Add Subtract 2B

Copyright 2006 - 2012 Taina Maria Miller. EDITION 1.5 All rights reserved. No part of this book may be reproduced or transmitted in any form or by any means, electronic or mechanical, or by any information storage and retrieval system, without permission in writing from the author. Copying permission: Permission IS granted to reproduce this material to be used with one (1)

teacher's students by virtue of the purchase of this book. In other words, one (1) teacher MAY make copies of these worksheets to be used with his/her students. Permission is not given to reproduce the material for resale. If you have other needs, such as school-wide licensing, contact the author at www.MathMammoth.com/contact.php.

Please visit www.MathMammoth.com for more information about ebooks and books by Maria Miller. Create free math worksheets at www.HomeschoolMath.net/worksheets/

2

Contents Introduction ...........................................................................

4

Adding with Whole Tens ...................................................... 7 Subtracting Whole Tens ....................................................... 10 Adding in Columns ............. .................................................. 12 Doubling ............................................................................... One-Half .............................................................................

14 16

Regrouping with Tens ........................................................ Going Over to The Next Ten ..............................................

18 21

Add with Two-Digit Numbers Ending in 9 ........................ 24 Add in Columns Practice ..................................................... 26 Add with Two-Digit Numbers Ending in 8 or 7 ................ 28 Addition Practice ................................................................. 30 Many Addends .................................................. ..................

32

Subtracting in Col umns ....................................................... 35 Regrouping (Bo rrowing), Part 1 .... ................................... 38 Regrouping (Bo rrowing), Part 2 .... ................................... 41 Regrouping (Borrowing), Part 3 .......................................

44

Graphs and Problems .......................................................... 46 Adding 2-Di git Numbers Ment ally ...... ................................ 49 Mental Subtraction Methods .............................................. More Mental Subtraction ....... ............................................. Euclid's Game ...................................................................... Review ....... ............................................................................

52 55 58 61

Answers ................................................................................. 64 More from Math Mammoth ................................................ 78

3

Introduction Math Mammoth Add & Subtract 2-B is a continuation to the book Math Mammoth Add & Subtract 2-A. The goal of this book is to study addition and subtraction within 0-100, both mentally and in

columns, especially concentrating on regrouping in addition (carrying) and in subtraction (borrowing).

Mental math Mental math is important because it builds number sense. This book includes many lessons that practice mental math. For example, the child practices adding and subtracting two-digit numbers when one of the −

numbers is a whole ten (problems such as 30 + 14, or 66 20). Also studied are problems such as 36 + 8 or 45 + 9. These problems use the idea of going over ten as in problems 6 + 8 and 5 + 9. The child knows that 6 + 8 fills the first ten and is four more than the ten. He/she will learn to use that fact when adding 36 + 8. The sum 36 + 8 fills the next whole ten (40), and is four more than that, or 44.

Regrouping in tens Simultaneously with this, the child learns adding two-digit numbers in columns, and regrouping with tens, or “carrying,” which is illustrated and explained in detail with the help of visual models. These visual models take the place of base-ten blocks or other manipulatives. You are welcome to use manipulatives to get the idea across, if you prefer. The main concept to understand is that 10 ones are regrouped to form a new ten, and this new ten is written using a little “1” in the tens column. As a “stepping stone” into the standard way to add, you can show the child the method below. This can be used if the child does not readily understand why the little “1” above the tens column corresponds to a ten. Below, the ones are added first, and the answer is written using both columns. Then, the tens are added and the answer is written under the sum of ones. Lastly, both sums are added. tens ones 3 6 1

8

add ones first → 1

+

4

tens ones 6 3 +

add tens here →

1

8

1 4

4

tens ones 3 6 +

0

total →

1

8

1 4

4

5

4

0

Regrouping in subtraction The next lessons teach subtracting in columns. First we only deal with the easy problems where you don't need to regroup (borrow). Then the following lessons practice in detail the process of regrouping or borrowing. You can use either term with your child, or even choose not to use either if you feel it is confusing. You can alternatively use the phrase “breaking a ten into ten ones.” First, the lesson Regrouping practices breaking down a ten into ten ones because we cannot subtract from the ones. It is crucial that the child understands what happens here. Otherwise, he/she might end up only memorizing the procedure, and will probably at some point misremember how it was done. That is why this lesson deals with the regrouping process in detail with plenty of visual exercises.

4

If you notice that the child does not understand the concept of regrouping, he/she may need more practice with concrete manipulatives or visual exercises before proceeding.

More mental math After learning regrouping, we practice mental subtraction in three separate lessons. One of them expounds on several methods for mental subtracting. Another is about Euclid's game—a fun game that also practices subtraction of two-digit numbers. I wish you success with math teaching! Maria Miller, the author

Helpful Resources on the Internet Use these free online resources to supplement the “bookwork” as you see fit. You can access an up-to-date online version of this list at www.mathmammoth.com/weblinks/add-subtract-2B.htm Base Blocks Addition

A virtual manipulative that shows regrouping in addition. You can either solve addition problems that are provided, or create your own. “Lasso” with a mouse ten units, ten tens, or ten hundreds to regroup them. Choose “Columns = 2” to restrict the work to two-digit numbers. http://nlvm.usu.edu/en/nav/frames_asid_154_g_1_t_1.html?from=category_g_1_t_1.html Base Blocks Subtraction

A virtual manipulative that helps teach borrowing in subtraction. Choose "Create Problem", then click on the blue whereas blocks tothe create a problem. TheBLUE number to be Click subtracted (theproblem subtrahend) is illustrated the red REDand blocks minuend is by the blocks. BEGIN to start solving. by Drag a red block on top of a blue to “subtract” —they cancel each other. Drag bigger place values to the column on their right to “break them up”—in other words regroup or borrow. http://nlvm.usu.edu/en/nav/frames_asid_155_g_1_t_1.html?from=category_g_1_t_1.html Callum's Addition Pyramid

Add the pairs of numbers to get a number on the next level and finally the top number. Three difficulty levels. http://www.amblesideprimary.com/ambleweb/mentalmaths/pyramid.html Techno Tortoise

Practice adding two two-digit numbers in parts on a number line. http://www.ictgames.com/technowithflock.html Mr. Martini's Classroom: Addition and Subtraction Inequalities

Compare expressions that involve addition and subtraction of one and two-digit numbers. http://www.thegreatmartinicompany.com/inequalities/number-comparison.html

and http://www.thegreatmartinicompany.com/inequalities/add-subtract-comparison.html

5

Mr. Martini's Classroom: Long Addition

Practice adding two-digit numbers in columns online. http://www.thegreatmartinicompany.com/longarithmetic/longaddition.html Mathionare Addition Quiz

Answer increasingly more difficult addition questions (one and two-digit numbers), and win a million! http://www.mathsisfun.com/games/mathionaire-addition-quiz.html Button Beach Challenge

Figure out what number the various colored buttons represent. http://www.amblesideprimary.com/ambleweb/mentalmaths/buttons.html Teaching Treasures - Year 2 Maths Worksheets

Simple online addition and subtraction worksheets where the student types in the answer and can check it. http://www.teachingtreasures.com.au/maths/maths_level2.html Euclid's Game

An online version of Euclid's game (a Java applet). http://www.cut-the-knot.org/blue/EuclidAlg.shtml Count on Convict

Practice “adding up” strategy for mental subtraction. First type the amount to move on to the next whole ten, then count on tens, then the rest. http://www.ictgames.com/countonconvict.html Double Digit Addition

Match the addition problem with the correct sum. Enjoy! http://www.quia.com/mc/818288.html Addition Level 2

A matching game where you add a one-digit number and a two-digit number. http://www.quia.com/mc/65798.html Speed Grid Addition

Find numbers on the grid that add up to the given number. This uses both single-digit and two-digit numbers. http://www.oswego.org/ocsd-web/games/SpeedGrid/Addition/urikares.html

6

Adding with Whole Tens 1. The numbers are shown with ten-sticks and one-dots. Write the sums.

+

+

a.

b.

54 + 10 = ______

______ + 20 = ______

+ c.

+ d.

______ + ______ = ______

______ + ______ = ______

+ e.

+ f.

______ + ______ = ______

______ + ______ = ______

Adding whole tens and another 2-digit number

Break down the other number into tens and ones. Add the tens. Then, add the ones. 2. Add. Break the second number into tens and ones first. Then add the tens. a.

10 + 34 = _______

b. 10

(10 + 30 + 4)

+ 28 = _______

c.

(10 + _____ + _____ )

20 + 24 = _______ (20 + _____ + _____ )

d.

30 + 21 = _______

e.

50 + 17 = _______

f.

40 + 33 = _______

g.

60 + 23 = _______

h.

30 + 37 = _______

i.

70 + 25 = _______

7

Math MammothAdd & Subtract 2-B (Blue Series)

3. Add. Break the first number into tens and ones first. Then add the tens. a.

45 + 20 = _______

b.

(40 + 5 + 20) d.

27 + 20 = _______

( _____ + _____ + 20 )

46 + 30 = _______

45 + 40 = _______

c.

( _____ + _____ + 40)

e.

16 + 50 = _______

f.

38 + 60 = _______

4. Add. a. 77

+ 10 = ______

b.

20 + 45 = ______

c.

16 + 10 = ______

d. 77

+ 20 = ______

e.

30 + 45 = ______

f.

16 + 30 = ______

50 + 48 = ______

h.

60 + 21 = ______

i.

19 + 20 = ______

g.

Remember rounding to the nearest ten?

Numbers ending in 1, 2, 3, or 4 are closer to the previous ten than the next, so they are rounded down.

Numbers ending in 6, 7, 8, or 9 are closer to the next ten so they are rounded up.

≈

≈

72 70 (72 is approximately 70)

46 50 (46 is approximately 50)

Middle numbers ending in 5 are rounded up. ≈

5

10

5. Round these numbers to the nearest ten. a.

23 ≈ ______

b.

54 ≈ ______

c.

78 ≈ ______

d.

96 ≈ ______

e.

65 ≈ ______

f.

95 ≈ ______

g.

8 ≈ ______

h.

3 ≈ ______

6. Gwen bought shoes for $39, a top for $8, and a skirt for $23. Round these prices to the nearest ten, and then add them to find the total cost. 7. Jacob had $61. Then he bought a toy for $29. Use rounded numbers to estimate how much money he has left.

8


Subtracting Whole Tens 1. Cross out as many ten-pillars as the problem indicates. What is left?

a.

b.

30 – 10 = ______

d.

47 – 20 = ______

50 – 30 = ______

e.

