Lesson 4.1 Skills Practice
Name_________________________________________________________ Date__________________________
Math Football
Using Models to Understand Integers
Problem Set
Determine the ending position by adding and subtracting the indicated steps from each
© 2011 Carnegie Learning
starting position.
Starting
Position
Steps
Backward
Steps
Forward
Ending
Position
1.
13
4
5
14
2.
17
6
2
13
3.
15
2
4
17
4.
0
5
8
13
5.
24
3
7
0
6.
11
7
9
13
7.
26
1
5
22
8.
22
5
6
21
9.
8
3
1
16
10.
29
2
4
27
Chapter 4 Skills Practice • 489
Lesson 4.1 Skills Practice
page 2
Write a number sentence to describe each set of steps forward and backward.
Starting Position
Steps
Backward
Steps
Forward
11.
12
4
7
12.
27
3
5
27 1 (23) 1 5 5 25
13.
16
9
4
16 1 (29) 1 4 5 11
14.
14
6
1
14 1 (26) 1 1 5 21
15.
25
2
9
25 1 (22) 1 9 5 12
16.
0
5
3
0 1 (25) 1 3 5 22
17.
23
1
4
23 1 (21) 1 4 5 0
18.
28
2
6
28 1 (22) 1 6 5 24
19.
0
8
2
0 1 (28) 1 2 5 26
20.
19
7
8
19 1 (27) 1 8 5 110
Number Sentence
12 1 (24) 1 7 5 15
21. 19 1 (24) 1 3 5 18
22. 22 1 (25) 1 8 5 11
23. 16 1 (28) 1 5 5 13
24. 0 1 (22) 1 7 5 15
25. 29 1 (21) 1 6 5 24
26. 13 1 (26) 1 5 5 12
27. 0 1 (27) 1 9 5 12
28. 11 1 (21) 1 9 5 19
29. 25 1 (23) 1 4 5 24
30. 23 1 (22) 1 8 5 13
490 • Chapter 4 Skills Practice
© 2011 Carnegie Learning
Calculate each sum.
Lesson 4.1 Skills Practice
page 3
Name_________________________________________________________ Date__________________________
Write a number sentence to describe the results of each roll of two number cubes (numbered 1 through
6). The result of the red number cube represents a negative number and the result of the black number
cube represents a positive number.
31. Your score starts at 0. You roll a red 5 and a black 3.
0 1 (25) 1 3 5 22
32. Your score is 4. You roll a red 3 and a black 6.
14 1 (23) 1 6 5 17
33. Your score is 22. You roll a red 4 and a black 1.
22 1 (24) 1 1 5 25
34. Your score is 7. You roll a red 6 and a black 2.
17 1 (26) 1 2 5 13
35. Your score is 25. You roll a red 2 and a black 4.
25 1 (22) 1 4 5 23
© 2011 Carnegie Learning
36. Your score is 1. You roll a red 5 and a black 3.
11 1 (25) 1 3 5 21
37. Your score starts at 0. You roll a red 6 and a black 1.
0 1 (26) 1 1 5 25
38. Your score is 23. You roll a red 1 and a black 5.
23 1 (21) 1 5 5 11
Chapter 4 Skills Practice • 491
Lesson 4.1 Skills Practice
page 4
Determine a roll of two number cubes (numbered 1 through 6) that will result in a final score of 10. Write
a number sentence to describe the results of each roll. The result of the red number cube represents a
negative number and the result of the black number cube represents a positive number.
Sample answers.
Roll of the
Red Number
Cube
Roll of
the Black
Number Cube
Number Sentence
39.
17
3
6
17 1 (23) 1 6 5 110
40.
18
1
3
18 1 (21) 1 3 5 110
41.
15
1
6
15 1 (21) 1 6 5 110
42.
19
3
4
19 1 (23) 1 4 5 110
43.
112
5
3
112 1 (25) 1 3 5 110
44.
16
1
5
16 1 (21) 1 5 5 110
45.
114
6
2
114 1 (26) 1 2 5 110
46.
110
5
5
110 1 (25) 1 5 5 110
© 2011 Carnegie Learning
Starting Score
492 • Chapter 4 Skills Practice
Lesson 4.2 Skills Practice
Name_________________________________________________________ Date__________________________
Walk the Line
Adding Integers, Part I
Problem Set
Use the number line to determine the number described by each statement. Explain your reasoning.
