Basic Mathematics - Walch · Unit 1:Addition and Subtraction • Basic Mathematics 8 Addition skills can help you do work around the house. Ellis wants to make some shelves for his

Basic Mathematics

Robert Taggart

®

PB MATH Basic Math TB 1/6/05 2:52 PM Page i

Table of ContentsTo the Student . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v

UUnniitt 11:: AAddddiittiioonn aanndd SSuubbttrraaccttiioonnLesson 1: Addition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3Lesson 2: Subtraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20Unit 1 Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37Unit 1 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

UUnniitt 22:: MMuullttiipplliiccaattiioonn aanndd DDiivviissiioonnLesson 3: Multiplication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47Lesson 4: Division . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69Unit 2 Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95Unit 2 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96

UUnniitt 33:: FFrraaccttiioonnss aanndd DDeecciimmaallssLesson 5: Fractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101Lesson 6: Decimals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131Unit 3 Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149Unit 3 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150

UUnniitt 44:: PPeerrcceennttss,, PPoowweerrss,, aanndd RRoooottssLesson 7: Percents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157Lesson 8: Powers and Roots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178Unit 4 Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197Unit 4 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199

Appendixes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202A. Review of Rules and Formulas . . . . . . . . . . . . . . . . . . . . . . . . . . 202B. Table of Squares and Square Roots . . . . . . . . . . . . . . . . . . . . . . 223

Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233

Power Basics: Basic Mathematics

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PB MATH Basic Math TB 1/6/05 2:52 PM Page iii

UNIT 1Addition and Subtraction

PB MATH Basic Math TB 1/6/05 2:52 PM Page 1

LESSON 1: Addition

GOAL: To review the addition of numbers to four digits withcarrying, and to use addition in word problems

WORDS TO KNOW

WWhhaatt IIss AAddddiittiioonn??

When you add, you combine two or more groups into one group.These groups can include one thing or more than one thing. Thenumber of things in one group can be added to the number ofthings in another group. Adding is quicker than counting.

You have three apples in one group below and two apples inthe other.

GGrroouupp OOnnee GGrroouupp TTwwoo

How many apples do you have altogether?

To answer this question, you can count:

1 2 3 4 5

Or, even faster, you can add:

3 + 2 = 5

Lesson 1: Addition • Basic Mathematics

3

ccaarrrryy

ccoolluummnn

ddiiggiitt

eeqquuaall ssiiggnn

pplluuss ssiiggnn

rrooww

ssuumm

ttoottaall


The sign for addition is + . It is called the pplluuss ssiiggnn.. The plussign tells you to add the numbers before and after the sign. Theanswer in an addition problem is called the ssuumm or ttoottaall.. Theresult of addition equals the sum or total. The eeqquuaall ssiiggnn is = .

Look at the examples below.

EExxaammppllee 11

3 + 7 = 10 Three plus seven equals ten. The sum or total is 10.

EExxaammppllee 22

8 + 4 = 12 Eight plus four equals twelve. The sum ortotal is 12.

■ PRACTICE 1: AdditionAnswer the question about each set of pictures. Write youranswer on the line after each question.

11.. Look at the apples below. How many apples are therealtogether? _____ apples

+ = ?

22.. Look at the circles below. How many circles are therealtogether? _____ circles

+ = ?

Unit 1: Addition and Subtraction • Basic Mathematics

4


Find the sum for each addition problem. Write your answer onthe line after each problem.

33.. 1 + 1 = _____ 44.. 2 + 1 = _____

55.. 2 + 2 = _____ 66.. 2 + 3 = _____

77.. 3 + 1 = _____ 88.. 4 + 3 = _____

AAddddiittiioonn PPrroobblleemmss iinn CCoolluummnnss

Addition problems can be written in different ways. You canwrite an addition problem in a rrooww,, in which the numbers arelined up horizontally. Look at the example below.

EExxaammppllee 11

8 + 6 = 14

However, you will more often write an addition problem in accoolluummnn.. Put the addition sign to the left of the last number to beadded. Then put a line under the last number, separating it fromthe total. Look at the example below.

EExxaammppllee 22

Addition problems are easier to solve when they are written incolumns, especially if you are adding large numbers.


5

8+ 6

14

The word sum comes from a Latin word thatmeans “highest.” So when we say “The sum of 6and 3 is 9,” we mean that the sum (9) is the highestnumber in the problem.

TIP


■ PRACTICE 3: Adding More Than Two NumbersFind the sum for each problem. Circle your answer when youhave finished.

