Math practice...

#### Description

Copyright 2007-2010 Taina Maria Miller. EDITION 1.4 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 for the teacher to reproduce this material to be used with students, not commercial resale, by virtue of the purchase of this book. In other words, the teacher MAY make copies of the pages to be used with students. Permission is given to make electronic copies of the material for back-up purposes only.

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

2

Contents Foreword .....................................................................

5

Chapter 1: Getting Started Introduction ...................................................................

6

Some Review .................................................................

8

Adding and Subtracting Within 0-100 .........................

10

Ordinal Numbers ..........................................................

13

Fact Families .................................................................

15

Dividing to Two Parts - Halves ....................................

17

Fourths and Other Parts ..............................................

19

Chapter 2: Clock Introduction ...................................................................

21

Review - Whole and Half Hours ..................................

23

The Minutes ...................................................................

24

Five-Minute Intervals ...................................................

27

How Much Time Passes? ..............................................

31

Half and Quarter Hours ...............................................

33

The Calendar ..................................................................

35

Review .............................................................................

37

Chapter 3: Addition and Subtraction Facts Within 0-18 Introduction ...................................................................

38

Review: Completing the Next Whole Ten ...................

41

Review: Going Over Ten ..............................................

43

Adding with 9 .................................................................

45

Adding with 8 .................................................................

47

Adding with 7 .................................................................

49

Adding with 6 .................................................................

51

Review - Facts with 6, 7, and 8 .....................................

52

Subtract to Ten ..............................................................

54

Subtraction and the Difference ......................................

56

Number Rainbows - 11 and 12 ................................

58

3

Fact Families - 11 and 12 .......................................

60

Number Rainbows - 13 and 14 .....................................

62

Fact Families - 13 and 14 ..............................................

63

Fact Families - 15 ..........................................................

66

Fact Families - 16 ..........................................................

68

Fact Families - 17 and 18 .............................................

70

Review ...........................................................................

73

Chapter 4: Addition and Subtraction With Two-Digit Numbers Introduction ....................................................................

75

Adding with Whole Tens ..............................................

78

Subtracting Whole Tens ................................................

81

Carrying to Tens ............................................................

83

Going Over to the Next Ten ..........................................

86

Two-Digit Numbers Ending in 9 ...................................

89

Add in Columns Practice ..............................................

91

Two-Digit Numbers Ending in 8 or 7 ...........................

93

95

97

Subtracting in Columns .................................................

100

Borrowing/Regrouping, Part 1 ......................................

101

Borrowing/Regrouping, Part 2 ......................................

104

Borrowing/Regrouping, Part 3 ......................................

107

Graphs and Problems ...................................................

109

Mental Subtraction Methods .........................................

112

Euclid's Game .................................................................

115

Mixed Review ................................................................

118

Chapter 5: Counting Money Introduction ...................................................................

120

Counting Coins Review ................................................

122

Change ...........................................................................

125

Dollars ............................................................................

128

Counting Change ..........................................................

131

4

5

Chapter 1: Getting Started Introduction The first chapter of the Math Mammoth Grade 2-A Complete Worktext has addition and subtraction review from the first grade, plus a few new topics that should be easy. The chapter starts out with review. Ordinal numbers are probably familiar from common language. The lesson Fact Families practices addition/subtraction connection, and introduces missing subtrahend problems such as __ − 5 = 4 where the total is missing. This is an early prelude to algebraic thinking. The last two lessons introduce some easy parts, such as one-half, one-fourth, two-fourths and threefourths. These lessons also practice finding half of a number or a fourth of a number. This is done for a good reason: First of all, the idea of finding part of a number is of paramount importance throughout elementary mathematics. Second, it prevents the fixation that half is “half of a pie” or that one-fourth is “one-fourth of a pie”, when halves and fourths apply to all kinds of “totals”. Third, the child will soon encounter the idea of a quarter of an hour when studying the clock, which is just one-fourth of an hour.

The Lessons in Chapter 1 page

span

Some Review ..........................................................................

8

2 pages

Adding and Subtracting Within 0-100 ...................................

10

3 pages

Ordinal Numbers ....................................................................

13

2 pages

Fact Families ..........................................................................

15

2 pages

Dividing to Two Parts - Halves .............................................

17

2 pages

Fourths and Other Parts .........................................................

19

2 pages

(hours)

Helpful Resources on the Internet Use these free online resources to supplement the “bookwork” as you see fit. Number Cracker Help Mr. Cracker obtain the secret code before the insidious Prof. Soup catches him by guessing what number comes next in a series of numbers. http://www.funbrain.com/cracker/index.html Squigly Squigly is hiding in one of the apples. Click on the ordinal number that tells the order of Squigly's apple. http://www.primarygames.com/squigly/start.htm MathBlox Click on two falling blocks that add up to the given number and they disappear. With various levels and number ranges. http://www.iknowthat.com/com/L3?Area=Mathblox

6

Number Jump Move the ball along the number line to smash the flies. http://www.carstensstudios.com/mathdoodles/numberjump.htm Connect Sums Click on the neighboring die-faces/numbers/coins so that the points add up to the given target sum. http://www.carstensstudios.com/mathdoodles/connectsums.html Sum Stacker Drag dies from stack to stack until the sums of each stack equal the sums given. http://www.carstensstudios.com/mathdoodles/sumsstacker.html

7

Some Review 1. The box with a “T” means a ten. Write the addition sentences.

a.

32

+

7

=

+

+

+

39

b. ____ + ____ = ____

c. ____ + ____ = ____

2. Add whole tens. You draw a ten-box, or some more ten-boxes to the picture.

+

+

+

a. 25 + 10 = _____

b. 14 + 10 = _____

c. 32 + 10 = _____

25 + 20 = _____

14 + 20 = _____

32 + 20 = _____

25 + 30 = _____

14 + 30 = _____

32 + 30 = _____

3. Subtract from whole tens. One of the tens is shown with 10 dots, instead of a ten-box. Cover some of the dots to subtract.

60 – 3 = _____

a.

b.

30 – 4 = _____

60 – 8 = _____

30 – 6 = _____

60 – 7 = _____

30 – 5 = _____

4. Add in columns. The two numbers to be added are shown with dots and ten-boxes. b.

a.

+

+

8

5. Cross out to subtract in (a) and (b). In (c) and (d), subtract in columns.

4

5

− 2

3

c.

a. 49 – 6 = _____

9

8

− 6

5

d.

b. 47 – 16 = _____

6. Add and subtract. a.

b.

c.

d.

70 + 6 = _____

30 + 4 + 4 = _____

90 + ____ = 94

60 + ____ = 90

50 + 9 = _____

50 + 7 + 2 = _____

40 + ____ = 47

40 + ____ = 80

e.

f.

g.

h.

70 − 1 = _____

5 − 5 = ____

88 − 8 = _____

50 + ____ = 56

100 − 5 = _____

24 − 4 = _____

57 − 7 = _____

30 + ____ = 39

7. Solve the word problems. a. Luis bought two boxes of crayon for \$6 each, and a stack of paper for \$3. What was his total cost?

b. Ernie has 7 marbles, and Jackie has 5. Jackie gives Ernie two of his. How many more marbles does Ernie have now than Jackie?

c. Jack has twenty shirts, and ten of them are white. How many are not white?

d. A book costs \$45. Can you buy it if you already have \$22 and your grandma gives you another \$20?

9

Adding and Subtracting Within 0-100 1. Skip-count by fives, starting at 5. Color these numbers light blue.

1

2

3

4

5

6

7

8

9

10

11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

2. Color yellow all the even numbers from 32 to 70.

31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

3. What can the last digit of an even number be? Even numbers end in ____, ____, ____, ____, or ____.

51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100

1

4. Skip-count by tens starting at 17. Color these numbers pink. What is similar about these numbers?

2

3

4

5

6

7

8

9

10

11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40

They all end in ____.

41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

5. Skip-count by tens backwards starting at 93. Color these numbers green. What is similar about these numbers?

61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90

They all end in ____.

91 92 93 94 95 96 97 98 99 100

1

6. Color purple all the odd numbers from 89 to 51.

2

3

4

5

6

7

8

9

10

11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40

7. What can the last digit of an odd number be?

41 42 43 44 45 46 47 48 49 50

Odd numbers end in ____, ____, ____, ____, or ____.

51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70

8. Skip-count by fours starting at 4. Color these numbers yellow.

71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100

10

9. Skip-count. First find by which number to skip-count - by 2s, by 5s, or by 10s. a. 40,

42, 44, _____, _____, 50, _____, _____, _____, _____, _____

b. _____,

_____, _____, _____, 48, 58, 68, _____, 88, _____

c. _____,

_____, _____, _____, 65, 63, 61, _____, _____, _____

d. _____,

_____, _____, 70, 65, 60, _____, _____, _____, _____

10. Write the addition sentences. The box with a “T” is a ten. Under each problem, there is another, similar, addition problem for you to solve. Can you see how it is similar?

+

+

+

a.

____ + ____ = ____

c.

____ + ____ = ____

e.

____ + ____ = ____

b.

34 + 3 = ____

d.

53 + 6 = ____

f.

32 + 5 = ____

11. Subtract by crossing some out. Under each problem, there is another, similar, problem.

a.

59 – 6 = _____

c.

47 – 5 = _____

e.

60 – 3 = _____

b.

39 – 6 = _____

d.

67 – 5 = _____

f.

50 – 3 = _____

12. Add and subtract. The problems in each box are similar. a.

b.

c.

d.

2 + 6 = _____

4 + 4 = _____

3 + 6 = _____

8 + 2 = _____

42 + 6 = _____

74 + 4 = _____

53 + 6 = _____

48 + 2 = _____

72 + 6 = _____

94 + 4 = _____

23 + 3 = _____

98 + 2 = _____

e.

f.

g.

h.

7 – 5 = _____

9 – 4 = _____

10 – 4 = _____

8 – 5 = _____

37 – 5 = _____

29 – 4 = _____

50 – 4 = _____

38 – 5 = _____

67 – 5 = _____

99 – 4 = _____

80 – 4 = _____

88 – 5 = _____

11

13. Draw more dots so you complete the next whole ten. Write an addition sentence.

+ a.

+

13 + ___ = 20

b.

+

____ + ___ = ____

c.

____ + ___ = ____

14. Complete the next whole ten. The problems in the bottom row are challenging! a.

32 + ___ = ____

b.

74 + ___ = ____

c.

48 + ___ = ____

d.

42 + 3 + ____ = 50

e.

37 + ____ + 1 = 40

f.

84 + ____ + 4 = 90

15. Subtract the same number each time.

a.

– 10

b.

– 20

c.

50

____

100

____

45

____

52

____

20

____

95

____

64

____

40

____

96

____

23

____

21

____

11

____

Find numbers for the boxes so that the sum of each row and of each column is a. 50 b. 80. a.

42

+

+ +

+ +

+ +

b.

+ +

+

–5

40

75

+

+

41

+ +

+

+

+

+

+ +

+

12

+

74

72 +

+

Ordinal Numbers The numbers 1, 2, 3, 4, and so on are called cardinal numbers. The fourth tree from the left is circled. It is also the second tree from the right.

But we also often use ordinal numbers. Ordinal numbers are used when talking about the order of things. List of some ordinal numbers:

The seventh letter of the word is S. Ordinal Number Name 1st first 2nd second 3rd third 4th fourth 5th fifth 6th sixth 7th seventh 8th eighth

Ordinal Number Name 9th ninth 10th tenth 11th eleventh 12th twelfth 13th thirteenth 14th fourteenth 15th fifteenth 16th sixteenth

1. Circle. a. The second car from the left. b. The fifth car from the right. c. The seventh snowflake

from the left. d. The fourth snowflake

from the right. e. The ninth letter from the left. f. The twelfth letter from

EXTRAORDINARY

the right.

13

2. Color.

a. The third flower from the left

b. The first three flowers on the left

c. The fifth flower from the right.

d. The first five flowers on the right.

3. Find the letters, and find out what Greg's surprise gift was. The second row from the top, the first letter from the left.

___

The fourth row from the top, the third letter from the left.

___

The first row from the top, the fifth letter from the right.

___

The fifth row from the bottom, the second letter from the right.

___

The 1st row from the bottom, the 1st letter from the left.

___

The sixth row from the top, the third letter from the right.

___

The 3rd row from the top, the 2nd letter from the left.

___

The 1st row from the top, the 2nd letter from the left.

___

E B W J Y U O

4. a. Choose the letters of the given word to make a new word.

___

10th 5th

___

L E K A Z T H

A N P U N S A

B I T D Y O V

G V L W I Q E

P S F M C R L

b. Put the letters in the given order

to make a new word. N D Y R T C I A I O 7th 1st 10th 9th 4th 3rd 2nd 8th 5th 6th

S U R P R I S I N G ___

S H N D K D T

___ ___

6th 9th 1st

14

Fact Families When you have two addition and two subtraction facts that use the same numbers, it is called a “fact family”. Sometimes in a subtraction problem, the total is asked:

4+5= 9

4 + 5 =9

5+4= 9

5 + 4 =9

− 8 = 20 You know 20 and 8 are the “parts”, and the total is missing. To find the total, just add the “parts”: 20 + 8 = 28

9 −5=4

9− 5 = 4

9 −4=5

9− 4 = 5

Notice the TOTAL. The subtraction sentences start with the total.

Notice the PARTS. The two parts make up the total.

1. Write two addition and two subtraction sentences - a fact family! a.

b.

c.

____ + ____ = ____

____ + ____ = ____

____ + ____ = ____

____ + ____ = ____

____ + ____ = ____

____ + ____ = ____

____ − ____ = ____

____ − ____ = ____

____ − ____ = ____

____ − ____ = ____

____ − ____ = ____

____ − ____ = ____

2. Fill in the missing numbers. The four problems form a fact family. a.

b.

=8

c.

____ + ____ = 10

____ + ____ = ____

+2=8

____ + ____ = 10

____ + ____ = ____

2+

10 − 7 =

8−2= 8−

=2

10 −

9 − =7

15

= 6

____ − ____ = ____

3. Write a matching addition sentence for the subtraction sentence. There are two possibilities. a.

____ + ____ = ____

b.

8 − 2 = 6

____ + ____ = ____

c.

20 − 7 = 13

____ + ____ = ____ 60 − 20 = 40

– 6 =2

When the first number is missing in a subtraction, it is the TOTAL that is missing.

The total is missing. 6 and 2 are the “parts”. So we add them. 2 + 6 = 8. The missing number is 8!

You can find the TOTAL by adding the two numbers (those are the “parts”).

It's like “adding backwards”:

4. The total is missing from the subtraction sentence. Solve. a.

– 5 = 4

b.

– 7 = 2

c.

b.

– 7 = 80

c.

– 7 = 10

5. Find the missing numbers. a.

–2=4 – 50 = 50

60 + 4 =

– 8 = 20

16 +

9–

=5

77 + = 20

= 78 – 9 = 60

Find the missing numbers. This time adding backwards will NOT work! a. 50 −

= 10

b. 100 −

= 91

c. 10 −

−2=1

33 −

= 31

76 −

= 72

9−

−5=2

16

Dividing into Two Parts — Halves If you divide something into two of the same size parts, or two equal parts, then either part is one-HALF of the whole. We write one-half this way:

1 2

You can also write one-half this way: 1/2 You can also find half of so-many objects. For example, you can find half of ten apples. It is five apples. You can also find half of a number. For example, half of 6 is 3.

1. a. Color one half of each shape.

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 items into two EQUAL groups. Write an addition sentence. Find half of the total.

10 balls

40

24

a. ____ + ____ = _____

b. ____ + ____ = _____

c. ____ + ____ = _____

1 of 10 is ____. 2

1 of 40 is ____. 2

1 of 24 is ____. 2

17

4. Remember your doubles? Fill in the chart.

1 + 1 = ____

1 2

of 2 is 1 .

6 + 6 = ____

1 2

of ___ is ____.

2 + 2 = ____

1 2

of 4 is 2 .

7 + 7 = ____

1 2

of ___ is ____.

3 + 3 = ____

1 2

of ___ is ____.

8 + 8 = ____

1 2

of ___ is ____.

4 + 4 = ____

1 2

of ___ is ____.

9 + 9 = ____

1 2

of ___ is ____.

5 + 5 = ____

1 2

of ___ is ____.

10 + 10 = ____

1 2

of ___ is ____.

5. Divide the items into two EQUAL groups. Write an addition sentence. Find half of the total.

a. ____ + ____ = _____

b. ____ + ____ = _____

c. ____ + ____ = _____

1 of ___ is ____. 2

1 of ___ is ____. 2

1 of ___ is ____. 2

6. Solve the word problems, and fill in another chart of doubles and halves to help you. a. Jack and Joe split \$60 between them.

10 + 10 = _____

1 2

of ___ is ____.

b. What is half of 60 minutes?

20 + 20 = _____

1 2

of ___ is ____.

c. Half of 100 students were sick.

