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Activities for Learning, Inc.

RIGHTSTART™ MATHEMATICS

ACTIVITIES FOR THE AL ABACUSA HANDS-ON APPROACH TO ARITHMETIC

Copyright ©1988, 2000 by Joan A.Cotter. All rights reserved. No partof this publication may be reproduced, stored in a retrieval system, ortransmitted, in any form or by any means, electronic, mechanical,photocopying, recording, or otherwise, without written permissionfrom the publisher except as permitted by the United States CopyrightAct of 1976.The publisher hereby grants permission to reproduce these worksheetsfor a single homeschooling family or a single teacher’s class use only.

Printed in the United States of America, November 2000.

Copies may be ordered from:Activities for Learning, Inc.P.O. Box 468; 321 Hill StreetHazelton, ND 58554-0468888-272-3291order@RightStartMath.comwww.RightStartMath.com

ISBN 978-0-9609636-4-5

.

ABOUT THE AUTHOR

Joan A. Cotter received her BSEE in electrical engineering from theUniversity of Wisconsin-Madison and worked in computer design.She received her Montessori diploma from the Montessori TrainingCenter of Minnesota in St. Paul, Minnesota and has administered andtaught in several Montessori schools.She also received a Masters in Curriculum and Instruction (MACI)from the College of St. Thomas, St. Paul. She has taught mathematicsto students from age three through grade eight.

PREFACE

Unit 1: Basic Concepts 1NAMING QUANTITIES 1-10 1Using fingers for 1 to 5 1Using fingers for 6 to 10 1 Quantities on the abacus 2Matching hands and abacuses 2Sorting 3Worksheets 3

MEMORIZING 1-10 4Memorizing the words 4Reading quantities on the abacus 4The stairs 4

COUNTING 5Counting a known quantity 5Counting to a number 5

LEARNING NUMERALS 6Using sandpaper numerals 6Writing the numerals 6Practice with the numerals 74 simple card games 7Introducing zero 8

MATCHING AND CONCENTRATION 8Matching with numerals 8 Matching Concentration 9In-order Concentration 9

EVENS AND ODDS 9Counting by twos 10Counting the dots 10Even or odd 10Evens-odds on abacus 11Counting beads by twos 12Counting with odds 12The middle 12

THE ORDINAL NUMBERS 13Ordinal numbers in general 13Ordinal numbers on the abacus 13 Writing ordinal numerals 14Applications (future review) 14

Unit 2: Introducing addition 15SIMPLE ADDITION 15Beginning adding 15 Practice 16

ADDING 1 17

THE COMMUTATIVE LAW 17Reversing the addends 17Application 18

THE WAYS TO MAKE 10 18Splitting 10 18Games 19Missing addends 19

SPLITTING NUMBERS 9-2 20More splitting 20Missing addends 20

Unit 3: Numbers from 11 to 100 21THE TENS 21Entering tens 21Reading the tens 22Adding tens 22 Splitting 100 22

TENS AND ONES 23Tens and ones on the abacus 23Practice 23Adding tens and ones 24

MORE TENS AND ONES 24Customary names 24Counting by tens 24 Tens and ones + ones 25

THE TEENS 25 The names 25Practice 26Adding with sums in the teens 26Adding double digits 27

VERTICAL ADDITION 28Adding with sums ten or less 28Adding with sums over ten 29

ADDING MORE THAN TWO 30 Make Tens game 30Adding three numbers 31

COUNTING TO 100 32Counting by 1s 32Counting by 2s 33Counting by 10s 33Counting by 5s 33

Contents

Unit 4: Mastering the addition facts 35EVENS + EVENS... 36Even + even 36Odd + odd 36Even + odd 37

ADDING 1 OR 2 38Adding 1 to a number 38Adding 2 to a number 38Adding 2 to an even number 39Adding 2 to an odd number 40

SUMS EQUAL TO 11 OR 9 40Facts equal to 11 40Facts equal to 9 41

THE DOUBLES GROUPS 42Doubles 42 Near doubles 42Middle doubles 43

ADDING NINE OR EIGHT 44Adding 10 to a number 44Adding 9 to a number 44Adding 8 to a number 46

Unit 5: Introducing subtraction 47SIMPLE SUBTRACTION 47Oral subtraction 47Written subtraction 48Subtracting from 10 48Subtracting 1 49

SUBTRACTIONS > 10 50Subtracting tens 50Subtracting single-digit numbers 51Subtracting double-digit numbers 52