26 – 10 = ______

c.

70 – 40 = ______

f.

55 – 30 = ______

What can you notice? 2. Count by tens backwards. a.

76, 66, ________ , ________ , ________ , ________ , ________

b.

_______ , ________ , 52, 42, ________ , ________ , ________

c.

________ , ________ , ________ , ________ , 27 , 17, ________

3. Subtract. a.

b.

c.

23 – 10 = ________

48 – 20 = ________

56 – 10 = ________

23 – 20 = ________

48 – 30 = ________

56 – 30 = ________

d.

e.

f.

75 – 10 = ________

31 – 10 = ________

81 – 40 = ________

75 – 20 = ________

31 – 20 = ________

81 – 50 = ________

10


4. Find the pattern and continue it. a.

88 – 10 = ______

b. 100

– 60 = ______

c.

34 – 10 = ______

88 – 20 = ______

90 – 50 = ______

44 – 20 = ______

88 – 30 = ______

80 – 40 = ______

54 – 30 = ______

88 – ______ = ______

_____ – _____ = _____

_____ – _____ = _____

88 – ______ = ______

_____ – _____ = _____

_____ – _____ = _____

88 – ______ = ______

_____ – _____ = _____

_____ – _____ = _____

88 – ______ = ______

_____ – _____ = _____

_____ – _____ = _____

5. Use rounded numbers to solve these problems. a. Three suitcases weigh 29 kg, 18 kg, and 31 kg. About how much is their total weight?

b. Dale Chairs cost $29ofapiece. Can $80? buy three them with

c. Henry received $50 for his birthday.

If he buys three books that cost $9 each, about how much will he have left?

Find numbers for the – puzzles.

+

= 90

–

–

+ +

= 30

= 30 = 30

11

= 40 + – =

30

= 80

= 10


2. Fill in the numbers and add. tens

a.

+

+

+

d.

+

f.

tens

ones

tens

ones

+

ones

+

ones

+

ones

+

+

+

b.

tens

e.

tens

+

tens

c.

ones

+

3. Add. a.

2 0 + 5 7

b.

6 2 + 3 6

f.

4 6 + 4 0

g.

7 1 + 2 4

k.

2 5 1 3 + 4 0

l.

4 1 3 2 + 2 4

c.

4 5 + 1 3

d.

3 7 + 3 2

e.

1 4 + 7 2

h.

3 2 + 5 5

i.

3 3 + 4 3

j.

6 4 + 2 5

m.

3 2 5 0 + 1 5

n.

3 3 1 2 + 4 3

o.

5 4 1 1 + 2 4

13


Doubling Doubling a number means adding it to itself. It is finding two times the number. Examples:

Double 7 is 7 + 7 is 14.

Double 20 is 20 + 20 is 40.

1. Find the double of these numbers. a.

Double 5

b.

_____ + _____ = _____

Double 30

c.

_____ + _____ = _____

Double 50

_____ + _____ = _____

2. Find the double of these numbers by adding in the boxes. a.

+

22 + 22

b.

Double 34

c.

+

13 + 13

d.

+

Double 41

+

3. Make a doubles chart. Notice it has a pattern!

Double 6 is 6 + 6 = _____. Double 13 is 13 + 13 = _____. Double 7 is 7 + 7 = _____. Double 14 is 14 + 14 = _____. Double 8 is 8 + 8 = _____. Double 15 is 15 + 15 = _____. Double 9 is 9 + 9 = 18.

Double 16 is 16 + 16 = 32.

Double 10 is 10 + 10 = 20.

Double 17 is 17 + 17 = 34.

Double 11 is 11 + 11 = 22.

Double 18 is 18 + 18 = 36.

Double 12 is 12 + 12 = 24.

Double 19 is 19 + 19 = 38.

14


We can use doubles chart to solve problems about equal sharing. Example. Two children need to clean 18 chairs. They divide the job equally.

How many chairs does each child clean? We can use the doubles chart. Since 9 + 9 = 18, each child will clean 9 chairs.

Solve the problems. You can use the doubles chart. 4. Mother tells two children to make 16 sandwiches. The children share the job How many sandwiches willequally. each child make? 5. You and your brother share equally 32 pieces of candy. How many pieces of candy will you get?

6. A batch of brownies makes 16 brownies. Mom makes a double batch. How many brownies will she make?

7. Two teachers divide 28 worksheets evenly. How many worksheets will each one get?

8. In a board game, you throw two dice and move that many spaces. Mary got double four. Andrea got double six. How many spaces did Mary move? How many spaces did Andrea move?

9. Mother and her friend need to make 20 dolls to sell. They share the job evenly. How many dolls will each woman make?

15


One-Half When you divide something into two equal parts, you have divided it into two halves. Each part is half of the whole. We write one-half this way:

1

,

2

or this way: 1/2 .

6 + 6 = 12

To find half of 10 apples, divide the ten into two equal parts. 5 + 5 = 10. Half of ten apples is five apples.

1. a. Color one half of each shape.

1 2 of 12 is 6.

b. Color two halves of each shape.

2. Draw a line through these shapes and divide them into two halves. Color one half.

b.

a.

e.

c.

d.

3. Divide the things into two EQUAL groups. Write an addition sentence. Find half of the total. a.

10

b.

40

____ + ____ = _____

____ + ____ = _____

1 2 of 10 is ____.

1 2 of 40 is _____.

16

c.

24

____ + ____ = _____ 1 of 24 is _____. 2


4. Fill in the doubles chart. Then use it to find one-half of the given numbers.

6 + 6 = _____

11 + 11 = _____

1 2

of 16 is _____.

7 + 7 = _____

12 + 12 = _____

1 2

of 28 is _____.

8 + 8 = _____

13 + 13 = _____

1 2

of 26 is _____.

1

9 + 9 = _____

14 + 14 = _____

10 + 10 = _____

15 + 15 = _____

2 1 2

of 30 is _____. of 22 is _____.

5. Divide the dots into two EQUAL groups. Find half of the total. a.

1 of 26 is ____. 2

c.

b.

1 of 30 is ____. 2

d.

1 of ____ is _____. 2

1 of ____ is _____. 2

6. Solve the word problems, and fill in another chart of doubles to help you. a. Jack and Joe split $60 between them. How many dollars did each one get? b. What is half of 60 minutes?

10 + 10 = ______ 20 + 20 = ______

c. Half of 100 students were sick.

30 + 30 = ______

How many were not sick?

40 + 40 = ______

d. Aunt Katie gave Missie half of $40.

Missie spent $10 on a toy. How many dollars does Missie have now?

50 + 50 = ______

e. The recipe called for 10

apples. That was exactly half of Mom's apples. How many apples had Mom bought srcinally?

17


When we make a new ten from the ones (cubes), we are regrouping. The ten little ones get grouped and become a ten.

tens ones

1

This is also called carrying to tens. Imagine someone “gathering” ten little cubes in his lap and “carrying” them over into the tens column as 1 ten.

3 + 2 6

5 7 2

To show this new ten, write a little “1” in the tens column above the other numbers. Then add in the tens-column as usual, adding the little “1” also. 2. Circle ten ones to make a new ten. Add the tens and ones in columns.

a.

tens 1

ones

1

3

+ 2

b.

9

tens 1

ones

2

4

+ 3

8

2 tens 1

ones

3

5

c.

tens 1

ones

2

4

+ 4

7

d.

+ 1

9

e.

f.

g.

h.

19


3. Add. If you can make a new ten from the ones, regroup the new ten with the other tens. a.

4 2 + 1 5

b.

2 7 + 4 5

c.

6 5 + 2 6

d.

8 3 + 1 5

e.

3 4 + 1 9

f.

5 2 + 4 1

g.

1 3 + 4 4

h.

6 3 + 2 7

i.

3 6 + 5 1

j.

6 6 + 2 9

k.

1 8 +4 0

l.

3 9 +3 6

m.

5 9 + 3 5

n.

7 2 + 2 2

o.

1 7 + 2 3

tens ones 2

Sometimes we can get or regroup two tens from all the ones (cubes). On the right, when you add the ones, you get 6 + 7 + 8 = 21. This makes two

3 6

new tens

. We need to add them with the other tens in the tens column. So, we write a little “2” above the tens column.

2 7 + 1 8 1

4. Add. Regroup the ones to make new tens. Add the new tens in the tens column. a.

3 4 1 9 + 2 6

b.

1 5 2 7 + 4 5

c.

1 8 2 7 + 2 6

d.

2 6 4 8 + 1 9

e.

3 4 2 0 + 1 9

5. Count by fours. a. 0,

4, _____ , _______ , _______ , _______, _______ , _______ , _______

b. 100,

96, 92, _______ , _______ , _______ , _______ , _______ , _______ 20


Going Over to the Next Ten Sums that go over to the next ten

Let's add 59 + 5 so that we first complete 60. 59 + 5 | \

59 + 1 + 4 60 + 4 = 64 The 5 is broken into two parts: 1 and 4. That is because 59 and 1 makes sixty. Then, we have 60 and 4. We get 64.

9 and 1 make a ten. We get 6 tens. 59 + 5 = 64

1. Circle ten little cubes to make a ten. Count the tens and ones. Write the answer.

a. 13

+ 9 = ______

b. 15

+ 8 = ______

c. 17

+ 7 = ______

d. 24

+ 7 = ______

e. 25

+ 6 = ______

f. 37

+ 9 = ______

g. 36

+ 6 = ______

h. 48

+ 4 = ______

i. 58

+ 5 = ______

21


2. Complete. Break the second number into two parts so that you complete the next ten.

28 + 8

a.

/

47 + 5

b. \

28 + 2 + ____

/

39 + 3 /

79 + 9 /

47 + 3 + ____

30 + ____ = ______ d.

c. \

79 + ____ + ____

50 + ____ = ______ 27 + 5

e. \

/

\

80 + ____ = ______ f.

38 + 7

\

/

\

39 + ____ + ____

27 + ____ + ____

40 + ____ = ______

______ + ____ = _____ ______ + ____ = _____

38 + ____ + ____

3. Continue the patterns. COMPARE the columns, and NOTICE what is the same.

8 + 1 = _______

a.

28 + 1 = _______

b.

78 + 1 = _______

c.

8 + 2 = _______

28 + 2 = _______

78 + 2 = _______

8 + 3 = _______

28 + 3 = _______

78 + 3 = _______

8 + 4 = _______

28 + 4 = _______

78 + 4 = _______

8 + ____ = _______

28 + ____ = _______

78 + ____ = _______

8 + ____ = _______

28 + ____ = _______

78 + ____ = _______

4. Fill the missing addends. a.

8 + _____ = 10

b.