11.. 22.. 1 + 5 + 3 + 2 = _______

33.. 44.. 4 + 2 + 1 + 3 = _______

55.. 66.. 3 + 4 + 2 + 6 = _______

Unit 1: Addition and Subtraction • Basic Mathematics

8

Addition skills can help you do work around thehouse. Ellis wants to make some shelves for hisliving room. He measures his living room wall anddecides that each shelf should be 4 feet long. At thelumber yard, he notices that boards are sold inlengths of 6 feet, 8 feet, 10 feet, 12 feet, and 16 feet.The salesperson tells him he can buy one piece ofwood and cut it into three pieces. If Ellis wantsthree shelves, each 4 feet long, which length ofboard should he buy? Write your answer on aseparate sheet of paper.

IN REAL LIFE

342

+ 6

134

+ 5

522

+ 7


AAddddiinngg TTwwoo--DDiiggiitt NNuummbbeerrss

A ddiiggiitt is any of the symbols used to write numbers: 0, 1, 2, 3, 4,5, 6, 7, 8, 9. So far we have added numbers with one digit.Numbers from 10 to 99 have two digits.

SSoommee OOnnee--DDiiggiitt NNuummbbeerrss SSoommee TTwwoo--DDiiggiitt NNuummbbeerrss

1, 3, 7, 6 10, 36, 21, 55

To add two-digit numbers, follow the steps below.

EExxaammppllee

35 + 54

SStteepp 11.. Line up the ones and tens digits in columns.

SStteepp 22.. Add the digits in the ones column.

SStteepp 33.. Add the digits in the tens column.

The sum is 89.


9

3 5+ 5 4

tens

ones

35+ 54

9

35+ 54

89


Basic Mathematics

WALCH PUBLISHING

Teacher’s Guide

®

Table of ContentsTo the Teacher . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viClassroom Management . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii

UUnniitt 11:: AAddddiittiioonn aanndd SSuubbttrraaccttiioonnUnit Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1Additional Activity Suggestions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

UUnniitt 22:: MMuullttiipplliiccaattiioonn aanndd DDiivviissiioonnUnit Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4Additional Activity Suggestions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

UUnniitt 33:: FFrraaccttiioonnss aanndd DDeecciimmaallssUnit Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7Additional Activity Suggestions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

UUnniitt 44:: PPeerrcceennttss,, PPoowweerrss,, aanndd RRoooottssUnit Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10Additional Activity Suggestions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

Answer Key . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13Graphic Organizers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19Student Book Appendixes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24Student Book Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

© 2005 Walch Publishing Basic Mathematics

iii

© 2005 Walch Publishing Teacher’s Guide • Basic Mathematics

1

This unit presents the operations of addition and subtraction. In Lesson 1, students learn the basicsof addition, how to add in columns, adding multi-digit numbers, carrying, and how to identify andsolve word problems involving addition. In Lesson 2, they learn about subtraction, includingsubtracting in columns, checking answers, subtracting numbers with different numbers of digits,borrowing, and how to identify and solve word problems involving subtraction.

Lesson 1—AdditionGoal: To review the addition of numbers to four digits with carrying, and to use

addition in word problems

WORDS TO KNOW

ccaarrrryy when the sum of a column is more than 9, to move numbers from that columnto the column of the next greater place value

ccoolluummnn numbers lined up vertically (up and down)

ddiiggiitt any one of the symbols 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, which are used to representnumbers

eeqquuaall ssiiggnn a sign used in place of the words “is equal to.” The sign looks like this: = .

pplluuss ssiiggnn a sign used to mean add. It looks like this: +.

rrooww numbers lined up horizontally (across)

ssuumm the answer to an addition problem

ttoottaall the answer to an addition problem; another word for sum

Lesson 2—SubtractionGoal: To review subtraction, including borrowing, and to use subtraction in

word problems

WORDS TO KNOW

ccoommmmuuttaattiivvee mathematical property that says that changing the order of the numbers to be pprrooppeerrttyy added or multiplied doesn’t change the answer

ddiiffffeerreennccee the answer in a subtraction problem

mmiinnuueenndd in a subtraction problem, the number that is being reduced, or subtracted from; in 4 – 1, the minuend is 4.

Unit 1: Addition and Subtraction

Teacher’s Guide • Basic Mathematics © 2005 Walch Publishing

2

mmiinnuuss ssiiggnn a sign used to show that the number after the sign is to be subtracted. It lookslike this: – .

ppllaaccee vvaalluuee the value of a digit within a number is shown by where it is placed in the number, that is, whether it stands for ones, tens, hundreds, thousands, and so forth.

ssuubbttrraaccttiioonn mathematical operation in which one number is taken away from another

ssuubbttrraahheenndd in a subtraction problem, the number to be subtracted, or taken away, to find the difference between two numbers; in 7 – 5, the subtrahend is 5.