SUBTRACTION RESULTS 53Greater than, equal to, or less than 53Remainders and differences 54Subtraction twins 55Equations 56Checking 57

SPECIAL EFFECTS 58Minuend decreased by 1 58Subtrahend decreased by 1 58Counting up 59

Unit 6: Mastering the subtraction facts 61

SUBTRACTING 1 OR 2 61Subtracting evens from evens... 61Subtracting 1 from a number 62Subtracting 2 from an even number 62Subtracting 2 from an odd number 63

SUBTRACTING CONSECUTIVES 63Subtracting consecutive ones 63Subtracting consecutive evens and odds 64

SUBTRACTING FROM 11 OR 9 64Subtracting from 11 64Subtracting from 9 65

SUBTRACTING 9 OR 8 65Subtracting 9 from a number 65Subtracting 8 from a number 66

THE DOUBLES GROUPS 67Doubles 67Near doubles 67

Unit 7: Adding and subtracting inthousands 69

TABLES 69Addition table 69Subtraction table 70Cotter Sum Line 71

HUNDREDS AND THOUSANDS 72The hundreds 72Adding with sums in the hundreds 73The thousands 75Adding in the thousands 76Subtracting in the thousands 77

BEAD TRADING 78Basic bead trading 78Variations 79

ADDITION ALGORITHM 79Adding tens without carrying 79Adding tens with carrying 80Adding hundreds with carrying 81Adding thousands with carrying 81Adding three numbers 82

SIMPLIFIED SUBTRACTION 83Subtracting tens without borrowing 83Subtracting tens with borrowing 83Subtracting hundreds with borrowing 84

Unit 8: Multiplication 87SKIP COUNTING 87On the abacus 87Patterns on the hundred chart 88Strategies for memorizing 88Review of adding and subtracting 89

INTRODUCING MULTIPLICATION 89Basic multiplying 89Multiplying with 0s and 1s 90Multiplying with take and give 91Writing multiplication tables 91Using the table 92 Guess the sign 92

MULTIPLICATION RESULTS 93Write the equation 93Changing the order (commutative law) 94Changing the grouping (associative law) 94Mastering the facts 95

MULTIPLICATION ALGORITHM 96Multiplying tens 96 Multiplying 2-digit numbers 96Multiplying 3-digit numbers 98Multiplying by multiples of 10 99Multiplying by 2-digit numbers 100

Unit 9: Division 101INTRODUCING DIVISION 101Division by counting 101Division by skip counting 102Division with take and give 102The dividing line 103 Repeated subtraction 103

DIVISION RESULTS 104 Writing equations 104Missing factors 105Remainders 105 Increasing dividends 106Increasing divisors 107 Comparing quotients 106Mastering the facts 107Dividing larger numbers 107

SHORT DIVISION 108Division without trading 108Division with trading 109Multivides 112

LONG DIVISION 112Division with a table 112Guess the multiple 113"Octopus" multiplying 113Single-digit quotients 114Multi-digit quotients 114

Unit 10: Other topics 115ROUNDING 115

COMMON MULTIPLES 116

PARENTHESES 117

NUMBER BASE OF 4 118Numeration 118Addition and subtraction 119Multiplication and division 120Converting between base 4 and base 10 120Other bases 121

FACTORS 121

MEASUREMENT 121

ON TO THE MILLIONS 123

SQUARES 123Introduction 124 Finding the next square 125Squaring a sum 126Dividing a square by a square 126

PERCENTAGE 126A fraction of a number 127A fraction of 100 127

AVERAGE 128

Unit 11: Japanese (Chinese) abacus 129

NUMERATION 129

ADDITION 130Adding without carrying 130Carrying with the 5-bead 131Carrying with tens 131Adding 6, 7, and 8 133Adding 9 134

Appendix

18 Introducing addition

Repeat with the Cs adding 4 + 6 and the Bs adding 6 + 4.Do you think this is always true? Ask the childrenfor two numbers to try.

2. Prepare worksheets (2-7 to 2-9) with problems such as4 + 5 and 5 + 4 in pairs and let the children work indepen-dently. Observe whether or not they are using the abacusfor the second sum. It takes time for children to prove tothemselves that it is always true.

3. For children who have mastered adding 1 to a numberand the commutative law, a worksheet with 1 plus a num-ber will be a challenge. Let each child decide whether ornot to use the abacus.

Application1. Adding water to containers provides an excellent exam-ple of the commutative law. Prepare four identical glass-es, two filled to the same lower level and two filled to thesame higher level as shown.

