r a g r a p h . This time you will need another column, because d a t a are given for two different years. We get our energy from several sources: coal, nuclear, oil, gas, and water. The world h a s changed a lot since 1970, with the use of these various sources changing as well. Coal use went from 46 percent of the energy generated in 1970 to 56 percent now. Nuclear energy use rose from 1.4 percent to 22.1 percent. Oil use dropped from 12 percent to 3.2 percent. Gas use decreased from 24.3 percent to 9.4 percent. Water use declined from 16.2 percent to 8.6 percent. (Data from StatisticalalAbstract of thee United States,s,1994.).) 4. Now let's m a k e sure you can go the other way. In complete sentences, write down the information from the table below in a p a r a g r a p h : Oil Spill Incidents In and Around U.S. Waters Year

Number of Incidents

Gallons Spilled

1973

11,054

15,289,188

1983

10,530

8,378,719

1993

8,790

1,503,862

Data from Statistical Abstract of the United States, 1994.

LESSON 9.1: TABLES / 107 5. Discussion. Possible questions include the following: Is it easier to understand data in a prose paragraph or in a table? Are you surprised at the family-of-four water use figures? If so, why? Hydroelectric (water) power is considered "clean" energy, unlike coal and nuclear, which create dangerous by-products. Why might nuclear power use be increasing so much, relative to the other sources? Are you surprised by the apparent trend in oil spills? Why?

108 / UNIT 9

LESSON 9.2: BAR GRAPHS • Teach m a k i n g and reading bar graphs • Social-context activities (about 40 minutes) Bar graphs are a n easy way to analyze d a t a t h a t have been organized into tables. 1. Make a b a r g r a p h from the following table: World Energy Consumption Region World

Kg per Person 2,026

United States

10,798

South America

1,080

Europe

4,650

Japan

4,754

Data from Statistical Abstract of the United States, 1994. 2. Discussion. Possible questions include the following: What would you conclude about U.S. energy use compared with t h a t of other countries? W h a t ways can you try to reduce energy use in your own life? 3. Make another b a r graph. This one will have two bars for each country—one for 1970 and one for 1991. World Energy Consumption Region

Kg per Person, 1970

World

1,208

2,026

United States

8,910

10,798

490

1,080

Europe

2,963

4,650

Japan

3,246

4,754

South America

Kg per Person, 1991

Data from Statistical Abstract of the United States, 1994.

LESSON 9.2: BAR GRAPHS / 109 4. Discussion. Possible questions include the following: W h a t facts are clear, from glancing at this bar graph? Why do you t h i n k energy use has gone up in all these areas? 5. Greenhouse gases are those gases t h a t can cause global warming, known as the greenhouse effect. These include carbon dioxide, m e t h a n e , and nitrous oxide. Carbon dioxide is the most abundant. Make another double b a r graph for the sources of CO2, 1985 and 1990, from the table below. Emissions of Carbon Dioxide Gases in the United States

Source

1985 Million Metric Tons Emitted

1990 Million Metric Tons Emitted

Energy sources

1,240.6

1,317.2

Cement production

9.6

8.8

Gas flaring

1.3

2.3

Other industrial

6.1

6.8

Other

15.3

16.6

Data from Statistical Abstract of the United States, 1994. 6. Discussion. Possible questions include the following: W h a t is one major difficulty in making a bar graph of this information? W h a t are two dangers of excess energy consumption? (Use the last two tables.) 7. H a n d out and explain homework.

110/UNIT 9

UNIT 9, LESSON 9.2 HOMEWORK 1. Make five s t a t e m e n t s based on the following b a r graph. Use complete sentences, and select w h a t you consider to be the most vital information. Percentage of Wastes Being Recycled

Data from Environmental Science, 1992.

2. Make a concluding observation, of fact or opinion or both, about the information in this b a r graph.

From Civic Mathematics. © 1996. Teacher Ideas Press. (800) 237-6124.

LESSON 9.3: LINE GRAPHS / 1 1 1

LESSON 9.3: LINE GRAPHS • Teach m a k i n g and reading line graphs • Social-context activities (about 40 minutes) 1. Go over Lesson 9.2 homework. 2. Make a line g r a p h from the following table: Spending on Pollution Abatement, 1975-1990 Year

Millions of Dollars

1975

28,424

1980

51,478

1985

70,941

1990

89,996

Data from Statistical Abstract of the United States, 1994. 3. Make a line g r a p h from the following table. This one should have two lines, one for federal and one for state and local. Spending on Pollution Abatement, 1975-1990 Year

Federal Spending (millions of dollars)

State and Local Spending (millions of dollars)

1975

432

1,752

1980

494

2,778

1985

1,225

4,324

1990

1,391

8,089

Data from Statistical Abstract of the United States, 1994. 4. Discussion. Possible questions include the following: How would you characterize spending on pollution a b a t e m e n t over the years? Are you surprised at the relative burden of responsibility between federal and state and local spending? Which do you t h i n k absorbs most of t h a t state and local spending—air, water, or solid waste?

112/UNIT 9 5. Make a line graph of the following table: Population, 1980-2000 Year

World Population

1980

4,456,531,000

1990

5,294,294,000

2000

6,165,079,000

Data from Statistical Abstract of the United States, 1994. 6. On the same graph, add lines for China and India from the table below: Year

China

India

1980

984,736,000

692,384,000

1990

1,136,626,000

852,656,000

2000

1,260,154,000

1,018,105,000

Data from Statistical Abstract of the United States, 1994. 7. Discussion. A possible question is the following: Do you t h i n k there is a problem with population growth? If so, describe. 8. H a n d out and explain homework.

UNIT 9, LESSON 9.3 HOMEWORK / 1 1 3

U N I T 9, LESSON 9.3 HOMEWORK 1. Make five s t a t e m e n t s based on the following line graph. Use complete sentences and select w h a t you consider to be the most vital information. U.S. Motor Fuel Consumption

Data from Statistical Abstract of the United States, 1994.

2. Make a concluding observation, of fact or opinion or both, about the information in this line graph.

From Civic Mathematics. © 1996. Teacher Ideas Press. (800) 237-6124.

114/UNIT 9

LESSON 9.4: CIRCLE GRAPHS • Teach m a k i n g and reading circle graphs • Social-context activities (about 40 minutes) 1. Go over Lesson 9.3 homework. 2. Make a circle graph out of the following table: World Endangered Species Species

Percentage

Plants

35%

Mammals

25%

Birds

18%

Reptiles

7%

Fish

5%

Other

10%

Data from Statistical Abstract of the United States, 1994. 3. Make a circle graph out of the following table, completing the percent column first. U.S. Nonfederal Land Use tUse

Total

Thousands of Acres

Percentage of Total

1,484,157

100%

Developed

77,305

Cropland

422,416

Pasture

129,021

Range

401,685

Forest

393,904

Other

59,826

Data from Statistical Abstract of the United States, 1994.