NNootteess oonn AApppplliiccaattiioonn AAccttiivviittiieess iinn SSttuuddeenntt TTeexxtt

AAddddiittiioonnaall AAccttiivviittyy SSuuggggeessttiioonnss ■ Have learners visit the admissions office of a nearby college or junior college they might consider

attending. Have them gather information on the costs of attending the school (including tuition,fees, books, dormitory housing if applicable, meals, parking permits, and so on) and find thetotal cost. They can also learn the number of credits needed to graduate and how much thecourses they would want to take count toward the total.

■ Have learners visit a local food bank or soup kitchen to learn the total cost of providing such aservice. They should ask about the renting of the space and the cost of the food (including theapproximate value of donated food), paper goods, cleaning service, paid staff (if any), andliability insurance. Have them total the expenses and research how much of the money neededcomes from organized charities (such as the United Way) and other sources. Learners may beable to suggest additional ways to procure donated food, labor, or money for the pantry orkitchen.

AAccttiivviittyy SSkkiillllss AApppplliieedd PPrroodduucctt

AA NNeeww CChheecckkiinngg AAccccoouunntt gathering information completed chart

critical thinking written opinion

computation skills

CCoouunnttiinngg AAnniimmaallss gathering information completed chart

critical thinking written conclusion

computation skills

YYoouurr MMoonntthhllyy BBuuddggeett gathering information completed chart

computation skills


3

■ Ask learners with access to cars to visit a service station for a tune-up. They should find out thebasic rate and also inquire about “extras” that add to the cost. Which extra services seemlegitimate, and which seem like padding? What is the total cost of the desired services? Learnerswithout access to a car might team up with those who do; they might also complete the sameassignment with a bicycle at a bicycle shop.

■ Have learners attend a town meeting, city council meeting, or their church’s annual meeting toobserve and participate in budget discussions. Most such meetings are open to observers.Learners could prepare for the meeting by interviewing the town or county planner orcomptroller (titles vary but basically they’re looking for the financial officers). Learners shouldalso obtain a copy of the proposed budget to study. If there is a desire to take this idea further,you could have an in-class debate about a municipal budget.

MMeennttaall MMaatthh■ Addition and subtraction lend themselves well to lively classroom games. One easy idea is to

split your learners into two teams. Then present the teams with a series of addition andsubtraction problems. Learners should not use paper, pencils, or calculators—all math shouldbe done in their heads. The first person to call out each correct answer wins a point for his or herteam. You can vary the game by adding a third team. Each team then takes a turn providingaddition and subtraction problems for the other two teams to solve in their heads.

DDiiffffeerreennttiiaattiioonn■ As you present new concepts, demonstrate them on the board or overhead, using metacognitive

strategies to explain out loud what you are thinking and doing throughout the process.■ For learners who find it difficult to think abstractly, use manipulatives to demonstrate the

principles of addition.■ Give students pages from catalogs with items they are likely to find appealing, such as

electronics, CDs, DVDs, and so forth. Have students work individually or in small groups tochoose items from the catalog and add their cost. You may ask students to choose a certainnumber of items and add their prices to find the total cost, or ask them to find a minimum ofthree items that add up to a certain dollar value. You may want to specify whether they shouldinclude or omit tax and shipping costs in their calculations.

■ To help students recall important new terms, use the Words to Know and definitions from eachlesson to prepare crossword puzzles or matching activities.

■ Ask students to brainstorm a list of all the ways they use addition in their daily lives. If you like,write the list on a corner of the board or on newsprint and post it in the classroom as areminder.


13

UUnniitt 11:: AAddddiittiioonn aanndd SSuubbttrraaccttiioonn

LLeessssoonn 11:: AAddddiittiioonn

PPrraaccttiiccee 11:: AAddddiittiioonn1. 9 apples 5. 42. 9 circles 6. 53. 2 7. 44. 3 8. 7

PPrraaccttiiccee 22:: AAddddiittiioonn PPrroobblleemmss iinn CCoolluummnnss1. 13 7. 112. 16 8. 143. 9 9. 104. 6 10. 115. 15 11. 146. 12 12. 17

PPrraaccttiiccee 33:: AAddddiinngg MMoorree tthhaann TTwwoo CCoolluummnnss1. 15 4. 102. 11 5. 163. 13 6. 15

IInn RReeaall LLiiffee,, ppaaggee 88:: Ellis should add the lengths of the three shelves together. 4 feet + 4 feet + 4 feet = 12 feet. Ellis should buy the board thatis 12 feet long.