8 + _____ = 11 d.

7 + _____ = 10 7 + _____ = 12

13 + _____ = 20

c.

13 + _____ = 21 e.

18 + _____ = 20 18 + _____ = 22 22

67 + _____ = 70 67 + _____ = 71

f.

86 + _____ = 90 86 + _____ = 92


5. Solve the problems. Write a number sentence for each problem, not just the answer. a.

Benjamin wants to buy a kite that costs $30. He has saved $22. How much more money will he need?

b.

Natasha had already saved $20. She earned $5 by selling eggs, and earned $5 more for selling fruit. How much money does she have now?

c.

Mom bought 28 fruit trees and has planted eight of them. How many still need planted?

d.

Thirty-seven people attended Uncle Sam's 50th birthday party. Thirty-two of them came before noon. How many came after noon?

e.

Dad bought a bunch of 40 grapes and ate half of them. Then, little sister ate seven grapes. How many are left now?

6. Continue the patterns. COMPARE the columns, and NOTICE what is the same. a.

9 + 1 = _______

b.

39 + 1 = _______

c.

59 + 1 = _______

9 + 2 = _______

39 + 2 = _______

59 + 2 = _______

9 + 3 = _______

39 + 3 = _______

59 + 3 = _______

9 + 4 = _______ 9 + ____ = _______

39 + 4 = _______ 39 + ____ = _______

59 + 4 = _______ 59 + ____ = _______

9 + ____ = _______

39 + ____ = _______

59 + ____ = _______

23


Add with Two-Digit Numbers Ending in 9 Imagine that 29 wants to be 30... so it “grabs” one from 5. Then, 29 becomes 30, and 5 becomes 4. The addition problem is changed to 30 + 4 = 34.

1. Circle the nine dots and one more dot to form a complete ten. Add.

a.

19 + 5 = ______

b.

29 + 7 = ______

c.

49 + 5 = ______

d.

29 + 8 = ______

e.

39 + 6 = ______

f.

49 + 9 = ______

2. Add. For each problem, write a helping problem using the “ones” from the first problem. a.

19 + 7 = _______

b.

49 + 3 = _______

9 + 7 = ______

____ + _____ = ______

39 + 4 = _______

c.

____ + _____ = ______

3. Add. Compare the problems. a.

9 + 3 = ________ 19 + 3 = ________

d.

b.

9 + 6 = ________

c.

39 + 6 = ________ e.

9 + 4 = ________

49 + 4 = ________ f.

9 + 7 = ________ 39 + 7 = ________

9 + 9 = ________ 69 + 9 = ________

9 + 5 = ________ 19 + 5 = ________

29 + 7 = ________

79 + 9 = ________

59 + 5 = ________

24


4. These problems review the basic facts with 9 and 8. By this time you should already remember these addition facts. Try to remember what number will fit, and not count.

a.

b.

c.

d.

9 + _____ = 14

4 + 9 = _____

8 + _____ = 15

7 + 8 = _____

9 + _____ = 15

8 + 9 = _____

8 + _____ = 17

8 + 8 = _____

9 + _____ = 13

2 + 9 = _____

8 + _____ = 12

5 + 8 = _____

9 + _____ = 18

5 + 9 = _____

8 + _____ = 14

6 + 8 = _____

9 + _____ = 12

6 + 9 = _____

8 + _____ = 13

3 + 8 = _____

9 + _____ = 17

9 + 9 = _____

8 + _____ = 18

9 + 8 = _____

9 + _____ = 16

7 + 9 = _____

8 + _____ = 16

4 + 8 = _____

5. Find the patterns and continue them! a.

+

40 b.

+

16 c.

+

+

+

48

53

61

+

+

+

27

34

21 +

_____

+

____

+

____

+

+

+

66

_____

+

+

42

+

_____

25

+

_____

_____ _____

+

_____

+

_____

+

_____ +

67

+

_____ _____

+

71

74

76


Add in Columns Practice 1. Add in columns. a.

9 + 7 1

b.

2 4 + 6 7

c.

5 5 + 3 6

d.

4 5 + 2 5

e.

3 8 + 1 4

f.

3 4 9 + 3 5

g.

2 5 4 2 + 4 9

h.

5 8 3 0 + 6

i.

2 9 4 4 + 1 2

j.

1 6 1 4 + 1 9

2. Write the numbers so that the ones and tens are in their own columns. Add. a.

f.

45 + 27

6 + 31 + 25

b.

g.

8 + 56

40 + 7 + 9

c.

h.

40 + 32

46 + 8 + 20

26

d.

i.

25 + 45

5 + 8 + 13

e.

j.

47 + 9

5 + 4 + 57


Here we have more than 10 tens. Ten tens make a hundred (100)! Add the tens: 8 + 7 = 14 tens. The “1” of the 14 goes in the hundreds' column, and the “4” stays in the tens column. The answer 149 is read “one hundred fifty-nine.” Another example. Add the tens normally: 1 + 5 + 6 = 12 tens. Write the 12 so that the “1” is in the hundreds' column, and the “2” is in the tens column. The 12 tens make 1 hundred and 2 tens. The answer 123 is read “one hundred twenty-three.” You will study more about hundreds later. 3. Add. You will have more than 10 tens. a.

27 + 80

b.

95 + 47

c.

29 + 75

d.

62 + 84

4. Add. a.

6 7 + 6 1

b.

9 0 + 6 5

c.

3 9 + 8 1

d.

8 5 + 6 2

e.

2 9 + 9 4

f.

6 5 1 8 + 2 6

g.

7 4 7 + 4 5

h.

6 8 4 7 + 3 2

i.

1 2 8 8 + 4 9

j.

8 5 0 + 7 9

27


Add with Two-Digit Numbers Ending in 8 or 7 Imagine that 38 wants to be 40, so it “grabs” two from 7. Then, 38 becomes 40, and 7 becomes 5. The addition problem is changed to 40 + 5 = 45.

1. Circle the eight dots and two more dots to form a complete ten. Add.

a.

18 + 6 = ______

b.

28 + 7 = ______

c.

48 + 8 = ______

d.

38 + 4 = ______

e.

38 + 6 = ______

f.

48 + 5 = ______

2. Add. For each problem, write a helping problem using the “ones” from the top problem. a.

18 + 7 = _______

b.

38 + 6 = _______

8 + 7 = ______

____ + _____ = ______

58 + 5 = _______

c.

____ + _____ = ______

3. Add. Compare the problems. What is similar about the problems in each box? a.

8 + 3 = _______ 18 + 3 = _______

d.

8 + 2 = _______ 38 + 2 = _______ 28 + 2 = _______

b.

8 + 6 = _______

c.

38 + 6 = _______ e.

8 + 9 = _______ 68 + 9 = _______ 78 + 9 = _______ 28

8 + 4 = _______

78 + 4 = _______ f.

8 + 5 = _______ 18 + 5 = _______ 58 + 5 = _______


4. Circle the seven dots and three more dots to make a new ten. Add.

a.

27 + 4 = ______

b.

47 + 5 = _______

37 + 7 = _______

c.

5. Add. For each problem, write a helping problem using the “ones” from the top problem. a.

75 + 7 = _______

b.

5 + 7 = ______

____ + _____ = ______

47 + 7 = _______

c.

57 + 6 = _______

____ + _____ = ______

6. Add. Compare the problems. What is similar about the problems in each box? a.

7 + 6 = ________

27 + 6 = ________ d.

7 + 9 = ________

b.

7 + 5 = ________

c.

77 + 5 = ________ e.

7 + 3 = ________

7 + 7 = ________

87 + 7 = ________ f.

7 + 10 = ________

67 + 9 = ________

37 + 3 = ________

17 + 10 = ________

87 + 9 = ________

77 + 3 = ________

47 + 10 = ________

7. Solve the word problems. a.

Jenny needed 24 eggs to make omelettes for her family. She already had 15 eggs. How many more does she need?

b.

Her large family eats lots of potatoes. Dad bought a 25-kilogram bag of potatoes. Now, only six kg are left. How many kilograms of potatoes have they eaten?

29


Addition Practice 1. Break the second number into tens and ones, and then add mentally.

20 + 34 = _______

a.

70 + 18 = _______

b.

(20 + ______ + ____ )

50 + 27 = _______

c.

(70 + ______ + ____ )

(50 + ______ + ____ )

2. Add mentally. a.

17 + 10 = _______

b.

16 + 20 = _______

c.

50 + 14 = _______

26 + 10 = _______

34 + 30 = _______

60 + 23 = _______

42 + 10 = _______

67 + 20 = _______

30 + 45 = _______

3. Find the pattern and continue it. This pattern “grows” at each step. +

+

1

3

+

7

+

13

+

21

+

+

31

_____

+

_____ _____

4. Add. a.

4 4 + 4 8

b.

c.

3 2 + 5 9

1 6 + 4 7

d.

2 3 + 6 7

e.

5 5 + 2 9

5. Compare the expressions and write < , > , or = . a.

8+3

40 + 5

b.

8+54

9+53

d.

2 + 36

29 + 7

e.

46+8

48+5

30

c.

5+6+56

61+6

85+9

6+88

f.


6. Explain why these are wrong:

33 + 48

55 + 39

711

814

7. Add. Compare the problems! a.

b.

c.

d.

7 + 8 = ______

4 + 9 = ______

8 + 4 = ______

7 + 9 = ______

17 + 8 = ______

14 + 9 = ______

48 + 4 = ______

57 + 9 = ______

37 + 8 = ______

44 + 9 = ______

78 + 4 = ______

37 + 9 = ______

8. Count in threes. a.

42, 45, _______, _______, _______, _______, _______, _______

b.

1, 4, _______, _______, _______, _______, _______, _______

9. Add. a.

b.

c.

d.

29 + 4 = _____

45 + 8 = _____

22 + 8 = _____

78 + 6 = _____

38 + 9 = _____

24 + 9 = _____

46 + 8 = _____

69 + 5 = _____

48 + 6 = _____

36 + 8 = _____

91 + 8 = _____

62 + 9 = _____

Figure out the missing numbers for these addition problems. a.

b.

+ 1

4

4

1

c.

+ 7

d.

e.

3

+ 2

5

+ 7

8

+ 2

6

1

5

1

9

1

6

1

31


Many Addends When adding the ones, you may get two or even three tens. Regroup.

Adding the ones we get 8 + 7 + 8 = 23.