LESSON 9.4: CIRCLE GRAPHS / 115 4. Discussion. Possible questions include the following: W h a t do you t h i n k have been some of the causes of species' becoming extinct? W h a t do you t h i n k would happen on the planet if h u m a n s became extinct? Does anything surprise you about the land use data? 5. From the following data, you will need to calculate the total and the percentage for each state before m a k i n g the circle graph. Top 5 States, National Priority List for Hazardous Waste Sites State

Number of Sites

New Jersey

109

Pennsylvania

99

California

95

New York

85

Michigan

76

Data from Statistical Abstract of the United States, 1994. 6. The circle g r a p h below is for your information in doing the activities following it. Sources of Hazardous Waste in United States

116/UNIT 9 7. Calculate the dollar amounts of each type of pollution, given that the total spending on cleanup by industry is $7,866,900,000. I n d u s t r i a l F u n d i n g for Cleanup

Calculate the dollar amounts of each type of pollution spending, given the total government spending is $21,998,000,000. Government Funding for Cleanup

8. Discussion. Possible questions include the following: Do you know the sources of hazardous wastes in your own home? Do you know the best way to dispose of an old can of paint in your community? Do you think the financial burden of cleanup is divided fairly between industry and taxpayers?

UNIT 9 LIBRARY RESEARCH ACTIVITY / 117

U N I T 9 LIBRARY RESEARCH A C T I V I T Y (ABOUT 80 MINUTES)

Divide into groups of two or three students. Pick one of the research questions below for each group. Use the guide to conduct your research. Reconvene as a whole class and have a spokesperson from each group share your results. Researchch Qstionsionsss 1. How does your state compare to the nation or with other states or both regarding some environmental issue—waste management, air or water health, or wildlife? 2. What is the situation with "clean" sources of energy—solar, hydroelectric, geothermal, wind? That is, how much are these sources being used, how clean are they, how much do they cost, and so on? 3. How have recycling practices improved over the years? 4. How does the United States compare with other nations regarding some environmental issue, such as recycling, energy use, and so on? 5. What is the situation with some environmental issue you care about—acid rain, endangered species, clean air, clean water, use of natural resources, and so on? Assessmentnttt For this activity you will be assessed on the following: seriousness in approach to library work (5%) quality of presentation of data, using appropriate graphs and calculations (50%) quality of explanation of graphs and data (20%) quality of final organization and presentation (20%) insight of concluding observation (5%)

From Civic Mathematics. © 1996. Teacher Ideas Press. (800) 237-6124.

118/UNIT 9

UNIT 9 LIBRARY RESEARCH GUIDE Researchh Qestionion 1. Locate sources containing information on your question. Write down the titles, authors, publishers, dates of publication.

Choose appropriate graphs for presenting your information—you may not copypyy graphs from your sources, but you may interpret graphs you find, to work into your report. Include three of the following in your report: table, line graph, bar graph, circle graph.

Write down the statements to accompany the graphs, for presenting to the wholeolee class, and organize the whole into an interesting and informative report.

4. Make at least one concluding observation, either factual or reflecting an opinion shared by the whole group, based on your data and on environmental issues in general.

From Civic Mathematics.cs© 1996. Teacher Ideas Press. (800) 237-6124.4.

Fourth Quarter

Teen Issues Skills Covered: • Mean • Median • Mode • Range • Percentage change • Percentage and probability • Odds • Adding and multiplying probabilities • Coordinate geometry • Negative numbers

This page intentionally left blank

UNIT

10

INTRODUCTION Social-ContexextTopicsCoveredredd Marriage and divorce Teen parenting Sexual harassment AIDS Causes of death Smoking, alcohol, and drug use Exercise

Mathematicacal Skills Coveredvered Mean Median Mode Range Percentage increase and decrease

Discussionnn Unit 10 begins the quarter on teen issues. Measures of central tendency are fairly straightforward, so they are joined in this unit in a way that reveals their comparative usefulness. Really, every social issue today is a teen issue: It is teens who are on the threshold of a life full of excitement and danger. This unit explores a few of those challenges.

121

122 / UNIT 10

LESSON 1 0 . 1 : MEAN, MEDIAN, MODE, RANGE • Teach averages, range • Social-context activities (about 40 minutes) "She's an average teenager." What does t h a t mean? Does she smoke, drink, t a k e drugs? Is she sexually active? Has she ever been arrested? Will she g r a d u a t e from high school? Get AIDS? Get pregnant? Has she been sexually h a r a s s e d at school? Does she live with both parents? Has she ever tried to commit suicide? With this lesson, we will begin to answer these questions, for both girls and boys. 1. Compute the m e a n and find the median for the d a t a on m a r r i a g e and divorce. Marriages and Divorces in the United States Year

Marriages

1970

2,159,000

708,000

1975

2,153,000

1,036,000

1980

2,390,000

1,189,000

1985

2,413,000

1,190,000

1992

2,362,000

1,215,000

Divorces

Data from Statistical Abstract of the United States, 1994. 2. What is the range for the marriage data? The divorce data? 3. Discussion. Possible questions include the following: If you wanted to make our divorce r a t e look as bad as possible, would you use the mean or median for these data? Twice in this span of years, the n u m b e r of marriages went down. W h a t happened to the n u m b e r of divorces?

LESSON 10.1: MEAN, MEDIAN, MODE, RANGE /123 4. Compute the mean, median, mode, and range for the divorce rates in the following countries: Divorce Rate (per 100 marriages)

Country Canada

40

Czechoslovakia

31

Denmark

44

France

31 7

Italy

48

United States

Data from Statistical Abstract of the United States, 1994. 5. Discussion. A possible question is the following: Which kind of average would you use if you wanted to make the U.S. figure look as close as possible to "average"? 6. Find the mean, median, mode, and range of both columns of the following: Births to Teens Under 15 in the United States Year

Number of Births

Number of Teens

1970

9,500

16,299,200

1980

9,000

15,178,800

1985

9,400

13,961,600

1990

10,700

13,812,400

1991

11,000

14,035,600

Data from Statistical Abstract of the United States, 1994. 7. Discussion. Possible questions include the following: Why is a rate more useful information than number of births? What trends do you see for divorce and teen parenting? Do you think the two are related? Why or why not? What factors influence whether a teen decides to become sexually active? To use birth control? To have a baby once pregnant? To keep a baby once having had one? Which kind of average do you think is a true representation of average? Is it always? Based on these data, do you think the average teen lives with both biological parents? Gets pregnant and has a baby, if female?

124 / UNIT 10

LESSON 10.2: PERCENT INCREASE OR DECREASE • Teach percentage increase or decrease • Social-context activities (about 40 minutes) We will revisit some of the social issues from the last lesson to gain a clearer picture of the "average" teen, t h e n move on to other topics. 1. Calculate the percentage of change, completing the last column in the table below. Indicate increase or decrease with a + or - , t h e n calculate the percentage living with both p a r e n t s in 1970 and in 1992. Families in the United States Children Aged 10-14

1970

1992

Total Number

20,804,000

18,100,000

Living with both parents

17,225,712

12,398,500

Living with mother only

2,434,068

4,072,500

Living with father only

332,864

633,500

Living with neither parent

821,356

996,000

Percentage of Change

Data from Statistical Abstract of the United States, 1994. 2. Calculate the percentage of increase or decrease in the n u m b e r of teens and n u m b e r of teen births, completing the last column in the table below. Then calculate the percentage of teens who had babies in 1980 and 1991. Births to Teenage Mothers, Aged 13-19

Total number of teens Births to teens

1980

1991

28,464,800

24,043,000

103,849

156,580

Percentage of Change

Data from Statistical Abstract of the United States, 1994. 3. Discussion. Possible questions include the following: Using the tool of finding percentage of increase or decrease, describe t h e t r e n d s in teen pregnancy. Based on these data, is the average teen living with both biological parents? Is the average teen girl having babies?