PPrraaccttiiccee 44:: AAddddiinngg TTwwoo--DDiiggiitt NNuummbbeerrss1. 86 6. 832. 37 7. 693. 95 8. 594. 38 9. 285. 88 10. 99

PPrraaccttiiccee 55:: AAddddiinngg TThhrreeee--DDiiggiitt NNuummbbeerrss1. 799 6. 6672. 687 7. 3883. 589 8. 9934. 959 9. 4975. 937 10. 762

PPrraaccttiiccee 66:: AAddddiinngg FFoouurr--DDiiggiitt NNuummbbeerrss1. 4799 6. 81872. 9795 7. 43643. 4243 8. 85374. 7977 9. 89175. 8998 10. 9999

TThhiinnkk AAbboouutt IItt,, ppaaggee 1166:: When numbers are lined up in columns, it is easy to see whichdigits are in the ones place, tens place, and so on. This makes itmuch easier to add. Also, one number is right below the other,

without signs or spaces between them.

PPrraaccttiiccee 77:: CCaarrrryyiinngg1. 1307 4. 53852. 10,307 5. 86753. 9011 6. 5754

TThhiinnkk AAbboouutt IItt,, ppaaggee 1188:: Shannon did not carry the 1 to the hundreds column. The correct answer is 314.

PPrraaccttiiccee 88:: WWoorrdd PPrroobblleemmss1. 396 CDs 6. 427 new restaurants2. 200 candy bars 7. 1984 miles3. $402 8. 4225 white cars4. 1066 workers 9. 22,518 patients5. $418

LLeessssoonn 22:: SSuubbttrraaccttiioonn

TThhiinnkk AAbboouutt IItt,, ppaaggee 2211:: The commutative property doesn’t work for subtraction. Youwill get a different answer if the order is changed. For example,5 – 3 = 2. But 3 – 5 = –2.

PPrraaccttiiccee 99:: SSuubbttrraaccttiioonn1. 4 4. 0 2. 6 5. 9 3. 7 6. 3

PPrraaccttiiccee 1100:: SSuubbttrraaccttiinngg iinn CCoolluummnnss1. 7 4. 12. 1 5. 63. 0 6. 5

PPrraaccttiiccee 1111:: CChheecckkiinngg YYoouurr AAnnsswweerrss1. 4, 4 + 4 = 8 3. 4, 4 + 5 = 92. 2, 2 + 3 = 5 4. 6, 6 + 2 = 8

TThhiinnkk AAbboouutt IItt,, ppaaggee 2255:: Ramón thought that since zero stands for nothing, he didn’tneed to put it in the column. He was wrong. The zero must beused because it “holds” the ones place. The 2 actually belongs inthe tens place. The correct answer is 33.

PPrraaccttiiccee 1122:: SSuubbttrraaccttiinngg TTwwoo--DDiiggiitt NNuummbbeerrss1. 62 8. 232. 11 9. 143. 33 10. 22 4. 17 11. 535. 44 12. 63 6. 52 13. 227. 20 14. 52

Answer Key


19

GGrraapphhiicc OOrrggaanniizzeerrssGraphic organizers are a versatile teaching and learning tool. They can help students clarify their thinking,integrate new knowledge, reinforce their understanding of a topic, and review material for quizzes and testsUsing graphic organizers, learners can understand content more clearly and can take clear, concise notes.Graphic organizers can also act as a visual aid to make abstract concepts more concrete.

The graphic organizers provided here can be used in many ways. You can use transparencies of theorganizers to introduce or review a topic with the entire class. You can photocopy the organizers and allowstudents to use them as they work through the student text. Here is a brief description of the organizers inthis section, and their uses.

SSttrruuccttuurreedd NNootteessThis organizer is one way of organizing notes as students read through the text. Students should write themain topic in the box at the top. In the boxes underneath they can write details about the topic, specificinformation, examples, and so forth.

CCoonncceepptt aanndd DDeeffiinniittiioonn CChhaarrttThis chart is used to keep track of new vocabulary and concepts as they are introduced in the text. Studentsshould write the word or concept in the box at the top of the chart. They should then fill in the information inthe rest of the boxes.