Write the new tens in the tens column.

Write the two new tens in the

2

4 8 2 7 + 1 8 9 3

tens column.

Adding the ones we get 9 + 9 + 7 + 6 = 31. Write the three new tens in the tens column.

3

1 1 2 + 2

9 9 7 6

9 1

1. Add mentally. First add the numbers that make 10 (if there are any).

8 + 4 + 5 = _______

a.

5 + 8 + 7 = _______

b.

9 + 9 + 9 = _______

9 + 2 + 6 = _______

c. 8

+ 5 + 6 + 4 = _______

4 + 9 + 5 + 6 = _______

2. Add. The answers are “hidden” in the list of numbers below the problems. a.

5 2 3 0 + 1 1

e.

i.

3 2 1 + 1

1 3 2 5

b.

c.

+ 5 4

6 7 8 6

f.

1 9

j.

+ 71 99

4 1 1 + 2

0 8 6 2

g.

5 6

k.

80

82

89

91

1 1 1 + 3

+ 1 9

5 7 8 9

h.

4 5

l.

+ 61 59

92

93

96

97

32

98

117

3 6 2 7

d.

+ 2 7

+ 32 29

74

3 3 3 8

1 2 2 + 1

2 9 5 4

5 1 + 17 59

117

122

129

145


3. Solve the problems. Write an addition or subtraction sentence for each one. You can add in columns if you need to. a.

A bus can seat 30 people. There were already 23 people. Is there room for nine more people?

b.

The first bus had 22 people on it, and the second bus had 25. What is the total number of people on the buses?

d.

A bus was full, but then six people got off. How many people were on it now?

Yes/No, because

c.

How many buses do you need if you have 57 people?

How many buses do you need if you have 88 people?

e.

A bus was full. First it dropped off 13 people. Then it dropped off seven more people. How many people were left on the bus?

f.

A bus had some people in it, and then 13 more got on. Now there are 29 people on the bus. How many were on the bus srcinally?

g.

A bus had 20 people on it. Then it dropped off eight people. Then five people got on. Now how many people are on the bus?

h.

A bus had some people on it. It picked up 12 people, and then seven people more. Then it was full. How many people were on the bus srcinally?

33


4. Add mentally. Try to find the easiest order. a.

30 + 2 + 40 + 8 = ________

c.

9 + 40 + 1 + 4 = ________

b.

50 + 4 + 10 + 7 = ________

d.

20 + 10 + 8 + 9 = ________

5. Add. Below each number, write “E” for an even number, and “O” for an odd number. a.

19 + 5 + 7 =3 1 OO

O

b.

25+ 7 + 3 =

e.

5 + 1 +1 1+ 9 =

_______

c.

7 + 11 + 23 =

_______

O

d.

57 + 21 =

g.

17 + 27 + 5 =

_______

_______

h.

_______

25 +1 3+ 3 + 1 =

_______

25 + 9 =

f.

i.

57+21=

_______

_______

Underline the correct choice in the sentences below. Can you think why it is that way? If I add two odd numbers, the answer is (even/odd). If I add three odd numbers, the answer is (even/odd). If I add four odd numbers, the answer is (even/odd). 4 7 + 2 9

5 2 1 7 + 1 4

6 0 + 1 6

Can you figure out how Mary is adding and why it works?

7 0 + 1 3

7 6

8 3 Use Mary's method with these problems: 1 3 1 5 + 4 8

2 7 2 8 + 3 1

1 6 2 5 + 4 7

34

4 6 2 5 + 1 2

3 6 2 7 + 3 4


Subtracting in Columns tens

ones

1. a.

tens

ones

6

1

1. b.

–

3

2

–

Cross out 3 tens and 2 ones.

Cross out 6 tens and 1 one.

It's easy: subtract the tens and ones in their own column. 2. Subtract. a.

5 7 – 1 0

b.

6 6 – 2 4

c.

7 8 – 4 4

d.

8 7 – 2 0

e.

5 5 – 1 1

f.

9 5 – 3 5

g.

2 8 – 2 5

h.

6 7 – 3 3

i.

7 6 – 3 2

j.

8 8 – 6 6

9 6

d.

2 7

e.

3. Figure out what was subtracted.

5 7

a.

4 8

b.

–

– 3 7

c.

– 2 5

– 3 3

7 6 –

1 2

3 3

4. Subtract and add. Compare the problems. a.

b.

c.

72 + 20 = _______

29 + 10 = _______

63 + 30 = _______

72 + 10 = _______

29 + 50 = _______

63 – 40 = _______

72 – 30 = _______

29 + 30 = _______

63 – 60 = _______

35


5. Kids gathered seashells on the beach, and counted how many each one got. Then they made a bar graph. a. Who gathered the least

seashells? __________________________ b. Who gathered the most?

__________________________ c. How many more did Luis gather than Linda? d. How many more did Annie gather than Mark? e. How many did Linda and Jane gather together?

________ more ________ more ________ seashells

f. Mark gave 10 of his to Linda.

Now how many does Linda have?

________ seashells

g. If Luis gives 10 of his to Annie,

will Luis and Annie have equal amount? ________________ 6. Count by six, seven, eight, and nine - and backwards by 5! a.

0, 6, ______, ______, ______, ______, ______, ______, ______

b.

0, 7, ______, ______, ______, ______, ______, ______, ______

c.

0, 8, ______, ______, ______, ______, ______, ______, ______

d.

0, 9, ______, ______, ______, ______, ______, ______, ______

e.

100, 95, ______, ______, ______, ______, ______, ______, ______

f.

77, 72, 67, ______, ______, ______, ______, ______, ______

36


7. Solve the word problems. Write an addition or subtraction sentence for each one. a.

There were 36 birds sitting on the telephone line. 15 of them flew away. How many were left?

b.

The teacher needed 34 red sheets of paper for the crafts class. She already had 21. How many more did she need?

c.

The paper sheets are sold in packages of 12. How many packages did the teacher need to buy?

d. Jane

saw 38 birds sitting on the telephone line. A little later she counted only 30 birds on the line. How many had flown away?

Find the missing numbers in these addition and subtraction problems!

7 – 3

5 –

2 3

8 2

+ 3

4 2

+ 1

7 3

8 – 1 5 0

3 + 1 7 5 0

2

6 8

4

+

9 –

6 2

37

4

7

+ 9 3 4

4 1 5

+ 4 8 2


Regrouping (Borrowing), Part 1 We will now study regrouping (“borrowing”) in subtraction.

Break a ten.

As a first step, we study breaking a ten-pillar into ten little cubes. This is called regrouping, 4 tens 5 ones because one ten “changes First we have 45. We groups” from the tens group “break” one ten-pillar into the ones. into little cubes. Here is another example. First we have 5 tens 3 ones. We “break” one ten-pillar into 10 little cubes. We end up with 4 tens 13 ones.

3 tens 15 ones Now we have 3 tens and 15 ones. It is still 45, but written in a different way.

Break a ten.

5 tens 3 ones

4 tens 13 ones

1. Break a ten into 10 ones. What do you get? Draw or use manipulatives to help.

a.

3 tens 0 ones

b.

___tens ____ones

___tens ___ones

c.

___tens ___ones

d.

___tens ____ones

___tens ___ones

e.

___tens ___ones

___tens ____ones

___tens ____ones

f.

___tens ____ones

___tens ___ones

38

___tens ____ones


Let's study subtraction. The pictures on the right illustrate 45 – 17.

Break a ten.

First, a ten is broken into 10 ones. So, 4 tens 5 ones becomes 3 tens 15 ones. After that, cross out (subtract) 1 ten 7 ones.

4 tens 5 ones

3 tens 15 ones

Cross out 1 ten 7 ones (from the second picture). What is left? ____ tens ____ ones

The pictures on the right illustrate 52 – 39.

Break a ten.

First, a ten is broken into 10 ones. So, 5 tens 2 ones becomes 4 tens 12 ones. After that, cross out (subtract) 3 tens 9 ones.

5 tens 2 ones

4 tens 12 ones

Cross out 3 tens 9 ones (from the second picture). What is left? ____ tens ____ ones

2. Fill in. Always subtract (cross out some) from the second picture. Break a ten.

3 tens 6 ones a.

Break a ten.

___ tens ___ ones

2 tens 16 ones

Subtract 8 ones (from the second picture).

b.

Subtract 2 tens 7 ones.

What is left? ____ tens ____ ones

What is left? ____ tens ____ ones Break a ten.

___ tens ___ ones c.

___ tens ___ ones

Break a ten.

___ tens ___ ones

___ tens ___ ones

Cross out 2 tens 5 ones.

d.


___ tens ___ ones

Cross out 4 tens 4 ones.


39


3. First, break a ten. Then subtract ones and tens separately. Look at the example. a.

b.

4 tens – 3 tens

5 tens 5 ones

3

tens

15 ones

___ te ns ___ ones

7 tens 2 ones

5 ones

8

–

5 ones

___ tens ___ ones

ones

c.

3 tens

d.

6 tens 0 ones

–

___ te ns ___ ones 2 tens

6 tens 4 ones

7 ones

–

___ tens ___ ones e.


8 ones

___ tens ___ ones f.

___ te ns ___ ones

7 tens 6 ones –

4 tens

___ te ns ___ ones

5 tens 0 ones

7 ones

–

___ tens ___ ones g.

2 tens

2 ones

___ tens ___ ones h.

8 tens 1 one –

___ tens ___ ones 6 tens

6 tens 3 ones

5 ones

–

___ tens ___ ones


8 ones

___ tens ___ ones

4. Jessica had 37 colored pencils. Then she gave 12 of them to her brother, and six to her sister. a.

How many pencils does Jessica have now?

b.

How many more pencils does Jessica have than her brother?

c.

How many more pencils does Jessica have than her sister?

40


Regrouping (Borrowing), Part 2 In columns:

5 tens, 3 ones

4 tens, 13 ones

Cross out 1 ten 6 ones. What is left? ____ tens ____ ones

4

13

5

3

– 1

6

3

7

When the subtraction is done in columns: 





We take (borrow) one ten from the 5 tens. There will be now only 4 tens in the tens column, so to show this, we cross the “5” in the tens column and write 4 above it. This new ten is now grouped with the ones. There were 3 ones, but with the 10 new ones there will be 13. To show this, we also cross the “3” in the ones column and write 13 above it. Then we subtract the tens and ones separately.

4 tens

3 tens, 10 ones

3

10

4

0

– 2

8

1

2

Cross out 2 tens 8 ones. What is left? ___ tens ___ ones Here is another example: 40 – 28. 