LESSON 10.2: PERCENT INCREASE OR DECREASE /125 Percentage of increase or decrease can also be thought of as percentage of difference, higher or lower. 4. Calculate the percentage of difference between boys and girls on these d a t a on sexual h a r a s s m e n t in school. Sexual Harassment in Schools Type of Harassment

Boys

Girls

Received sexual comments or looks

457

620

Were touched, grabbed, or pinched in sexual way

343

530

Had sexual rumors spread about them

277

343

Were shown, given, or left sexual material

277

253

Total number

816

816

Boys

Girls

Not wanting to go to school

98

269

Not wanting to talk in class

106

261

Finding it hard to pay attention

106

228

49

139

816

816

Reaction to Harassment

Thinking about changing schools Total number

Percentage Higher or Lower for Girls

Percentage Higher or Lower for Girls

Survey reported in The New York Times, June 6, 1993. 5. Discussion. Possible questions include the following: Is t h e r e anything t h a t surprises you about these data? How are things in your school regarding sexual h a r a s s m e n t ? What do you t h i n k teachers should do? W h a t do you t h i n k you should do? You are told the percentage of increase in the number of teens becoming p a r e n t s . W h a t else do you need to know before drawing any conclusions? 6. H a n d out and explain homework.

126 / UNIT 10

UNIT 10, LESSON 10.2 HOMEWORK AIDS Deaths Year

Age 13-29

1985

1,329

6,177

505

7,682

1986

2,286

10,557

980

11,537

1987

3,012

13,921

1,530

15,451

1988

3,794

17,551

2,106

19,657

1989

4,801

23,394

2,763

26,157

1990

5,021

24,936

3,124

28,060

1991

5,292

27,048

3,545

30,593

1992

3,809

20,110

2,565

22,675

All Males

All Females

Total

Data from Statistical Abstract of the United States, 1994. 1. What is the good news here?

2. What is the percentage of decrease in each category from 1991 to 1992? Age 13-29:

Females:

Males:

Total Deaths:

3. What is the percentage of increase in each category from 1985 to 1992? Age 13-29:

Females:

Males:

Total Deaths:

From Civic Mathematics. © 1996. Teacher Ideas Press. (800) 237-6124.

UNIT 10 LIBRARY RESEARCH ACTIVITY / 127

U N I T 10 LIBRARY RESEARCH A C T I V I T Y (ABOUT 80 MINUTES)

Divide into groups of two or three. Pick one of the research questions below for each group. Use the guide to conduct your research. Reconvene as a whole class and have a spokesperson from each group share your results.

Researchh Questionsons 1. What is the trend in dropping out of high school?

2. What sports do teens participate in?

3. How do teens spend their leisure time—reading, TV, studying, sports, and so on?

4. How many eligible teens become drivers? How many accidents do they become involved in, and so on?

Assessmenntt For this activity you will be assessed on the following: seriousness in approach to library work (5%) quality of statements based on data (20%) quality of application of math skills to statements (30%) quality of revised statements (20%) quality of final organization (20%) thoroughness and insight of "typical teen" description (5%)

From Civic Mathematics. © 1996. Teacher Ideas Press. (800) 237-6124.

128 / UNIT 10

UNIT 10 LIBRARY RESEARCH GUIDE Researchch Questionnn 1. Write down the titles, authors, publishers, and dates of publication for your sources.

2. Write down, in complete sentences, five to 10 s t a t e m e n t s of fact based on the data. For example: "In 1980 there were 5,212,000 high-schoolers dropping out, and in 1992 t h e r e were 3,468,000."

3. Perform the following m a t h skills on the s t a t e m e n t s , using each at least once in all: finding

mean

finding median finding mode finding range finding percentage of increase finding percentage of decrease For example, given the s t a t e m e n t above, you might say, "There was a 33 percent decrease in the number of high school dropouts from 1980 to 1992." 4. Organize your new s t a t e m e n t s into an orderly, logical, and interesting whole, so t h a t they m a k e sense for presenting to the class. 5. Compose a description of a typical teen, based on all we have studied in this unit, as well as on your own research. The subject areas include: m a r r i a g e and divorce teen pregnancy sexual h a r a s s m e n t AIDS your research topic

From Civic Mathematics. © 1996. Teacher Ideas Press. (800) 237-6124.

UNIT

11

INTRODUCTION Social-Contexext Topics Coveredred Violence Suicide Exercise Expectations about marriage Causes of death Cigarette smoking Abuse of other substances

Mathematicacal Skills Coveredvered Probability Changing percentage to probability Odds Adding probabilities Multiplying probabilities

Discussionn This unit covers some of the most talked-about issues regarding adolescents in the United States today, and though much of the data are often frightening, there are some encouraging trends. Substance abuse, violence, and other social ills pose a huge challenge to young people, but fortunately these problems still are not part of the life of the "typical teen." The tools of probability help to bring these issues to a personal level and make the statistics a meaningful warning to students.

129

130/UNIT 11

LESSON 1 1 . 1 : PROBABILITY • Teach probability • Social-context activities (about 40 minutes) You can m a k e a probability s t a t e m e n t based on current statistics. For example, if four out of five high school students g r a d u a t e , you could say a student h a s a probability of g r a d u a t i n g of V5, t a k i n g no other factors into consideration. 1. Give the probabilities, based on the d a t a below (round and reduce). Victims of Violent Crime per 1,000 People in Age Group Age

1991

1992

12-15

63

76

16-19

91

78

20-24

75

70

25-34

35

38

35-49

20

21

50-64

10

10

4

5

>64

Data from Statistical Abstract of the United States, 1994. 2. Do the same for the d a t a below. Arrest Rates for Aggravated Assault for People Under 18 (per 100,000 Arrests) | Year

Rate

1980

250

| 1992

450

j

Data from Statistical Abstract of the United States, 1994. Arrest Rates for Murder for People Under 18 (per 100,000 Arrests) Year

Rate

1980

12

1992

23

Data from Statistical Abstract of the United States, 1994.

LESSON 11.1: PROBABILITY / 131 3. Discussion. Possible questions include the following: W h a t factors influence whether you will be a victim of violent crime and therefore alter a statistical probability for you? W h a t factors influence your becoming a violent criminal? Which h a s a greater impact on you—being told the rate of violent crime victimization for your age, or being told the probability of your being the victim of a violent crime? 4. Suicide is another form of violence. Complete the last column, rounding and reducing, of the table below. Suicide Rates, Age 15-19 Country

Rate per 100,000 Youths

New Zealand

16

Canada

14

United States

11

Austria

10

Ireland

8

Japan

4

Probability

Data from The New York Times, July 15, 1995. 5. Make several probability s t a t e m e n t s about the data below. Suicide Rates by Age per 100,000 Year

Age 10-•14

1980

1

1990 1991

Age 15-•19

Age 65 and Over

9

19

1.5

11

22

1.5

11

24

Data from Statistical Abstract of the United States, 1994. 6. Discussion. Possible questions include the following: Do you view suicide as a violent crime? Why or why not? W h a t do you find surprising about any of the data? 7. A percentage can be viewed as a probability, because every percentage can be changed to a fraction. If 15 percent of people charged with m u r d e r are younger t h a n 18, t h e n a person charged with m u r d e r has a 15 /ioo or 3/20 chance of being under 18.