30 + 30 = _____

1 2

of ___ is ____.

40 + 40 = _____

1 2

of ___ is ____.

50 + 50 = _____

1 2

of ___ is ____.

How many dollars did each get?

How many were not sick? d. Aunt Katie gave Missie half of \$40.

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

e. The recipe called for 10 apples. That was exactly half of Mom's apples.

How many apples had mom bought originally?

18

Fourths and Other Parts 1 4 A square is divided into four equal parts. One part is colored. The colored part is one-fourth:

1 of the circle 4

1 of the stars 4

1 of the rectangle 4

1 of the hearts 4

1 4

We also write one-fourth as 1/4. If you need to find 1/4 of any thing, first divide it into four equal groups.

1 4 one-fourth

2 4

3 4

4 4

two-fourths

three-fourths

four-fourths

1. Color the part indicated.

a.

1 2

b.

1 4

c.

3 4

d.

2 2

e.

2 4

f.

1 2

g.

3 4

h.

4 4

i.

1 4

j.

1 2

19

2. Divide these items into four EQUAL groups. Find one-fourth of the total. 12 balls

8 balls

a.

1 of 8 is ____. 4

b.

40

1 of 12 is ____. 4

c.

16

1 of 40 is ____. 4

d.

1 of 16 is ____. 4

1 of 100 is _____. 4

3. a. Here you see 100 little squares. Color 1/4 of them.

1 of 60 is _____. 4

b. Here you see 60 little squares.

Color 1/4 of them.

3 of 80 is _____. 4

c. Here you see 80 little squares.

Color 3/4 of them.

1 dollar = 100 pennies

4 quarters = 1 dollar 4. Remember the quarter coin? The word “quarter” means one-fourth.

=

Four quarters makes one dollar, or 100 cents. 1 of 100 cents is _____ cents = 1 quarter. 4 1 of 100 cents is _____ cents = 2 quarters. 2 3 of 100 cents is _____ cents = 3 quarters. 4

20

Chapter 2: Clock Introduction The second chapter of the Math Mammoth Grade 2-A Complete Worktext deals with reading the clock to the five-minute intervals, and finding simple time intervals. It is helpful to have a practice clock, such as an alarm clock, where the child can turn the clock hands. First we practice telling time in the hours:minutes form (such as 10:20), and then using the colloquial phrases “ten after”, “quarter till”, and so on. Also studied are simple time intervals, or how much time passes. When practicing these, tell the child to imagine moving the minute (or hour) hand on a clock. He/she can initially use a practice clock for this. The section also has one lesson about the calendar. Of course the calendar and the months are best learned just in the context of everyday life, as the months pass. Hang a wall calendar on the wall and instruct your child to look at it every day, and to cross out days as they pass.

The Lessons in Chapter 2 page

span

Review - Whole and Half Hours ..................

23

1 page

The Minutes ..................................................

24

3 pages

Five Minute Intervals ..................................... 27

4 pages

How Much Time Passes? ..............................

31

2 pages

Half and Quarter Hours .................................

33

2 pages

The Calendar ................................................

35

2 pages

Review .........................................................

37

1 page

Helpful Resources on the Internet Use these free online resources to supplement the “bookwork” as you see fit. Analog and Digital Clocks These clocks show you the current time, side by side. Useful for illustration. http://nlvm.usu.edu/en/nav/frames_asid_316_g_2_t_4.html What Time Will it Be? Move the hands on the clock to show what time it will be after a certain amount of minutes. http://nlvm.usu.edu/en/nav/frames_asid_318_g_2_t_4.html Match Clocks Make the digital clock to show the time given with the analog clock. http://nlvm.usu.edu/en/nav/frames_asid_317_g_2_t_4.html

21

Time Flies Practice telling time with two types of watches. In the second part, practice what you have learned by selecting the digital time that matches the time displayed. http://www.alfy.com/Games/playgame.aspx?gameID=354&gameName=Time+Flies Flashcard Clock Read the analog and type in the time in digital form. Very clear clock and good fast response! http://www.teachingtreasures.com.au/maths/FlashcardClock/flashcard_clock.htm Telling Time Practice Interactive online practice: you drag the hands of the clock to show the correct time. http://www.worsleyschool.net/socialarts/telling/time.html Teaching Time Analogue/digital clock games and worksheets. Also an interactive “class clock” to demonstrate time. http://www.teachingtime.co.uk/ Time-for-time Resource site to learn about time: worksheets, games, quizzes, time zones. http://www.time-for-time.com/default.htm A Matter of Time Lesson plans for telling time, interactive activities, and some materials to print. http://www.fi.edu/time/Journey/JustInTime/contents.html Elapsed Time Line This interactive tool shows 2 clocks that have draggable fingers to set a "from" and "to" time, and a number line. You can demonstrate how to use a number line to calculate elapsed time. www.teacherled.com/2008/10/05/elapsed-time-line/ Clockwise Plug in a time, and the clock runs till it, or clock runs to a time and you type it in. http://www.shodor.org/interactivate/activities/clock2/index.html Clock (evaluation version words across the screen) Use the buttons to advance the clock in 5, 10, 15, 30 minute increments or drag the hands. Shows digital time also. For illustrations only, does not have any quiz or questions. http://www.interactive-resources.co.uk/mathspack1/clock/clock.html The Right Time A couple of interactive exercises about reading the clock. http://www.pitara.com/activities/math/time/time.asp?QNum=3 What Time Is It? Look at the analog clock and pick the digital clock that shows the same time. http://www.primarygames.com/time/start.htm

22

Review - Whole and Half Hours 1. Write or say the time using the expressions o'clock or half past.

a.

b.

c.

d.

2. Write the time in two ways: using the expressions o'clock or half past, and with numbers.

a. _____ o'clock _____ : _____

b. half past _____

c. half past _____

_____ : _____

_____ : _____

d. _____ o'clock _____ : _____

3. Write the time an hour later. Use numbers. Now it is:

a. 6:00

b. 11:30

c. 3:00

d. 2:30

e. 9:30

c. 12:30

d. 10:00

e. 1:30

An hour later, it is: 4. Write the time a half-hour later. Use numbers. Now it is:

a. 5:00

b. 7:30

A half-hour later, it is:

23

The Minutes When the hour hand moves from one number to the next (from 1 to 2, or from 6 to 7, etc.), it takes one hour to do that. In that same one hour of time, the minute hand travels from 0 to 60 minutes. So one hour is 60 minutes. A half-hour is 30 minutes. When you read the minute hand, you use the green numbers. They go by fives, and are not normally marked on clocks. You need to know them. (Just skip-count by fives!)

The hour hand is past 8. The minute hand is at 15. The time is 8:15.

The hour hand is past 3. The minute hand is at 25. The time is 3:25.

1 hour = 60 minutes. 1/2 hour = 30 minutes.

The hour hand is past 11. The minute hand is at 10. The time is 11:10.

1. The arrow shows how much the minute hand travels. How many minutes of time passes?

a. _____ minutes

b. _____ minutes

c. _____ minutes

24

d. _____ minutes

2. Write the time.

a. ____ : _____

b. ____ : _____

c. ____ : _____

d. ____ : _____

e. ____ : _____

f. ____ : _____

g. ____ : _____

h. ____ : _____

3. Find the clock that shows 11:25 and the clock that shows 11:05.

a.

b.

c.

d.

4. Write the time that the clock shows, and the time 5 minutes later.

5 min. later →

a. ____ : _____

b. ____ : _____

c. ____ : _____

d. ____ : _____

____ : _____

____ : _____

____ : _____

____ : _____

25

Notice! The hour hand looks like it is pointing to 10. But the minute hand has not yet reached 60 minutes, so it is not yet 10 o'clock. We still say it is 9 hours (and some minutes). The minute hand is at 55. The time is 9:55.

5. Write the time. Note: the hour hand is close to some number, but it has not reached that yet.

a. ____ : _____

b. ____ : _____

c. ____ : _____

d. ____ : _____

e. ____ : _____

f. ____ : _____

g. ____ : _____

h. ____ : _____

6. Write the time that the clock shows, and the time 5 minutes later.

5 min. later →

a. ____ : _____

b. ____ : _____

c. ____ : _____

d. ____ : _____

____ : _____

____ : _____

____ : _____

____ : _____

26

Five-Minute Intervals When the MINUTE hand travels from one number to the next on the clock face, 5 minutes of time passes. Each interval is five minutes. That is why you skip-count by fives, when figuring out the minutes.

1. Continue writing the times at each five-minute interval. You can use your practice clock.

a.

b.

c.

d.

8 : 20

_____ : _____

_____ : _____

_____ : _____

8 : 25

_____ : _____

_____ : _____

_____ : _____

_____ : _____

_____ : _____

_____ : _____

_____ : _____

_____ : _____

_____ : _____

_____ : _____

_____ : _____

_____ : _____

_____ : _____

_____ : _____

_____ : _____

_____ : _____

_____ : _____

_____ : _____

_____ : _____

_____ : _____

_____ : _____

_____ : _____

_____ : _____

_____ : _____

_____ : _____

_____ : _____

_____ : _____

_____ : _____

_____ : _____

_____ : _____

_____ : _____

_____ : _____ _____ : _____ _____ : _____

_____ : _____ _____ : _____ _____ : _____

27

We can also tell the time by saying how many minutes it is past the whole hour, or how many minutes it is till the next whole hour. Use the expression “so-many minutes past” only if the minutes are less than 30. After that, use “so-many minutes till” the next whole hour.

20 past 1

10 till 7

“20 minutes past 1 o'clock”. “10 minutes till 7 o'clock.”

2. How many minutes is it past the whole hour, or till the next whole hour?

a. It is ____ minutes past 2 o'clock.

b. It is ____ minutes past 3 o'clock.

c. It is ____ minutes past ____ o'clock.

d. It is ____ minutes past _____ o'clock.

e. It is ____ minutes till 7 o'clock.

f. It is ____ minutes till ____ o'clock.

g. It is ____ minutes till ____ o'clock.

h. It is ____ minutes till ____ o'clock.

i. ____ past ___

j. ____ past ___

k. ____ past ___

l. ____ past ___

m. ____ till ___

n. ____ till ___

o. ____ till ___

p. ____ till ___

28

3. Write the time using the wordings “past”, “till”, “half past” or “o'clock”, and the time 5 minutes later.

a. ____ till ___

b. ____ till ___

c. ____ past ___

d. ____ past ___

____ till ___

____ till ___

____ past ___

____ past ___

5 min. later →

e.

f.

g.

h.

i.

j.

k.

l.

5 min. later →

5 min. later → 4. Write the time using the hours:minutes way. Use your practice clock to help. a. 10 past 8 ______:______ e. 9 o'clock ______:______

b. 15 till 7

c. 25 past 12

______:______

______:______

f. 20 till 6

g. 5 till 11

______:______

______:______

29

d. half-past 7 ______:______ h. 25 till 4 ______:______

5. Write the time using the expressions “past”, “till”, or “half past”. a. 6:45

b. 9:30

c. 12:10

d. 4:55

e. 8:35

f. 1:40

g. 2:15

h. 11:50

6. How many minutes does the minute hand “cover”, or “pass through”, on the clock?

a. From 10:00 till 10:15

b. From 1:20 till 1:35

c. From 5:50 till 6:10

d. From 2:05 till 2:40

______ minutes

______ minutes

______ minutes

______ minutes

7. Write the later times.

a.

c.

e.

z

15 min. later ____:_____

z

15 min. later ____:_____

z

20 min. later ____:_____

z

20 min. later ____:_____

z

30 min. later ____:_____

z

30 min. later ____:_____

z

15 min. later ____:_____

z

15 min. later ____:_____

z

20 min. later ____:_____

z

20 min. later ____:_____

z

30 min. later ____:_____

z

30 min. later ____:_____

z

15 min. later ____:_____

z

15 min. later ____:_____

z

20 min. later ____:_____

z

20 min. later ____:_____

z

30 min. later ____:_____

z

30 min. later ____:_____

b.

d.

f.

30

How Much Time Passes? 1. How many minutes till 2:30? Till 8:05? a.

b.

It is 2:00. → ______ minutes till

It is 7:30. → ______ minutes till

It is 2:10. → ______ minutes till

It is 7:35. → ______ minutes till

It is 2:20. → ______ minutes till

It is 7:45. → ______ minutes till 2:30

It is 2:25. → ______ minutes till

It is 7:50. → ______ minutes till

8:05

2. The class ends at 1:00. How many minutes of class is left at these times?

a.

b.

c.

d.

_______ minutes

_______ minutes

_______ minutes

_______ minutes

3. How many minutes pass? Imagine turning the minute hand on a clock. from

1:45

1:55

1:40

1:45

1:55

to

1:55

2:05

2:05

2:15

2:10

minutes

10 minutes

from

2:00

7:05

8:45

6:40

11:15

to

2:35

7:15

9:05

7:10

11:30

minutes 4. a. The bus trip started at 10 past 4, and ended at half past 4. How many minutes did it take? b. Joshua started math homework at 20 till 5, and ended at 5 past 5.

How much time did he spend? c. Music class starts at 10:15, and ends at 10:45. How long is it?

31

5. How many hours is it? from to

8 AM

7 AM

9 AM

11 AM

10 AM

12 noon

1 PM

4 PM

11 PM

7 PM

4 PM

7 PM

12 AM

9 AM

7 AM

12 midnight

12 midnight

12 midnight

12 midnight

12 midnight

hours 6. How many hours till midnight? from to hours 7. a. Dad's workday starts at 8:00 in the morning, and ends at 5 PM. How many hours is Dad at work? b. Mary's school day starts at 9 AM and ends at 2 PM. How long is her school day? c. The airplane took off at 10 AM and landed at 1 PM. Then it again took off again

at 2 PM and landed at 6 PM. How many hours was the airplane in the air? d. How many hours are there in 1 day-night period?

8. a. The turkey needs to cook 3 hours in the oven to be ready at 7 PM. When should it be put into the oven? b. It takes 2 hours to mow the lawn. Jim wants to be done at 1 PM.

When should he start mowing? c. Mom needs 7 hours of sleep tonight. She wants to wake up at 6 AM.

When should she go to bed? 9. Imagine the minute hand going all the way around on the clock - or full hours. Fill in how many whole hours pass. from

10:30

10:30

1:40

5:45

3:20 AM

to

11:30

12:30

4:40

11:45

12:20 PM

full rounds or hours

32

Half and Quarter Hours The clock face is divided into four equal parts. Each part is one-fourth. We can see that one-fourth of 60 minutes is 15 minutes. The word “quarter” means one-fourth. When we say, “A quarter past 6”, we mean one-fourth of an hour past 6 o'clock, or 15 minutes past 6. When we say, “A quarter till 6”, we mean one-fourth of an hour till 6 o'clock, or 15 minutes till 6. When we say, “Half-past 6”, we mean a half-hour past 6 o'clock, or 30 minutes past 6.

15 past 4, OR a quarter past 4

1 hour = 60 minutes. 1/2 hour = 30 minutes. 1/4 hour = 15 minutes.

15 till 8, OR a quarter till 8

half past 10

1. Write the time using “a quarter past”, “a quarter till”, “half past”, or “o'clock”.

a.

b.

c.

d.

e.

f.

g.

h.

33

2. Write the times using hours:minutes. a. a quarter till 5

b. a quarter past 12

c. a quarter till 9

d. a quarter past 3

_____ : ______

_____ : ______

_____ : ______

_____ : ______

e. half past 11

f. a quarter till 12

g. a quarter past 8

h. a quarter till 1

_____ : ______

_____ : ______

_____ : ______

_____ : ______

3. Write the time using “a quarter past”, “a quarter till”, “half past”, or “o'clock”. a. 7:30

b. 5:15

c. 5:45

d. 9:45

e. 12:15

f. 12:30

g. 11:45

h. 7:45

4. Which clock shows the time a half-hour later than the given time? a. a quarter past 5 b. half past 4 c. 3 o'clock

1.

2.

3.

4.

5.

6.

d. a quarter till 6 e. a quarter till 7 f. a quarter past 4

5. a. Mom started cooking rice at a quarter past 5. It needs to cook for 30 minutes. When will it be ready? b. A rain storm lasted half an hour, starting at a quarter till 2. When did it end? c. The class ends at 2 o'clock. Now there are still 15 minutes left of class time.

What time is it now?