We take (borrow) one ten from the 4 tens. There will be now only 3 tens in the tens column, so to show this, we cross the “4” in the tens column and write 3 above it. This new ten is now grouped with the ones. There were 0 ones, but with the 10 cross the “0”

new ones there will be and write 10 above it. 10. To show this, we also 

in the ones column

Then we subtract the tens and ones separately in columns.

41


2. Subtract. Check by adding the result and what was subtracted. a.

b.

Check:

4 16

1

5 6 – 2 7

2 9 + 2 7

2 9

5 6

Check:

Check:

9 0 – 2 8

c.

4 2 – 1 5

+ 2 8

d.

9 0 – 3 5

e.

8 2 – 2 5

f.

6 5 – 3 9

g.

5 2 – 1 4

h.

6 5 – 2 6

i.

7 0 – 4 8

.

5 5 – 1 7

k.

3 1 – 1 8

l.

6 6 – 2 8

+ 1 5

Figure out the missing numbers in these subtractions! You might need to regroup.

3 – 1 7

8 –

5

1

0 7

– 3

6

4

43

2

– 1

4

6

8

6

2

5

3

–


Regrouping (Borrowing), Part 3 You can subtract

How do we know when to break a ten into 10 ones, and when not to? From six cubes, we can cross out 0, 1, 2, 3, 4, 5, or 6 cubes. We cannot cross out 7, 8, 9, etc. because

6–0 6–1 6–2

there are not that many cubes to begin with.

You would go into debt 6 – 7 6 – 11 6 – 8 6 – 12 6 – 9 6 – 13

6–3 6–4 6–5 6–6

6 – 10

etc.

1. Cross out the subtractions that would “make you go into debt”. Do you notice any patterns? (You can also write how much you would go into debt; for example –4 is a negative 4.) 3–0 3–1 3–2 3–3 3–4 3–5 3–6 3–7

4–0 4–1 4–2 4–3 4–4 4–5 4–6 4–7

5–0 5–1 5–2 5–3 5–4 5–5 5–6 5–7

6–0 6–1 6–2 6–3 6–4 6–5 6–6 6–7

7–0 7–1 7–2 7–3 7–4 7–5 7–6 7–7

8–0 8–1 8–2 8–3 8–4 8–5 8–6 8–7

3–8 3–9

4–8 4–9

5–8 5–9

6–8 6–9

7–8 7–9

8–8 8–9

2. Look at the ones' digits. Do you need to regroup (borrow a ten to ones' column)? a. Do you need

to regroup?

6 1 – 2 6

Y/N

d. to Doregroup? you need

Y/N

b. Do you need

to regroup?

7 4 – 2 3

Y/N

– 35 24

c. Do you need

to regroup?

5 0 – 2 5

Y/N

e. to Doregroup? you need

Y/N

– 58 62

f. Do you need to regroup?

– 29 70

Y/N

44


If you subtract in columns and you don't have enough ones, you have regroup one ten to the ones' column. 3. Do you need to regroup? Find the answers in the line of numbers below.

a. Do you need

to regroup?

6 0 – 1 6

b. Do you need

to regroup?

Y/N

d. Do you need

to regroup?

to regroup?

c. Do you need

to regroup?

Y/N

8 0 – 2 8

to regroup?

9 7 – 2 5

f. Do you need

to regroup?

Y/N

5 0 – 1 0

8 8 – 7 7

Y/N

h. Do you need

to regroup?

Y/N

4 3 – 1 7

Y/N

e. Do you need

Y/N

g. Do you need

5 7 – 3 2

3 7 – 2 7

i. Do you need

to regroup?

Y/N

6 0 – 4 1

Y/N

35 44 26 19 25 11 63 22 72 49 10 26 51 52 78 30 25 40

4. Subtract. Regroup if necessary. Check by adding! a.

5 4 – 3 7

b.

9 4 – 3 4

c.

8 2 – 2 5

d.

6 2 – 2 9

e.

9 9 – 5 7

f.

4 0 – 2 3

45


Graphs and Problems 1. The graph shows how many newspapers Jack sold at his newspaper stand from Monday through Sunday. a. For each day, find about how

many newspapers Jack sold. Look how tall each column is, and round to the nearest ten.

Day

Mon

Tues

Wed

Thurs

Fri

Sat

Sun

about

about

about

about

about

about

about

______

______

______

______

______

______

______

Newspapers

b.

About how many newspapers did Jack sell on Saturday and Sunday together? ______

c.

About how many more newspapers did Jack sell on Sunday than on Monday? ______

2. The table lists the eye colors of a group of 50 children.

9

4

10

16

11

blue

green

gray

brown

hazel

a. Draw the bars for the bar

graph. b. How many children have

either brown or hazel eyes?

c. How many children have

either eyes? blue, green, or gray

46


3. a. How many Arctic animals does the zoo have? How many rain forest birds? b.

How many European and Arctic animals does the zoo have together?

c.

How many more African animals does the zoo have than Australian animals?

4. Break the number you are subtracting into tens and ones, and subtract in parts. a.

45 – 23 / \ 45 – 20 – 3 = ______

b.

76 – 15 / \ 76 – 10 – 5 = ______

c.

47 – 15

5. Solve the word problems. Add or subtract in columns if you need to. a.

Jim has 62 marbles, Peter has 28, and Ed has 33 marbles. Peter and Ed put their marbles together. Now do they have more than Jim?

b.

You were on page 48 in a book that has a total of 95 pages. Then you read ten more pages. How many pages have you read now? How many pages do you have left to read?

47


Adding 2-Digit Numbers Mentally Strategy 1: Break the second addend in parts

Break the 27 into tens and ones. First add 45 and 20. Then add 7.

45 +

27 / \ 45 + 20 + 7 65 + 7 = 72

1. Add by breaking the second addend into tens and ones. a.

52 +

b.

26

38 +

52 + 20 + 6 ____ +

35

6

= _____

57

25 + ____ + ____

____ + ____ = ____

____ + ____ = ____

e.

19

48 +

62 + ____ + ____

f.

36

54 +

48 + ____ + ____

____ + ____ = ____

39

54 + ____ + ____

____ + ____ = ____

g.

17 +

25 +

38 + ____ + ____

d.

62 +

c.

____ + ____ = ____

h.

64

44 +

17 + ____ + ____

i.

38

29 +

44 + ____ + ____

____ + ____ = ____

23

29 + ____ + ____

____ + ____ = ____

____ + ____ = ____

2. Add mentally. a.

b.

c.

d.

34 + 35 = ______

15 + 29 = ______

44 + 46 = ______

19 + 18 = ______

47 + 12 = ______

8 + 12 = ______

43 + 18 = ______

13 + 17 = ______

33 + 56 = ______

47 + 36 = ______

56 + 25 = ______

34 + 18 = ______

27 + 26 = ______

50 + 33 = ______

12 + 19 = ______

45 + 35 = ______

49


Adding three numbers

The basic strategy is to simply break the numbers into parts, and add them little by little. You can add all the tens and ones separately. Or, you can add with rounded numbers, and lastly correct the rounding errors. Just do whatever works! Add tens and ones separately:

Add with rounded numbers. Then correct the final answer.

33 + 28 + 16 (30 + 20 + 10) + (3 + 8 + 6) 60 + 17 = 77

27 + 39 + 38 27 is 23 less less than than 40. 30. 39 is 1 less than 40. 38 is

Add first those numbers that form a ten:

So, 27 + 39 + 38 is exactly 6 less than 30 + 40 + 40, or 6 less than 110, which is 104.

15 + 27 + 45 (5 + 5 + 10 + 40) + 27 60 + 27 = 87

5. Add mentally, and find the answer to the riddle. Use any strategy. L

22 + 43 + 38 = ______

V

52 + 14 + 18 = ______

L

28 + 18 + 36 = ______

C

37 + 18 + 15 = ______

E 47

+ 32 + 21 = ______

E

50 + 15 + 16 = ______

E

22 + 44 + 38 = ______

L 19

+ 17 + 25 = ______

B

64 + 12 + 17 = ______

R

24 + 13 + 25 = ______

W

55 + 14 + 28 = ______

O

16 + 60 + 20 = ______

W

54 + 16 + 22 = ______

E

E

50 + 31 + 19 = ______

27 + 11 + 21 = ______

Father: “How were your test scores?” Son: “Underwater.” Father: “What do you mean underwater?” 97 100 62 59

93 81 103 96 92

70

82 104 84 100 61

Son: They...

51


Mental Subtraction Methods Method 1:

Subtract in two parts

53 – 8 =5 3 – 3 – 5 = 50 – 5 = 45

72 – 6 = 72 – 2 – 4 = 70 – 4 = 66

Subtract 8 in two parts: first 3, then 5.

Subtract 6 in two parts: first 2, then 4.

(In other words, first subtract to the previous whole ten, then the rest.)

1. Subtract the elevated number in parts (first subtract to the previous whole ten; then the rest). −

5

/ a.

−

( 51 − 1 ) − 4 = ______ −

6

d.

−

5 \

( 92 − ____ ) − ____ = ______ −

\

/

( 75 − ____ ) − ____ = ______ /

g.

−

/

( 33 − ____ ) − ____ = ______ −

\

( 62 − ____ ) − ____ = ______

\

/ e.

b.

4

/ c.

7

/

\

f.

−

\

/ d.

\

( 63 − ____ ) − ____ = ______

7

( 35 − ____ ) − ____ = ______

7

5 \

( 74 − ____ ) − ____ = ______

2. First subtract the balls that are not in the ten-groups. a.

51 − 7 = _______

b.

−

42 − 4 = _______ −

51 5 = _______ 51 − 3 = _______

42 5 = _______ 42 − 3 = _______

51 − 6 = _______

42 − 6 = _______ 52


Method 2:

Use known subtraction facts

Since 14 – 6 = 8, we know that the answer to 74 – 6 will end in 8, but it will be in the sixties (sixty-something). So it is 68. Since 15 – 8 = 7, we know that the answer to 55 – 8 will end in 7, but it will be in the forties (forty-something). So it is 47. 3. Subtract. The first problem in each box is a “helping problem” for the others. b.

f.

14 – 9 = _______

c.

d.

17 – 8 = _______

12 – 9 = _______

24 – 9 = _______

27 – 8 = _______

52 – 9 = _______

44 – 9 = _______

37 – 8 = _______

32 – 9 = _______

15 – 9 = _______

g.

13 – 8 = _______

h.