132 /UNIT 11 Complete the last column of the table below. Killings in the United States Type of Homicide

Percentage

Victims of any age of a juvenile gang killing

3.5%

Victims age 15-19 who were killed with firearms

85%

Victims as percent of all deaths in 15-24 age group

22%

Victims of all ages involving firearms

68%

Probability

Data from The New York Times, December 5, 1994, and December 13, 1994, and Statistical Abstract of the United States, 1994. 8. Discussion. Possible questions include the following: Does anything about this set of d a t a surprise you? W h a t do you t h i n k about guns—their accessibility, the laws, and so on?

LESSON 11.2; ODDS, MULTIPLYING PROBABILITIES, ADDING PROBABILITIES / 133

LESSON 11.2: ODDS, MULTIPLYING PROBABILITIES, ADDING PROBABILITIES • Teach odds, multiplying and adding probabilities • Social-context activities (about 40 minutes) The same extension of probabilities to statistics is true for odds: If you have a V5 chance of graduating, the odds of your graduating are 4 to 1. We will use probability skills in this lesson to explore some issues affecting teens. 1. From the data below, first go to a probability, then to odds, completing the last column. Statement

Probability of Event

Odds of Event

35% of ninth-grade girls exercise regularly

7

7 to 13

/20

50% of ninth-grade boys exercise regularly 63% of teens age 13-17 expect to get married 55% expect to have kids 86% of girls age 13-17 expect to work outside home 58% of boys expect wife to work outside home

Data from The New York Times, January 4, 1995, and July 11, 1994. 2. Make three and statements from the table below, using probability (not including the "any cause" data). For example: "The probability of dying in a car accident and being near death from cancer is V50,000,000." Then make three or statements, such as "The probability of dying of homicide or AIDS is 13/60,000."

134/UNIT 11 Leading Causes of Death, Age 15-24 Cause

Rate/Probability

Any cause

Hooo

Accident

1

/2,500

Homicide

1

/5,000

Suicide

1

Cancer

1

/20,000

Heart disease

1

/35,000

AIDS

1

/7,500

/60,000

Data from Statistical Abstract of the United States, 1994. 3. From the d a t a below, make five and s t a t e m e n t s and five or s t a t e m e n t s , using probability. Substance Abuse in Teens 12th-graders who smoke cigarettes lOth-graders who smoke cigarettes 8th-graders who smoke cigarettes 12th-graders offered an illegal drug at school lOth-graders offered an illegal drug at school 8th-graders who used marijuana at school 8th-graders who used alcohol at school Seniors who h a d seen classmates drunk at school Seniors who h a d seen classmates high on other drugs at school C u r r e n t user of marijuana, age 12-17 C u r r e n t user of alcohol, age 12-17 C u r r e n t user of cocaine, age 12-17

31% 25% 19% 23% 18% 3% 4% 50% 42% 4% 16% .3%

Data from The New York Times, July 20, 1995, and Statistical Abstract of the United States, 1994. 4. Discussion. Possible questions include the following: Share s t a t e m e n t s made about all d a t a in this lesson and discuss. Would you prefer to be told the percent of occurrence of an event, its probability, or the odds of it occurring? Does a n y t h i n g surprise you about the leading causes of death in your age group? Does anything surprise you about the d a t a on substance use and abuse?

UNIT 11 LIBRARY RESEARCH ACTIVITY / 135

U N I T 11 LIBRARY RESEARCH A C T I V I T Y (ABOUT 80 MINUTES)

Divide into groups of two or three students. Pick one of the research questions below for each group. Use the guide to conduct research. Reconvene as a whole class and have a spokesperson from each group share results. Researchch Questionsnss 1. What is the recent trend in youth violence? 2. What is the recent trend in youth substance abuse? 3. What is the trend in youth crimes overall? 4. What information can you find about gangs? 5. What geographical factors (region, city or rural, etc.) seem to make a difference in youth violence or substance abuse? 6. What are some other specific age correlations on any of the topics? 7. What health factors are associated with adolescence (e.g., diet, exercise)? Assessmenentt For this activity you will be assessed on the following: seriousness in approach to library work (5%) quality of statements based on data (20%) quality of application of math skills to statements (30%) quality of revised statements (20%) quality of final organization and presentation (20%) thoroughness and insight of "typical teen" description (5%)

From Civic Mathematics.cs,

© 1996. Teacher Ideas Press. (800) 237-6124.

136/UNIT 11

UNIT 11 LIBRARY RESEARCH GUIDE Researchh Questionestion 1. Write down the titles, authors, publishers, and dates of publication of your sources.

2. Write down, in complete sentences, 5 to 10 statements of fact based on your data. For example: "Forty-five percent of vandalism arrests were of people under 18."

3. Perform the following mathematical analyses on the statements, at least one of each: probability changing a percentage to a probability statement finding odds adding probabilities multiplying probabilities

For example, given the statement above, you might say, "If someone is arrested for vandalism, that person has a 9/20 chance of being under 18."

4. Organize your new statements into an orderly, logical, and interesting whole so that they make sense for presenting to the class.

From Civic Mathematics. © 1996. Teacher Ideas Press. (800) 237-6124.

UNIT 11 LIBRARY RESEARCH GUIDE / 137 5. Compose a description of a typical teen, based on the findings from your work in this unit and your research regarding the following: violence and suicide health and nutrition causes of death substance abuse (including cigarettes and alcohol)

From Civic Mathematics. © 1996. Teacher Ideas Press. (800) 237-6124.

UNIT

12

INTRODUCTION Social-Contextext Topics Coveredvered Nutrition Exercise Skin cancer Heart rate Gas mileage Garbage and compost, revisited Mathematicaical Skills Coveredovered Negative numbers Coordinate geometry Graphing equations

Discussiononn The last unit in this quarter draws on health and nutrition topics and revisits related topics from the third quarter, the environment. It is especially valuable to see how algebra and coordinate geometry can be used to better understand topics already covered.

138

LESSON 12.1: NEGATIVE NUMBERS / 139

LESSON 1 2 . 1 : NEGATIVE NUMBERS • Teach negative numbers and the number line • Social-context activities (about 30 minutes) This lesson will focus upon health and nutrition, with the concept of negative numbers applied to data. 1. Calories—or food energy—can be used by your body or turned into fat. Consider 0 to be the ideal number of calories needed for you to function, including exercise. Consider any number to the right (positive) as extra calories, or stored as fat, and any number to the left as used up, or burned, calories.

If you consume a piece of chocolate cake, to the tune of 350 calories, then go dancing for one hour, you burn up that 350 calories and are nicely back at 0. Figure out where you stand at the end of the following school day, completing the appropriate columns. Calorie Consumption and Burning

Eat a bowl of cereal, slice of toast with butter and jam, and glass of orange juice for breakfast (525 calories) Walk to school 15 minutes (burn 60 calories) Eat a hamburger, french fries, and soda for lunch (645 calories) Go to a PE class for 30 minutes (burn 330 calories) Snack after school on a Snickers bar (85 calories) Walk home (burn 60 calories)

You burn some calories just to stay alive and breathe—about 3 per minute. Estimate 1,000 burned during the rest of the time, so far. Should you have a bowl of popcorn or go jogging?

140 / UNIT 12 2. There are other factors to consider for good health besides calories: vitamins and minerals. Consider 0 to be the recommended amount, to the positive direction extra, and to the negative direction a deficit.