SStteeppss iinn aa PPrroocceessss CChhaarrttThis graphic organizer is used to show information in order. Students will find this organizer particularlyuseful when taking notes of mathematical processes, showing the steps in order. They should write theprocess in the box at the top of the chart, then break the process down into steps and write one step in onebox, adding or deleting boxes as needed.

TTaabblleeThis graphic organizer has many uses. Students should label each column, then write relevant information ineach cell of the chart.

Graphic Organizers


21

Concept and Definition Chart

CCoonncceepptt

CChhaarraacctteerriissttiiccss

WWhhaatt iiss iitt lliikkee?? WWhhaatt iiss iitt nnoott lliikkee??

DDeeffiinniittiioonn EExxaammpplleess

Basic Mathematics

WALCH PUBLISHING

Workbook

Table of Contents


iii

To the Student . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii

AAccttiivviittyy 11Addition 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

AAccttiivviittyy 22Magic Squares . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

AAccttiivviittyy 33Addition Bingo . . . . . . . . . . . . . . . . . . . . . . . . . . 3


AAccttiivviittyy 55Tug-of-War . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5


AAccttiivviittyy 77Estimating Addition 1 . . . . . . . . . . . . . . . . . . . . . 7

AAccttiivviittyy 88Estimating Addition 2 . . . . . . . . . . . . . . . . . . . . . 8

AAccttiivviittyy 99Adding Out Loud . . . . . . . . . . . . . . . . . . . . . . . . . 9

AAccttiivviittyy 1100Perimeter Practice . . . . . . . . . . . . . . . . . . . . . . . 10

AAccttiivviittyy 1111Vending Machine Math . . . . . . . . . . . . . . . . . . . 11

AAccttiivviittyy 1122Breaking the Code . . . . . . . . . . . . . . . . . . . . . . . 12

AAccttiivviittyy 1133Solving One-Step Equations Using Addition . 13

AAccttiivviittyy 1144Subtraction 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

AAccttiivviittyy 1155Number Code . . . . . . . . . . . . . . . . . . . . . . . . . . 15


AAccttiivviittyy 1177Estimating Subtraction . . . . . . . . . . . . . . . . . . 17


AAccttiivviittyy 1199Find the Missing Part . . . . . . . . . . . . . . . . . . . . 19

AAccttiivviittyy 2200Estimation and Exact Answers . . . . . . . . . . . . . 20

AAccttiivviittyy 2211Addition and Subtraction Puzzle . . . . . . . . . . . 21

AAccttiivviittyy 2222Tug-of-War with Subtraction . . . . . . . . . . . . . . 22

AAccttiivviittyy 2233Solving One-Step Equations Using Subtraction 23

AAccttiivviittyy 2244Multiplication Bingo . . . . . . . . . . . . . . . . . . . . . 24

AAccttiivviittyy 2255Partner Facts . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

AAccttiivviittyy 2266Multiplication Chart . . . . . . . . . . . . . . . . . . . . . 26

AAccttiivviittyy 2277Deciding Out Loud . . . . . . . . . . . . . . . . . . . . . . 27

AAccttiivviittyy 2288Multiplication 1 . . . . . . . . . . . . . . . . . . . . . . . . . 28

AAccttiivviittyy 2299Using Multiplication to Find Area . . . . . . . . . . 29

AAccttiivviittyy 3300Growing Volume . . . . . . . . . . . . . . . . . . . . . . . . 30

AAccttiivviittyy 3311Bringing Down the Zero . . . . . . . . . . . . . . . . . . 31

AAccttiivviittyy 3322Estimating Answers . . . . . . . . . . . . . . . . . . . . . . 32

AAccttiivviittyy 3333Multiplication 2 . . . . . . . . . . . . . . . . . . . . . . . . . 33

AAccttiivviittyy 3344Write First . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

AAccttiivviittyy 3355Keyword Scramble . . . . . . . . . . . . . . . . . . . . . . 35

UUnniitt 22:: MMuullttiipplliiccaattiioonn aanndd DDiivviissiioonn

UUnniitt 11:: AAddddiittiioonn aanndd SSuubbttrraaccttiioonn

Basic Mathematics © 2005 Walch Publishing

iv

Table of Contents, continuedAAccttiivviittyy 3366

Solving One-Step Equations Using Multiplication 36

AAccttiivviittyy 3377Divisibility Rules . . . . . . . . . . . . . . . . . . . . . . . . 37

AAccttiivviittyy 3388Number Code . . . . . . . . . . . . . . . . . . . . . . . . . . 38