34

The Calendar January Su Mo Tu 1 6 7 8 13 14 15 20 21 22 27 28 29

We 2 9 16 23 30

Th 3 10 17 24 31

Fr 4 11 18 25

Sa 5 12 19 26

February

March

Su Mo Tu We Th Fr Sa 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29

Su Mo Tu We Th Fr Sa 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31

May

June

April Su Mo Tu 1 6 7 8 13 14 15 20 21 22 27 28 29

We 2 9 16 23 30

Th 3 10 17 24

Fr 4 11 18 25

Sa 5 12 19 26

Su Mo Tu We Th 1 4 5 6 7 8 11 12 13 14 15 18 19 20 21 22 25 26 27 28 29

July Su Mo Tu 1 6 7 8 13 14 15 20 21 22 27 28 29

We 2 9 16 23 30

Th 3 10 17 24 31

Th 2 9 16 23 30

Sa 3 10 17 24 31

Su 1 8 15 22 29

Mo 2 9 16 23 30

August Fr 4 11 18 25

Sa 5 12 19 26

Su Mo Tu We Th Fr 1 3 4 5 6 7 8 10 11 12 13 14 15 17 18 19 20 21 22 24 25 26 27 28 29 31

October Su Mo Tu We 1 5 6 7 8 12 13 14 15 19 20 21 22 26 27 28 29

Fr 2 9 16 23 30

Sa 4 11 18 25

We 4 11 18 25

Th 5 12 19 26

Fr 6 13 20 27

Sa 7 14 21 28

Fr 5 12 19 26

Sa 6 13 20 27

Fr 5 12 19 26

Sa 6 13 20 27

September Sa 2 9 16 23 30

Su Mo 1 7 8 14 15 21 22 28 29

November Fr 3 10 17 24 31

Tu 3 10 17 24

Su Mo Tu We Th Fr Sa 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

Tu 2 9 16 23 30

We 3 10 17 24

Th 4 11 18 25

December Su Mo 1 7 8 14 15 21 22 28 29

Tu 2 9 16 23 30

We 3 10 17 24 31

Th 4 11 18 25

Discuss with your teacher: 1. What do the letters “Su Mo Tu We Th Fr Sa“ mean? 2. (Use the calendar above.) What day of the week is... a. April 4th

b. October 13th

c. December 3rd

d. May 28th

e. September 1st

f. February 19th

h. today

i. your mom's birthday

35

3. a. List here all the months that have 31 days.

b. List here all the months that have 30 days.

c. Which month is the shortest month? ________________________

How many days does it have? ____ 4. Write the dates, using the form (month) (day), like in problem (2). The day number is an ordinal number! a. today's date

b. tomorrow's date

d. your mom's birthday

e. Monday next week

f. the first Monday of June

5. Write the date exactly one week (7 days) later than these dates: a. January 3rd

b. February 11th

c. May 22nd

d. June 5th

e. August 30th

f. November 26th

g. March 13th

h. September 28th

6. a. Let's say it is now April first. How many months is it till June? Till August? Till December? Till October? b. Let's say it is now January first. How many months is it till February? Till April?

Till July? Till September? 7. If you have already had your birthday for this year, how many months ago was it? If you haven't had it yet, how many months is it from today until your birthday? 8. Mary goes to a swimming club every Thursday. List here the May dates when Mary goes swimming. 9. Jack ordered a passport on July 3rd. He is supposed to pick it up two weeks later. What date is that?

36

Review - Clock to the Nearest Five Minutes 1. Write the time with hours:minutes, and using “past”, “till”, “half past” or “o'clock”.

a. ____ : ______

b. ____ : ______

c. ____ : ______

d. ____ : ______

________________

________________

f. ____ : ______

g. ____ : ______

h. ____ : ______

________________

________________

________________

_____ till ____

_____ past ____

e. ____ : ______

_____ till ____

2. Write the later time. Time now 15 min. later

2:30

6:55

____ : _____

____ : _____

Time now 20 min. later

9:05

5:40

____ : _____

____ : _____

3. How many minutes pass? Imagine turning the minute hand on a clock. from

1:45

1:55

1:40

1:45

1:55

to

1:55

2:05

2:05

2:15

2:10

8 AM

7 AM

9 AM

11 AM

10 AM

12 noon

1 PM

4 PM

11 PM

7 PM

minutes

10 minutes

4. How many hours is it? from to hours

37

Chapter 3: Addition and Subtraction Facts Within 0-18 Introduction The third chapter of the Math Mammoth Grade 2-A Complete Worktext provides lots of practice for learning and memorizing the basic addition facts of single-digit numbers where the answer is between 10 and 18, and learning to use them with subtraction.

Completing the ten - concept This concept is important to learn. The child learns what number is needed to complete the next whole ten. For example, what number do you add to 23 to get 30, or 23 + __ = 30. The next step is to study what happens when the sum goes over the next ten. In the lesson “Going Over Ten”, the child learns to add 8 + 5 by first adding 8 + 2 (which completes the ten) and then the “leftover” 3. These prepare the child for addition facts where the sum is more than 10.

Memorizing the facts The National Council of Teachers of Mathematics (NCTM) recommends in their Grade 2 Curriculum Focal Points that children “...develop quick recall of basic addition facts and related subtraction facts”. Mathematics builds upon previously learned concepts and facts. Learning addition and subtraction facts is essential for later study. For example, the child will soon study double-digit addition and subtraction, and needs to be able to add and subtract small numbers efficiently. The next lessons in the book provide lots of practice for learning and memorizing the addition facts. There are 20 such facts: 9 + 2 till 9 + 9: 8 + 3 till 8 + 8: 7 + 4 till 7 + 7: 6 + 5 till 6 + 6:

8 facts 6 facts 4 facts 2 facts

After those lessons, we reverse the process and practice subtracting. First, the child subtracts TO ten with problems such as 16 − __ = 10. Then come subtraction problems which “cross” the ten the other direction, such as 16 − 7. Again the student first practices these by subtracting in two parts: First subtracting to ten, then the rest. For example, 16 − 7 becomes 16 − 6 − 1. The various lessons about the fact families give lots of practice and further reinforce memorizing the facts. These lessons also include many word problems. You can choose to skip some of these lessons or problems, or use them later for review. They do not contain any new concepts. Alongside this book, you can also use math games or flashcards to reinforce the addition and subtraction facts. You can find a list of some free online games at www.homeschoolmath.net/math_resources_2.php

38

The Lessons in Chapter 3 page

span

Review: Completing the Next Whole Ten ......

41

2 pages

Review: Going Over Ten ................................

43

2 pages

Adding with 9 .................................................

45

2 pages

Adding with 8 .................................................

47

2 pages

Adding with 7 .................................................

49

2 pages

Adding with 6 .................................................

51

1 page

Review - Facts with 6, 7, and 8 ......................

52

2 pages

Subtract to Ten ...............................................

54

4 pages

Subtraction and the Difference ......................... 56

2 pages

Number Rainbows- 11 and 2 .........................

58

2 pages

Fact Families - 11 and 12 ..............................

60

2 pages

Number Rainbows - 13 and 14 ......................

62

1 page

Fact Families - 13 and 14 ...............................

63

3 pages

Fact Families - 15 ...........................................

66

2 pages

Fact Families - 16 ...........................................

68

2 pages

Fact Families - 17 and 18 ................................

70

3 pages

Review .............................................................

73

2 pages

Helpful Resources on the Internet Use these free online resources to supplement the “bookwork” as you see fit. Space Jumps Adding two single-digit numbers, first jump to ten, then the rest to the spaceship. Practices addition that goes over ten. http://www.ictgames.com/spacejumps.html Bridging Shuttle Bridging Through Ten means the same as adding to ten first, then the rest. Get a “flight plan”, then first add to ten by typing the number needed into the oval, and press the red button. Then type the rest that the shuttle needs to go, into the other oval, and press the red button. http://www.ictgames.com/bridging.html Speedy Sums Click on numbers that add to the target sum. The more numbers you use, the higher your score will be. http://www.mathplayground.com/speedy_sums.html

39

40

Review: Completing the Next Whole Ten 1. Write the previous and next whole ten. Circle the ten that is nearer the number. a. ____,

56, ____

b. ____,

____, 37, ____

72, ____

c. ____,

____, 25, ____

94, ____

____, 31, ____

2. Write the previous and next whole tens. Below, write the two differences: the difference between the previous whole ten and the number, and the difference between the number and the next whole ten. See the example. a.

b.

c.

60 , 63 , 570

_____ , 46 , _____

_____ , 95 , _____

7

3

Differences:

____

____

____

____

d.

e.

f.

_____ , 72 , _____

_____ , 41 , _____

_____ , 44 , _____

Differences:

____

____

____

____

____

____

3. Complete the next ten. Below, write the same kind of problem within numbers 0-10. a.

17 + ____ = 20

b.

62 + ____ = ____

7 + ____ = 10

c.

2 + ____ = ____

94 + ____ = ____ 4 + ____ = ____

4. Complete the next ten. Think of the corresponding problem within the range of 0-10. a.

42 + ____ = 50

b.

22 + ____ = ____

c.

66 + ____ = ____

55 + ____ = ____

97 + ____ = ____

32 + ____ = ____

61 + ____ = ____

34 + ____ = ____

83 + ____ = ____

41

5. Fill in the missing numbers. Compare the top and bottom problems! a.

73 + ____ = 80

b.

73 + ____ = 81

35 + ____ = 40

c.

35 + ____ = 41

14 + ____ = 20 14 + ____ = 21

6. Find your way through the maze! Start at the top. You can only go on a square where the sum is a whole ten.

13 + 6

54 + 6

73 + 8

45 + 7

99 + 4

15 + 9

14 + 8

15 + 5

13 + 6

32 + 7

45 + 7

73 + 7

64 + 5

82 + 9

16 + 7

30 + 12

39 + 1

74 + 6

73 + 9

52 + 7

46 + 7

32 + 7

31 + 9

86 + 4

65 + 4

92 + 4

21 + 8

24 + 7

22 + 8

32 + 6

83 + 6

11 + 7

98 + 2

57 + 3

17 + 9

44 + 9

12 + 8

95 + 6

38 + 5

53 + 9

71 + 9

34 + 4

36 + 7

19 + 4

28 + 11

53 + 7

29 + 2

26 + 6

78 + 6

32 + 5

7. Complete the next whole ten. a.

17 + ____ + 1 = 20

b.

35 + ____ + 2 = 40

c.

41 + ____ + 6 = 50

12 + ____ + 4 = 20

32 + ____ + 3 = 40

44 + ____ + 3 = 50

13 + ____ + 4 = 20

36 + ____ + 3 = 40

42 + ____ + 5 = 50

8. Find as many different sums as you can to make one hundred!

90 + ____ + ____ = 100

90 + ____ + ____ = 100

90 + ____ + ____ = 100

90 + ____ + ____ = 100

90 + ____ + ____ = 100

90 + ____ + ____ = 100

90 + ____ + ____ = 100

90 + ____ + ____ = 100

90 + ____ + ____ = 100

42

Review: Going Over Ten Sums that go over 10 Let's add 8 + 6 so that we first make a ten.

Let's add 9 + 7 so that we first make a ten.

8+ 6 | \ 8+2+4

9+ 7 | \ 9+1+6

10 + 4 = 14

10 + 6 = 16

The 6 is broken into two parts: 2 and 4. That is because 8 and 2 make a ten. Then, we have 10 and 4. We get 14.

The 7 is broken into two parts: 1 and 6. That is because 9 and 1 make a ten. Then, we have 10 and 6. We get 16.

1. Circle all the blue balls and some of the red ones so that you get a ten. Then add the rest of the red balls. a.

c.

8

8

+

4

10

+ 2

+

b.

9

7

+

5

10 + ____ = ____

= ____

6

d.

9

10 + ____ = ____ e.

+

+

3

10 + ____ = ____

5

f.

10 + ____ = ____

9

+

8

10

+ ____ =

____

2. Write a number on the empty line that completes ten. Then add the last number. a. ( 7 + 3 ) + 2 =

b. ( 5 + ___ ) + 3 =

c. ( 8 + ___ ) + 4 =

d. ( 6 + ___ ) + 4 =

e. ( 9 + ___ ) + 7 =

f. ( 7 + ___ ) + 5 =

43

3. Complete. Break the second number into two parts so that you get a ten. a.

8 + 7 / \ 8 + 2 + ____

b.

8 + 9 / \ 8 + 2 + ____

10 + ____ = ____ d.

c.

8 + 5 / \ 8 + 2 + ____

10 + ____ = ____

9 + 4 / \ 9 + 1 + ____

e.

10 + ____ = ____

9 + 6 / \ 9 + ___ + ____

10 + ____ = ____

9 + 9 / \ 9 + ___ + ____

f.

10 + ____ = ____

10 + ____ = ____

4. Add up to 10, 11, 12 and notice the patterns! a.

b.

c.

d.

8 + ___ = 10

7 + ___ = 10

9 + ___ = 10

6 + ___ = 10

8 + ___ = 11

7 + ___ = 11

9 + ___ = 11

6 + ___ = 11

8 + ___ = 12

7 + ___ = 12

9 + ___ = 12

6 + ___ = 12

15

24

58

89

99

5. Circle the even numbers.

40

51

6. Solve the word problems. a. You have \$8 and you buy a toy for \$5 and candy for \$2.

How much money do you have now? b. Cassie had \$8. Then she found \$5 in her piggy

bank, and her mom gave her \$2. How much money does she have now? c. Matthew had \$8. He spend \$3 on a bottle of juice.

Later he found \$2 on the street. How much money does he have now?

44

67

100

2

Adding with 9 9 wants to be a 10! So, it takes one from the other number (from 3). So, 9 becomes 10, and 2 are left over.

Imagine that 9 really wants to be a 10! It takes one from the other number (from 5). So, 9 becomes 10, and 4 are left over.

+ 9

+

= 5

=

= 10 + 4

=

+ 14

9

+

= 3

=

= 10 + 2 =

Use the list on the right to practice. Don't write the answers there. Just point to different problems and say the answer aloud.

12

9+1=

1. Add. First encircle the ten.

9+2= 9+3= 9+4=

a. 9 + 5

b. 9 + 4

c. 9 + 7

10 + 4 = ____

10 + ____ = ____

10 + ____ = ____

9+5= 9+6= 9+7=

d. 9 + ___

e. 9 + ___

f. 9 + ___

9+8=

10 + ____ = ____

10 + ____ = ____

10 + ____ = ____

9+9=

2. It is good to memorize the doubles, also. Fill in. 2 + 2 = ____

5 + 5 = ____

8 + 8 = ____

3 + 3 = ____

6 + 6 = ____

9 + 9 = ____

4 + 4 = ____

7 + 7 = ____

10 + 10 = ____

45

3. Add to nine. Think how 9 wants to be a ten, and takes 1 from the other number. a. 9 + 6

b. 9 + 8

10 + 5 = ____

c. 9 + 5

10 + ____ = ____

e. 9 + 7

10 + ____ = ____

f. 9 + 9

10 + 6 = ____

d. 9 + 2

g. 9 + 8

10 + ____ = ____ h. 9 + 3

10 + ____ = ____

10 + ____ = ____

10 + ____ = ____

4. Here are addition facts with nine. Do not write the answers down, but just practice the sums.

9+0=

9+5=

9+9= 9+4=

9+3=

9+6=

9+1= 9 + 10 =

9+7=

9+8=

9+2=

5. Add. Remember, you can add both ways. For example, 7 + 9 = 9 + 7. a. 9 + 4 = ____

b. 9 + 7 = ____

c. 3 + 9 = ____

d. 5 + 9 = ____

8 + 9 = ____

4 + 9 = ____

9 + 2 = ____

8 + 9 = ____

9 + 5 = ____

9 + 4 = ____

9 + 9 = ____

9 + 6 = ____

a. 9 + ____ = 13

b. 9 + ____ = 16

c. 9 + ____ = 17

d. 9 + ____ = 12

9 + ____ = 15

9 + ____ = 14

9 + ____ = 11

9 + ____ = 18

6. What is missing?

You can use this same "trick" with 19, 29, 39, 49, and so on. Imagine that 49 really wants to be 50, and so it "steals" 1 from the other number. Solve. a. 49 + 7 = _____

b. 59 + 5 = _____

c. 69 + 3 = _____

19 + 6 = _____

89 + 9 = _____

29 + 6 = _____

46

Adding with 8 Imagine that 8 wants to be a 10! It takes two from the other number (from 3). So, 8 becomes 10, and only 1 is left over.

+ 8

+

= 3

=

8 wants to be a 10! So, it takes two from the other number (from 5). So, 8 becomes 10, and 3 are left over.

= 10 + 1

=

+ 11

=

=

8 + 5 = 10 + 3 =

Use the list on the right to practice. Don't write the answers there. Just point to different problems and say the answer aloud.

13

8+1=

1. Add. First, circle the ten.

8+2= 8+3= 8+4=

a. 8 + 5

b. 8 + 4

c. 8 + ____

10 + 3 = ____

10 + ____ = ____

10 + ____ = ____

8+5= 8+6= 8+7=

d. 8 + ____ =

e. 8 + ____ =

f. 8 + ____ =

8+8=

10 + ____ = ____

10 + ____ = ____

10 + ____ = ____

8+9=

2. It is good to memorize the doubles, also. Fill in. 2 + 2 = ____

5 + 5 = ____

8 + 8 = ____

3 + 3 = ____

6 + 6 = ____

9 + 9 = ____

4 + 4 = ____

7 + 7 = ____

10 + 10 = ____

47

Here are addition facts with eight. Do not write the answers down, but just practice the sums.