The recommended daily allowance of vitamin C for teens is 55 mg. If you smoke, you run about 25 percent low on vitamin C, so add 25 percent on. If you consumed the following vitamin C amounts over the course of a week, did you do okay? Complete the table. Amount Credit Need

Consumed

Day 1

185 mg.

Day 2

45 mg.

Day 3

600 mg.

Day 4

30 mg.

Day 5

120 mg.

Day 6

185 mg.

Day 7

50 mg.

+

Weekly Total:

Amount Deficit

-

or

3. Discussion. Possible questions include the following: What factors besides exercise influence how many calories you should consume? Does it make any difference whether you get your calories from protein, carbohydrates, or fats? Do you eat a healthful diet? How could you improve it? Do you get enough exercise? Are negative numbers helpful in thinking about these relationships? Why or why not? 4. Hand out and explain homework.

UNIT 12, LESSON 12.1 HOMEWORK / 141

U N I T 1 2 , LESSON 12.1 HOMEWORK Below is a table that is all mixed up as to whether the items represent burning calories (-) or consuming calories (+). 1. Complete the appropriate + or - column by putting the number of calories in the column. +

-

Eating 2 scrambled eggs (220) Eating 2 scrambled egg whites (30) Drinking 1 glass of orange juice (110) Dancing 15 minutes (75) Eating 1 piece of toast (60) Eating 1 tablespoon butter (70) Walking 15 minutes (60) Sitting 5 minutes (15) Having 2 slices bacon (90) Eating 1 orange (65) Eating 6 pancakes (360) Jogging 15 minutes (165) Bicycling 15 minutes (120) Swimming 15 minutes (150) Running 15 minutes (285) Eating 1 bowl of oatmeal, with milk and sugar (190) Eating 1 doughnut (165) Drinking 1 glass of milk (200) Drinking 1 cup of coffee with cream (30)

2. Pick out a breakfast and a way of getting to school (dancing, walking, riding in a car, jogging, bicycling, swimming, or running) that exactly or nearly cancel each other out, calorie-wise.

From Civic Mathematics. © 1996. Teacher Ideas Press. (800) 237-6124.

142 / UNIT 12

LESSON 12.2: COORDINATE GEOMETRY AND GRAPHING EQUATIONS • Teach graphing equations • Social-context activities (about 40 minutes) 1. Go over Lesson 12.1 homework. 2. A health issue often talked about is skin cancer—especially relevant to teens. The s u n b u r n s you get now can lead to skin cancer later. S P F m e a n s "sun protection factor" and is used as a sunscreen rating. Let x = n u m b e r of minutes you can stay in the sun without burning. Let y = S P F number (lotion number). Then xy = n u m b e r of minutes you will be protected by the lotion. Make a table of values for x and y if you want to stay in the sun 120 minutes: xy = 120. Graph the equation. Read the graph to answer the following questions: If you can stay in the sun 15 minutes without burning, w h a t number lotion do you need to stay in the sun safely for 120 minutes? If you b u r n in 10 minutes, w h a t number lotion do you need to stay in the sun 120 minutes? 3. To figure out w h a t your h e a r t r a t e should be, subtract your age from 220, t h e n take 80 percent. (220-age) x .80 = HR Make a table of values for the equation, if your age is x and your h e a r t r a t e is y. .80(220-x) = y Graph the equation. Should your h e a r t rate go up or down as you get older? 4. To figure how many gallons of gas you will use on a trip, you divide the n u m b e r of miles you drive by the car's fuel efficiency (miles per gallon). miles driven „ 1 = gallons used mpg If x = miles driven, and y = gallons used, and your fuel efficiency is 30 mpg, t h e n V30 = y

LESSON 12.2: COORDINATE GEOMETRY AND GRAPHING EQUATIONS / 143 Graph this equation, making a table of values. Read the g r a p h to complete the table for these trips: Miles Driven

Gallons Used

150 300 500 5. Discussion. Possible questions include the following: Why doesn't t h e S P F graph ever go into the negatives for x or y? Why doesn't the h e a r t r a t e graph ever go into the negatives for x or y? Why doesn't the fuel consumption graph ever go into the negatives for x or y? 6. All those wonderful formulas you used for figuring out volumes of garbage, volume of a compost bin, area of a lake or pond, and so on are graphable equations. Try three: A = s2 A = 7cr

p

V=

TI

r2h

V=

TI

r2h

2 For A = s , let A = y and s = x. Make a table of values and g r a p h it. Read the graph. When the side (x) is 2, w h a t is the area (y)? When x is 8, w h a t is y? 2 For A = 7C r , let A = y and r = x. Make a table of values and g r a p h it. 2 For V = n r h, you can ask the question you asked in the last quarter: If I need a volume of 500 cubic feet, what dimensions can I use for a cylindrical compost bin? so 500 = n r 2 h Let r = x and h = y. Make a table of values and graph. Read the graph to find a few possible values for radius (x) and height (y).

144 / UNIT 12

U N I T 12 LIBRARY RESEARCH A C T I V I T Y (ABOUT 80 MINUTES)

Divide into groups of two or three students. Pick one of the research topics below for each group. Use the guide to conduct your research. Reconvene as a whole class and have a spokesperson from each group share results. Researchch Topicscs 1. Car fuel efficiency over the years. 2. Consumption of fats or other nutrients or both over the years. 3. Teens and their nutrient intake. 4. Garbage, compost, or water use, or any combination of these three. 5. Exercise. Assessmenentt For this activity you will be assessed on the following: seriousness in approach to library work (5%) appropriateness of formula for data (30%) quality of use of formula and graphing (40%) quality of presentation (25%)

From Civic Mathematics. © 1996. Teacher Ideas Press. (800) 237-6124.

UNIT 12 LIBRARY RESEARCH GUIDE / 145

UNIT 12 LIBRARY RESEARCH GUIDE Researcch TTopic 1. Write down title, author, publisher, and date of publication of your source.

2. Write down a formula that will apply to your data from the following: Heart rate: .80(220-age) = HR „,««.. „ , miles driven Fuel efficiency: gallons used = m PS Area of square: A = s 2 Volume of cube: V = s3 olumeme oof recangular soid: V = lwh1wh Volume of cylinder: V = n r h Area of circle: A = n r2 Any other formula you can work out and get approved by your teacher

3. Prepare a report on your data that includes an explanation of your formula and a graph.

From Civic Mathematics. © 1996. Teacher Ideas Press. (800) 237-6124.