16 – 8 = _______

65 – 9 = _______

33 – 8 = _______

86 – 8 = _______

45 – 9 = _______

93 – 8 = _______

36 – 8 = _______

4. Use either method from this lesson to subtract. a.

b.

c.

d.

34 – 5 = ______

65 – 9 = ______

51 – 8 = ______

62 – 7 = ______

73 – 7 = ______

36 – 8 = ______

93 – 6 = ______

83 – 8 = ______

5. a. Terry is on page 56 of her book. The book has a total of 92 pages. How many pages does she have left to read? b. Terry reads nine pages more. Now how many

pages does she have left to read?

53


Method 3:

Add.

You can “add backwards”. This works well if the two numbers are close to each other. Instead of subtracting, think how much you need to add to the number being subtracted (the subtrahend) in order to get the number you're subtracting from (the minuend). Think: 84 + ____ = 92

(84 and how many more makes 92?)

Think: 25 + ___ = 75

+____

(25 and how many more makes 75?)

92 – 84 = _____

+___ 75 – 25 = _____

6. To find these differences, think of adding more.

+ 8 a. 92

+____

– 84 =______

b. 51

(Think: 84 + ____ = 92)

+____

– 49 =______

c. 76

(Think: 49 + ___ = 51)

– 69 =______

(Think: 69 + ___ = 76)

g.

32 – 28 = ______

j.

90 – 83 = ______

m.

100 – 95 = ______

h.

22 – 14 = ______

k.

64 – 56 = ______

n.

64 – 55 = ______

i.

l.

53 – 46 = ______

o.

72 – 65 = ______

44 – 37 = ______

7. Fill in, and find what was subtracted. –

–

78

77

–

72

–

70

–

65

–

60

–

57

–

53

46

The triangle and square represent “mystery numbers.” Find them. Guess and check! Then change your guess. a.

+

+ 10 = 34

= ______

b.

c.

+ – = _____,

= 22 =4 = _____

54

+ + = _____,

= 22 = 36 = _____


More Mental Subtraction 1. Break the number you are subtracting into two parts (tens and ones). Subtract in parts.

45 – 32 / \ 45 – 30 – 2 = _______

b.

81 – 45 / \ 81 – 40 – 5 = _______

c.

d.

e.

f.

a.

52 – 34 = _______

55 – 22 = _______

74 – 21 = _______

88 – 53 = _______

g.

70 – 34 = _______

h.

50 – 27 = _______

i.

66 – 27 = _______

j.

73 – 33 = _______

k.

94 – 27 = _______

l.

60 – 36 = _______

2. What is the difference? Solve whichever is easier.

35 + _____ = 42 42 − 35 = _______

a.

71 + _____ = 78 78 − 71 = _______

b.

3 + _____ = 42 42 − 3 = ______

d.

c.

10 + _____ = 33 33 − 10 = _______

3. Solve. a.

78 + _____ = 85

b.

63 − 55 = ______

c.

5 + ______ = 43

d.

76 − 69 = ______

e.

95 − 65 = ______

f.

8 + ______ = 96

g.

20 + ______ = 75

h. 11

+ ______ = 86

4. Subtract in the easiest order! a.

b.

c.

40 − 4 − 20 − 2 = ________

74 − 20 − 4 − 5 = _______

72 − 8 − 60 − 2 = _______

50 − 8 − 10 − 20 = _______

91 − 7 − 10 − 3 = _______

66 − 20 − 2 − 5 = _______

60 − 2 − 6 − 4 = ________

82 − 5 − 7 − 11 = _______

86 − 8 − 5 − 20 = _______

55


5. Solve the word problems. a.

Mariana had 64 marbles. She gave 8 to her brother. Then her brother gave her 4 back. How many marbles does Mariana have now?

b.

In a store, one chair is 64 cm wide, and another is 55 cm wide. How much wider is the first chair?

c.

Mary had 50 cards, and Jack had 5. Mary gave 20 cards to Jack. How many cards does Jack have now?

d. Mary had 40 marbles, and Jack had 5.

Mary gave half of her marbles to Jack. How many marbles does Jack have now?

e.

Ken has collected 34 stamps. Bill has collected 57 stamps. Brian has collected 94 stamps. If Ken and Bill combine their collections, will they together have more than Brian?

6. Connect each problem to its answer with a line.

39 + _____ = 44

56 + _____ = 64

36 + _____ = 44

7

70 + _____ = 74

18 + _____ = 24

9

58 + _____ = 64

30 + _____ = 34

6

29 + _____ = 34

15 + _____ = 24

5

58 + _____ = 64

79 + _____ = 84

8

35 + _____ = 44

85 + _____ = 94

4

69 + _____ = 74

67 + _____ = 74

27 + _____ = 34

56


Review 1. Complete the next ten. a.

b.

c.

16 + _____ = 20

47 + ____ = ______

75 + ____ = ______

64 + _____ = 70

38 + ____ = ______

92 + ____ = ______

2. Add. a.

4 3 + 2 8

b.

3 3 + 3 9

c.

2 4 + 4 7

d.

2 3 + 3 7

e.

5 5 +1 7

f.

3 8 1 3 + 4 2

g.

3 9 1 0 + 4 6

h.

4 1 1 4 + 3 6

i.

3 8 2 9 + 2 3

j.

1 8 1 9 +5 5

3. Add. a.

b.

c.

d.

25 + 8 = ______

76 + 5 = ______

88 + 3 = ______

82 + 8 = ______

81 + 8 = ______

72 + 7 = ______

42 + 9 = ______

54 + 9 = ______

24 + 9 = ______

50 + 6 = ______

34 + 7 = ______

10 + 9 = ______

4. Find the missing addends. a.

25 + _____ = 35 87 + _____ = 93

b.

44 + _____ = 51

c.

67 + _____ = 75

17 + _____ = 26 79 + _____ = 85

61

d.

34 + _____ = 41 21 + _____ = 30


5. For each problem, write one where you subtract from 11, 12, 13, 14, 15, 16, 17, or 18. a.

55 – 7 = ____ 15 – 7 = 8

d.

72 – 7 = ____ ____ – ___ = ____

74 – 8 = ____

b.

c.

____ – ___ = ____ 51 – 3 = ____

e.

93 – 5 = ____ ____ – ___ = ____

f.

____ – ___ = ____

33 – 4 = ____ ____ – ___ = ____

6. Solve the problems. a.

There are some people in the bus. At the next bus stop, 13 people come in. Now there are 52 people in the bus. How many were there srcinally?

b. Molly

has 23 stuffed toys that she likes to play with, and 16 stuffed toys that she does not care for. Her little sister Annie has 17 stuffed toys. Molly gives the 16 toys to her little sister. How many does Annie have now? Who has more stuffed toys now? How many more?

c. There

are 24 hours in a day-night period. An elephant typically eats for about 16 hours a day, and sleeps for about 6 hours a day. How many hours a day can an elephant spend on other activities?

d. Andy

has $47 in his wallet. He earns $15 by selling lemonade. Can he now buy a remote-controlled toy car for $65? If yes, how much money would have have left after buying it? If not, how much more money would he need?

62


7. Subtract. – 8

77

– 9

______

– 6

88

– 10

______

– 9

______

– 5

______

– 10

______

– 4

______

– 7

______

– 3

38

______

– 8

______

– 5

______

43

8. Subtract. Check by adding. a.

d.

Check:

8 8 – 5 4

b.

+ 5 4

6 6 – 1 7

e.

Check:

6 3 – 4 8

c.

+ 4 8

7 1 – 2 2

f.

Check:

6 9 – 2 7

+ 2 7

8 4 – 4 9

9. Compare the problems, and find a way to do them. Place a letter in the box next to each problem according to the right answer. Read the words vertically. a.

b.

c.

______ – 28 = 45

______ + 12 = 45

______ + 12 + 13 = 45

______ – 33 = 29

______ + 23 = 99

______ + 23 + 19 = 96

______ – 37 = 55

______ + 66 = 100

______ + 67 + 4 = 88

______ – 41 = 50

______ + 24 = 50

______ + 24 + 26 = 80

ADE

E HKM

NOORT

W W

62 20 30 99 91 26 73 17 54 76 34 92 85 33

63


Subtracting Whole Tens, p. 10 1. a. 20 b. 20 c. 30 d. 27 e. 16 f. 25. The ones digit does not change. 2. a. 76, 66, 56, 46, 36, 26, 16 b. 72, 62, 52, 42, 32, 22, 12 c. 67, 57, 47, 37, 27, 17, 7 3. a. 13, 3

b. 28, 18

c. 46, 26

d. 65, 55

e. 21, 11

f. 41, 31

4. a. 88 – 10 = 78 88 – 20 = 68 88 – 30 = 58 88 – 40 = 48

b. 100 – 60 = 40 90 – 50 = 40 80 – 40 = 40 70 – 30 = 40

88 88 –– 50 60 = = 38 28 88 – 70 = 18

c. 34 – 10 = 24 44 – 20 = 24 54 – 30 = 24 64 – 40 = 24

60 50 –– 20 10 = = 40 40 40 – 0 = 40

74 84 –– 50 60 = = 24 24 94 – 70 = 24

5. a. 30 + 20 + 30 = 80. So they weigh about 80 kg. b. $30 + $30 + $30 = $90. No, he cannot. c. $50 – $10 – $10 – $10 = $20. He has about $20 left. Puzzle corner: Answers vary. There are many solutions for both puzzles. 40 + 50 =9 0 –

5 0 – 10 =4 0

–

10 + 20 = 30 = 30

= 30

= 80

30 + 60 =9 0 –– 0 = 30

+

+

30 –

0

= 30

= 10 45 –

5

= 40

++ + 30= = 30

30

35 – = 10

= 80

5

= 30

Adding in Columns, p. 12 1. a.

20 + 30

b.

50 2. a.

32 + 14 46

10 + 50

c.

60 b.

54 + 5 59

32 d. + 20 52

c.

41 d. + 27 68

43 + 33

e.

76 65 + 13 78

e.

35 f. + 12

57 g. + 22

26 h. + 51

47

79

77

31 f. + 40

43 + 34 77

25 + 33

71

58

3. a. 77 b. 98 c. 58 d. 69 e. 86 f. 86 g. 95 h. 87 i. 76 j. 89 k. 78 l. 97 m. 97 n. 88 o. 89

65


Doubling, p. 14 1. a. 5 + 5 = 10

b. 30 + 30 = 60

c. 50 + 50 = 100

2. a. 2 2 + 2 2

b. 3 + 3

4 4

c. 1 + 1

3 3

d. 4 1 + 4 1

4 4

6

8

2

6

8 2

3. Double 6 is 6 + 6 = 12. Double 7 is 7 + 7 = 14 Double 8 is 8 + 8 = 16. Double 9 is 9 + 9 = 18. Double 10 is 10 + 10 = 20. Double 11 is 11 + 11 = 22. Double 12 is 12 + 12 = 24.