8+0=

8+5=

8+8=

8+9=

8+3=

8+7=

8+1=

8+4=

8 + 10 =

8+1=

8+6=

8+2=

3. Add and fill in what is missing. a. 8 + 4 = ____

b. 8 + 8 = ____

c. 8 + ____ = 14

8 + 6 = ____

8 + 5 = ____

8 + ____ = 16

8 + 2 = ____

8 + 7 = ____

8 + ____ = 17

d. 8 + ____ = 13

e. 5 + 8 = ____

f. 6 + 8 = ____

8 + ____ = 12

8 + 7 = ____

8 + 9 = ____

8 + ____ = 11

3 + 8 = ____

8 + 8 = ____

4. Find the pattern and continue it. a.

b.

8 + 2 = ____

18 + 2 = ____

1 2

of 0 is ____.

8 + 4 = ____

18 + 4 = ____

1 2

of 2 is ____.

8 + 6 = ____

18 + 6 = ____

1 2

of 4 is ____.

1 2

of ____ is ____.

1 2

of ____ is ____.

1 2

of ____ is ____.

1 2

of ____ is ____.

8 + ____ = ____

18 + ____ = ____

____ + ____ = ____

____ + ____ = ____

____ + ____ = ____

____ + ____ = ____

____ + ____ = ____ ____ + ____ = ____

____ + ____ = ____ ____ + ____ = ____

48

c.

Adding with 7 We have already studied these addition facts with 7:

These are the new facts with 7:

7 + 4 = ____ 7 + 8 = ____

8 + 7 = ____ 7 + 5 = ____

7 + 9 = ____

9 + 7 = ____

7 + 10 = ____

10 + 7 = ____

7 + 6 = ____ 7 + 7 = ____

1. First circle ten balls. Then add.

7+1= a. 7 + 7

b. 7 + 5

10 + ___ = ____

10 + ___ = ____

c. 7 + 6

7+2= 10 + ___ = ____ 7+3= 7+4=

Use the list on the right to practice. Don't write the answers there. Just point to different problems and say the answer aloud.

7+5= 7+6=

2. Let's practice doubles - and doubles plus one more.

7+7= a. 6 + 6 = ____

b. 7 + 7 = ____

c. 8 + 8 = ____

6 + 7 = ____

7 + 8 = ____

8 + 9 = ____

7+8= 7+9=

d. 9 + 9 = ____

d. 5 + 5 = ____

d. 4 + 4 = ____

9 + 10 = ____

6 + 5 = ____

4 + 5 = ____

49

Here are some addition facts where we add to seven. Do not write the answers down but just go over them until you remember them easily.

7+0=

7+5=

7+6=

7+9=

7+3=

7+9=

7+7=

7+4=

7 + 10 =

7+8=

7+1=

7+2=

3. Fill in the missing numbers. a. 7 + 4 = ____

b. 8 + 7 = ____

c. 7 + ____ = 14

d. 7 + ____ = 12

6 + 7 = ____

7 + 10 = ____

7 + ____ = 13

7 + ____ = 16

7 + 5 = ____

3 + 7 = ____

7 + ____ = 15

7 + ____ = 11

e. 7 + 7 = ____

f. 4 + 7 = ____

g. 8 + ____ = 13

h. ____ + 7 = 17

9 + 7 = ____

7 + 9 = ____

8 + ____ = 16

____ + 7 = 10

7 + 8 = ____

3 + 7 = ____

8 + ____ = 17

____ + 7 = 12

+7 4. Try these boxes! Add 7 each time. Add 8 each time. Add 9 each time.

+8

+9

4

11

3

11

2

____

7

____

6

____

4

____

8

____

5

____

7

____

10

____

7

____

8

____

5

____

9

____

3

____

3

____

2

____

6

____

9

____

4

____

5

____

50

6

+

=

+ 5

= ____

6

+

=

+ 6

= ____

Here are addition facts where we add to six. Do not write the answers down. Just go over the problems until you remember them easily.

6+0=

6+5=

6+9= 6+6=

6+3=

6+7=

6+4= 6+8=

6 + 10 =

6+1=

6+2=

1. Fill in the missing numbers. a.

b.

c.

d.

6 + 4 = _____

6 + 8 = _____

6 + ____ = 14

6 + ____ = 13

6 + 6 = _____

6 + 9 = _____

6 + ____ = 16

6 + ____ = 15

6 + 5 = _____

6 + 7 = _____

6 + ____ = 12

6 + ____ = 11

e.

f.

g.

h.

5 + 6 = _____

9 + 6 = _____

7 + ____ = 14

___ + 6 = 13

6 + 7 = _____

8 + 6 = _____

8 + ____ = 14

___ + 6 = 14

4 + 6 = _____

6 + 6 = _____

9 + ____ = 14

___ + 6 = 15

2. Do not forget adding many numbers, either. a. 6 + 6 + 2 = _____

10 + 4 + 5 = _____

b. 8 + 6 + 3 = _____

20 + 2 + 5 = _____

51

c. 6 + 9 + 3 = _____

50 + 6 + 4 = _____

Review - Facts with 6, 7, and 8 1. Here are the 20 addition facts with single-digit numbers where the sum is between 10 and 20. Connect the problems to the right answer.

6+6

8+6 11

5+8

5+7

9+9

15

7+9 9+5

9+2

12

5+6

16

8+7

17

9+8

4+7 13

3+9

9+4

8+8 7+7

6+7

14

8+3

18

6+9

4+8

2. Figure out the pattern and continue it. a.

b.

c.

9 + ____ = 19

____ + 16 = 17

6 + ____ = 6

8 + ____ = 18

____ + 14 = 17

6 + ____ = 8

7 + ____ = 17

____ + 12 = 17

6 + ____ = 10

____ + ____ = ____

____ + ____ = ____

____ + ____ = ____

____ + ____ = ____

____ + ____ = ____

____ + ____ = ____

____ + ____ = ____

____ + ____ = ____

____ + ____ = ____

____ + ____ = ____

____ + ____ = ____

____ + ____ = ____

____ + ____ = ____

____ + ____ = ____

____ + ____ = ____

____ + ____ = ____

____ + ____ = ____

____ + ____ = ____

52

3. Fill in the addition table.

+

6

2

8

4

5

1

7

3

9

3 5 7 9 4. Try your skills! a. 6 + 9 = _____

b. 8 + 9 = _____

c. 5 + 9 = _____

d. 6 + 6 = _____

9 + 8 = _____

9 + 2 = _____

9 + 3 = _____

9 + 4 = _____

4 + 9 = _____

7 + 6 = _____

4 + 8 = _____

3 + 9 = _____

6 + 5 = _____

7 + 5 = _____

9 + 7 = _____

8 + 7 = _____

When you add lots of numbers, first add the numbers that form a ten. It makes adding easier!

8+6+4

5+6+2+5

= 8 + 10 = 18

= 10 + 8 = 18

5. Add in the easiest order. First find numbers that make 10! a. 1 + 6 + 9 = _____

b. 3 + 6 + 6 = _____

c. 4 + 7 + 3 + 5 = _____

5 + 4 + 7 = _____

3 + 5 + 7 = _____

6 + 5 + 1 + 4 = _____

8 + 6 + 4 = _____

7 + 8 + 2 = _____

8 + 3 + 6 + 2 = _____

5 + 6 + 5 = _____

3 + 6 + 4 = _____

9 + 6 + 1 + 4 = _____

53

Subtract to Ten 1. Subtract the "ones" that are not in the whole ten-groups. You should only have tens left!

a.

b.

c.

d.

13 − 3 = 10

15 − ____ = 10

26 − ____ = ____

38 − ____ = ____

e. 17 − ____ = 10

f. 21 − ____ = 20

g. 19 − ____ = 10

h. 64 − ____ = 60

Subtracting in parts Let's subtract 13 − 5. First we subtract so many balls that we have only 10 left. So, we take away 3 balls. 13 − 3 = 10. Then, we subtract the rest, which means we subtract 2 more. 10 − 2 = 8.

13 − 5 /

\

13 − 3 − 2 10 − 2 = 8

2. First subtract so many that you have only 10 left. Then subtract the rest. b. 13 − 8

a. 15 − 7 /

\

15 − 5 − 2 10 − 3 = ____ d. 14 − 9 /

/

c. 13 − 4 \

13 − ___ − ____ 10 − ____ = ____ e. 12 − 5

\

14 − ___ − ____ 10 − ___ = ____

/

/

\

13 − ___ − ____ 10 − ____ = ____ f. 16 − 8

\

/

12 − ___ − ____ 10 − ___ = ____

\

16 − ___ − ____ 10 − ___ = ____

3. First subtract to 10. Then subtract some more. a. 13 − 6

b. 14 − 9

c. 15 − 8

/ \ 13 − 3 − 3 = ____

/ \ 14 − ____ − ____ = ____

/ \ 15 − ____ − ____ = ____

54

4. First subtract to 10. Then subtract some more. a. 16 − 7 /

b. 12 − 4 \

/

d. 13 − 6 \

/

\

16 − ____ − ____ = ____

12 −____ − ____ = ____

13 − ____ − ____ = ____

d. 11 − 3

e. 12 − 7

f. 15 − 8

/

\

/

11 − ____ − ____ = ____

\

/

12 − ____ − ____ = ____

\

15 − ____ − ____ = ____

5. First subtract those that are not in the ten-group. Compare the top and bottom problems.

a.

15 − 7 = ____

b.

13 − 6 = ____

c.

16 − 9 = ____

d.

25 − 7 = ____

e.

23 − 6 = ____

f.

26 − 9 = ____

6. Subtract. a.

12 − 4 =

b.

15 − 6 =

14 − 5 =

c.

12 − 5 =

15 − 9 =

14 − 8 =

12 − 3 =

15 − 7 =

14 − 7 =

12 − 6 =

15 − 8 =

14 − 6 =

7. Subtract a number so that the answer is 10 or 9. Do you notice a shortcut? a. 13 − ____ = 10

13 − ____ = 9

b. 11 − ____ = 10

c. 15 − ____ = 10

d. 12 − ____ = 10

11 − ____ = 9

15 − ____ = 9

12 − ____ = 9

8. Subtract in two steps. First subtract to the previous whole ten. Then, subtract some more. How much did you subtract (take away) all totaled? a. 29 − ____ = 20

b. 34 − ____ = 30

c. 72 − ____ = 70

20 − 5 = ____

30 − 3 = ____

70 − 6 = ____

I subtracted a total of ____.

I subtracted a total of ____.

I subtracted a total of ____.

55

Subtraction and The Difference The difference of two numbers on the number line means how far apart they are from each other. The difference of 7 and 3 is 4, because 7 and 3 are four steps apart.

We can solve the difference of two numbers in two ways:

Let's find the difference of 12 and 8 in two ways. 1. Subtract:

1. Subtract the numbers. 2. Write a “how many more” addition (missing addend).

12 – 8 = ____.

2. Think: “8 and how many more makes 12?” You can write an addition 8 + ____ = 12 Either way, the answer is 4 .

1. Find the difference of the numbers by subtracting.

Numbers

Subtraction

Difference

7

2

7–2=5

5

10 9

Numbers

6

3

4

10

5

5

9

6

Subtraction

Difference

2. Think of adding more to find the difference of two numbers. a. The difference of 10 and 6

b. The difference of 7 and 12

c. The difference of 9 and 4

6 + ____ = 10

7 + ____ = 12

4 + ____ = 9

d. The difference of 15 and 8

e. The difference of 5 and 12

f. The difference of 9 and 17

8 + ____ = 15

5 + ____ = 12

9 + ____ = 17

3. Subtract. Think of the differences or “how many more”.

+3

+__

+__

a. 15 – 12 = ____

b. 11 – 9 = ____

c. 16 – 11 = ____

12 and how many more makes 15?

9 and how many more makes 11?

11 and how many more makes 16?

56

4. Solve these subtraction problems by thinking of the differences or “how many more”.

+__ a. 14 – 11 = ____

+__ e. 20 – 15 = ____

+__

+__ b. 20 – 19 = ____

+__

c. 17 – 15 = ____

+__

+__

+__

f. 15 – 11 = ____

d. 13 – 10 = ____

g. 12 – 8 = ____

h. 18 – 14 = ____

5. Subtract by thinking how far apart the two numbers are (the difference). a. 20 – 16 =

b. 40 – 38 =

c. 65 – 61 =

d. 33 – 31 =

e. 100 – 99 =

f. 87 – 84 =

g. 53 – 50 =

h. 79 – 78 =

6. Find what is missing. a. 6 + ____ + 4 = 14

b. 2 + ____ + 2 = 8

c. 10 + ____ + 4 = 17

8 + ____ + 3 = 13

3 + ____ + 3 = 9

10 + ____ + 2 = 15

7. Solve the word problems. Write number sentences for them. a. Jen is on page 20 and Mark is on page 17 of the same book.

How many more pages has Jen read?

b. Mom had one dozen eggs plus five in another carton.

She used 6 eggs. How many does she have now?

c. Ingrid is reading a 50-page book. She's on page 42.

How many more pages does she have left to read?

d. In family A, the kids are 13 and 9 years old. In family B, the kids are 15 and 12.

In which family is there a bigger difference in the kids' ages?

57

Number Rainbows - 11 and 12 This is a number rainbow for 11. If two numbers are connected with an arc, they add up to 11. Use the number rainbow to help you with addition and subtraction facts! 1. Practice subtraction from 11. Don't write the answers below; just think them in your head.

11 – 6 =

11 – 7 =

11 – 8 =

11 – 2 =

11 – 3 =

11 – 9 =

11 – 4 =

11 – 5 =

2. Similarly, practice subtraction from 12.

12 – 5 =

12 – 7 =

12 – 10 =

12 – 6 =

12 – 9 =

12 – 4 =

12 – 3 =

12 – 8 =

58

3. Fill in and color the number rainbows. Don't look at the previous page! Then practice the subtraction problems.

11 – 4 =

11 – 2 =

11 – 3 =

11 – 9 =

11 – 8 =

11 – 5 =

11 – 6 =

11 – 7 =

12 – 8 =

12 – 3 =

12 – 4 =

12 – 9 =

12 – 6 =

12 – 10 =

12 – 7 =

12 – 5 =

For more practice, make your own number rainbows and subtraction problems on empty paper!

59

Fact Families - 11 and 12 1. Fill in. Color the balls, using two colors, so that the coloring matches the numbers. Fact families with 11

10, 1, 11

___, ___, 11

10 + 1 = ___

11 – 10 = ___

7 + ___ = 11

___ – ___ = ___

1 + 10 = ___

11 – 1 = ___

___ + ___ = ___

___ – ___ = ___

9, ___, 11

___, ___, 11

9 + ___ = 11

___ – ___ = ___

6 + ___ = 11

___ – ___ = ___

___ + ___ = ___

___ – ___ = ___

___ + ___ = ___

___ – ___ = ___

___, ___, 11

8 + ___ = 11

___ – ___ = ___

___ + ___ = ___

___ – ___ = ___

2. Find the pattern and continue it. a.

b.

c.

11 – 0 = ____

0 + 11 = ____

11 – 1 = ____

11 – 2 = ____

2 + 9 = ____

11 – 3 = ____

11 – 4 = ____

4 + 7 = ____

11 – 5 = ____

___ – ___ = ____

____ + ____ = ____

___ – ___ = ____

___ – ___ = ____

____ + ____ = ____

___ – ___ = ____

___ – ___ = ____

____ + ____ = ____

___ – ___ = ____

60

3. Fill in. Color the balls, using two colors, so that the coloring matches the numbers. Fact families with 12

10, 2, 12

___, ___, 12

10 + 2 = ___

12 – 10 = ___

7 + ___ = 12

___ – ___ = ___

2 + 10 = ___

12 – 2 = ___

___ + ___ = ___

___ – ___ = ___

9, ___, 12 9 + ___ = 12

___ – ___ = ___

___ + ___ = ___

___ – ___ = ___

___, ___, 12 6 + ___ = 12

12 – ___ = ___

___, ___, 12 8 + ___ = 12

___ – ___ = ___

___ + ___ = ___

___ – ___ = ___

4. Subtract from 11 and 12. a.

12 – 10 = ____

b.

11 – 8 = ____

c.

12 – 6 = ____

d.

12 – 3 = ____

11 – 9 = ____

12 – 7 = ____

11 – 4 = ____

12 – 10 = ____

12 – 8 = ____

11 – 3 = ____

12 – 9 = ____

11 – 5 = ____

11 – 6 = ____

12 – 5 = ____

12 – 4 = ____

11 – 7 = ____

5. Let's practice missing addends as well! a.

6 + ____= 11

b.

7 + ____= 12

c.

9 + ____= 11

d.