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Appendix X Solutions to Selectedd Problemss Lesson 1.1 Activity 1: Rounded 262.8 128.3 134.5 217.5

33.1 2.2 26.5 9.8

Activity 2: White Black Hispanic

Asian American Indian

Activity 4: JRounded 9.84 9.39 8.83 8.37 9.78

9.42 9.26 9.50

Homework: Roundedd 1 4 5 9 15

5 4 8 9

Lesson 1.2 Activity 1 0answers may vary): 120 or 125 300 175 or 200 40 50 375 50 80 550 450

2,750 or 3,000 170 or 200 200 250 70 30 40 50 30 30

147

77 or 80 40 140 25 400 or 450 70 135 250 20 125

148 / APPENDIX

Activity 4: 10 10

2

Lesson 1.3

Activity 1: Men— .609 million Women— .148 million Difference: 2.46 (M) .077 (M) 1.42 (M) .211 (M) .341 (M) .12 (M)

Men— 1.668 million Women— .171 million .116(M) .421 (M) .021 (F) Writers 12.668-7.523 = 5.145

Lesson 1.4

Activity 1: Number of Rapes 3249.8 654.0 99.6 309.3 Homework: Number of Bias Crimes 24.3 12.8 3.4 8.1

375.9 60.8 182.7 186.4 10.8 1.3 6.7

Lesson 1.5

Activity 2: Hourly Rate $11.58 $12.87 $9.89 Activity 3: $113.56 $196.98

$11.97 $9.26 $8.38 $232.19

Lesson 1.6 Activity 1: 14,531,000 4,635,000 3,550,000

7,815,000 8,312,000

APPENDIX/149 Activity 2: Blacks 3,639,000.0 8,834,000.0 11,891,000.0 15,042,000.0 26,683,000.0 33,117,000.0

Whites 19,553,000.0 66,809,000.0 110,287,000.0 134,942,000.0 194,713,000.0 218,334,000.0

Activity 3: 102.0 165.8

22.6 15.8

Lesson 2.1 Activity 1: / 2 63

2

/263

27

/263

10

/263

37

V 4 63

134 218 33

/263

/263

Activity 2: 51

%63 3 396/ 4 6 3 479

335/ 4 6 3

/463

Activity 4: 14 7

/623

/623

392 210

/623 /623

Activity 6: Black or Hispanic

Women

24

19

/435

21

/435

29 30 34

/435 /435 /435 /435

366

/435 388

/435 555

/435

22

/435

24

/435

25

/435

26

/435

48

/435

150/APPENDIX Homework: (1)

16

(3) V612

/519

(2) 47 / 62

(4) 1 ' 5 6 7 /i,572

Lesson 2.2 Activity 2: Total: 196 Rounded

Fraction

Equivalent

90

90

9

100

100

160

16

20 20

/200

/20

%00

v2 v5

20

/200

V10

20

/200

V10

/200

200 Activity 4: Rounded

Fraction

Equivalent

9

9

Vioo

10

10

7

7

/l,000

Vioo

/l,000

Vioo

/l,000

Homework:: Fraction

Equivalent

33

7

V5o 7

/l,000

/i,ooo

18

/l,000

/200 = V20

Vioo V50

APPENDIX / 151 L e s s o n 2.3 Activity

2:

Rounded Rounded Male Female

Total Male + Female

28,000

9,000

12,000

Fraction Male

Fraction Female

Male Equivalent

Female Equivalent

37,000

28,000 37,000

9,000 37,000

28 37

9 37

4,000

16,000

12,000 16,000

4,000 16,000

3 4

1 4

7,000

1,000

8,000

7,000 8,000

1,000 8,000

7 8

1 8

4,000

1,000

5,000

4,000 5,000

1,000 5,000

4 5

1 5

Activity 4: Rounded Black

Rounded White

Total

270,000

1,869,000

13,000

Fraction Black

Fraction White

2,139,000

270,000 2,139,000

1,869,000 2,139,000

74,000

87,00()

13,000 87,000

74,000 87,000

13,000

13,000

26,000

13,000 26,000

13,000 26,000

2,000

28,000

30,000

2,000 30,000

28,000 30,000

Equivalent Black

Equivalent White

270

1'86%,139

13

/2)139

/87

74

/87

v2

Vi Vl5

14

Homework: (1) Whites—289/50C) Blacks—9/20 Hispanics—V7

/l5

(2) l e a s t - Blacks most—-males (4) males

152 / APPENDIX

Lesson 3.1 Activity Activity 1: Fraction Fraction

Hourly Hourly

518 518/ 40 /40 425 4() 425/ /40

12.9^ 12.91ft

416 416/40

10.4^ 10.4%

/40

10.63^ 10.6%

373 373/ 40 /40

9.33^ 9.3%

332 332/ 40 /40

8.39^ 8.3%

260 260/ 40 /40 236/4Q

6 50 6.5% - /l

674/ 674 40 /40

16.8% 16.8^

2 2,476/40 >47%0

61.91^ 61.9%

Activity 3: $40 $270

5.99^ 5.9%

$500 $1,050

Lesson 3.2 Activity 1: Ratio

I61

20 3

33 5

3 2

19 2

6 1 1

5 22

10 3

41 3

11 n. 3

5 2

7 1

Activity 3: 11

11 11

-2

high graduation high school graduation

3

i

6

APPENDIX / 153

Homework: (1) $900 $1,400 $1,500 $1,600 $1,900

$2,500 $3,200 $5,600 $4,500

Lesson 3.3 Activity 2:

United States 5 10 15 10 5

Russia 5 20 55 50 55

Activity 3: 5 _ 1 15 3

5 _ 1 55 11

10 _ 1 20 ~ 2

5 _ 1 5 1

10 _ 1 50 5

15 _ 3 55 11

Activity 5:

Rounded

Ratio

10

10 100

20

20 100

50

50 100

55

55 100

10

10 100

Activity 6:

Vio

V5 V2

V2 Vio

154/APPENDIX Lesson 4.1 Activity 1: Decimal

Fraction

Reduced

.19

19

19

.02

2

/ioo

V50

.03

3

/ioo

3

.05

5

/ioo

V20

.04

4

/ioo

V25

.05

5

/ioo

/ioo

/l00

/ioo

V20

.07

Vioo

Vioo

.02

2

V50

.10

10

/ioo

Vio

/ioo

Activity 3: Decimal .15 .10 .17 .15 .17 .16 .10

Percentage 15% 10% 17% 15% 17% 16% 10%

Activity 5: Decimal

Fraction

.17

17

.16

4

/25

.15

3

/20

.14

7

/50

/ioo

Lesson 4.2 Activity 1: rent— 1 %o 15

phone—V40

car— /4o

miscellaneous—V40

food—8/40

savings—V40

APPENDIX/155 Activity 3: 1960—4/i6

1970—2/i6

1965—3/i6

1975—2/i6

1992—3/ie

1980—2/i6

Lesson 4.3 Activity 1: savings—%Q = V15 Activity 2: under 18—7/i8

35-54— 3 /is

18-34— 5 /is

55 and up—3/i8

Activity 3: 3

/20

17

V5 21

/ioo

/ioo

2

Vioo

%o

V5 Homework: (1) V5 ~ V25 = 4 / 25

(2) 16/i00

V5 - V20 = 3/20

15

l/ 5 - 2/ 2 5

12/ 1 0 0

=

3/ 2 5

V5 - 9/ioo = n /ioo 1:L

V5 - 9/ioo =

/ioo

9

V5 - V50 = /50

/l00

11/

ioo

1:L

/ioo

18

/l00

Lesson 4.4 Activity 2: 4,993 3,338

3,729 4,197

156 / APPENDIX Activity 4:

$600 $300 $120 Activity 5: Had 37 5 37 18 43 23

$240 $120 $420 Didn't Have 49 20 49 5 31 7

Lesson 5.1 Activity 1:

Expression 3x 4x 6x 3x 5x 3x 8x 2x lOx 2x 6x 5x 6x

Cost $3.27 $3.20 $6.90 $1.23 $7.50 $2.79 $11.12 $6.80 $7.60 $3.76 $3.00 $1.55 $3.00 $65.50

Activity 2:

$256 $248 $240 $232 $224

$216 $208 $200 $192

Lesson 5.2 Activity 1:

a + 3c = FS 2a + 2c = FS 2a + 7c = FS a + 5c = FS

$262.50 $275.00 $587.50 $387.50

APPENDIX / 1 5 7 Activity

2:

160 175 190 205 220 235

250 265 280 295 310

L e s s o n 5.3 Activity 1: $53.13 $65.63 $68.75 Activity

2:

Formula 30x 15x 20x 18x

= = = =

90 60 180 90

Activity

$146.88 $96.88

Max. Wt. 3.43 lbs. 3 lbs. 4 lbs. 9 lbs. 5 lbs.