AAccttiivviittyy 3399Find the Quotient 1 . . . . . . . . . . . . . . . . . . . . . . 39

AAccttiivviittyy 4400Find the Quotient 2 . . . . . . . . . . . . . . . . . . . . . . 40

AAccttiivviittyy 4411Estimating Quotients . . . . . . . . . . . . . . . . . . . . 41

AAccttiivviittyy 4422Think About It: Estimating . . . . . . . . . . . . . . . . 42

AAccttiivviittyy 4433Shorthand Division . . . . . . . . . . . . . . . . . . . . . . 43

AAccttiivviittyy 4444Multiplication and Division Puzzle . . . . . . . . . 44

AAccttiivviittyy 4455Solving One-Step Equations Using Division . . 45

AAccttiivviittyy 4466Reducing Fractions . . . . . . . . . . . . . . . . . . . . . . 46

AAccttiivviittyy 4477Find the Better Buy . . . . . . . . . . . . . . . . . . . . . . 47

AAccttiivviittyy 4488Comparing Fractions . . . . . . . . . . . . . . . . . . . . . 48

AAccttiivviittyy 4499Fractions 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

AAccttiivviittyy 5500Finding the GCF . . . . . . . . . . . . . . . . . . . . . . . . 50


AAccttiivviittyy 5522To Borrow or Not to Borrow? . . . . . . . . . . . . . . 52


AAccttiivviittyy 5544Scale Drawings . . . . . . . . . . . . . . . . . . . . . . . . . 54

AAccttiivviittyy 5555Unit Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

AAccttiivviittyy 5566A Grading Dilemma . . . . . . . . . . . . . . . . . . . . . 56

AAccttiivviittyy 5577Solving One-Step Equations Using the Reciprocal 57

AAccttiivviittyy 5588Fraction Rap . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

AAccttiivviittyy 5599Fraction Puzzle . . . . . . . . . . . . . . . . . . . . . . . . . 59

AAccttiivviittyy 6600Comparing Decimals . . . . . . . . . . . . . . . . . . . . 60

AAccttiivviittyy 6611Decimals 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

AAccttiivviittyy 6622Decimals 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

AAccttiivviittyy 6633Draw It . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

AAccttiivviittyy 6644Find the Missing Piece . . . . . . . . . . . . . . . . . . . 64

AAccttiivviittyy 6655Fractions and Equivalent Decimals . . . . . . . . . 65

AAccttiivviittyy 6666Decimal Puzzle . . . . . . . . . . . . . . . . . . . . . . . . . 66

AAccttiivviittyy 6677Unlimited Options? . . . . . . . . . . . . . . . . . . . . . . 67

AAccttiivviittyy 6688What to Do with That Decimal? . . . . . . . . . . . 68

AAccttiivviittyy 6699Writing About History . . . . . . . . . . . . . . . . . . . 69

AAccttiivviittyy 7700Percents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

AAccttiivviittyy 7711Percent Increase or Decrease? . . . . . . . . . . . . . 71

UUnniitt 44:: PPeerrcceennttss,, PPoowweerrss,, aanndd RRoooottss

UUnniitt 33:: FFrraaccttiioonnss aanndd DDeecciimmaallss

Table of Contents, continued


v

AAccttiivviittyy 7722Pie Charts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

AAccttiivviittyy 7733Percent Decimal Chart . . . . . . . . . . . . . . . . . . . 73

AAccttiivviittyy 7744Commission . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

AAccttiivviittyy 7755A Quick Way to Tip . . . . . . . . . . . . . . . . . . . . . . 75

AAccttiivviittyy 7766Sales Tax . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76

AAccttiivviittyy 7777Simple Interest . . . . . . . . . . . . . . . . . . . . . . . . . 77

AAccttiivviittyy 7788Percent Puzzle . . . . . . . . . . . . . . . . . . . . . . . . . . 78

AAccttiivviittyy 7799Unscramble the Letters . . . . . . . . . . . . . . . . . . . 79

AAccttiivviittyy 8800Solving Percent Problems Using Proportions . 80

AAccttiivviittyy 8811Solving Percent Problems Using MathematicalSentences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81

AAccttiivviittyy 8822Zero Power . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

AAccttiivviittyy 8833Multiplying Negative Numbers . . . . . . . . . . . . 83

AAccttiivviittyy 8844Scientific Notation . . . . . . . . . . . . . . . . . . . . . . 84

AAccttiivviittyy 8855Powers and Roots . . . . . . . . . . . . . . . . . . . . . . . 85