6 + ____= 12

8 + ____ = 11

8 + ____ = 12

7 + ____ = 11

9 + ____ = 12

5 + ____ = 11

5 + ____ = 12

4 + ____ = 11

4 + ____ = 12

61

Number Rainbows - 13 and 14 1. Fill in and color the number rainbows. Then practice the subtraction problems.

13 – 7 =

13 – 4 =

13 – 9 =

13 – 10 =

13 – 5 =

13 – 6 =

13 – 11 =

13 – 8 =

14 – 8 =

14 – 3 =

14 – 7 =

14 – 6 =

14 – 5 =

14 – 9 =

14 – 11 =

14 – 4 =

For more practice, make your own number rainbows and subtraction problems on empty paper! 62

Fact Families - 13 and 14 1. Fill in. Color the balls, using two colors, so that the coloring matches the numbers. Fact families with 13

10, 3, 13

___, ___, 13

10 + 3 = ___

13 – 10 = ___

8 + ___ = 13

___ – ___ = ___

3 + 10 = ___

13 – 3 = ___

___ + ___ = ___

___ – ___ = ___

9, ___, 13

___, ___, 13

9 + ___ = 13

___ – ___ = ___

7 + ___ = 13

___ – ___ = ___

___ + ___ = ___

___ – ___ = ___

___ + ___ = ___

___ – ___ = ___

2. Subtract. a. 13 – 8 = ____

b. 13 – 5 = ____

c. 12 – 7 = ____

d. 12 – 9 = ____

13 – 6 = ____

13 – 4 = ____

13 – 7 = ____

13 – 9 = ____

3. Connect with a line the problems that are from same fact family. You don't need to write the answers.

13 – 7 = 5+

= 12

11 – 3 = 8+

= 13

12 – 3 = 7+

= 11

' ' ' ' ' ' ' '

11 – 4 =

12 – 7 =

11 – 8 =

13 – 6 =

5+

3+

= 13

= 12

12 – 5 =

13 – 5 =

6+

= 13

3+

= 11

9+

= 12

4+

= 11

63

4. Fill in. Color the balls, using two colors, so that the coloring matches the numbers. Fact families with 14

___, ___, 14

10, 4, 14 10 + ___ = ___

___ – 10 = ___

8 + ___ = 14

___ – ___ = ___

___ + 10 = ___

___ – 4 = ___

___ + ___ = ___

___ – ___ = ___

9, ___, 14

___, ___, 14

9 + ___ = 14

___ – ___ = ___

___ + ___ = ___

___ – ___ = ___

7 + ___ = 14

14 – ___ = ___

5. For each addition problem, write a subtraction problem using the same numbers so that the numbers in the boxes end up being the same. a. 9 +

= 14

14 – 9 = d. 9 +

= 13

= 11

____ – ____ = j. 5 +

= 14

14 – 6 =

____ – ____ = g. 5 +

b. 6 +

= 14

____ – ____ =

e. 7 +

____ – ____ = = 12

____ – ____ = k. 8 +

= 13

____ – ____ =

64

= 12

12 – 6 = = 14

h. 7 +

c. 6 +

f. 6 +

= 15

____ – ____ = i. 4 +

= 14

____ – ____ = l. 6 +

= 11

____ – ____ =

6. Solve the word problems. a. Jack arranged his toy cars in rows. The first row had seven cars, the second had

7, and the third row had 4. How many cars does Jack have?

b. If you have 14 strawberries and I have 8, how many more do you have?

c. Dad has six cherries and Mom has five more than him. How many cherries

does Mom have?

d. At first Mom had 20 apples to make an pie, but she gave each of the four kids

one apple before she made the pie. How many apples did she have for the pie?

7. Figure out the patterns and continue them!

a.

+

40

b.

+

48

+

17

+

56

+

21

+

64

+

25

+

+

+

+

____

____

____

+

+

+

+

____

____

____

____

72

+

29

65

____

____

Fact Families - 15 1. Fill in. Color the balls, using two colors, so that the coloring matches the numbers. Fact families with 15

___, ___, 15

10, 5, 15 10 + ___ = ___

15 – 10 = ___

8 + ___ = 15

___ – ___ = ___

___ + 10 = ___

15 – ___ = ___

___ + ___ = ___

___ – ___ = ___

9, ___, 15

9 + ___ = 15

___ – ___ = ___

___ + ___ = ___

___ – ___ = ___

2. Subtract. For each problem write a corresponding addition fact. a.

b.

c.

d.

15 – 5 = ___

15 – 8 = ___

15 – 4 = ___

15 – 3 = ___

___ + ___ = ___

___ + ___ = ___

___ + ___ = ___

___ + ___ = ___

e.

f.

g.

h.

15 – 2 = ___

15 – 6 = ___

15 – 7 = ___

15 – 9 = ___

___ + ___ = ___

___ + ___ = ___

___ + ___ = ___

___ + ___ = ___

3. Count by threes. + 3

9

+ 3

____

+ 3

____

+ 3

____

+ 3

____ 66

+ 3

____

+ 3

____

+ 3

____

33

4. Solve the word problems. a. At first Mom had 17 peaches to make an pie, but she gave each of the three kids

one peach before she made the pie. How many peaches did she have for the pie?

b. Jill, Tom, and Nancy made a stack of school books. Jill had three books, Nancy

had seven, and Tom had five. How many books were in the stack?

c. Now Jill took her books out of the stack.

How many are left in the stack?

d. Five kids came to play ball. Then, six more kids came. Then, one child had to

go home. How many kids are playing ball now?

5. For each addition problem, write a subtraction problem using the same numbers so that the numbers in the boxes end up being the same. a.

9+

= 15

15 – 9 = d.

5+

8+

6+

= 14

____ – ____ = = 11

____ – ____ = g.

b.

= 15

____ – ____ =

e.

7+

= 15

____ – ____ = h.

8+

= 12

____ – ____ =

67

c.

6+

= 15

____ – ____ = f.

7+

= 13

____ – ____ = i.

7+

= 11

____ – ____ =

Fact Families - 16 1. Fill in. Color the balls, using two colors, so that the coloring matches the numbers. Fact families with 16

10, 6, 16

8, ___, 16

10 + ___ = ___

16 – 10 = ___

8 + ___ = 16

___ – ___ = ___

___ + 10 = ___

16 – ___ = ___

___ + ___ = ___

___ – ___ = ___

9, ___, 16 9 + ___ = 16

___ – ___ = ___

___ + ___ = ___

___ – ___ = ___

2. Subtract. a.

15 – 10 = ___

b.

13 – 9 = ___

c.

14 – 8 = ___

d.

15 – 7 = ___

13 – 10 = ___

16 – 9 = ___

13 – 8 = ___

16 – 7 = ___

16 – 10 = ___

14 – 9 = ___

16 – 8 = ___

13 – 7 = ___

3. Connect with a line the problems to the answer.

15 – 9 15 – 10

3 4

14 – 9 14 – 10 13 – 9

17 – 9 16 – 9

7 8

16 – 10 5 6

18 – 9 17 – 10

68

17 – 9 16 – 9 18 – 9

9 10

19 – 10 19 – 9

4. Figure out the patterns and continue them! +

a.

6

b.

+

9

+

12

+

+

12

+

16

15

+

+

+

+

+

____

____

____

____

+

+

+

+

____

____

____

____

+

20

24

____

____

5. Solve the word problems. a. A class has 24 kids. Two of them

b. If you have \$10, and mom gives

were sick one day and two had to leave to go to the dentist. How many kids were in class that day?

you \$4 more, can you buy a book for \$13?

d. Jenny has saved \$12. She wants to

c. You had \$20 and you bought shoes for

buy a gift that costs \$16. How much more money does she need?

\$17. How many dollars do you have left?

6. Compare the expressions and write , or = . a.

35

20 + 5

b.

23 + 5

23 + 6

c.

16 – 8

15 – 8

d.

15

6+7

e.

31 + 4

31 + 3

f.

15 – 9

16 – 9

g.

36

30 + 7

h.

20 + 8

30 + 5

i.

15 – 6

14 – 6

69

Fact Families - 17 and 18 1. Fill in. Color the balls, using two colors, so that the coloring matches the numbers. Fact families with 17

Fact families with 18

10, ___, 17

10, ___, 18

10 + ___ = ___

17 – 10 = ___

10 + ___ = 18

___ – ___ = ___

___ + 10 = ___

17 – ___ = ___

___ + ___ = ___

___ – ___ = ___

9, ___, 17

9, ___, 18

9 + ____ = 17

___ – ___ = ___

9 + ___ = 18

___ – ___ = ___

___ + ___ = ___

___ – ___ = ___

___ + ___ = ___

___ – ___ = ___

b. 15 – 9 = ____

c. 14 – 6 = ____

d. 12 – 9 = ____

17 – 9 = ____

15 – 8 = ____

14 – 7 = ____

12 – 8 = ____

18 – 10 = ____

16 – 9 = ____

13 – 6 = ____

11 – 9 = ____

18 – 9 = ____

16 – 8 = ____

13 – 7 = ____

11 – 8 = ____

2. Subtract and add. a. 17 – 10 = ____

e. 6 + 6 = ____

f. 9 + ____ = 19

g. 8 + 9 = ____

h. 7 + ____ = 14

7 + 7 = ____

9 + ____ = 15

8 + 7 = ____

7 + ____ = 16

8 + 8 = ____

9 + ____ = 18

8 + 5 = ____

7 + ____ = 18

9 + 9 = ____

9 + ____ = 17

8 + 3 = ____

7 + ____ = 13

70

3. Write , or = . You can often compare the expressions without calculating! a. 8 + 9

d. 45 + 8

g.

1 2

of 16

j.

1 2

of 40

8+8

b. 20 – 9

20 – 8

45 + 7

e. 50 – 6

50 – 8

1 2

m. 31 + 7

of 14

h. 14 – 2

1 2

20 + 20

k.

31 + 9

n. 25 – 8

of 50

1 2

of 14

1 2

of 60

c.

25 – 9

1 2

of 12

12

f. 15 – 8

17 – 8

i. 10 + 5

20 – 5

l.

1 2

of 80

20 + 20

o.

1 2

of 20

10

4. Continue the patterns. a.

b.

c.

17 – 10 = ____

20 – 10 = ____

1 2

of 20 + 10 = 20

16 – 9 = ____

30 – 20 = ____

1 2

of 18 + 9 = ____

15 – 8 = ____

40 – 30 = ____

1 2

of 16 + 8 = ____

____ – ____ = ____

____ – ____ = ____

1 2

of ____ + ____ = ____

____ – ____ = ____

____ – ____ = ____

1 2

of ____ + ____ = ____

____ – ____ = ____

____ – ____ = ____

1 2

of ____ + ____ = ____

____ – ____ = ____

____ – ____ = ____

1 2

of ____ + ____ = ____

____ – ____ = ____

____ – ____ = ____

1 2

of ____ + ____ = ____

____ – ____ = ____

____ – ____ = ____

1 2

of ____ + ____ = ____

71

5. Solve the word problems. a. A baby slept 4 hours and woke up to nurse. Then she slept

another 2 hours and woke up to nurse. Then she slept 3 hours more and nursed again. Then she slept 3 hours till the morning. How many hours did the baby sleep?

b. A new jacket costs 18 dollars. John

c. The temperature outside is 50 degrees

has saved 9 dollars. How much more does he need?

Fahrenheit, and inside it is 70 degrees. What is the difference in temperature?

d. Mom needs 16 eggs. Eggs are sold in cartons of 12.

How many cartons does she need to buy? How many eggs will she have left over?

6. Fill in the addition table.

+

1

3

5

7

2

4

6

10

9

8

11

31

6 8 5

7. Find the missing numbers. Try to work backwards, starting from 60! –10

100

–1

___

–5

___

–4

___

–2

___

72

–8

___

–5

___

–5

___

60

Review 1. Complete the next ten. a.

b.

c.

d.

13 + ____ = 20

42 + ____ = 50

29 + ____ = ____

65 + ____ = ____

88 + ____ = 90

28 + ____ = 30

15 + ____ = ____

82 + ____ = ____

74 + ____ = 80

26 + ____ = ____

73 + ____ = ____

49 + ____ = ____

2. UNDERLINE the problems where the answer is ten. CIRCLE the ones where the answer is more than ten. a.

b.

c.

d.

e.

5 + 1 = ___

6 + 1 = ___

7 + 1 = ___

8 + 1 = ___

9 + 1 = ___

5 + 2 = ___

6 + 2 = ___

7 + 2 = ___

8 + 2 = ___

9 + 2 = ___

5 + 3 = ___

6 + 3 = ___

7 + 3 = ___

8 + 3 = ___

9 + 3 = ___

5 + 4 = ___

6 + 4 = ___

7 + 4 = ___

8 + 4 = ___

9 + 4 = ___

5 + 5 = ___

6 + 5 = ___

7 + 5 = ___

8 + 5 = ___

9 + 5 = ___

5 + 6 = ___

6 + 6 = ___

7 + 6 = ___

8 + 6 = ___

9 + 6 = ___

5 + 7 = ___

6 + 7 = ___

7 + 7 = ___

8 + 7 = ___

9 + 7 = ___

5 + 8 = ___

6 + 8 = ___

7 + 8 = ___

8 + 8 = ___

9 + 8 = ___

5 + 9 = ___

6 + 9 = ___

7 + 9 = ___

8 + 9 = ___

9 + 9 = ___

Compare the columns! What do you notice? 3. Find the missing steps. –5

75

–5

__

–2

__

–3

__

–6

__ 73

–3

__

–1

__

–10

__

40

4. Solve the puzzle. What happened to the teddy bear in the desert?

Key:

5+9 7+8

13 – 8 2 + 9 10 + 5

9+7

4+7

9+6

____ ____

____

____

____

____

7 + 7 13 – 6

19 – 4 11 + 5 13 – 7

3 + 13 11 – 5 13 – 4

6+9

____ ____

____

____

____

A 9

____

____

____

____

____

____

E I O G H T W N 6 14 11 5 16 15 8 7

5. Solve the word problems. a. Jack has 13 tennis balls and Robert has 20. How many do they have together? How many more does Robert have than Jack?

b. You have saved 20 dollars to buy a big Lego set that costs \$28. How much will you still need to save? A neighbor pays you 2 dollars to mow the lawn. So you do. Do you now have enough money to buy the Lego set? How much do you still need? How about if you mow the lawn a second time? A third time?

c. In a board game, you need to move 18 more squares to get to the end of the game. You roll 6 and 5 on two dice. How many more squares do you need to go to get to the end? What kind of numbers on the two dice would get you to the end?

74

Chapter 4: Adding and Subtracting with Two-Digit Numbers Introduction The fourth chapter of the Math Mammoth Grade 2-A Complete Worktext deals with addition and subtraction within 0-100, both mentally and in columns, especially concentrating on how to carry when adding in columns (trading) and how to borrow when subtracting in columns (regrouping).

Mental math Mental math is important because it builds number sense. Chapter 4 includes many lessons that practice mental math. For example, the child practices adding and subtracting 2-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 connect with the idea of going over ten as in problems 6 + 8 and 5 + 9. So, just as the child knows that 6 + 8 fills the first ten and is 14, he/she will learn that 36 + 8 fills the next whole ten (40) and is 44.

Carrying to tens Simultaneously with this, the child learns adding two-digit numbers in columns, and “carrying” to tens, which is illustrated and explained in detail with the help of pictures. Some people call it trading, as in trading 10 ones into 1 ten. As a “stepping stone” into the usual way of adding in columns with a carry, you can show the child the method below. This can be used if the child does not readily understand why the little “1” that is carried corresponds to a ten. In the process below, the ones are added, and the answer is written using both columns. Then, the tens are added and the answer is written under the sum from ones. Lastly, both sums are added. tens ones 3 6 1

8

add ones first → 1

4

+

tens ones 6 3 1

8

1 add tens here → 4

4

+

tens ones 3 6 +

0

total →

1

8

1 4

4

5

4

0

The lesson Add in Columns Practice contains problems where the sum is more than 100.

Borrowing or regrouping 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 (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,

75

he/she might end up learning the procedure of borrowing as a memorized algorithm only, 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. If you notice that the child does not understand the concept of borrowing, 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.

The Lessons page

span

78

3 pages

Subtracting Whole Tens ..................................... 81

2 pages

Carrying to Tens ..............................................

83

3 pages

Going Over to the Next Ten ...........................

86

3 pages

Two-Digit Numbers Ending in 9 ....................

89

2 pages

Add in Columns Practice ................................

91

2 pages

Two-Digit Numbers Ending in 8 or 7...............

93

2 pages

95

2 pages

97

3 pages

Subtracting in Columns ...................................... 100

1 page

Regrouping, Part 1 ...........................................

101

3 pages

Regrouping, Part 2 ...........................................

104

3 pages

Regrouping, Part 3 ...........................................

107

2 pages

Graphs and Problems ......................................