Double 13 is 13 + 13 = Double 14 is 14 + 14 = Double 15 is 15 + 15 = Double 16 is 16 + 16 = Double 17 is 17 + 17 = Double 18 is 18 + 18 = Double 19 is 19 + 19 =

26. 28. 30 32. 34. 36. 38.

4. Each child will make 8 sandwiches. 5. You each get 16 pieces of candy. 6. A double batch of brownies makes 32 brownies. 7. Each teacher will get 14 worksheets. 8. Mary moved 8 spaces. Andrea moved 12 spaces. 9. Each woman will make 10 dolls.

One-Half, p. 16 1. a.

b.

2.a.

b.

c.

d.

e.

3. a. 5 + 5 = 10

b. 20 + 20 = 40

c. 12 + 12 = 24

1 of 10 is 5. 2

1 of 40 is 20. 2

1 of 24 is 12. 2

4. 1

6 + 6 = 12

11 + 11 = 22

7 + 7 = 14

12 + 12 = 24

2 1 2

of 16 is 8. of 28 is 14.

1

8 + 8 = 16 9 + 9 = 18

13 + 13 = 26 14 + 14 = 28

2

10 + 10 = 20

15 + 15 = 30

1

1 2 2

of 26 is 13. of 30 is 15. of 22 is 11.

66


5. b.

a. 1 of 26 is 13. 2

c. 1 of 48 is 24. 2

1 of 30 is 15. 2

6. a. Each one got $30.

d. 1 of 32 is 16. 2

10 + 10 = 20

b. Half of 60 minutes is 30 minutes.

20 + 20 = 40

c. 50 students were not sick.

30 + 30 = 60 40 + 40 = 80

d. Missie has $10 now.

50 + 50 = 100

e. Mom had 20 apples srcinally.

Regrouping with Tens, p. 18 1. a.

33 + 9 42

2. a.

13 + 29 42

2. g.

25 + 55 80

25 b. + 8 33 24 b. + 38 62

38 c. + 9 47

27 d. + 7 34

35 c. + 19 54

36 e. + 18 54

24 d. + 47 71

25 f. + 27 52

44 e. + 17 61

26 f. + 36 62

39 h. + 35 74

3. a. 57 b. 72 c. 91 d. 98 e. 53 f. 93 g. 57 h. 90 i. 87 j. 95 k. 58 l. 75 m. 94 n. 94 o. 40 4. a. 79 b. 87 c. 71

d. 93 e. 73

5. a. 0, 4, 8, 12, 16, 20, 24, 28, 32 b. 100, 96, 92, 88, 84, 80, 76, 72, 68

Going Over to the Next Ten, p. 21 1. a. 22 b. 23 c. 24 d. 31 e. 31 f. 46 g. 42 h. 52 i. 63 2. a. 28 + 8 / \ 28 + 2 + 6 30 + 6 = 36 d. 39 + 3 / \ 39 + 1 + 2 40 + 2 = 42

b. 47 + 5 / \ 47 + 3 + 2

c. 79 + 9 / \ 79 + 1 + 8

50 + 2 = 52 e. 27 + 5 / \ 27 + 3 + 2

80 + 8 = 88 f. 38 + 7 / \ 38 + 2 + 5

30 + 2 = 32

40 + 5 = 45

67


3. a. 8 +1 = 9 8 + 2 = 10 8 + 3 = 11 8 + 4 = 12 8 + 5 = 13 8 + 6 = 14

28 28 28 28 28 28

b. + 1 = 29 + 2 = 30 + 3 = 31 + 4 = 32 + 5 = 33 + 6 = 34

c. 78 + 1 = 79 78 + 2 = 80 78 + 3 = 81 78 + 4 = 82 78 + 5 = 83 78 + 6 = 84

What do you notice? The two patterns are similar. The ones digits are the same. 4. a. 2, 3 b. 7, 8 c. 3, 4 d. 3, 5 e. 2, 4 f. 4, 6 5. a. $22 + $8 = $30 or $30 – $22 = $8. Benjamin needs $8 more. b. $20 + $5 + $5 = $30. Natasha has $3. c. 28 – 8 = 20 fruit trees left to plant. d. 37 – 32 = 5 came later. e. Half of 40 is 20. 40 – 20 – 7 = 13 grapes are left. 6. 9 9 9 9 9 9

a. + 1 = + 2 = + 3 = + 4 = +5 = + 6 =

10 11 12 13 14 15

39 39 39 39 39 39

b. + 1 = + 2 = + 3 = + 4 = + 5= + 6=

40 41 42 43 44 45

59 59 59 59 59 59

c. + 1 = + 2 = + 3 = + 4 = + 5 = + 6=

60 61 62 63 64 65

Add with Two-Digit Numbers Ending in 9, p. 24 1.

a. 19 + 5 = 24

b. 29 + 7 = 36

c. 49 + 5 = 54

d. 29 + 8 = 37

e. 39 + 6 = 45

f. 49 + 9 = 58

2. a. 19 + 7 = 26 9 + 7 = 16

b. 49 + 3 = 52 9 + 3 = 12

c. 39 + 4 = 43 9 + 4 = 13

3. a. 12, 22 b. 15, 45 c. 13, 53 d. 16, 46, 36 e. 18, 78, 88 f. 14, 24, 64 The answers to the problems in each box end in the same digit. 4. a. 5, 6, 4, 9, 3, 8, 7 b. 13, 17, 11, 14, 15, 18, 16 c. 7, 9, 4, 6, 5, 10, 8 d. 15, 16, 13, 14, 11, 17, 12

68


5.

a.

+

8

40 b.

+

+ 32

5

48 5

16 c.

+

8

53 +

+

7

27 +

5

+

+

49

7

+

8

66 8

34

8

41

+

61

6

21 9

+

+

42 +

56

6 62

+

+

5

74

79

9

+ 10

51

61

5

+

67

+

8

+

87

92

+ 11

+ 12

72

4

+

71

5

84 3

+

74

2

76

Add in Columns Practice, p. 26 1. a. 80

b. 91

c. 91

d. 70

e. 52

f. 78

g. 116

h. 94

i. 85

j. 49

2. a. 72

b. 64

c. 72

d. 70

e. 56

f. 62

g. 56

h. 74

i. 26

j. 66

3. a. 107

b. 142

c. 104

d. 146

4. a. 128

b. 155

c. 120

d. 147

e. 123

f. 109 g. 126

h. 147

i. 149

j. 137

Add with Two-Digit Numbers Ending in 8 or 7, p. 28 1.

a. 18+ 6 = 24

b. 28 + 7 = 35

c. 48 + 8 = 56

d. 38 + 4 = 42

e. 38 + 6 = 44

f. 48 + 5 = 53

b. 38 + 6 = 44 8 + 6 = 14

c. 58 + 5 = 63 8 + 5 = 13

2. a. 18 + 7 = 25 8 + 7 = 15

3. a. 11, 21 b. 14, 44 c. 12, 82 d. 15, 95 e. 10, 40, 30 f. 17, 77, 87 g. 13, 23, 63 h. 16, 36, 96 The answers to the problems in each box end in the same digit. 4. a. 31 b. 52 c. 44 5. a. 75 + 7 = 82 5 + 7 = 12

b. 47 + 7 = 54 7 + 7 = 14

c. 57 + 6 = 63 7 + 6 = 13

6. a. 13, 33 b. 12, 82 c. 14, 94 d. 16, 76, 96 e. 10, 40, 80 f. 17, 27, 57 The answers to the problems in each box end in the same digit. 7. a. She needs nine eggs. b. They have eaten 38 pounds of potatoes.

69


Addition Practice, p. 30 1. a. 20 + 34 = 54 (20 + 30 + 4)

b. 70 + 18 = 88 (70 + 10 + 8 )

2. a. 27, 36, 52 b. 36, 64, 87

c. 50 + 27 = 77 (50 + 20 + 7 )

c. 64, 83, 75

3. At each step, we add two more than we added in the previous step.

+ 2 1

+ 4 3

+ 6

+ 8

+ 10

1 3

21

31

7

+ 12

+ 14

4 3

57

+ 16

73

4. a. 92 b. 91 c. 63 d. 90 e. 84 5. a. <

b. =

c. =

d. > e. > f. =

6. The person did not carry to the tens, but instead wrote the sum of the ones down in its completeness, and then wrote the sum of the tens next to it. 7. a. 15, 25, 45 b. 13, 23, 53 c. 12, 52, 82 d. 16, 66, 46 8. a. 42, 45, 48, 51, 54, 57, 60, 63 b. 1, 4, 7, 10, 13, 16, 19, 22, 25 9. a. 33, 47, 54 b. 53, 33, 44 c. 30, 54, 99 d. 84, 74, 71 Puzzle corner. a.

b.

2 7 + 1 4

+

c.

6 8 3

4 1

d.

2 6 + 2 5

7 1

1 3 + 7 8

5 1

e.

3 5 + 2 6

9 1

6 1

Many Addends, p. 32 1. a. 17, 27 b. 20, 17 c. 23, 24 2. a. 93 b. 92 c. 98 d. 82 e. 97 f. 96 g. 89 h. 80 i. 117 j. 117 k. 129 l. 145 3. a. No, because 23 plus 9 is more than 30. It can only hold 7 more people. b. 47 people total. c. 2 buses for the 57 people and 3 buses for 88 people. d. 30 – 6 = 24. e. 30 – 13 – 7 = 10. f. 16 people g. 20 – 8 + 5 = 17, so there are 17 people now. h. 30 – 7 – 12 = 11, so there were 11 people on the bus srcinally. 4. a. 80 b. 71 c. 54 d. 47 5.a. 19 + 5 + 7 = 31 OO

O

d. 57 + 21 = 78 O

O

E

g. 17 + 27 + 5 = 49 OO

O

b. 25 + 7 + 3 = 35

O

O

O e. 5 O

+

O 1

O

c. 7 + 11 + 23 = 41

O

O

+ 11 +

OOO

9

=2 6

E

h. 25 + 13 + 3 + 1 = 42 OOO

O

E

OO

O

f. 25 +

9

O

O

= 34 E

i. 57 + 21 = 78 O

O

E

Underline the correct choice in the sentences below. Can you think why it is that way?