AAccttiivviittyy 8866What Went Wrong? . . . . . . . . . . . . . . . . . . . . . 86

AAccttiivviittyy 8877Matching the Steps . . . . . . . . . . . . . . . . . . . . . . 87

AAccttiivviittyy 8888Write to Remember . . . . . . . . . . . . . . . . . . . . . . 88

AAccttiivviittyy 8899Using Factor Trees to Find Square Roots . . . . . 89

AAccttiivviittyy 9900Defend Your Choice! . . . . . . . . . . . . . . . . . . . . . 90

AAccttiivviittyy 9911Powers and Roots Puzzle . . . . . . . . . . . . . . . . . 91

AAccttiivviittyy 9922Pythagorean Theorem . . . . . . . . . . . . . . . . . . . 92

Unit 2: Multiplication and Division • Basic Mathematics © 2005 Walch Publishing

24

Your class has decided to play a game of multiplication bingo. Your teacher will roll the two diceand will multiply the two numbers together. Your teacher will continue to do this until someonehas bingo. You are allowed to fill out the spaces of your bingo card with the numbers 1 to 36.Numbers can be repeated on your card up to five times.

11.. On a separate sheet, create a chart showing all of the possible products of the two dice.

22.. Would any numbers in the range you’re allowed to use be more useful on a bingo card thanothers? Explain.

________________________________________________________________

33.. Are any numbers between 1 and 36 impossible to get? Explain.

________________________________________________________________

________________________________________________________________

44.. How would you fill out your card?

UNIT 2 • ACTIVITY 24MMuullttiipplliiccaattiioonn BBiinnggoo

NAME:

Free Space

© 2005 Walch Publishing Unit 2: Multiplication and Division • Basic Mathematics

25

Choose a partner for the following activity. Plan to help each other learn multiplication facts!

First, as a team, write down every multiplication fact from 0 to 12. This means you need to writedown 0 � 0 = 0, 0 � 1 = 0, through 12 � 0 = 0. Then write down 12 � 1 = 12 through 12 � 12 = 144. Write each fact on a separate slip of paper. Placed all the slips face down.

Next, you will take turns quizzing each other using these slips of paper.

Decide who will go first. The other partner will then choose a slip of paper and quiz the firstplayer. For instance, you may pick up the slip of paper that reads: 6 � 7 = 42. You would say: “Sixtimes seven equals . . .” and wait for your partner to answer. If your partner answers correctly,choose another slip of paper and read the problem. Continue for 2 minutes or until your partnerhas given three incorrect responses. If your partner answers incorrectly, write the completecorrected multiplication fact below.

Once 2 minutes is up (or three wrong answers have been given), change roles. The quizzer willnow give answers. Whoever answers more problems correctly during his or her turn wins theround.

After each round, discuss your wrong answers and review the correct multiplication facts youwrote below. Try to help each other improve. Continue to play until your teacher ends the game.

Correct multiplication fact 1: ______________________________



UNIT 2 • ACTIVITY 25PPaarrttnneerr FFaaccttss

NAME:

Unit 2: Multiplication and Division • Basic Mathematics © 2005 Walch Publishing

26

Complete the multiplication chart by filling in the missing values.

UNIT 2 • ACTIVITY 26MMuullttiipplliiccaattiioonn CChhaarrtt

NAME:

11.. Are there any patterns that you found? ________________________________________

_____________________________________________________________________

22.. What do you notice about the middle diagonal starting at the top left corner?____________

_____________________________________________________________________

� 1 2 3 4 5 6 7 8 9 10 11 12 13

1 1 2 3 4 5 6 7 8 9 10 11 12 13

2 2 6 10 12 18 22

3 12 15 30

4 8 24 44 52

5 10 25 40 50

6 6 18 30 42 72

7 21 49 77 91

8 8 32 48 72

9 27 90 108

10 10 50 80 110

11 11 33 77 143

12 48 84 120

13 26 65 117 169

Basic Mathematics

WALCH PUBLISHING

Test Pack

Table of ContentsTo the Teacher . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v

Testing Students Who Do Not Test Well . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vi

Test-Taking Strategies for Power Basics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii

PPrreetteesstt .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 11

UUnniitt 11 TTeesstt:: AAddddiittiioonn aanndd SSuubbttrraaccttiioonn .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 77

UUnniitt 22 TTeesstt:: MMuullttiipplliiccaattiioonn aanndd DDiivviissiioonn .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 1122

UUnniitt 33 TTeesstt:: FFrraaccttiioonnss aanndd DDeecciimmaallss .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 1177

UUnniitt 44 TTeesstt:: PPeerrcceennttss,, PPoowweerr,, aanndd RRoooottss .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 2233

PPoosstttteesstt .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 2277

Answer Key . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

Student Record-Keeping Form . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

Strategies for Standardized Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

© 1997, 2000, 2005 Walch Publishing Basic Mathematics Test Pack

iii

Circle the correct answer for the problem. Show your work.