While pointing to the first arrangement, ask the children,When I add the water from this container, howhigh will the water be? Have the children venture aguess before pouring the water.

Then ask the same question while pointing to the secondarrangement. [The levels will be the same.] Set up the ex-periment at a learning center where the children can per-form it for themselves.

2. Addition problems can be worked with water using asmall marked beaker, a larger marked beaker, and a pitch-er of water.

THE WAYS TO MAKE 10Ten is an important number in our number system and thefacts that make 10 are also very helpful to know. Severalgames will be presented to help the children master thesefacts in a non-stressful atmosphere.

Splitting 101. Enter 10 on the top wire. Separate the right bead byone-half inch (1 cm) and ask a child to state the fact. [9 +1 = 10] Move over another bead and ask another child tostate that fact. [8 + 2 = 10] Continue to 1 + 9.

2. Give the children a blank worksheet and ask them touse their abacuses and record the combinations that make10. After they are written, have the children find the“twins”; for example, 1 + 9 and 9 + 1. Each set of twinscan be circled with a different color. Or the facts can becut apart and the twins pasted together on another sheet ofpaper. One fact, 5 + 5, is called a "double" and does nothave a twin.

4 + 5 = 5 + 4 =

8 + 2 = 2 + 8 =

5 + 1 = 1 + 5 =

3 + 6 = 6 + 3 =

1 + 4 = 1 + 6 = 1 + 1 = 1 + 3 = 1 + 2 = 1 + 7 = 1 + 9 = 1 + 5 = 1 + 8 =

+ = + =

+ =+ =+ =+ =+ =+ =+ =

+ = + =

+ =+ =+ =+ =+ =+ =+ =

9 1 108 2 107 3 106 4 105 5 104 6 103 7 102 8 101 9 10

Introducing addition 19

Games1. HANDSHAKING GAME. Distribute among ten chil-dren one of each number 1 to 9, but two 5s. Build thestairs on the abacus; move the remaining beads near thestairs to narrow the gap, as shown. Touch the top wireand read the fact, 1 + 9. The children having those num-bers shake hands gently. Continue to 9 + 1. Then ask,Who shook hands twice? [All but those with the 5s]Who shook hands only once? Why?

2. FINDING THE PAIRS. This game for two or threeplayers uses the same cards as the Handshaking Game.Spread the cards out face up. Without regard to turn, eachplayer picks up a card, for example 2, and enters thatnumber on the abacus. Next he slides over the remainingbeads in the row leaving a finger's width. Ask, Howmany beads are needed to make 10? [8] Tell thechild to find the 8-card and to set the pair aside.

3. MATCHING MEMORY. Use the same cards to playMemory. When the first card is turned over, the playerstates what card is needed to make 10 before turning overthe second card.

4. GO TO THE DUMP. The pairs for this game, playedsimilar to Go Fish, are the combinations that make 10.

Missing addends1. Write 7 + __ = 10 and say, Seven plus whatequals ten. Put 7 on the top wire and 10 on the secondwire. How many beads do you have to add tomake these equal? [3] The children can either countthe missing spaces or count the beads as they move themover. So seven plus three equals ten. Write the 3 inthe blank. Repeat for another example: 4 + __ = 10.

Give the children a prepared worksheet (2-10 and 2-11).

2. ORAL PROBLEMS.

A. Carlos is trying to get 10 gold stars. If he already has6, how many more must he receive? [4 stars]

B. Kay has 10 houses on her block. If she has walked by6 houses, how many more must she walk by before shereaches the end of the block? [4 houses]

C. Tracy learned the names of 2 more of her classmates.She already knew 5 names. Now how many names doesshe know? [7 names]

D. What even number comes after 6? [8]

E. What odd number comes after 7? [9]

F. What even number comes before 6? [4]

E. What odd number comes before 7? [5]

1

2

3 4

5

6

7

8

95

7 + = 10 4 + = 10 9 + = 10 2 + = 10 5 + = 10 8 + = 101 + = 10 6 + = 10 3 + = 10

72 Adding and subtracting in the thousands

HUNDREDS AND THOUSANDSChildren need to experience the quantities of 100, 200,and so forth separately before combining with tens andones to form numbers like 582. The AL abacus with 100beads can be used for this as well as Base 10 PictureCards, shown simplified at the left.

The hundreds1. Ask the children, How many beads are on an ab-acus? [one hundred] Hold up two abacuses and ask,How many beads do you think are on two aba-cuses? [two hundred]

Say, You know how we write one hundred; howdo you think we write two hundred? Show theplace value card of 200 found in the appendix. Point tothe 2 while saying two, to the middle 0 while sayinghun-, and the last 0 while saying -dred. Repeat forquantities 300 and 400.