109

3 pages

Mental Subtraction Methods .............................. 112

3 pages

Euclid's Game....................................................

115

3 pages

Mixed Review ..................................................

118

2 pages

Adding with Whole Tens ..................................

Helpful Resources on the Internet Use these free online resources to supplement the “bookwork” as you see fit.

Base Blocks Addition A virtual manipulative that shows regrouping in addition. 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

76

77

Adding with Whole Tens 1. One of the numbers is a whole ten. Add.

+ a.

+

32 + 10 = 42

b.

+

+

54 + 10 = ____

c.

____ + 20 = ____

+

d. ____ + ____ = ____

+

+

e. ____ + ____ = ____

f. ____ + ____ = ____

+

g. ____ + ____ = ____

+

h. ____ + ____ = ____

Adding whole tens and another 2-digit number Break down the other number into tens and ones. Add the tens. Then, add the ones.

i. ____ +

50 + 26 / \ 50 + 20 + 6 70 + 6 = 76

____ = ____

39 + 40 / \ 30 + 9 + 40 70 + 9 = 79

2. Add. You can break the second number into tens and ones first. a. 10 + 34 = ____

b. 10 + 28 = ____

c. 20 + 24 = ____

d. 30 + 21 = ____

(10 + 30 + 4)

(10 + ____ + ____ )

(20 + ____ + ____ )

(30 + ____ + ____ )

e. 50 + 17 = ____

f. 40 + 33 = ____

g. 60 + 23 = ____

h. 30 + 37 = ____

(50 + ____ + ____ )

78

3. Add. You can break the first number into tens and ones first. a. 45 + 20 = ____

b. 27 + 20 = ____

(40 + 5 + 20)

( ____ + ___ + ____ )

e. 46 + 30 = ____

f. 16 + 50 = ____

c. 45 + 40 = ____

d. 62 + 30 = ____

g. 38 + 60 = ____

h. 78 + 10 = ____

4. Add. a. 77 + 10 = ____

b. 20 + 45 = ____

c. 16 + 10 = ____

d. 30 + 37 = ____

77 + 20 = ____

30 + 45 = ____

16 + 30 = ____

20 + 37 = ____

Remember rounding to the nearest ten? Numbers ending in 1, 2, 3, or 4 are 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

46 ≈ 50

(72 is approximately 70)

(46 is approximately 50)

The 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. Amy 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 her total bill.

7. Jacob has \$61. Then he buys a toy airplane for \$29. Use rounded numbers to estimate how much money he has left.

79

8. Fill in the missing numbers and find how many tens were added. a. 10 + ____ = 60

b. 12 + ____ = 22

c. 45 + ____ = 65

d. 23 + ____ = 63

30 + ____ = 50

12 + ____ = 52

45 + ____ = 55

23 + ____ = 53

10 + ____ = 90

12 + ____ = 42

45 + ____ = 75

23 + ____ = 93

9. Add 10, 20, 30, or 40. In the box below the number, write “E” if the number is even, and “O”, if the number is odd. What can you notice?

+ 20

+ 10

12

22

E

E

19

+ 40

23

+ 30

____

32

58

____

37

+ 20

+ 30

____

+ 40

7

____

____

+ 10

____

85

____

How many different solutions can you find for this puzzle? Find at least two. All numbers are whole tens.

+ +

+ +

+ +

+

+ = 100

+ +

+

+ +

= 100

+

+ +

+ = 80

= 70

+ = 70 = 80

80

+ +

+ +

= 60

= 70

= 100 +

+ = 100

= 70 = 60

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

a. 30 – 10 = 20

b. 40 – 20 = ____

c. 50 – 30 = ____

d. 70 – 40 = ____

e. 33 – 10 = 23

f. 47 – 20 = ____

g. 26 – 10 = ____

h. 55 – 30 = ____

The ____________ digit does not change.

2. Count by tens backwards. a. 76, 66, ______ , ______ , ______ , ______ , ______, ______ b. _____ , ______ , 52, 42, ______ , ______ , ______ , ______ c. _____ , ______ , ______ , ______ , ______ , ______ , 17, ______

3. Subtract. a. 23 – 10 = ____

b. 48 – 20 = ____

c. 56 – 10 = ____

d. 87 – 20 = ____

23 – 20 = ____

48 – 30 = ____

56 – 30 = ____

87 – 40 = ____

e. 75 – 10 = ____

f. 31 – 10 = ____

g. 81 – 40 = ____

h. 74 – 40 = ____

75 – 20 = ____

31 – 20 = ____

81 – 50 = ____

74 – 20 = ____

81

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 – ____ = ____

____ – ____ = ____

____ – ____ = ____

____ – ____ = ____

____ – ____ = ____

____ – ____ = ____

____ – ____ = ____

____ – ____ = ____

____ – ____ = ____

____ – ____ = ____

____ – ____ = ____

____ – ____ = ____

____ – ____ = ____

____ – ____ = ____

5. Use rounded numbers to solve these problems. a. Three suitcases weigh 29 kg, 18 kg, and 31 kg. About how much do they weigh in total? b. Garden chairs cost \$29 apiece. Can Charlene buy three of them with \$80? c. Michael 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

= 40 +

= 30

= 80

82

= 30 = 10

Carrying to Tens tens ones

When adding 3 + 9, we can circle ten cubes to form a ten. We write “1” in the tens column. There are two little cubes left over, so we write “2” in the ones column.

+ 1

When adding 35 + 8, we can circle ten little cubes to form a ten. There already are three tens, so in total we now have four tens. These are written as “4” in the tens column.

3 9 2

tens ones

3 +

There are three little cubes left over, so we write “3” in the ones column.

4

5 8 3

1. Circle ten cubes to make a whole ten. Count the whole tens, including the one you made by circling the cubes. Count the ones. Write the tens and ones in their own columns. tens ones

a.

3 3 + 9

tens ones

2 b.

tens ones

tens ones

3 c.

+

8 9

d.

tens ones

e.

3 + 1

6 8

2 7 + 7

tens ones

f.

83

+

5 8

2 + 2

5 7

tens ones

When we form a new ten from the ones (little cubes), we are trading or exchanging the ten ones into 1 ten.

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 1 new ten. Add the tens and ones in columns. tens ones 1

tens ones 1

1 3 + 2 9 2

a.

2 4 + 3 8

b.

tens ones 1

3 5 + 1 9 4

c.

e.

g.

tens ones 1

2 4 + 4 7 1

d.

f.

+

h.

+

84

+

+

3. Add. If the ones go over ten, carry one whole ten to the tens column. a.

42 + 15

b.

27 + 45

c.

65 + 26

d.

83 + 15

e.

34 + 19

f.

52 + 41

g.

13 + 44

h.

63 + 27

i.

36 + 51

j.

66 + 29

k.

18 +40

l.

39 +36

m.

59 + 35

n.

72 + 22

o.

17 + 23

2

Sometimes we can get two tens from all the ones (little cubes). On the right, when you add the ones, you get 6 + 7 + 8 = 21. So, we carry two tens to the tens column and write a little “2” above the tens column.

3 2 + 1

6 7 8 1

4. Add. Carry to the tens column. a.

34 19 + 26

b.

15 27 + 45

c.

18 27 + 26

d.

26 48 + 19

e.

34 20 + 19

5. Count by fours. a. 0, 4, _____ , _____ , _____ , _____ , _____ , _____ , _____ , _____ , _____ , _____ b. 100, 96, 92, _____ , _____ , _____ , _____ , _____ , _____ , _____ , _____ , _____

85

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 = ______

86

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

28 + 8 /

b. \

/

28 + 2 + ____

39 + 3 /

c.

/

e.

27 + 5 /

39 + 1 + ____

80 + ____ = ____ f.

38 + 7

\

/

27 + ____ + ____

____ + ____ = ____

\

79 + 1 + ____

50 + ____ = ____

\

79 + 9

\

47 + 3 + ____

30 + ____ = ____ d.

47 + 5

\

38 + ____ + ____

____ + ____ = ____

____ + ____ = ____

3. Continue the patterns. COMPARE the columns. a.

b.

8 + 1 = ____

28 + 1 = ____

5 + 4 = ____

15 + 4 = ____

8 + 2 = ____

28 + 2 = ____

5 + 5 = ____

15 + 5 = ____

8 + 3 = ____

28 + 3 = ____

5 + 6 = ____

15 + 6 = ____

8 + 4 = ____

28 + 4 = ____

5 + ___ = ____

15 + ___ = ____

8 + ___ = ____

28 + ___ = ____

5 + ___ = ____

15 + ___ = ____

8 + ___ = ____

28 + ___ = ____

___ + ___ = ___

___ + ___ = ____

What do you notice?

4. Fill the missing addends. a. 8 + ____ = 10

b. 13 + ____ = 20

c. 67 + ____ = 70

8 + ____ = 11

13 + ____ = 21

67 + ____ = 71

d. 7 + ____ = 10

e. 18 + ____ = 20

f. 86 + ____ = 90

7 + ____ = 12

18 + ____ = 22

86 + ____ = 92

87

5. Solve the word problems. Write a number sentence for each problem, not just the answer. a. Ben wants to buy a bicycle that costs \$30.

He has saved \$22. How much more money will he need?

b. Jill had already saved \$20. She earned five dollars for

raking the yard, and another five dollars for weeding. How much money does she have now?

c. Mom bought 28 rosebushes and has planted eight of them.

How many still need planted?

d. Thirty-seven people attended Uncle Jim's 50th birthday

party. Thirty-two of them came before noon. How many came after?

e. Dad bought a bunch of 40 grapes and ate half of them. Then,

little sister ate 7 grapes. How many are left now?

6. Add and compare. Notice the patterns. a.

b.

6 + 2 = ____

36 + 2 = ____

9 + 1 = ____

29 + 1 = ____

6 + 3 = ____

36 + 3 = ____

9 + 2 = ____

29 + 2 = ____

6 + 4 = ____

36 + 4 = ____

9 + 3 = ____

29 + 3 = ____

6 + ___ = ___

36 + ___ = ____

9 + 4 = ____

29 + 4 = ____

6 + ___ = ___

36 + ___ = ___

9 + ___ = ___

29 + ___ = ___

6 + ___ = ___

36 + ___ = ____

9 + ___ = ___

29 + ___ = ___

___ + ___ = ____

___ + ___ = ____

___ + ___ = ____

___ + ___ = ____

88

Two-Digit Numbers Ending in 9 1. Circle the dots to form a complete ten. Compare to the problem with the ones' digits.

a. 19 + 5 = ____

b. 29 + 7 = ____

c. 49 + 5 = ____

9 + 5 = ____

9 + 7 = ____

9 + 5 = ____

The answer goes to the next ten!

2. Add. For each problem, write down the corresponding problem with just the ones' digits. a. 19 + 7 = ____

b. 49 + 9 = ____

c. 59 + 5 = ____

d. 39 + 4 = ____

___ + ___ = ____

___ + ___ = ____

___ + ___ = ____

___ + ___ = ____

e. 59 + 8 = ____

f. 19 + 2 = ____

g. 49 + 3 = ____

h. 79 + 5 = ____

___ + ___ = ____

___ + ___ = ____

___ + ___ = ____

___ + ___ = ____

3. Add. Compare the problems.

9 + 3 = ____

b. 9 + 6 = ____

c. 9 + 4 = ____

d. 9 + 7 = ____

19 + 3 = ____

39 + 6 = ____

49 + 4 = ____

29 + 7 = ____

29 + 3 = ____

59 + 6 = ____

79 + 4 = ____

89 + 7 = ____

e. 9 + 2 = ____

f. 9 + 9 = ____

g. 9 + 5 = ____

h. 9 + 8 = ____

39 + 2 = ____

69 + 9 = ____

19 + 5 = ____

29 + 8 = ____

29 + 2 = ____

79 + 9 = ____

59 + 5 = ____

89 + 8 = ____

a.

89

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

a.

b.

c.

d.

9 + ____ = 14

4 + 9 = ____

8 + ____ = 11

7 + 8 = ____

9 + ____ = 15

8 + 9 = ____

8 + ____ = 15

2 + 8 = ____

9 + ____ = 13

2 + 9 = ____

8 + ____ = 17

8 + 8 = ____

9 + ____ = 18

5 + 9 = ____

8 + ____ = 12

5 + 8 = ____

9 + ____ = 12

6 + 9 = ____

8 + ____ = 14

6 + 8 = ____

9 + ____ = 17

3 + 9 = ____

8 + ____ = 13

3 + 8 = ____

9 + ____ = 11

1 + 9 = ____

8 + ____ = 18

1 + 8 = ____

9 + ____ = 16

9 + 9 = ____

8 + ____ = 16

9 + 8 = ____

9 + ____ = 10

7 + 9 = ____

8 + ____ = 10

4 + 8 = ____

5. Find the pattern and continue it!

a.

+

40

b.

+

48

+

16

53 +

21 +

____

____

+

61 +

27

+

c.

+

66 +

34 +

____

+

+

____

____

+

42 +

____

+

+

+

____

____

+

____

90

+

67

+

____ +

____

+

71

____

____

+

74

76

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

9 + 71

b.

24 + 67

c.

55 + 36

d.

45 + 25

e.

38 + 14

f.

58 + 25

g.

29 + 38

h.

79 + 15

i.

62 + 28

j.

37 + 35

k.

34 9 + 35

l.

25 42 + 49

m.

58 30 + 6

n.

29 44 + 12

o.

16 14 + 19

2. Write the numbers under each other so that the ones and tens are in their own columns. Add. a. 45 + 27

b. 8 + 56

tens ones

tens ones

+

f. 6 + 31 + 25

+

+

g. 40 + 7 + 9

+

c. 40 + 32

d. 25 + 45

e. 47 + 9

+

+

+

h. 46 + 8 + 20

+

i. 5 + 8 + 13

+

91

j. 5 + 4 + 57

+

In the tens column, you add 1 + 5 + 6 = 12. The “1” of 12 is in the hundreds' column, and the “2” of 12 is in the tens column.

+

Ten tens makes a hundred. 12 tens makes more than a hundred - a hundred and 2 tens. In the tens column, you add 8 + 7 = 15. The “1” of 15 is in the hundreds' column, and the “5” of 15 is in the tens column.

+

Ten tens makes a hundred. 15 tens makes more than a hundred - a hundred and 5 tens. 3. Add. You will have more than 10 tens. a. 27 + 80

b. 95 + 47

+

c. 29 + 75

+

+

d. 62 + 84

+

67 + 61

b.

90 + 65

c.

39 + 81

d.

85 + 62

e.

29 + 94

f.

57 + 72

g.

70 + 68

h.

85 + 78

i.

86 + 15

j.

96 + 90

k.

65 18 + 26

l.

74 7 + 45

m.

68 47 + 32

n.

12 88 + 49

o.

8 50 + 79

92

Two-Digit Numbers Ending in 8 or 7 1. Circle dots to complete a ten. Compare it to the problem below with the ones' digits.

+

+

____ + __ = ____ 8

+

18 + 5 = ____

____ + ___ = ____

8 + 5 = 13

8 + 9 = 17

+ 6 = 14

The answer goes to the next ten!

2. Add. For each problem, write the corresponding problem with just the ones' digits. a. 68 + 7 = ____

b. 58 + 2 = ____

c. 38 + 6 = ____

d. 48 + 4 = ____

8 + 7 = 15

___ + ___ = ____

___ + ___ = ____

___ + ___ = ____

e. 14 + 8 = ____

f. 72 + 9 = ____

g. 65 + 8 = ____

h. 55 + 9 = ____

___ + ___ = ____

___ + ___ = ____

___ + ___ = ____

___ + ___ = ____

3. Add. Compare the problems. a. 8 + 3 = _____

b. 8 + 6 = _____

c. 8 + 4 = _____

d. 8 + 7 = _____

18 + 3 = _____

38 + 6 = _____

48 + 4 = _____

28 + 7 = _____

28 + 3 = _____

58 + 6 = _____

78 + 4 = _____

88 + 7 = _____

e. 8 + 2 = _____

f. 8 + 9 = _____

g. 8 + 5 = _____

h. 8 + 8 = _____

38 + 2 = _____

68 + 9 = _____

18 + 5 = _____

28 + 8 = _____

28 + 2 = _____

78 + 9 = _____

58 + 5 = _____

88 + 8 = _____

93

4. Add. Circle dots to form a ten. Note the answer goes over to the next ten.

a. 27 + 4 = ____

b. 47 + 5 = ____

c. 37 + 7 = ____

5. Add. For each problem, write the corresponding problem with just the ones' digits. a. 75 + 7 = ____

5 + 7 = 12

b. 47 + 7 = ____

c. 57 + 6 = ____

d. 37 + 4 = ____

___ + ___ = ____

___ + ___ = ____

___ + ___ = ____

6. Add. Compare the problems. a. 7 + 6 = ____

b. 7 + 5 = ____

c. 7 + 4 = ____

d. 7 + 7 = ____

17 + 6 = ____

47 + 5 = ____

17 + 4 = ____

67 + 7 = ____

27 + 6 = ____

77 + 5 = ____

47 + 4 = ____

87 + 7 = ____

e. 7 + 9 = ____

f. 7 + 3 = ____

g. 7 + 8 = ____

h. 7 + 10 = ____

67 + 9 = ____

37 + 3 = ____

57 + 8 = ____

17 + 10 = ____

87 + 9 = ____

77 + 3 = ____

27 + 8 = ____

47 + 10 = ____

7. Solve the word problems. a. Jeanine needed 24 eggs to make an omelet 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 50-pound

bag of potatoes. There are only 12 pounds remaining. How many pounds of potatoes have they eaten?