3:

Formula X + 87 = 700 X + 125 = 700 X + 98 = 700 X + 55 = 700 X + 136 = 700

Solution $613 $575 $602 $645 $564

L e s s o n 6.1 Activity 1: $47,275.76 million $87,689.35 million

$119,141.37 million

Activity 2: $22,576.85 million $51,605.75 million

$64,815.72 million

Activity 4: $277,996.53 million $304,472.39 million

$264,758.60 million $13,237.93 million

158 / APPENDIX Lesson 6.2 Activity 1: 38% 8% 1%

32%% 4%

Activity 2: 15% 10% 15%

2% 17%

Activity 3: 25% Activity 5: 46% 8% 1% 9% 1%

0.2% 7% 6% 1% 2%

Lesson 6.3 Activity 1: $14,085.00 $22,989.00 $27,660.00 $34,906.00 Activity 3: $33,308.00 $37,964.00 $43,450.00 Activity 5: $4,255.0 million $2,742.0 million $2,444.0 million Lesson 6.4 Activity 1: $216,000 Activity 2: $342,614

$60,156.00 $85,714.00 $290,254.00 $2,438,403.00

$44,427.00 $24,133.00

$46,027.0 million $29,826.0 million $16,169.0 million

Activity 4: Interest $3,334.50 $3,234.60 $5,003.46 $4,692.60

Cost $10,834.50 $12,234.60 $18,303.46 $21,192.60

$5001.75 $4,851.90 $7,505.19 $7,038.90

$12,501.75 $13,851.90 $20,805.19 $23,538.90

$955.00 $791.55 $1,718.93 $2,302.20

$3,455.00 $3,791.55 $6,018.93 $8,302.20

Activity 5: $.83 $.91 $.21 $1.73 $.49 $.39 $3.61 Activity 6: $258.08 billion $294.64 billion $326.64 billion Activity 7: $9,352,000,000 per year $779,333,333 per month

$6.51 $.30 $.53 $5.00 $20.51

$348.08 billion $374.08 billion

$194,833,333 per week $38,966,666 per day

Lesson 7.1 Activity 1: 1975 30 X 30 mi. 57 X 57 mi. 57 X 57 mi. 52 x 52 mi. 75 X 75 mi. 50 X 50 mi.

2000 26 X 26 mi. 57 x 57 mi. 55 X 55 mi. 49 X 49 mi. 73 x 73 mi. 49 x 49 mi.

Activity 2: 6,928 mi. 7,500 mi.

2,068 mi. 3,136 mi.

160/APPENDK Activity 3: 1975 262 mi. 914 mi. 920 mi. 765 mi. 1,609 mi. 705 mi.

2000 186 mi. 904 mi. 856 mi. 680 mi. 1,516 mi. 676 mi.

Lesson 7.2 Activity 1: 55,800 sq. mi. 12,000 sq. mi.

2,344 sq. mi. 360 sq. mi.

48 X 48 mi. 19 x 19 mi.

Activity 2: 3,732,000 sq. mi. 54,000 sq. mi. 56,000 sq. mi. 267,500 sq. mi.

69 337 50 67

Activity 3: 75,000 sq. ft. 240,000 sq. ft. 140,000 sq. ft. 175,000 sq. ft.

48 lbs. 154 lbs. 90 lbs. 112 lbs.

Homework: (1) 34,552,960 acres 5,257,600 acres 787,840 acres 36,016,640 acres 101,676,160 acres (2) 108,160 (3) area 1,849 676 196 121

acres 1,183,360 432,640 125,440 77,440

Lesson 8.1 Activity 1: V = 9 cu. ft. 2 lbs. 1.6 cu. ft.

1.8 cu. ft. 2.2 cu. ft.

55 mi. 21 mi.

APPENDIX / 161

Activity 3: 1,570 lbs. 785 cu. ft. Activity 4: 298,205,000 cu. ft. 149,102,500 cu. ft.

9 ft. x 9 ft. x 9 ft.

530 ft. X 530 ft. x 530 ft. 2,229 ft. x 2,229 ft. x 30 ft.

Lesson 8.2 Activity 1: 24% 377 lbs. 189 cu. ft. d = 7 ft. Activity 2: New Haven—533,200 lbs. 127,968 lbs. 63,984 cu. ft. 4,075 64 ft. 128 ft.

Abilene—464,400 lbs. 111,456 lbs. 55,728 cu. ft. 3,550 60 ft. 120 ft.

Independence—485,900 lbs. 116,616 lbs. 58,308 cu. ft. 3,714 61 ft. 122 ft.

D.C.—2,515,500 lbs. 603,720 lbs. 301,860 cu. ft. 19,227 139 ft. 278 ft.

Activity 4: 3,140,000 cu. ft.

6,280,000 lbs.

Activity 5: V small cans: 125.6 cu. in. V large can: 141.3 cu. in. Surface area of 2 small cans: 176.24 sq. in. Surface area large can: 150.52 sq. in. Buy 1 large can Lesson 10.1 Activity 1: Marriages 2,295,400 2,362,000

Divorces 1,067,600 1,189,000

162/APPENDIX Activity 2: 260,000

507,000

Activity 4: 34 36

31 41

Activity 6: Number of Births 9,920 9,500

Number of Teens 14,657,520 14,035,600

2,000

2,486,800

Lesson 10.2 Activity 1: -13% -28% + 67%

+90% +21%

Activity 2: -16% +51%

1980—.4% 1991—.7%

Activity 4: 36% higher 55% higher 24% higher 9% lower same

174% 146% 115% 184% same

Homework: (2) Age 13-29—28% Males—26% Females—28% Total—26%

(3) Age 13-29—187% Males—226% Females—408% Total—195%

Lesson 11.1 Activity 1: 1991

1992

Vie

Vis

Vn

V13

Vl3

Vl4

v29

V26

higher higher higher higher

APPENDK/163

v50

v 48

Vioo

Vioo

V250

V200

Activity 2: 1980—V400

1980—y 8 ,333

1992—V222

1992—V4.348

Activity 4: V6,250

Vio.OOO

V7.143

Vl2,500

Vg.OQl

V25,000

Activity

7:

V29

VB

17

17

/20

/25

Lesson 11.2 Activity

1:

V2 63

/l00

1

V20

1 to 1 63 to 37 11 to 9

43

/50

43 to 7

29

/50

29 to 21

Lesson 12.1 Activity 1: +525 -60 +645 -330

+85 -60 +805 Eat popcorn

164 / APPENDIX Activity 2: Need 55 or 69 55 or 69 55 or 69 55 or 69 55 or 69 55 or 69 55 or 69 Homework: +220 +30 +110 -75 +60 +70 -60 -15 +90 +65

+130 or 116

10 or 24

545 or 531

25 or 39

65 or 51 130 or 116

5 or 19

830 or 732 +360 -165 -120 -150 -285 +190 +165 +200 +30

Lesson 12.2 Activity 2: #8

#12

Activity 3: down Activity 4: 5 10

17

Bibliography Editorial Projects in Education, Inc. Education Week. Washington, DC, September 29,1993. Enger, Eldon D., and Bradley F. Smith. Environmental ships, 4th ed. Dubuque, IA: Wm. C. Brown, 1992.