Place 100 identical items in a container; show it to thechildren and tell them that it is 100. Then show them con-tainers with 200, 300, or other multiples of 100 and askthe children to guess the quantities.

2. Hold up the various hundred cards one at a time andask the children to read them. Also ask them to show thequantities. If extra abacuses are unavailable, use copies ofthe “abacus” cards, found in the appendix, to representone hundred. Along with the hundred cards, hold up tencards and one cards for them to read.

3. Show a quantity such as 245 by setting up two abacus-es, each showing 100, and a third abacus showing 45.Pick up the 200, the 40, and the 5 cards; combine them byoverlapping to make 245. Provide each child or group ofchildren a set of place value cards. Give them other com-binations to construct with abacuses and place valuecards, such as 381 and 179.

4. Comparison of two quantities can help the children ap-preciate the relative magnitudes. Write on the board

321 123

Have the children work with a partner. Give each child anabacus and 9 abacus cards; each pair also needs a “greaterthan or less than” card. The child on the left enters the leftquantity while the child on the right enters the quantity onthe right. Then they decide which quantity is greater andplace the sign accordingly.

Give them two examples

452 402 512 517

before giving them a worksheet (7-1) to be done with apartner. After correctly placing the < or > sign, they cantake turns copying it on to the worksheet.

2 0 04 0

5

2 0 04 05 2 4 5

2 0 02 0 0two hun dred

321 123975 683526 543669 907463 364 28 288943 953753 750101 110

Thousand Hundred Ten One

Adding and subtracting in the thousands 73

FUTURE REVIEW. After the children have worked withthe < and > signs for the hundreds, ask them if they fig-ured out the rules to do the work without the abacuses.Ask, Which number do you look at first? [the hun-dreds] Then ask, If the hundreds are the same,what do you look at next? [the tens] Lastly ask, I fboth the hundreds and the tens are the same,what do you do? [look at the ones]

Write a few sets on the board for them to do without aba-cuses. Discuss following the rules.

Adding with sums in the hundreds1. The purpose of this activity is to introduce carryingwith sums beyond one hundred. It is not necessary at thispoint that the children start with the ones.

Write on the board

87+ 45

and ask the children to try it on an abacus. Then ask,What is the problem? [The sum will not fit on one ab-acus? Use two abacuses with the second placed directlybelow the first. Start the addition by entering 8 tens on thefirst abacus and 7 ones near the bottom of the second aba-cus. Next enter the 4 tens by filling the first abacus andcontinuing into the second. Finally enter the 5 ones andconstruct the sum 132 with the place value cards.

Let the children work in pairs to find the sums for 75 +52, 97 + 68, and 45 + 86. Then give them worksheets (7-2).

ORAL PROBLEMS. A. A ball costs 69ç. Tou wantedtwo balls; what would they cost? [$1.38]

Now is a good time to explain that a DOLLAR is 100cents, so the answer would be 1 dollar and 38 cents.

B. Ser had 300 pennies. How many dollars is this? [3]

C. Mee bought a scarf at a sale for 49ç. She also boughtsome buttons for 75ç. What did the two items cost?[$1.24]

D. Amanda bought two gifts, one costing 86ç and the oth-er 55ç. What was the total cost? [$1. 41]

E. Vang had 23 days of vacation from school. Eighteendays have gone by. How many days does he have beforeschool starts again? [5 days]

F. Jonathan had saved $13 for a special gift that cost $20.How much more did he have to save? [$7]

G. David walked for 28 minutes on Monday, 35 minuteson Wednesday, and 37 minutes on Friday. How manyminutes did he walk that week? [100 minutes]

87 63 26+ 45 + 89 + 74

37 58 47+ 69 + 94 + 63

52 73 68+ 76 + 28 + 39

90 Multiplication

(The term “times” will be introduced later.) Ask, Howmuch is it? [15] Ask a child to write the answer.

Write on the board 6 × 4 =__. Ask the children to read it[6 taken 4 times], then to enter it on their abacuses, and tofind the answer. Then ask to enter 7 × 8. Encourage themto see the tens groupings as shown.

Next, ask them to find 9 × 5. Since they know 10 × 5,subtracting 5 from 50 will give the product of 45.Thisalso works for multiplying by 8s.

Give them a page (8-6, 8-7) of problems, letting themfind the answers in any manner they choose.