−15
−10
−5
0
5
10
15
1. Determine the number that is 3 more than 25.
The number that is 3 more than 25 is 22. Go to 25 on the number line and then move 3 units
to the right.
2. Determine the number that is 9 more than 24.
The number that is 9 more than 24 is 5. Go to 24 on the number line and then move 9 units to
the right.
3. Determine the number that is 12 more than 28.
The number that is 12 more than 28 is 4. Go to 28 on the number line and then move 12 units
to the right.
© 2011 Carnegie Learning
4. Determine the number that is 10 more than 21.
The number that is 10 more than 21 is 9. Go to 21 on the number line and then move 10 units
to the right.
5. Determine the number that is 7 less than 3.
The number that is 7 less than 3 is 24. Go to 3 on the number line and then move 7 units
to the left.
Chapter 4 Skills Practice • 493
Lesson 4.2 Skills Practice
page 2
6. Determine the number that is 13 less than 6.
The number that is 13 less than 6 is 27. Go to 6 on the number line and then move 13 units to
the left.
7. Determine the number that is 10 less than 2.
The number that is 10 less than 2 is 28. Go to 2 on the number line and then move 10 units to
the left.
8. Determine the number that is 4 less than 1.
The number that is 4 less than 1 is 23. Go to 1 on the number line and then move 4 units
to the left.
Use the number line to determine each sum.
–3
8
9. 23 1 8 5 5 –15
–10
–5
0
5
10
15
0
5
10
15
0
5
10
15
10
15
3
–8
3 1 (28) 5 25 –15
–10
–5
–3
23 1 (28) 5 211 –15
–10
–5
3
8
3 1 8 5 11 –15
494 • Chapter 4 Skills Practice
–10
–5
0
5
© 2011 Carnegie Learning
–8
Lesson 4.2 Skills Practice
page 3
Name_________________________________________________________ Date__________________________
9
–2
10. 9 1 (22) 5 7 –15
–10
–5
0
5
10
15
0
5
10
15
–9
2
29 1 2 5 27 –15
–10
–5
9
2
9 1 2 5 11 –15
–10
–5
0
5
10
15
0
5
10
15
5
10
15
0
5
10
15
0
5
10
15
10
15
–9
–2
29 1 (22) 5 211 –15
–10
–5
–4
10
11. 24 1 10 5 6 –15
–10
–5
0
4
–10
4 1 (210) 5 26 –15
–10
–5
© 2011 Carnegie Learning
–4
–10
24 1 (210) 5 214 –15
–10
–5
4
10
4 1 10 5 14 –15
–10
–5
0
5
Chapter 4 Skills Practice • 495
Lesson 4.2 Skills Practice
page 4
5
–7
12. 5 1 (27) 5 22 –15
–10
–5
0
5
10
15
0
5
10
15
–5
7
25 1 7 5 2 –15
–10
–5
5
7
5 1 7 5 12 –15
–10
–5
0
5
10
15
0
5
10
15
0
5
10
15
0
5
10
15
–5
–7
25 1 (27) 5 212 –15
–10
–5
6
–8
13. 6 1 (28) 5 22 –15
–10
–5
–6
8
26 1 8 5 2 –15
–10
–5
6
–15
–10
–5
0
5
10
15
0
5
10
15
–6
–8
26 1 (28) 5 214 –15
496 • Chapter 4 Skills Practice
–10
–5
© 2011 Carnegie Learning
8
6 1 8 5 14 Lesson 4.2 Skills Practice
page 5
Name_________________________________________________________ Date__________________________
–12
3
14. 212 1 3 5 29 –15
–10
–5
0
5
10
15
12
–3
12 1 (23) 5 9 –15
–10
–5
0
5
10
15
0
5
10
15
–12
–3
212 1 (23) 5 215 –15
–10
–5
12
3
12 1 3 5 15 –15
–10
–5
0
5
10
15
Write the absolute values for each pair of integers and explain what they mean.
15. |4| 5 4 16. |15| 5 15 |24| 5 4 © 2011 Carnegie Learning
Each integer is 4 units from 0.
|215| 5 15 Each integer is 15 units from 0.