Science: A Study of Interrelation-

Hopkins, Nigel J., John W. Maybe, and John R. Hudson, eds. The Numbers You Need. Detroit: Gale Research, 1992. Lowe, Bob, and Rita Tenorio, eds. Rethinking Schools. Milwaukee, WI: Rethinking Schools, 1995. The New York Times. October 3,1989; October 5,1989; June 2,1993; July 11,1994; December 5, 1994; December 13, 1994; December 30, 1994; January 4, 1995; July 15, 1995; and July 20, 1995. U.S. Bureau of the Census. Statistical Abstract of the United States. Washington, DC: U.S. Government Printing Office, 1993, 1994. Whitmore, T.C. An Introduction Press, 1990.

to Tropical Rain Forests. New York: Oxford University

165

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IndexX Acid rain, 90 Acres, conversion to, 92 AFDC, 63, 64, 76 Age, and earnings, 49 population by, 5 and poverty level, 54-58 violent crimes by, 130 Alcohol. See Substance abuse Algebra, expressions and sentences in, 64-65 equations in, 68-69 formulas in, 142-43 and graphing equations, 142-43 Area, 90-92 Bar graphs, 108-10 Bias Crimes, 12 Births, teen, 123-24 Budgets, household, 52, 54, 58, 68, 78 national, 74, 75, 116 Circle graphs, 114-16 Circumference, 88-89 Compost. See Solid waste Coordinate geometry, 142-43 Cost of living, 43-44, 64-65 and automobiles, 79-80 and household budgets, 52, 54, 58, 68 over time, 51 Credit card rates, 80 Death, causes of, 29, 30, 126, 134 rates, in U.S., 27 Debt, credit card, 80 national, 81 Decimals, adding and subtracting, 10 dividing, 13-14 multiplying, 11, 12 Divorce. See Marriage Dropouts, high school, 127 by gender, 17 Drug abuse. See Substance abuse Earnings, 50 by age, 49 by education level, 42 by gender, 13, 22, 49 by occupation, 38 by race, 13, 14, 22, 49 and tax rates, 39 over time, 46 Education, and earnings, 42 by race, 9

and unemployment, 41 Elected officials, Hispanic, 23, 24 Employment, by gender, 10, 25 by occupation, 10, 25 by race, 25 Endangered species, 114 Energy, fuel consumption, 113, 142 sources of, 106 world consumption of, 108 Estimating, 7-9 Families, U.S., 124 Farming chemicals, 90-91 Federal budget, 74 national debt, 81 receipts, 75 Fertilizers, in farming, 90-91 Food stamps, 64-66, 76 Formulas, graphing of, 143 Fractions, adding and subtracting, 54-56 comparing, 52-53 and decimals and percentages, 49-51 finding equivalent, 26-28 making, 21-25 multiplying, 57-59 simplifying, 29-30 Garbage. See Solid waste Global warming, 109 Graphing, 142-43 Greenhouse effect, 109 Hazardous waste, government spending for, 116 sites, 115 sources of, 115 Health characteristics, 139-40 by gender, 31, 126 heart rate, 142 by race, 31 sunburn, 142 Herbicides, in farming, 90-91 Homicide. See Violent crimes Immigration, U.S., 6-8, 15 Infant mortality, 28 Interest, computing, 79 Landfills. See Solid waste Land use, U.S., 114 Line graphs, 111-13

167

168 / INDEX Marriage and divorce, U.S., 122 world, 123 Mean, 122-23 Median, 122-23 Minimum wage earners, 49 Mode, 122-23 Negative numbers, 139-41 Occupations. See Employment Odds, 133 Oil spills, 106 Percentage increase or decrease, 124-26 Percentage, 73-78 Perimeter, 88-89 Pesticides, in farming, 90-91 Pollution, and Aral Sea, 93 spending on, 111 See also Farming chemicals Population, U.S., by age, 5 in college, 16, 26 density, 90 by gender, 4, 5, 21 by race, 4, 15, 21 Population, world, 112 Poverty level, U.S., by age, 54-58 defined, 52 people below, 53 Powers often, multiplying and dividing, 15 16 Probability, 130-34 Proportions, 43-45 Public assistance, 63, 72 AFDC, 63, 64 budget for, 73, 76 food stamps, 64-66 funding for, 72 Race, and causes of death, 30 death rates by, 27 and earnings, 13, 14, 22 and education, 9 and employment, 25 elected officials, and, 23, 24 and health characteristics, 31 and infant mortality, 28 population by, 4, 15, 21 Rain forest land, 88-89 Range, 122-23 Rape, rate, by city, 11 Rates, 11, 38-39 Ratios, 40-42 Recycling, of solid wastes, 110 Rounding, 4-6

Scale, calculating, 93 School spending, by state, 40 Schools, sexual harassment in, 125 Sexual harassment, 125 Social services. See Public assistance Solid waste, composition of, 99-100 composting of, 99-100 recycling of, 110 volume of, 97-98 State and local budgets, 73, 75, 78 Substance abuse, and teens, 134 Suicide, teenage, 131 Surface area, of cylinder, 100-101 Tables, for data, 106-7 Taxes, by family type, 78 Federal, 74, 75, 77 for pollution abatement, 116 programs funded by, 64, 72 for public assistance, 73 state and local, 73, 75, 78 Tax rates, 39 Teenagers, 122-24, 130-35 average, 122 births to, 123, 124 characteristics of, 133 causes of death of, 134 and gangs, 135 and substance abuse, 134 and suicide, 131 and violent crimes, 130, 132 See also Age Unemployment, by education level, 41 Violent crimes, by age, 130 victims of, 132 Volume, of cylinders, 99-100 of rectangular solids, 97-98 Water, household use of, 106 oil spills in, 106 sources of, 106 Welfare. See Public assistance Women, causes of death of, 29 and death rates, 27 earnings of, 13, 22 and employment, 10, 25 health characteristics of, 31 population of, 5, 21

About the

Author

Terry Vatter received her M.S. degree in Education from Elmira College in 1993. Throughout her teaching career, which began in 1988, she has taught at-risk youth. Building upon a desire to make a contribution to society, and upon her own troubled high school experience, Ms. Vatter continues to work with these young people. She now teaches at an alternative high school in Ithaca, New York, and has published articles about her work inMMathematics Teacher. She is married and has three sons.

169

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from Teacher Ideas Press CELEBRATING THE EARTH: Stories, Experiences, Activities Norma J. Livo Invite young readers to observe, explore, and appreciate the natural world through engaging activities. Livo shows you how to use folk stories, personal narrative, and a variety of learning projects to teach students about amphibians, reptiles, mammals, constellations, plants, and other natural phenomena. Designed to build a Naturalist Intelligence in young learners, these stories and activities are packed with scientific information. All Levels. xvii, 174p. 8>/2xll paper ISBN 1-56308-776-6

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