FUTURE REVIEW. To help the children see these factsvisually, enter an array and show it to the children for 2-3seconds. Then ask them to state the multiplication fact andthe product. (For the classroom, an overhead abacus isavailable from the publisher.)

Multiplying with 0s and 1s1. The object of this lesson is that the children discoverand learn the rules associated with multiplying with zeroesand ones. Work with them only long enough to be surethey understand how to do it. Ask them to look forpatterns.

Write on the board

0 × 3 = __

and ask, How much do we enter each time? [0]How many times do we enter it? [3] Go through themotions of entering nothing on 3 wires. So what is theanswer? [0]

Next write on the board

8 × 0 = __

Give the children time to think how they would do it be-fore showing them. How much do we enter eachtime? [8] How many times do we enter it? [0]Move 8 beads on the top wire a slight distance, stop, andsay, We cannot enter it even once. So how muchis 8 ×××× 0? [0]

If necessary give them more examples, 0 × 4, 9 × 0. Thengive them a worksheet (8-8) with 0s.

FUTURE REVIEW. After the “0” worksheet is complet-ed, ask what happens when there is a 0 in a multiplicationproblem. [The answer is 0.]

2. Tell the children that now they will work with multiply-ing 1s. There is no confusion with problems like 1 × 7,but 7 × 1 can cause difficulties. Write on the board

7 × 1 =

0 x 3 = __9 x 0 = __5 x 0 = __0 x 7 = __4 x 0 = __0 x 10 = __6 x 0 = __0 x 2= __0 x 8 = __7 x 0 = __0 x 6 = __0 x 0 = __1 x 0 = __0 x 9 = __

9 x 3 = __7 x 5 = __ 5 x 3 = __8 x 8 = __6 x 9 = __6 x 3 = __9 x 10 = __9 x 4 = __ 5 x 9 = __8 x 5 = __9 x 9 = __5 x 6 = __9 x 5 = __8 x 6 = __

7 x 1 = __1 x 5 = __8 x 1 = __1 x 3 = __1 x 7 = __9 x 1 = __1 x 9 = __5 x 1 = __4 x 1 = __0 x 1 = __1 x 2 = __10 x 1 = __1 x 1 = __1 x 4 = __

6 x 4

7 x 8

9 x 5

Multiplication 91

Ask, How many times do we enter the 7? [1] Askthem to find the answer. Assign the worksheet (8-8).

FUTURE REVIEW. After the work with the “1” work-sheet is completed, ask, What happens when youmultiply by 1? [The answer is the number being multi-plied by 1.]

Multiplying with take and giveReview the names given to answers. Ask, What do wecall the answer in addition? [sum] What do wecall the answer in subtraction? [remainder or differ-ence] The answer in multiplication is called thePRODUCT. In the problem of 3 taken 2 timesequals 6, what is the 6 called? [product]

Another way to find the product is called “take and give.”Younger children often enjoy working with the take andgive that they ask for more of the “harder” problems.

Tell the children that you are going to show them a short-cut for solving problems with higher numbers. Write onthe board

9 × 3 = __

and ask them to enter the problem. Explain that the prod-uct can be read easily if the rows are tens. Therefore, tomake the first row a ten, TAKE a bead away from the lastrow and GIVE it to the first row. Do the same thing forthe second row. Then the product can be read as 27.

Ask them to work problems, 7 × 8 and 8 × 9. Any num-ber of beads may be removed at a time as long as the samenumber is restored on another wire. Provide worksheets(8-9, 8-10).

Also give them worksheets (8-11) with the problems writ-ten in the vertical form; tell the children that they areworked the same way. Also tell them that there is anotherway to read a multiplication problem; 9 × 3 can be read as“9 times 3.”

Writing multiplication tables 1. Say to the group that they will be writing the multipli-cation tables. Although there are no new facts, the tablesorganize all the multiplication facts, which they need tolearn. They already know some of them. After the tables(8-12 to 16) are completed, they can be fastened together.

Write on the board a sample table, for example, the 2s asshown on the mini worksheet shown on the right.

To start, enter the first 2 and record the product. Subse-quently add another 2 and write the result. Do not clearuntil the entire table is completed.