17. |213| 5 13 18. |7| 5 7 |13| 5 13 Each integer is 13 units from 0.
|27| 5 7 Each integer is 7 units from 0.
19. |28| 5 8 20. |9| 5 9 |8| 5 8 Each integer is 8 units from 0.
|29| 5 9 Each integer is 9 units from 0.
Chapter 4 Skills Practice • 497
Lesson 4.2 Skills Practice
page 6
Complete each number line model and then determine the unknown addend.
15
–7
21. 15 1 27 58
–15
–10
–5
0
5
10
15
5
10
15
5
10
15
5
10
15
0
5
10
15
0
5
10
15
0
5
10
15
0
5
10
15
3
–12
22. 3 1 212 5 29
–15
–10
–5
0
–4
23. 24 1 9 9
55
–15
–10
–5
0
–1
–10
24. 21 1 210 5 211
–15
–10
–5
0
6
25. 6 1 28 –8
5 22
–15
–10
–5
–13
5 27
–15
–10
–5
8
27. 8 1 211 –11
5 23
–15
–10
–5
–7
28. 27 1 23 –3
5 210
–15
498 • Chapter 4 Skills Practice
–10
–5
© 2011 Carnegie Learning
26. 213 1 6 6
Lesson 4.3 Skills Practice
Name_________________________________________________________ Date__________________________
Two-Color Counters
Adding Integers, Part II
Vocabulary
Define the term in your own words.
1. additive inverses
Additive inverses are two numbers with the sum of zero.
Problem Set
Determine each sum using the number line model or two-color counters.
1. 5 1 (25) 5 0 5
–5
–15
–10
2. (212) 1 12 5 0 –5
0
5
10
15
0
5
10
15
0
5
10
15
–12
12
© 2011 Carnegie Learning
–15
–10
–5
3. (22) 1 2 5 0 –2
2
–15
–10
–5
Chapter 4 Skills Practice • 499
Lesson 4.3 Skills Practice
page 2
4. 9 1 (29) 5 0 −
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5. 4 1 (24) 5 0 Lesson 4.3 Skills Practice
page 3
Name_________________________________________________________ Date__________________________
6. (26) 1 6 5 0 −
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Write a number sentence to represent each model. Cancel out the pairs of counters to show the
answer.
7. 2 1 (29) 5 27 or 29 1 2 5 27
8. 5 1 (21) 5 4 or 21 1 5 5 4
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© 2011 Carnegie Learning
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Chapter 4 Skills Practice • 501
Lesson 4.3 Skills Practice
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10. 3 1 (23) 5 0 or 23 1 3 5 0
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page 4
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12. 6 1 0 5 6 or 0 1 6 5 6
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502 • Chapter 4 Skills Practice
Lesson 4.3 Skills Practice
page 5
Name_________________________________________________________ Date__________________________
13. 1 1 (26) 5 25 or 26 1 1 5 25
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Draw a picture with two-color counters to represent and solve each number sentence. Cancel out the
pairs of counters to show the answer.
© 2011 Carnegie Learning
15. 29 1 3 5 26 16. 23 1 9 5 6 −
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Chapter 4 Skills Practice • 503
Lesson 4.3 Skills Practice
17. 29 1 (23) 5 212 page 6
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504 • Chapter 4 Skills Practice
Lesson 4.3 Skills Practice
page 7
Name_________________________________________________________ Date__________________________
21. 211 1 7 5 24 −
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22. 27 1 11 5 4 +
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23. 211 1 (27) 5 218 24. 25 1 12 5 7 −
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© 2011 Carnegie Learning
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Chapter 4 Skills Practice • 505
Lesson 4.3 Skills Practice
page 8
Complete each model and determine the unknown addend. Circle all of the zero pair counters to show
the answer.
26. 24 1 7 56
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25. 8 1 22 Lesson 4.3 Skills Practice
page 9
Name_________________________________________________________ Date__________________________
29. 23 1 25 30. 25 1 5 5 28
50
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Determine each sum.