94

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

b.

20 + 34 /

\

/

20 + ____ + ____ =

c.

70 + 18

50 + 27

\

/

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

+

____

+

____

____

44 + 48

b.

32 + 59

c.

16 + 47

d.

23 + 67

e.

55 + 29

5. Compare the expressions and write < , > , or = . a. 8 + 3

40 + 5

b. 8 + 54

9 + 53

c. 5 + 6 + 56

61 + 6

d. 2 + 36

29 + 7

e. 46 + 8

48 + 5

f. 85 + 9

6 + 88

95

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 by threes. a. 42, 45, _____, _____, _____, _____, _____, _____, _____, _____, ____ b. 1, 4, _____, _____, _____, _____, _____, _____, _____, _____, ____

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.

+

d.

e.

3

+ 2 5

+ 7 8

+ 2 6

7 1

5 1

9 1

6 1

96

Many Addends When adding the ones, you may get two or even three tens. Carry them to the tens' column.

Adding the ones we get 8 + 7 + 8 = 23. Carry 2 tens to the tens column.

2

48 27 + 18 93

Adding the ones we get 9 + 9 + 7 + 6 = 31. Carry 3 tens to the tens column.

3

19 19 27 + 26 91

1. Add mentally. First add the numbers that make 10 (if there are any). a. 8 + 4 + 5 =

b. 5 + 8 + 7 =

c. 8 + 5 + 6 + 4 =

9+9+9=

9+2+6=

4+9+5+6=

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

52 30 + 11

b.

13 25 + 54

c.

33 38 + 27

d.

36 27 + 19

e.

36 27 18 + 16

f.

40 18 16 + 22

g.

15 17 18 + 39

h.

12 29 25 + 14

i.

19 79 + 19

j.

56 32 + 29

k.

45 65 + 19

l.

51 15 + 79

129

145

74

80

82

89

91

92

93

96

97

97

98

117

117

122

3. Solve the problems. Write an addition or subtraction sentence or a missing addend sentence for each one. You can add in columns if you need to. a. A bus can seat 30 people. There were

b. The first bus had 22 people on it, and

already 23 people. Is there room for nine more people?

the second bus had 25. What is the total number of people on the buses?

Yes/No, because

c. How many buses do you need if you

d. A bus was full, but then six people

have 57 people?

got off. How many people were on it now?

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

e. A bus was full. First it dropped off

f. A bus had some people in it, and then

13 people. Then it dropped off 7 more people. How many people were left on the bus?

13 more got on. Now there are 29 people on the bus. How many were on the bus originally?

g. A bus had some people on it. Then 9

h. A bus had some people on it. It picked

people got on. Then 15 people got off. Now there are 17 people on the bus. How many were on it originally?

up 12 people, and then 7 people more. Then it was full. How many people were on the bus originally?

98

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 the numbers, write “E” if the number is even, and “O”, if the number is odd. a. 19 + 5 + 7 = 31

O

O

O

b. 25 + 7 + 3 = ____

c. 7 + 11 + 23 = ____

O

d. 57 + 21 = ____

g. 17 + 27 + 5 = ____

e. 5 + 1 + 11 + 9 = ____

h. 25 + 13 + 3 + 1 = ____

f. 25 + 9 = ____

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).

47 + 29 60 + 16

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

76

52 17 + 14 70 + 13 83

Use Mary's method with these problems:

13 15 + 48

27 28 + 31

16 25 + 47

99

46 25 + 12

36 27 + 34

Subtracting in Columns tens ones

1. a.

– 3

tens ones

b.

2

Cross out 3 tens and 2 ones. What is left? __ tens and __ ones

Cross out 6 tens and 1 one. What is left? __ tens and __ ones

You can simply subtract the tens in the tens-column and the ones in the ones-column.

2. Subtract. a.

57 – 10

b.

66 – 24

c.

78 – 44

d.

87 – 20

e.

55 – 11

f.

95 – 35

g.

28 – 25

h.

67 – 33

i.

76 – 32

j.

88 – 66

c.

96

d.

27

e.

76

3. Figure out what was subtracted.

57

a.

48

b.

– 37

– 25

– 33

– 12

33

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

72 + 20 = ____

b.

29 + 10 = ____

c.

55 – 20 = ____

d.

63 + 30 = ____

72 + 10 = ____

29 + 50 = ____

55 + 20 = ____

63 – 40 = ____

72 – 10 = ____

29 – 10 = ____

55 + 40 = ____

63 – 20 = ____

72 – 30 = ____

29 + 30 = ____

55 – 30 = ____

63 – 60 = ____

100

Borrowing/Regrouping, Part 1 Break a ten.

We will now study “borrowing” in subtraction. As a first step, we study breaking a ten-pillar into ten little cubes. 4 tens 5 ones This is also called “regrouping”, because one ten “changes groups” First we have 45. We from the tens group into the ones. “break” one ten-pillar into little cubes.

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.

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. 5 tens 3 ones

4 tens 13 ones

1. Break a ten into 10 ones. What do you get? You can draw ten-pillars and cubes to help. Break a ten. a. 3 tens 0 ones

Break a ten. b. __tens __ones

2 tens ___ ones Break a ten.

c. __tens __ones

Break a ten.

__tens __ones

d. __tens __ones

Break a ten. e. __tens __ones

__tens __ones

__tens __ones Break a ten.

__tens __ones

f. __tens __ones

101

__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.

4 tens 5 ones

After that, cross out (subtract) 1 ten 7 ones.

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

The pictures on the right illustrate 52 – 39.

3 tens 15 ones

Break a ten.

First, a ten is broken into 10 ones. So, 5 tens 2 ones becomes 4 tens 12 ones.

5 tens 2 ones

After that, cross out (subtract) 3 tens 9 ones.

Cross out 3 tens 9 ones from the second picture. What is left? ___ tens ___ ones

4 tens 12 ones

2. Fill in.

Break a ten.

3 tens 6 ones

Break a ten.

2 tens 16 ones

___ tens ___ ones

a. Cross out 8 ones from the second picture. What is left? ___ tens ___ ones

b. Cross out 2 tens 7 ones from the second

picture. What is left? ___ tens ___ ones

Break a ten.

___ tens ___ ones

___ tens ___ ones

Break a ten.

___ tens ___ ones

___ tens ___ ones

___ tens ___ ones

c. Cross out 2 tens 5 ones from the second

d. Cross out 4 tens 4 ones from the second

picture. What is left? ___ tens ___ ones

picture. What is left? ___ tens ___ ones

102

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

a. 5 tens 5 ones

4 tens 15 ones – 1 ten 7 ones

– 1 ten 7 ones

b. 7 tens 2 ones

– 3 tens 5 ones

3 tens 8 ones

c. 6 tens 0 ones

– 2 tens 7 ones

__ tens __ ones

__ tens __ ones 2 tens 7 ones

d. 6 tens 4 ones

– 3 tens 8 ones

__ tens __ ones

e. 7 tens 6 ones

– 4 tens 7 ones

– 6 tens 5 ones

__ tens __ ones 3 tens 8 ones __ tens __ ones

__ tens __ ones 4 tens 7 ones

f. 5 tens 0 ones

– 2 tens 2 ones

__ tens __ ones

g. 8 tens 1 one

__ tens __ ones 3 tens 5 ones

__ tens __ ones 2 tens 2 ones __ tens __ ones

__ tens __ ones 6 tens 5 ones

h. 6 tens 3 ones

– 2 tens 8 ones

__ tens __ ones

__ tens __ ones 2 tens 8 ones __ tens __ ones

4. Jessica had 37 colored pencils. Then she took a set of 12 different colored pencils and gave those to her brother, and another set of 6 pencils and gave those 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?

103

Borrowing/Regrouping, Part 2 The picture illustrates subtracting 16 from 53. First, we break a ten into ten ones. Then we cross out 1 ten 6 ones. When the subtraction is written down in columns, we cross the “5” in the tens-column and write 4 above it. We also cross the “3” in the ones column and write 13 above it.

5 tens, 3 ones

This shows the same thing as the pictures: one of the tens is "broken down" into ten ones, so there is one less ten in the tens column, and 10 more ones in the ones column.

4 tens, 13 ones

Cross out 1 ten 6 ones from the second picture. What is left? ___ tens ___ ones

Then we can subtract tens and ones separately.

4

13

5 – 1 3

3 6 7

Here is another example. The picture illustrates subtracting 28 from 40. First, we break a ten into ten ones. Then we cross out 2 tens 8 ones. When the subtraction is written down in columns, we cross the “4” in the tens-column and write 3 above it, because one of the tens was "moved" or "borrowed" into the ones column.

4 tens

3 tens, 10 ones

Cross out 2 tens 8 ones from the second picture. What is left? ___ tens ___ ones

We also cross the “0” in the ones column and write 10 above it, because there are now 10 new ones that came from the ten that was "borrowed".

3

10

4 – 2 1

0 8 2

1. Borrow from the tens, then subtract. a. 6 tens 3 ones → 5 tens 13 ones

Take away 1 ten, 7 ones.

b. 5 tens 2 ones → ___ tens ___ ones

5

13

6 – 1

3 7

Take away 2 tens, 7 ones.

104

5 – 2

2 7

c. 6 tens 0 ones → ___ tens ___ ones

6 – 3

Take away 3 tens, 9 ones.

d. 7 tens 1 one → ___ tens ___ ones

0 9

e. 3 tens, 5 ones → ___ tens ___ ones

3 – 1

Take away 1 ten, 7 ones.

7 – 4

1 6

f. 8 tens → ___ tens ___ ones

5 7

8 – 3

Take away 3 tens, 4 ones.

g. 7 tens, 6 ones → ___ tens ___ ones

Take away 4 tens, 8 ones.

7 – 1

Take away 1 ten, 6 ones.

0 4

h. 9 tens → ___ tens ___ ones

Take away 5 tens, 1 one.

6 8

9 – 5

i. 5 tens, 4 ones → ___ tens ___ ones

j. 8 tens → ___ tens ___ ones

Take away 2 tens, 5 ones.

Take away 4 tens, 7 ones.

0 1

k. 7 tens, 4 ones → ___ tens ___ ones

l. 4 tens 7 ones → ___ tens ___ ones

Take away 3 tens, 8 ones.

Take away 2 tens, 9 ones.

105

2. Subtract. Check by adding the result and what was subtracted. The sum should be the number you subtracted from. a.

4 16

Check:

56 – 27

1

29 + 27

29

56

b.

90 – 28

d.

c.

Check:

42 – 15

+ 28

e.

40 – 35

65 – 39

h.

52 – 14

i.

65 – 26

j.

70 – 48

k.

55 – 17

+ 15

f.

82 – 25

g.

Check:

l.

31 – 18

66 – 28

Figure out the missing numbers in these subtraction problems! You might need to borrow from the tens.

3 – 1

8 –

7 5

– 2 3 4 7

0 7

6 2 – 1 4

– 3

1 6

4 2

6 8

7 0

5

1

– 3 4 5

2 7

106

– 1 3 7

– 5 3 8 –

9 4 4

Regrouping/Borrowing, Part 3 You can subtract

How do we know when to break down a ten into 10 ones, and when not to?

6–0 6–1 6–2

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 there are not that many cubes to begin with.

You would go into debt

6–3 6–4 6–5 6–6

6 – 7 6 – 11 6 – 8 6 – 12 6 – 9 6 – 13 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 3–8 3–9

4–0 4–1 4–2 4–3 4–4 4–5 4–6 4–7 4–8 4–9

5–0 5–1 5–2 5–3 5–4 5–5 5–6 5–7 5–8 5–9

6–0 6–1 6–2 6–3 6–4 6–5 6–6 6–7 6–8 6–9

7–0 7–1 7–2 7–3 7–4 7–5 7–6 7–7 7–8 7–9

8–0 8–1 8–2 8–3 8–4 8–5 8–6 8–7 8–8 8–9

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

61 26

Y/N

d. Do you need to regroup? Y/N

b. Do you need to regroup?

74 23

Y/N

54 32

c. Do you need to regroup?

50 25

90 27

Y/N

e. Do you need to regroup? Y/N

82 56

f. Do you need to regroup? Y/N

107

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

60 16

b. Do you need to regroup?

Y/N

57 32

c. Do you need to regroup?

Y/N

d. Do you need to regroup?

80 28

97 25

f. Do you need to regroup?

Y/N

g. Do you need to regroup?

50 10

60 41

Y/N

h. Do you need to regroup?

Y/N

88 77

Y/N

e. Do you need to regroup?

Y/N

43 17

37 27

i. Do you need to regroup?

Y/N

Y/N

35 44 26 19 25 11 63 22 72 49 10 26 51 52 78 30 25 40 4. Subtract. Borrow from the tens when needed. Check by adding!

a.

54 – 37

b.

94 – 34

c.

82 – 25

d.

62 – 29

e.

99 – 57

f.

40 – 23

g.

76 – 48

h.

83 – 63

i.

89 – 17

108

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 find the nearest whole-ten number. Newspapers

Day

Mon

Tues

Wed

Thurs

Fri

Sat

Sun

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. Break the number you're subtracting into tens and ones, and subtract in parts. a. 45 – 23

b. 76 – 15

/ \ 45 – 20 – 3 = ____

/ \ 76 – 10 – 5 = ____

d. 60 – 35

e. 88 – 38

f. 70 – 16

g. 90 – 28

h. 73 – 32

i. 64 – 33

c. 47 – 15

109

3. Solve the word problems. Write an addition or subtraction sentence for each question. You can add or subtract in columns if you need to. a. Jim has 62 marbles, Peter has 28, and Ed has 33 marbles.

How many more marbles does Jim have than Peter? How many more marbles does Jim have than Ed? If Peter and Ed combined their marbles, will they have more than Jim?

b. Mom had \$72. She bought a gadget for \$44.

How many dollars does she have left?

c. You're on page 48 in your book that has a total of 95

pages. You read ten more pages. Now how many pages do you have left to read?

4. 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?

110

5. The teacher made a chart that shows how many books the children read each month. Books read

Jan

Feb

Mar

Apr

Annie

13

21

18

14

Freddie

8

5

11

9

Lisa

8

13

16

18

Jonathan

10

8

14

15

Total

a. How many books did Jonathan read in March? b. Who read the most books in February?

In April?

c. How many more books did Annie read in February than in January? d. How many more books did Lisa read in April than Freddie? e. Find how many books each child read in all. Put the number in the “total” column. Annie

+

Freddie

Lisa

+

+

f. How many more books in all did Annie read than Freddie?

111

Jonathan

+

Mental Subtraction Methods Method 1: Subtract in two parts

53 – 8 = 53 – 3 – 5 = 50 – 5 = 45

6 72 – = 72 – 2 – 4 = 70 – 4 = 66

Subtract 8 in two parts: first 3, then 5. In other words, first subtract to the previous whole ten, then the rest.

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 /

−7

\

/

a. ( 51 − 1 ) − 4 =

/

−7 \

/

e. ( 75 − ___ ) −___ =

−7 g. ( 35 − ___ ) −___ =

/

\

f. ( 63 − ___ ) −___ =

−6 \

\

c. ( 33 − ___ ) −___ =

−6 \

d. ( 92 − ___ ) −___ =

/

/

b. ( 62 − ___ ) −___ =

−5 /

−4 \

−5 \

/

h. ( 74 − ___ ) −___ =

\

i. ( 52 − ___ ) −___ =

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

c.

51 − 7 = ____

b.

42 − 4 = ____

51 − 5 = ____

42 − 5 = ____

51 − 3 = ____

42 − 3 = ____

51 − 6 = ____

42 − 6 = ____

34 − 8 = ____

d.

65 − 6 = ____

34 − 5 = ____

65 − 9 = ____

34 − 7 = ____

65 − 7 = ____

34 − 9 = ____

65 − 8 = ____

112

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. Compare the problems. a. 18 – 4 = ____

b. 14 – 9 = ____

c. 17 – 8 = ____

d. 12 – 9 = ____

48 – 4 = ____

24 – 9 = ____

27 – 8 = ____

52 – 9 = ____

78 – 4 = ____

44 – 9 = ____

37 – 8 = ____

32 – 9 = ____

e. 11 – 6 = ____

f. 15 – 9 = ____

g. 13 – 8 = ____

h. 16 – 8 = ____

51 – 6 = ____

65 – 9 = ____

33 – 8 = ____

86 – 8 = ____

71 – 6 = ____

45 – 9 = ____

93 – 8 = ____

36 – 8 = ____

4. Now you think of the “helping problem” yourself. a. 34 – 5 = ____

b. 65 – 9 = ____

c. 51 – 8 = ____

d. 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 9 pages more. Now how many pages does she have left to read?