9 x 3 = __7 x 5 = __ 5 x 3 = __8 x 8 = __6 x 9 = __6 x 3 = __9 x 10 = __9 x 4 = __ 5 x 9 = __8 x 5 = __9 x 9 = __5 x 6 = __9 x 6 = __8 x 6 = __

6 9 3x 5 x 3 10

8 6 6x 4 x 3 x 6

5 2 7x 9 x 1 x7

4 7 8x 1 x 3 x 2

2 x 1 = __2 x 2 = __2 x 3 = __2 x 4 = __2 x 5 = __2 x 6 = __2 x 7 = __2 x 8 = __2 x 9 = __2 x 10 = __

Division 101

INTRODUCING DIVISIONDivision will be studied from several different perspec-tives, including counting, skip counting, and the inverseof multiplication.

Division by countingTell the children that now they will start division. Posethis problem, If three friends have 12 pens thatthey want to share evenly, how can they sharethem? Guide them to the solution of passing them out, 3at a time, until they are gone. Repeat with other objects,such as 18 books shared evenly among 6 children.

Show 12 ÷ 3 on the abacus. Use golf tees or markersfrom a game to represent the persons (3 for this example).Enter beads evenly until the total quantity (12) is reached.Point to the first wire, or marker and ask, How manydid this one receive? [4] Repeat for the second andthird wires. See the figures.

Show them how to write it saying, This is one waywe write it. Write on the board

12 ÷ 3 = 4

while saying, Twelve divided by 3 equals 4.

Guide them through two other examples, such as, 14 ÷ 2and 20 ÷ 4 before giving them worksheets (9-1).

Unit 9Division

Division answers two questions; for example, 24 divided by 3 tells either how many 3s are in 24 or howmuch is in each of 3 groups. In this unit, the children will be shown different ways of dividing numbers.During this work, they will memorize many of the facts. Later in the unit, the children will be tested to de-termine how many facts they know, and strategies can be given for those they still need to learn.

Division has a profusion of signs to represent it, namely, ÷, , —, and /. The first of these, the divisionsign, primarily is used to show numeric calculations in arithmetic; it is often found on calculators. The sec-ond symbol, the “doghouse,” is reserved for calculating with paper and pencil. The third symbol, the di-viding line, is widely used in most branches of mathematics; it is also extensively used in divisions result-ing in quotients less than 1, usually referred to as fractions. The fourth symbol, the slanted line, is used inprint, including recipes, on highway signs, and in work on computers.

Division by 0 is a topic that does not need to be introduced to primary students. The older child can appre-ciate the impossibility. Help a child to understand by asking how many 0s are in the number: it makes nosense, so we say it is impossible.

Short division is a skill that is frequently needed and should be mastered first. Long division, however, isseldom done by hand today because of the widespread use of calculators. In this unit, it is approached asan extension of short division.

12 ÷ 3 = __10 ÷ 2 = __12 ÷ 4 = __15 ÷ 5 = __16 ÷ 4 = __21 ÷ 7 = __14 ÷ 2 = __30 ÷ 10 = __35 ÷ 5 = __8 ÷ 4 = __

)

102 Division

FUTURE REVIEW. After they have completed the work-sheets, write and ask them how they would do 0 ÷ 3,How much would each person receive? [0]

Division by skip countingTell the children that there is another way to write divi-sion. Write on the board

4 24

and explain that it is read as 24 divided by 4 and meanshow many 4s in 24. One way to find the answer is to en-ter and count by 4s until 24 is reached. The number ofwires tells how many 4s are in 24. Show them where towrite the answer, above the ones place of the 24.

Repeat for 3 18 and 5 20. Then give them worksheets(9-2) for practice.

Division by take and giveDivision by counting and by skip counting are somewhattedious, but many children enjoy division by take andgive. It consists of rearranging a quantity into the desiredarray in one of two methods.

1. Write on the board

7 28

and ask the children to enter 28. Tell them, We want tofind out how many 7s are in 28, so we wantonly 7 on each wire. Ask the children to remove theextra beads by take and give. See the figures. So howmany 7s are in 28? [4]

Repeat for 5 20 and 9 18. Then assign them similarworksheets (9-3).

2. The second method involves arranging the beads even-ly on 7 wires. Say, We want to find out how muchis on each of 7 rows. Again write on the board

7 28

and ask the children to enter 28. Tell them that we want todistribute the 28 over 7 wires. Use take and give; start atthe 7th wire with the transferring. Although 4 beads weretransferred at a time in the figures below, any quantity canbe transferred at a time. See the figures. The worksheet(9-4) is similar to the last one.

4 24 4 32

5 50 2 16

3 12 7 28

4 28 10 90

5 20 6 18

8 40 7 35

5 15 4 8

7 28 8 56

4 16 3 18

3 21 9 72

6 30 2 16

5 25 3 24

8 32 7 42

4 28 2 14

64 24

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