ANSWER KEY Grades 3-5
Chapter One: Addition and Subtraction Concepts
Total and Parts 1
Part A
3 + 5 + 4 = 12
8 + 1 + 3 = 12
6 + 4 + 2 = 12
Part B
4+3+2=9
5 + 1 + 4 = 10
3 + 8 + 6 =17
Total and Parts 2
Part A
2 + 2 + 6 = 10
3 + 3 + 4 = 10
5 + 3 + 2 = 10
Part B
2+2+4=8
6 + 3 + 3 = 12
2 + 5 + 3 = 10
Counting On and Counting Back 1
Part A
David won with a score of 50
Kolby lost with a score of 49
Part B
48 + 4 – 5 + 3 = 50
52 + 2 – 4 – 1 = 49
Counting on and Counting Back 2
Part A
Kirkland lost with a score of 48
Joey won with a score of 50
Part B
47 + 3 – 1 + 3 = 48 or 47 – 3 + 1 + 3 = 50
54 + 2 – 4 – 2 = 50 or 54 – 2 – 4 + 2 = 50
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Joining Sets 1
Part A
Various equations with three addends that equal 12
Part B
Swing
Slide
Jump Rope
Soccer
4
2
3
3
Joining Sets 2
Part A
Various equations with three addends that equal 12
Part B
Swing
Slide
Jump Rope
Soccer
4
2
3
3
10
5
1
1
2
1
7
7
Number Line Proficiency 1
Part A
65 66 67 68 69 70 71 72 73 74
Part B
60 70 80 90 100 110 120 130 140 150
Counting by multiples of ten.
Number Line Proficiency 2
Part A
72 73 74 75 76 77 78 79 80 81
Part B
35 40 45 50 55 60 65 70 75 80
Counting by multiples of five.
Take Away Subtraction 1
Part A
35 – 3 = 32 or 40 – 8 = 32
22 – 2 = 20 or 40 – 20 = 20
Part B
Hungry Frog eats a total of 26 flies in the first week. 5 + 3 + 4 + 6 + 2 + 5 + 1 = 26
There are 14 flies left because 40 – 26 = 14
Hungry frog eats 13 flies the next week because half of 26 is 13.
There will be 1 fly left because 14 – 13 = 1
©2016, Taylor and Francis
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Take Away Subtraction 2
Part A
44 – 3 = 41 or 50 – 9 = 41
34 – 4 – 30 or 50 – 20 = 30
Part B
Hungry Frog eats a total of 22 flies in the first week. 2 + 4 + 3 + 5 + 2 + 4 + 2 = 22
There are 28 flies left because 50 – 22 = 28
Hungry frog eats 22 flies the next week.
There will be 6 flies left because 28 – 22 = 6
Missing Part Subtraction 1
Part A
18 – 6 = 12
18 – 8 = 10
18 – 13 = 5
18 – 7 = 11
18 – 3 = 15
18 – 4 = 14
18 – 2 = 16
Part B
18 – 1 = 17
18 – 9 = 9
Missing Part Subtraction 2
Part A
20 – 15 = 5
20 – 10 = 10
20 – 13 = 7
20 – 17 = 3
20 – 12 = 8
20 – 14 = 6
20 – 19 = 1
Part B
20 – 18 = 2
20 – 16 = 4
20 – 11 = 9
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Comparison Subtraction 1
Part A
12 – 4 – 8
15 – 9 = 6
Part B
Joey’s fish compared to Kolby’s fish 12 – 9 = 3
Kirkland’s fish compared to Joey’s fish  15 – 12 = 3
Comparison Subtraction 2
Part A
11 – 9 = 2
16 – 7 = 9
Part B
Mac’s fish compared to Lilly’s fish 16 – 5 = 11
Adding and Subtracting Tens 1
Part A
25, 35, 37, 47, 48, 49, 59
Part B
36 – 1 = 35
33 – 10 = 25
36 + 1 = 37
37 + 10 = 47
47 + 1 = 48
48 + 1 = 49
49 +10 = 59
Adding and Subtracting Tens 2
Part A
42, 52, 54, 64, 65, 66, 76
Part B
53 – 1 = 52
52 – 10 = 42
53 + 1 = 54
54 + 10 = 64
64 + 1 = 65
65 + 1 = 66
66 + 10 =76
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Adding Doubles and Near Doubles 1
Part A
12, 4, 10
Part B
No. I do not agree with James.
7 + 8 = 15 because 8 + 8 = 16 and 16 – 1 = 15
Adding Doubles and Near Doubles 2
Part A
10, 6, 8
Part B
Yes. I agree with Kirk.