11..

aa.. 1180bb.. 1260cc.. 1270dd.. 1280


22.. (542 + 727) – 215 = ?aa.. 400bb.. 1054cc.. 1344dd.. 1484

Solve the following problem, and write your answer on the line. Show your work.

33.. Mr. and Mrs. Cordero have three vacations planned for this year. The first vacation costs $1435.The second costs $4989. The third costs $2750. How much will they spend on vacations duringthe year? $ __________


44.. 4145× 139

?aa.. 576,045bb.. 576,155cc.. 587,255dd.. 672,555

BASIC MATHEMATICS • PRETESTNAME: DATE:

© 1997, 2000, 2005 Walch Publishing Pretest • Basic Mathematics Test Pack

1

147756

+ 377?

Pretest • Basic Mathematics Test Pack © 1997, 2000, 2005 Walch Publishing

2


55.. 45,512 × 17 = ? ______________


66.. Mr. Johnson has $5500 in his bank account. He has three bills to pay. Each bill is for $400. How much will he have left in his bank account after he pays the three bills?

aa.. $4300bb.. $5100cc.. $5300dd.. $5380


77.. Mrs. Paletta gets a pension of $450 each month. She also gets $620 each month from SocialSecurity. How much does she get each year?

aa.. $5400bb.. $7400cc.. $10,740dd.. $12,840


88..

aa.. 34 R 3bb.. 22 R 9cc.. 202 R 9dd.. 2029


99.. 82,698 ÷ 33 = ?aa.. 2312bb.. 2506cc.. 2016dd.. 3506

NAME: DATE:

?344317

NAME: DATE:

12


11..

?

aa.. 29bb.. 46cc.. 204dd.. 354


22..

? __________


33.. 569 × 95 = ? __________


44.. 48 × 785 = ?aa.. 37,680bb.. 37,737cc.. 737dd.. 36,680

UNIT 2 TEST • MULTIPLICATION AND DIVISION

Unit 2 Test • Basic Mathematics Test Pack © 1997, 2000, 2005 Walch Publishing

12× 17

26× 42

© 1997, 2000, 2005 Walch Publishing Unit 2 Test • Basic Mathematics Test Pack

13


55..

?

aa.. 5844bb.. 308,271cc.. 32,142dd.. 207,271


66..

? __________


77.. 825 × 37 = ?aa.. 8200bb.. 8250cc.. 29,395dd.. 30,525


88.. 145 × 6562 = ?aa.. 951,290bb.. 951,497cc.. 951,490dd.. 45.25

NAME: DATE:

1461× 211

98× 53

NAME: DATE:

27


11..

? __________


22.. (128 + 404) – 499 = ? __________


33.. Janek is a car salesman. He sold three cars this month. He made $1324 for his first commission,$1560 for his second, and $1233 for his third. How much did he make in commissions thismonth?

aa.. $3997bb.. $4007cc.. $4237dd.. $4117


44.. 1625 – 1228 = ?aa.. 397bb.. 407cc.. 497dd.. 2853

BASIC MATHEMATICS • POSTTEST

© 1997, 2000, 2005 Walch Publishing Posttest • Basic Mathematics Test Pack

12453299

+ 309

Posttest • Basic Mathematics Test Pack © 1997, 2000, 2005 Walch Publishing

28

NAME: DATE:


55.. Yin bought three pairs of socks for $2 a pair. He also bought a pair of shoes for $40 and two tiesfor $12 each. What was his total bill? ___________


66.. 469 × 92 = ?aa.. 4315bb.. 41,480cc.. 42,148dd.. 43,148


77..

?

aa.. 253,004bb.. 263,004cc.. 263,994dd.. 277,900


88.. Petra paid $2200 a month for her office space last year. This year she moved to larger offices.She is now paying $2650 a month. How much more will she pay in rent this year compared tolast year?

aa.. $450bb.. $4500cc.. $5400dd.. $31,800

1302× 202

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Basic Mathematics - Walch · Unit 1:Addition and Subtraction • Basic Mathematics 8 Addition skills can help you do work around the house. Ellis wants to make some shelves for his