6. Find what was subtracted. –

78

77

72

70

65

113

60

57

53

46

Method 3:

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 =

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

+8

+__

+__

a. 92 – 84 =

b. 51 – 49 =

c. 76 – 69 =

Think: 84 + ___ = 92

Think: 49 + ___ = 51

Think: 69 + ___ = 76

+__

+__

+__

d. 43 – 35 =

e. 70 – 61 =

f. 84 – 78 =

g. 32 – 28 =

j. 90 – 83 =

m. 100 – 95 =

h. 22 – 14 =

k. 64 – 56 =

n. 64 – 55 =

i. 53 – 46 =

l. 72 – 65 =

o. 44 – 37 =

The triangle and square represent “mystery numbers”. Find what the mystery numbers are in each case. a.

+

+ 10 = 34

= ______

b.

+

= 22

=4

= ____,

114

= ____

c.

+ +

= ____,

= 22 = 36 = ____

Euclid's Game Euclid's game is simple, fun, and lets you practice finding the difference of two numbers! Rules: 1. The first player chooses any number on the 100-chart and circles or colors it. 2. The next player chooses any other number on the 100-chart and circles or colors it. After this, the numbers get marked by crossing them out. At his turn, each player has to find the difference of any two numbers already marked, and mark that number. The player can choose any two numbers for this; they just have to be already marked numbers. The player who cannot find any more numbers to mark is the loser.

Use the 100-chart on the next page as a game board. You can print it anew for every new game. Alternatively you may write the 100-chart on paper, of course. Example. Initially Jane chooses 28 and Joe chooses 9. After that:

9

10

11 12 13 14 15 16 17 18 19

20

21 22 23 24 25 26 27 28 29

30

31 32 33 34 35 36 37 38 39

40

41 42 43 44 45 46 47 48 49

50

You can continue Jane's and Joe's play if you'd like.

51 52 53 54 55 56 57 58 59

60

Eventually you should see all of the numbers from 1 to 28 marked, with Jane as the loser.

61 62 63 64 65 66 67 68 69

70

71 72 73 74 75 76 77 78 79

80

81 82 83 84 85 86 87 88 89

90

Jane: I mark 19 since it's the difference of 28 and 9. Joe: I mark 10 since it's the difference of 19 and 9. Jane: I mark 18 since it's the difference of 28 and 10. Joe: I mark 1 since it's the difference of 19 and 18. ... and so on.

1

2

3

4

5

6

7

8

91 92 93 94 95 96 97 98 99 100

Questions to ponder after you have played a few games: 1. Let's say that 28 and 9 are chosen as the initial numbers, like in Jane's and Joe's game. Can Jane and Joe ever mark a number that is more than 28? 2. Let's say that the two initial numbers are both even. What can you say about the numbers that get marked in the game? 3. Let's say that the two initial numbers are both multiples of 5, such as 55 and 30. What can you say about the numbers that get marked in the game? 4. Can you mark off all of the the numbers on the 100-chart during the game, if the initial numbers are (you can try these out): a. 90 and 7? b. 100 and 1? c. 100 and 10? d. 100 and 13?

115

100-Charts for Euclid's game or other uses 1

2

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52

53

54

55

56

57

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74

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76

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78

79

80

81

82

83

84

85

86

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88

89

90

91

92

93

94

95

96

97

98

99 100

1

2

3

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5

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7

8

9

10

11

12

13

14

15

16

17

18

19

20

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25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

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41

42

43

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45

46

47

48

49

50

51

52

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55

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99 100

116

1

2

3

4

5

6

7

8

9

10

1

2

3

4

5

6

7

8

9

10

11 12 13 14 15 16 17 18 19 20

11 12 13 14 15 16 17 18 19 20

21 22 23 24 25 26 27 28 29 30

21 22 23 24 25 26 27 28 29 30

31 32 33 34 35 36 37 38 39 40

31 32 33 34 35 36 37 38 39 40

41 42 43 44 45 46 47 48 49 50

41 42 43 44 45 46 47 48 49 50

51 52 53 54 55 56 57 58 59 60

51 52 53 54 55 56 57 58 59 60

61 62 63 64 65 66 67 68 69 70

61 62 63 64 65 66 67 68 69 70

71 72 73 74 75 76 77 78 79 80

71 72 73 74 75 76 77 78 79 80

81 82 83 84 85 86 87 88 89 90

81 82 83 84 85 86 87 88 89 90

91 92 93 94 95 96 97 98 99 100

91 92 93 94 95 96 97 98 99 100

1

1

2

3

4

5

6

7

8

9

10

2

3

4

5

6

7

8

9

10

11 12 13 14 15 16 17 18 19 20

11 12 13 14 15 16 17 18 19 20

21 22 23 24 25 26 27 28 29 30

21 22 23 24 25 26 27 28 29 30

31 32 33 34 35 36 37 38 39 40

31 32 33 34 35 36 37 38 39 40

41 42 43 44 45 46 47 48 49 50

41 42 43 44 45 46 47 48 49 50

51 52 53 54 55 56 57 58 59 60

51 52 53 54 55 56 57 58 59 60

61 62 63 64 65 66 67 68 69 70

61 62 63 64 65 66 67 68 69 70

71 72 73 74 75 76 77 78 79 80

71 72 73 74 75 76 77 78 79 80

81 82 83 84 85 86 87 88 89 90

81 82 83 84 85 86 87 88 89 90

91 92 93 94 95 96 97 98 99 100

91 92 93 94 95 96 97 98 99 100

117

Mixed Review 1. Complete the next ten. a.

b.

c.

d.

16 + ____ = 20

47 + ____ = ____

39 + ____ = ____

75 + ____ = ____

64 + ____ = 70

38 + ____ = ____

27 + ____ = ____

92 + ____ = ____

43 + 28

b.

33 + 39

c.

24 + 47

d.

23 + 37

e.

55 + 17

f.

38 13 + 42

g.

39 10 + 46

h.

41 14 + 36

i.

38 29 + 23

j.

18 19 + 55

b.

c.

d.

25 + 8 = ____

76 + 5 = ____

88 + 3 = ____

82 + 8 = ____

24 + 9 = ____

50 + 6 = ____

34 + 7 = ____

10 + 9 = ____

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

55 – 7 = ____

b.

15 – 7 = 8 d.

72 – 7 = ____ ____ – ___ = ____

74 – 8 = ____

c.

____ – ___ = ____ e.

51 – 3 = ____ ____ – ___ = ____ 118

93 – 5 = ____ ____ – ___ = ____

f.

33 – 4 = ____ ____ – ___ = ____

5. Subtract. – 6

88

– 9

____

– 10

____

– 7

____

– 8

____

– 5

____

– 7

____

– 3

____

33

6. Subtract. Check by adding. a.

d.

Check:

88 – 54

66 – 17

b.

+ 54

e.

Check:

63 – 48

c.

+ 48

71 – 22

f.

Check:

69 – 27

84 – 49

7. Solve the problems. a. There are some people on the bus. At the bus stop, 13 people come in.

Now there are 52 people in the bus. How many were there originally?

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. 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?

119

+ 27

Chapter 5: Counting Money Introduction The fifth chapter of the Math Mammoth Grade 2-A Complete Worktext covers counting quarters, dimes, nickels, and pennies. Also, the one-dollar bill and the five-dollar bill are introduced.

Counting Coins The main goal of this chapter is to be able to count coins and find the amount of money in cents or dollars. Also practiced is finding change by counting up. Only small money amounts are used. In one lesson, the one-dollar bill and the five-dollar bill are introduced, and the student learns to write money amounts using dollars and cents, with the decimal point in between. The latter part of second grade also includes a lesson about adding money amounts.

The Lessons page

span

Counting Coins Review ................................. 122

3 pages

Change............................................................ 125

3 pages

Dollars ........................................................... 128

3 pages

Counting Change ........................................... 131

2 pages

120

Helpful Resources on the Internet Use these free online resources to supplement the “bookwork” as you see fit. Change Maker Determine how many of each denomination you need to make the exact change. Good and clear pictures! Playable in US, Canadian, Mexican, UK, or Australian money. http://www.funbrain.com/cashreg/index.html Using Money Drag the right amount of coins and bills (US) to the answer space to match the given amount. The pictures look a little fuzzy. http://www.mathcats.com/microworlds/usingmoney.html Counting Money Activity from Harcourt Count the coin value and type it into the box and click “Check”. http://www.hbschool.com/activity/counting_money/ Cash Out Give the correct change by clicking on the bills and coins. http://www.mrnussbaum.com/cashd.htm Piggy bank When the coins fall from the top of the screen, choose those that add up to the given amount, and the piggy bank fills. http://fen.com/studentactivities/Piggybank/piggybank.html Money Instructor Checkbook math exercises and worksheets. Includes a checkbook to print, writing dollars and cents worksheet, checking account deposit, checkbook transactions, and word problems. http://www.moneyinstructor.com/checks.asp

121

Counting Coins Review

A quarter 25 cents

Count up →

A dime 10 cents

20 ¢

A nickel 5 cents

A penny 1 cent

25 ¢ 26 ¢ 27 ¢

10 ¢

25 ¢ 35 ¢ 45 ¢ 50 ¢ 51¢

75 ¢

1. How much money? Write down the amount in cents. a. b.

c.

e.

2 quarters 50 cents

d.

f.

g. h.

122

3quarters 75 cents

20 ¢

21 ¢

80 ¢ 85 ¢

You may count each two nickels as ten.

2. How much is the total if you have: a. a quarter and three dimes

b. three quarters and a dime

c. four nickels and four dimes

d. a quarter, a dime, six pennies

e. nine pennies and eight dimes

f. three quarters, two dimes, a penny

3. Cross out the coins you need to buy the item. Write how many cents you have left.

a.

b.

17 ¢

92 ¢ c.

Left ____¢

Left ____¢

d.

58 ¢

e.

Left ____¢

Left ____¢

123

Left ____¢

f.

64 ¢

33 ¢

95 ¢

Left ____¢

Often you have several ways to make a given amount. For example, to make 54 cents, you can use two quarters and four pennies. Or, you may use five dimes and four pennies. Are there any other ways to do it? 4. Find two ways to make these amounts. Use either real money, or draw. a. 26¢

b. 37¢

c. 43¢

d. 53¢

e. 61¢

f. 88¢

5. Remember \$1 means 1 dollar, which is 100 cents. How much more is needed to make \$1? a.

b.

c.

92¢ + ____¢ = 100¢

70¢ + ____¢ = \$1

40¢ + ____¢ = \$1

80¢ + ____¢ = \$1

74¢ + ____¢ = \$1

33¢ + ____¢ = \$1

79¢ + ____¢ = \$1

64¢ + ____¢ = \$1

45¢ + ____¢ = \$1

50¢ + ____¢ = \$1

58¢ + ____¢ = \$1

31¢ + ____¢= \$1

124

Change When you buy something in a store, you often do not have the exact amount of money to pay for it. Instead, you give the clerk more money than what the item costs. The clerk then gives you some money back. This is called your change. A pen costs 40¢. You don't have the coins to make exactly 40¢, so you give the clerk 50¢. That is 10¢ too much! But then the clerk gives you back 10¢ — your change. You give:

50¢

10¢

Price: 40¢

The clerk gives you back the difference between the price and what you paid. In each problem below, find the change you get back. Think of the DIFFERENCE between the price and what you pay. Or, think how many cents you paid “too much”. That will be your change. You can set up a “play store” to do these problems, using real money, one person as a clerk, and one person as a customer. 1. Write how many cents you give, and how many cents is your change. a.

You give: Your change:

b.

You give:

Price: 20¢

______¢

Price: 30¢

______¢

______¢

______¢

c.

You give: Your change:

Price: 35¢

______¢

______¢

125

d.

You give: Your change:

Price: 17¢

______¢

______¢

e.

You give: Your change:

Price: 22¢ ______¢

______¢

g.

You give:

Price: 60¢

______¢

______¢

f.

You give: Your change:

Price: 11¢

______¢

______¢

h.

You give:

Price: 80¢

______¢

______¢

2. Circle the coins you use to pay. Write how many cents your change is. You have: a. You buy a drink for 55¢.

Change: ______ ¢

You have: b. You buy raisins for 33¢.

Change: ______ ¢

You have: c. You buy a toy for 46¢.

Change: ______ ¢

You have: d. You buy a book for 88¢.

Change: ______ ¢

You have: e. You buy a basket for 75¢.

Change: ______ ¢

You have: f. You buy crayons for 63¢.

Change: ______ ¢

126

3. Practice some more! Figure out the change. a. Paper costs 70¢.

b. A banana costs 41¢.

c. A book costs 94¢.

You give \$1.

You give 50¢.

You give \$1.

Change: _____¢

Change: _____¢

Change: _____¢

d. A toy costs 20¢.

e. A drink costs 70¢.

f. A towel costs 62¢.

You give 50¢.

You give \$1.

You give 75¢.

Change: _____¢

Change: _____¢

Change: _____¢

4. Now you buy many items. First add their prices to find the total. Then find the change. Draw the coins that could be your change. a. A magazine costs 20¢. You buy three of them. You give \$1.

Total cost: 60¢ Change: 40¢ b. A toy costs 15¢ and another toy 20¢. You give 50¢.

Total cost: _____ ¢ Change: _____ ¢ c. A lollipop costs 8¢. You buy two of them. You give 20¢.

Total cost: _____ ¢ Change: _____ ¢ d. A pencil costs 5¢. You buy four of them. You give 25¢.

Total cost: _____ ¢ Change: _____ ¢ e. An eraser costs 35¢ and a pencil 10¢. You give 50¢.

Total cost: _____ ¢ Change: _____ ¢

127

Dollars = \$1.20 This is one dollar. It is worth 100 cents. \$1 or \$1.00

= \$5.26 This is a five-dollar bill. It is worth 500 cents. \$5 or \$5.00

Write first the dollars, then a point, then the cents. Use the “\$” symbol in front of dollar amounts. Do not use the ¢ symbol.

1. How much money? Write the amount.

a. \$________

b. \$________

c. \$________

d. \$________

e. \$________

f. \$________

g. \$________

h. \$________

128

2. Write the dollar amount.

\$2.15

b. \$________

c. \$________

d. \$________

a.

e. \$________

f. \$________

If you don't have any dollars, put a zero in the dollars place.

1¢ or \$0.01

35¢ or \$0.35

6¢ or \$0.06

3. Write the amount using the dollar symbol and a decimal point. a.

b.

c.

\$________

\$________

\$________

d.

e.

f.

\$________

\$________

\$________

129

Sometimes you have more than 100 cents. That means you have more than 1 dollar, because 1 dollar is 100 cents.

100¢ or \$1.00

105¢ or \$1.05

121¢ or \$1.21

4. Write the amount in dollars.

a.

b.

\$________

\$________

c.

d.

\$________

\$________

5. Draw bills and coins for these amounts. a. \$1.32

b. \$2.06

c. \$2.54

d. \$3.80

130

Counting Change When you buy an item, you might not have the exact coins and bills for the amount it costs. You can then pay with a bigger bill, and get back some change. To give change, or to check the change you are given, count up from the price of the item until you reach the amount the customer gives.

Customer gives \$1

Count up from the price →

69¢ Customer gives \$1

Count up from the price →

34¢

35 ¢ 40 ¢ 50 ¢

75 ¢

70 ¢ 80 ¢ 90 ¢ 100 ¢

100 ¢

The change is these coins. The change is 66 cents.

The change is these coins. The change is 31 cents.

1. Draw the coins for the change.

a.

78¢

Change: _______

Customer gives \$1

b.

65¢

Change: _______

Customer gives \$1

c.

47¢ Change: _______

Customer gives \$1

d.

52¢ Change: _______

Customer gives \$1

131

2. Draw the coins for the change.

a.

\$1.15

Customer gives \$2

b.

Change: _______

\$2.30

Customer gives \$2.50

c.

Change: _______

\$1.78

Customer gives \$2

d.

Change: _______

\$2.32 Customer gives \$3

Change: _______

3. Find the change. You can draw coins or use real money to help. a. A toy: \$1.44

b. A drink: \$0.88

Customer gives \$1.50

Customer gives \$1

Change \$________

Change \$________

c. Coffee: \$0.97

d. A pencil set: \$1.55

Customer gives \$1.00

Customer gives \$1.75

Change \$________

Change \$________

e. A book: \$3.25

f. A postcard: \$0.35

Customer gives \$4

Customer gives \$0.50

Change \$________

Change \$________

132