Fact Families—Addition and Subtraction 1
Part A
4 + 8 = 12
Part B
Answers may vary, but should include 2 related addition and 2 related subtraction facts. For
example, 9 + 3 = 12, 3 + 9 = 12, 12 – 3 = 9, 12 – 9 = 3
Fact Families—Addition and Subtraction 2
Part A
11 – 5 = 6
Part B
Answers may vary, but should include 2 related addition and 2 related subtraction facts. For
example, 7 + 4 = 11, 4 + 7 = 11, 11 – 4 = 7, 11 – 7 = 4
Partial Sums 1
Part A
39 + 25 = 50 + 14
Part B
28 + 45 = 60 + 13
Partial Sums 1
Part A
28 + 17 = 30 + 15
Part B
21 + 33 = 50 + 4
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Partial Differences 1
Part A
84 – 37 = 50 – 3
Part B
84 – 39 = 50 – 5
Partial Differences 2
Part A
73 – 45 = 30 – 2
Part B
73 – 49 = 30 – 6
Near Tens for Addition and Subtraction 1
Part A
56 – 39 = 56 – 40 + 1
Part B
Erasers 83 – 59 = 83 – 60 + 1
Notebooks 34 – 29 = 34 – 30 + 1
Near Tens for Addition and Subtraction 2
Part A
73 – 49 = 73 – 50 + 1
Part B
Erasers 92 – 69 = 92 – 70 + 1
Notebooks 58 – 39 = 58 – 40 + 1
Equal Differences 1
Part A
Kayla is correct.
Markings on number line may vary but should include the equal differences.
Part B
62 – 39 = 63 – 40
Part C
73 – 41 = 72 – 40
Equal Differences 2
Part A
Joey is correct.
Markings on number line may vary but should include the equal differences.
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Part B
86 – 39 = 87 – 40
Part C
65 – 31 = 64 – 30
Chapter Two: Multiplication and Division Concepts
Repeated Addition Multiplication 1
Part A
8+8+8+8+8
5x8
Part B
5 x 6 = 30
Repeated Addition Multiplication 2
Part A
9+9+9+9+9
5 x 8 = 40
Part B
Repeated Subtraction Division 1
Part A
24 ÷ 8 = 3
24 – 6 – 6 – 6 – 6 = 0
24 – 12 – 12 = 0
Part B
20 ÷ 4 = 5
20 ÷ 5 = 4
20 ÷ 10 = 2
20 ÷ 2 = 10
Repeated Subtraction Division 2
Part A
30 ÷ 3 = 10
30 – 15 – 15 = 0
30 ÷ 10 = 3
30 – 6 – 6 – 6 – 6 – 6 = 0
Part B
18 ÷ 2 = 9
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18 ÷ 9 = 2
18 ÷ 3 = 6
18 ÷ 6 = 3
Fair Shares Division 1
Part A
50 ÷ 2 = 25
50 ÷ 5 = 10
50 ÷ 10 = 5
50 ÷ 25 = 5
Part B
Agree
60 ÷ 5 = 12
Fair Shares Division 2
Part A
40 ÷ 2 = 20
40 ÷ 4 = 10
40 ÷ 10 = 4
40 ÷ 20 = 2
40 ÷ 8 = 5
40 ÷ 5 = 8
Part B
Agree
42 ÷ 6 = 7
Rectangular Arrays for Multiplication and Division 1
Part A
6 logs with 3 frogs on each log  Total number of frogs is 18
or
3 logs with 6 frogs on each log  Total number of frogs is 18
Part B
Array should represent 12 x 2 = 24 or 6 x 4 = 24
Rectangular Arrays for Multiplication and Division 2
Part A
5 logs with 4 frogs on each log  Total number of frogs is 20
or
4 logs with 5 frogs on each log  Total number of frogs is 20
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Part B
Array should represent 14 x 3 = 42 or 7 x 6 = 42
Multiplying and Dividing by Ten 1
Part A
50, 30, 90, 70
Part B
7, 5, 6
70 ÷ 10 = 7
50 ÷ 10 = 5
60 ÷ 10 = 6
Multiplying and Dividing by Ten 2
Part A
60, 40, 90, 80
Part B
8, 2, 3
80 ÷ 10 = 8
20 ÷ 10 = 2
30 ÷ 10 = 3
Perfect Squares and Near Perfect Squares 1
Part A
25, 16, 49
Part B
No. 6 x 7 = 42 because perfect square 6 x 6 and one more group of 6 is 42
Perfect Squares and Near Perfect Squares 2
Part A
16, 49, 64
Part B
Yes. 7 x 8 = 56 because perfect square 7 x 7 and one more group of 7 is 56
Near Tens for Multiplication 1
Part A
9 x 8 = (10 x 8) – (1 x 8)
Part B
9 x 7 = (10 x 7) – (1 x 7)
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Part C
72 + 63 = 135
Near Tens for Multiplication 2
Part A
9 x 6 = (10 x 6) – (1 x 6)
Part B
9 x 9 = (10 x 9) – (1 x 9)
Part C
81 + 54 = 135
Fact Families—Multiplication and Division 1
Part A
6 x 7 = 42
Part B
1 x 42 = 42
42 x 1 = 42
42 ÷ 1 = 42
42 ÷ 42 = 1
or
2 x 21 = 42
21 x 2 = 42
42 ÷ 21 = 2
42 ÷ 2 = 21
or
3 x 14 = 42
14 x 3 = 42
42 ÷ 14 = 3
42 ÷ 3 = 14
Part C
Answers may vary but should include something related to inverse operations.