70


If I add two odd numbers, the answer is (even/odd). If I add three odd numbers, the answer is (even/odd). If I add four odd numbers, the answer is (even/odd). Each odd number is actually some even number plus one. In other words, each odd number of items can be organized into pairs so that one item is left over. When we have two odd numbers, we can put those two items together to form another pair. That is why the sum of two odd numbers is even. If we have three odd numbers, from those we can form one pair but one item will be left over. So, the sum is odd. Similarly with adding two odd numbers, adding four odd numbers gives us an even sum. Puzzle Corner. Can you explain how Mary is adding and why it works? First she adds all of the tens and writes that under the line. Then she adds the ones and writes those under the tens' sum. Lastly, she adds the two sums. 13 27 16 46 15 28 25 25 + 48 + 31 + 47 + 12

36 27 + 34

60 + 16

70 + 16

70 + 18

70 + 13

80 + 17

76

86

88

83

97

Subtracting in Columns, p. 35 1. a. 55 –32 = 33. 2. a. 47

b. 42

b. 73 c. 34

– 61 = 12. d. 67

e. 44

f. 60

g. 3

h. 34

i. 44

j. 22

3. a. 20 b. 23 c. 63 d. 15 e. 43 4. a. 92, 82, 42 b. 39, 79, 59 c. 93, 23, 3 5. a. Linda b. Luis c. 33 more d. 3 more

e. 87 seashells f. 45

g. no

6. a. 0, 6, 12, 18, 24, 30, 36, 42, 48 b. 0, 7, 14, 21, 28, 35, 42, 49, 56 c. 0, 8, 16, 24, 32, 40, 48, 56, 64 d. 0, 9, 18, 27, 36, 45, 54, 63, 72 e. 100, 95, 90, 85, 80, 75, 70, 65, 60 f. 77, 72, 67, 62, 57, 52, 47, 42, 37, 32 7. a. 21 flew away b. She needed 13 sheets of paper. c. The teacher needed to buy 2 packages. d. 8 had flown away. Puzzle corner: –

5

7

3

4

–

5

4

1

2

2 3

–

6

8

1

8 5 0

+

3

8

3

5

4 2

+

3

3

1

7 5 0

+

5 1

3

4

2

8 6 2

+

2 6

6 8

7 3

+

4 4

–

9

9

8

4 1 5

71

7 6 9 3

+

3

4

4

8 8 2


Regrouping (Borrowing), Part 1, p. 38 1. a. 3 tens 0 ones → 2 tens 10 ones b. 3 tens 6 ones → 2 tens 16 ones c. 5 tens 1 one → 4 tens 11 ones d. 5 tens 5 ones → 4 tens 15 ones e. 4 tens → 3 tens 10 ones f. 3 tens 7 ones → 2 tens 17 ones 2. a. What is left? 2 tens 8 ones b. 5 tens 4 ones → 4 tens 14 ones. What is left? 2 tens 7 ones. c. 4 tens 3 ones → 3 tens 13 ones. What is left? 1 ten 8 ones. d. 6 tens 1 one → 5 tens 11 ones. What is left? 1 ten 7 ones. 3. a.

b.

5 tens 5 ones –

4 tens 3 tens 1 tens

15ones 5 ones

7 tens 2 ones –

10 ones

c.

6 t ens 3 tens 3 tens

12 ones 5 ones 7 ones

d.

6 tens 0 ones –


10 ones 7 ones

6 tens 4 ones –

3 ones

e.



f.

7 tens 6 ones –


16 ones 7 ones

5 tens 0 ones –

9 ones

g.



h. 7 tens

8 tens 1 one –

6 tens 1 tens

11 ones

5 tens

6 tens 3 ones

5 ones

–

6 ones

2 tens 3 tens


4. a. 19 pencils b. 7 more pencils c. 13 more pencils

72


Regrouping (Borrowing), Part 3, p. 44 1.

2. a. YES; 35 b. NO; 51 c. YES; 25

d. NO; 22 e. YES; 26 f. YES; 63

3. a. 44 h.b.NO; NO;10 25 i.c.YES; YES;1926 d. YES; 52 g. YES; NO; 40

e. NO; 72 f. NO; 11

4. a. 17 b. 60 c. 57 d. 33 e. 42 f. 17

Graphs and Problems, p. 46 1. a. Mon Tues Wed Thurs Fri

Day Newspapers

Sat

Sun

about about about about about about about 30 40 40 40 50 30 70

b. about 100

c. about 40 more.

2.

a.

b. 27 children c. 23 children

3. a. 35 Arctic animals, 90 rain forest birds b. 85 4. a. 22

b. 61

c. 35 more

c. 32

5. a. 28 + 33 = 61. No they don't have more than Jim. b. You have read now 48 + 10 = 58 pages. You have 95 – 58 = 37 pages left. 6. a. 14 books b. Annie, Lisa c. 8 more d. 9 more e. Books read Jan Feb Mar Apr Total Annie

13

21

18

14

66

Freddie

8

5

11

9

33

Lisa

8

13

16

18

55

Jonathan

10

8

14

15

47

f. 33

74


Adding 2-Digit Numbers Mentally, p. 49 1. a. 78 b. 73 c. 82 d. 81 e. 84 f. 93 g. 81 h. 82 i. 52 2. a. 69, 59, 89, 53

b. 44, 20, 83, 83 c. 90, 61, 81, 31

d. 37, 30, 52, 80

3. a. 58 b. 90 c. 91 d. 79 e. 72 f. 110 g. 63 h. 95 4. WHITTLE BY WHITTLE 5. ...WERE BELOW C LEVEL.

Mental Subtraction Methods, p. 52 1. a. ( 51 − 1 ) − 4 = 46 −

b. ( 62

−

−

2 ) − 5 = 55

−

c. ( 33

−

−

3 ) − 1 = 29

−

e. ( 75 5 ) 1 = 69 f. ( 63 3 ) 4 = 56 2. a. 44, 46, 48, 45 b. 38, 37, 39, 36

g. ( 35

d. ( 92

−

5 ) 2 = 28

−

2 ) − 3 = 87

−

h. ( 74

−

4 )

2 = 68

3. a. 5, 15, 35 b. 9, 19, 29 c. 3, 43, 23 d. 6, 56, 36 e. 5, 25, 85 f. 8, 78, 28 4. a. 29; 66

b. 56; 28 c. 43; 87

d. 55; 75

5. a. 36 pages b. 27 pages 6. + 8

+2

+7

a. 92 – 84 = 8

b. 51 – 49 = 2

c. 76 – 69 = 7

(Think: 84 + 8 = 92)

(Think: 49 + 2 = 51)

(Think: 69 + 7 = 76)

d. 32 – 28 = 4 g. 22 – 14 = 8 j. 53 – 46 = 7

e. 90 – 83 = 7 h. 64 – 56 = 8 k. 72 – 65 = 7

f. 100 – 95 = 5 i. 64 – 55 = 9 l. 44 – 37 =7

7. –1, –5, –2, –5, –5, –3, –4, –7 Puzzle Corner: a.

= 12

b.

= 9,

= 13

c.

= 4,

= 18

More Mental Subtraction, p. 55 1. a. 13 b. 36 c. 53 d. 18 e. 33 f. 35 g. 36 h. 23 i. 39 j. 40 k. 67 l. 24 2. a. 7 b. 7 c. 39 d. 23 3. a. 7

b. 8

c. 38 d. 7 e. 30 f. 88

g. 55

h. 75

4. a. 14, 12, 48 b. 45, 71, 59 c. 2, 39, 53 5. a. 64 – 8 + 4 = 60. She has 60 marbles. b. 64 cm – 55 cm = 9 cm. The chair is 9 cm wider. c. 50 – 30 = 20. 5 + 20 = 25. Jack has 25 cards now. d. 1/2 of 40 is 20. 5 + 20 = 25. Jack has 25 marbles now. e. Ken's stamps plus Bill's stamps equal 34 + 57 = 91 stamps. 91 is less than 94. No, they will not have more than Brian.

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6.

7. a. 54 – 45 = 9

b. 99 – 11 = 88

c. 100 – 50 = 50

63 – 36 = 27

88 – 22 = 66

99 – 51 = 48

72 – 27 = 45

77 – 33 = 44

98 – 52 = 46

81 – 18 = 63

66 – 44 = 22

97 – 53 = 44

90 – 09 = 81

55 – 55 = 0

96 – 54 = 42

8. Y O U ' R E A S U P E R S U B T R A C T E R!

Puzzle corner:

7 2

7 4

– 2 3

– 5 7

7 5 – 5 1

5 4 – 1 8

8 2 – 4 8

4 9

1 7

2 4

3 6

3 4

Euclid's Game, p. 58 1. No. 2. All the numbers that get marked are also even. 3. All the numbers that get marked will also be multiples of 5. 4. a. No. You cannot mark numbers that are greater than 90. b. Yes. c. No. You will only get to mark multiples of 10. d. Yes.

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Review, p. 61 1. a. b. c. 16 + 4 = 20 47 + 3 = 50 75 + 5 = 80 64 + 6 = 70 38 + 2 = 40 92 + 8 = 100 2. a. 71

b. 72

c. 71 d. 60 e. 72 f. 93

3. a. 33, 89, 33 b. 81, 79, 56 4. a. 10, 6 b. 7, 8

c. 9, 6

g. 95

h. 91

i. 90 j. 92

c. 91, 51, 41 d. 90, 63, 19

d. 7, 9

5. a. 55 – 7 = 48 b. 74 – 8 = 66 c. 93 – 5 = 88 15 – 7 = 8 14 – 8 = 6 13 – 5 = 8 d. 72 – 7 = 65 12 – 7 = 5

e. 51 – 3 = 48 f. 33 – 4 = 29 11 – 3 = 8 13 – 4 = 9

6. a. There were 39 people srcinally. b. Annie has now 33 toys. Annie has more toys; 10 more toys than Molly. c. about 2 hours d. He cannot buy the car. He needs $3 more. 7. 77 88

→

→

69 → 60 82

→

73

→

50

→

45

→

41

→

38

→

63

→

56

→

48

→

43

8. a. 34 b. 15 c. 42 d. 49 e. 49

f. 35

9. MATH WORK DONE. In set a., add the numbers. For example, to solve ___ – 28 = 45, add 28 and 45. In set b. and c., subtract. For example, to solve ___ + 12 = 45 , subtract 45 – 12. To solve ___ + 12 + 13 = 45, subtract 45 – 12 – 13.

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