31. 242 1 79 5 37 32. 219 1 19 5 0 33. 29 1 (238) 5 29 34. 117 1 (299) 5 18 35. 286 1 51 5 235 36. 243 1 80 5 37 37. 237 1 (264) 5 2101 38. 2106 1 78 5 228 © 2011 Carnegie Learning
Determine each unknown addend.
39. 259 1 41 5 218
40. 256 1 228 5 284
41. 262 1 71 5 9
42. 30 1 260 43. 16 1 249 44. 35 45. 212 5 233
1 25 5 13
5 230
1 (214) 5 21
46. 249 1 32 5 217
Chapter 4 Skills Practice • 507
© 2011 Carnegie Learning
508 • Chapter 4 Skills Practice
Lesson 4.4 Skills Practice
Name_________________________________________________________ Date__________________________
What’s the Difference?
Subtracting Integers
Vocabulary
Define the term in your own words.
1. zero pair
Using two-color counters, a zero pair is a pair consisting of one positive counter and one
negative counter. The sum of the counters in a zero pair is equal to zero.
Problem Set
Draw two other models to represent each integer.
1. 23
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© 2011 Carnegie Learning
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Chapter 4 Skills Practice • 509
Lesson 4.4 Skills Practice
page 2
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© 2011 Carnegie Learning
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Lesson 4.4 Skills Practice
page 3
Name_________________________________________________________ Date__________________________
Complete the two-color counter model for each subtraction problem. Circle the subtracted portion and
write the difference.
7. 23 2 6 5 29 −
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8. 23 2 (26) 5 3 Chapter 4 Skills Practice • 511
Lesson 4.4 Skills Practice
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512 • Chapter 4 Skills Practice
Lesson 4.4 Skills Practice
page 5
Name_________________________________________________________ Date__________________________
Draw a number line model to solve each subtraction problem.
15. 25 2 7 5 212 –5
–(+7)
–15
–12 –10
–5
16. 25 2 (27) 5 2 0
5
10
15
5
10
15
5
10
15
–5
–(–7)
–15
–10
–5
0
2
17. 5 2 7 5 22 +5
–(+7)
–15
–10
–5
–2
0
18. 5 2 (27) 5 12 +5
–(–7)
–15
–10
–5
0
19. 3 2 (211) 5 14 5
10
12
15
+3
–(–11)
–15
–10
–5
0
5
10
14 15
0
5
10
15
0
5
10
15
10
15
20. 3 2 11 5 28 +3
–(+11)
© 2011 Carnegie Learning
–15
–10
–8
–5
21. 23 2 11 5 214 –3
–(+11)
–15 –14
–10
–5
22. 23 2 (211) 5 8 –3
–(–11)
–15
–10
–5
0
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8
Chapter 4 Skills Practice • 513
Lesson 4.4 Skills Practice
page 6
Rewrite each subtraction expression using addition. Then calculate the result.
23. 13 2 (29) 5 13 1 9 5 22 24. 222 2 15 5 222 1 215 5 237 25. 31 2 17 5 31 1 217 5 14 26. 210 2 (28) 5 210 1 8 27. 5 2 (216) 5 5 1 16 28. 14 2 23 5 14 5 22 5 21 1 223 5 29 29. 220 2 (232) 5 220 1 32 30. 22 2 19 5 22 1 219 5 12 5 221 Determine the unknown integer in each number sentence.
2 (26) 5 27
32. 33 1 (26) 5 27
33. 221 2 6 5 227
34. 4 2 (227) 5 31
35. 4 2 35 5 231
36. 28 1 (230) 5 238
37. 8 2 46 38. 28 1 46 5 38
5 238
39. 62 1 (212) 5 50
40. 38 2 (212) 5 50
Determine each absolute value.
41. |5 2 9| 5 4 42. |25 2 9| 5 14 43. |5 2 (29)| 5 14 44. |25 2 (29)| 5 4 45. |27 2 15| 5 22 46. |7 2 (215)| 5 22 47. |27 2 (215)| 5 8 48. |7 2 15| 5 8 514 • Chapter 4 Skills Practice
© 2011 Carnegie Learning
31. 21 Lesson 4.5 Skills Practice
Name_________________________________________________________ Date__________________________
What Do We Do Now?
Adding and Subtracting Rational Numbers
Problem Set
Calculate each sum.