Fact Families—Multiplication and Division 2
Part A
6 x 8 = 48
Part B
1 x 48 = 48
48 x 1 = 48
48 ÷ 1 = 48
48 ÷ 48 = 1
©2016, Taylor and Francis
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or
2 x 24 = 48
24 x 2 = 48
48 ÷ 24 = 2
42 ÷ 2 = 24
or
3 x 16 = 48
16 x 3 = 48
48 ÷ 16 = 3
48 ÷ 3 = 16
or
4 x 12 = 48
12 x 4 = 48
48 ÷ 12 = 3
48 ÷ 4 = 12
Part C
Answers may vary.
Partial Products 1
Part A
21 + 280 + 60 + 800
Part B
(40 x 20) + (20 x 7) + (40 x 7) + (7 x 7)
Partial Products 2
Part A
(30 x 50) + (30 x 7) + (2 x 50) + (2 x 7)
Part B
(30 x 50) + (30 x 9) + (2 x 50) + (2 x 9)
Partial Quotients 1
Part A
19 bags
Part B
$12.00
Partial Quotients 2
Part A
17 bags
Part B
$10.50
©2016, Taylor and Francis
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Equal Products 1
Part A
6 x 35 = 3 x 70
Part B
Agree.
12 x 75 = 6 x 150 (double and half once)
6 x 150 = 3 x 300 (double and half two twice)
Equal Products 2
Part A
4 x 55 = 2 x 110
Part B
Agree.
8 x 45 = 4 x 90 (double and half once)
4 x 90 = 2 x 180 (double and half two twice)
Chapter Three: Multifaceted Number Concepts
Expanded Form 1
Part A
(5 x 100) + (7 x 100) + (9 x 10) + (1 x 3)
5,000 + 700 + 30 + 9
Part B
9,753 = (9 x 1,000) + (7 x 100) + (5 x 10) + (3 x 1)
3,579 = (3 x 1,000) + (5 x 100) + (7 x 10) + (9 x 1)
Expanded Form 2
Part A
7,000 + 900 + 80 + 6
(7 x 100) + (9 x 100) + (6 x 10) + (1 x 8)
Part B
9,876 = (9 x 1,000) + (8 x 100) + (7 x 10) + (6 x 1)
6,789 = (6 x 1,000) + (7 x 100) + (8 x 10) + (9 x 1)
Thousands and Millions 1
Part A
927,854,301
Part B
Answers will vary
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Thousands and Millions 2
Part A
738,965,412
Part B
Answers will vary
Commutative and Associative Properties 1
Part A
(7 x 3) x 2 = 7 x (3 x 2)
(3 x 7) x 2 = 3 x (7 x 2)
Part B
No.
(100 ÷ 2) – 23 = 27
100 ÷ (2 – 23) ≠ 27
Commutative and Associative Properties 2
Part A
4 x 14 = 14 x 4
Part B
Yes.
12 + 14 + (15 x 2) = 56
(2 x 15) + 14 + 12 = 56
Prime and Composite Numbers 1
Part A
42, 6
Part B
42
21 2
7 3
42
14 3
7 2
Part C
1 x 42
2 x 21
3 x 14
6x7
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Prime and Composite Numbers 2
Part A
24, 6, 4
Part B
24
12 2
6 2
23
24
6 4
3 2 22
24
8 3
4 2
22
Part C
1 x 24
2 x 12
3x8
6x4
Finding Common Multiples 1
Part A
9
Part B
18, 27, 36, 45, 54, 63, . .
Answers may vary, for example
3 x 6 = 18 9 x 2 = 18
3 x 9 = 27 9 x 3 = 27
3 x 12 = 36 9 x 4 = 36
3 x 15 = 45 9 x 5 = 45
3 x 18 = 54 9 x 6 = 54
3 x 21 = 63 9 x 7 = 63
Part C
11, 12
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Finding Common Multiples 2
Part A
12
Part B
24, 36, 48, 60, 72, 84, . . .
Answers may vary, for example
4 x 6 = 24 6 x 4 = 24
6 x 6 = 36 4 x 9 = 36
6 x 8 = 48 4 x 12 = 48
6 x 10 = 60 4 x 15 = 60
6 x 12 = 72 4 x 18 = 72
6 x 14 = 84 4 x 21 = 84
Part C
11, 7
Finding Common Factors 1
Part A
Total People
Male Crabs
Female Crabs
1
2
4
5
10
20
40
20
10
8
4
2
20
10
5
4
2
1
Part B
7 trays
Each tray has 3 extra large crabs and 7 large crabs
3 x 7 = 21 7 x 7 = 49
Finding Common Factors 2
Part A
Total People
Male Crabs
Female Crabs
1
2
3
5
10
30
30
15
10
6
3
1
60
30
20
12
6
2
©2016, Taylor and Francis
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Part B
5 trays
Each tray has 3 extra large crabs and 10 large crabs
5 x 3 = 15 5 x 10 = 50
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