​ 3 ​1 5__
​ 1 ​5
1. 2__
8
4
2 ​ 5
1 ​ 1 4​ __
2. 7​ __
6
3
1  ​1 4​ __
5 ​ 
2 ​ 5 11​ __
7​ __
3
6
6
3  ​1 5​ __
5 ​ 
1 ​ 5 7​ __
2​ __
4
8
8
3 ​ 5 2​ __
3 ​ 
2​ __
8
8
1 ​ 5 7​ __
1 ​ 
7​ __
6
6
1  ​5 5​ __
2 ​ 
15​ __
4
8
2 ​ 5 4​ __
4 ​ 
14​ __
3
6
5 ​ 
7​ __
8
5  ​
11​ __
6
(  )
3  ​ 
2 ​ 1 ​ 23​ __
1 ​   ​5 9​ ___
12​ __
5 (
4)
20
1 ​  ​5
2  ​1 ​23​ __
3. 12​ __
5
4
© 2011 Carnegie Learning
8  ​ 
2  ​5 12​ ___
12​ __
5
20
5  ​ 
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23​ __
4
20
4. 5.3 1 (27.45) 5
5.3 1 (27.45) 5 22.15
7.45
25.3
2.15
3  ​ 
9​ ___
20
Chapter 4 Skills Practice • 515
Lesson 4.5 Skills Practice
5
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page 2
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5)
5 (
2 ​ 1 ​22​ __
3 ​   ​5
7. 23​ __
5
5
8. 218.76 1 (211.23) 5
218.76 1 (211.23) 5 229.99
118.76
2  ​
3​ __
5
111.23
29.99
3 ​ 
12​ __
5
(  )
2 ​   ​5 8​ ___
7  ​ 
1 ​ 1 ​ 25​ __
14​ __
4 (
3)
12
2 ​   ​5
1 ​ 1 ​25​ __
9. 14​ __
4
3
1  ​5 14​ ___
3  ​ 5 13​ ___
15 ​ 
14​ __
12
12
4
8  ​ 
2  ​5 5​ ___
25​ __
3
12
7  ​ 
8​ ___
12
516 • Chapter 4 Skills Practice
10. 220.245 115.12 5
220.245 1 15.12 5 25.125
20.245
215.12
5.125
© 2011 Carnegie Learning
5  ​5 6
5 ​ __
5
Lesson 4.5 Skills Practice
page 3
Name_________________________________________________________ Date__________________________
Calculate each difference.
​ 3 ​2 5__
​ 1 ​5 11. 2__
8
4
12. 28.38 211.29 5
3  ​2 5​ __
1 ​ 5 22​ __
7 ​ 
2​ __
4
8
8
10 ​ 
1  ​5 5​ __
2 ​ 5 4​ ___
5​ __
4
8
8
3 ​ 5
22​ __
8
3 ​ 
2​ __
8
28.38 2 11.29 5 219.67
11.29
18.38
19.67
7 ​ 
2​ __
8
(  )
2 ​  2 ​ 24​ __
1 ​   ​5 7​ __
2 ​ 1 4​ __
1 ​ 5 11​ ___
11  ​
7​ __
4)
4
3 (
3
12
​ 2 ​2 ​24__
​ 1 ​ ​5
13. 7__
3
4
8  ​ 
2  ​5 7​ ___
7​ __
3
12
3  ​ 
1  ​5 4​ ___
14​ __
4
12
14. 32.85 2 (210.65) 5
32.85 2 (210.65) 5 32.85 1 10.65 5 43.50
32.85
110.65
43.50
© 2011 Carnegie Learning
11 ​ 
11​ ___
12
5  ​2 6​ __
2 ​ 5
15. 24​ __
6
3
5 ​ 2 6​ __
2 ​ 5 211​ __
1 ​ 
24​ __
6
3
2
5  ​5 4​ __
5 ​ 
4​ __
6
6
2 ​  5 6​ __
4 ​ 
16​ __
3
6
16. 219.01 2 10.91 5
219.01 2 10.91 5 229.92
19.01
110.91
29.92
9 ​  5 11​ __
3 ​ 5 11​ __
1 ​ 
10​ __
6
6
2
Chapter 4 Skills Practice • 517
Lesson 4.5 Skills Practice
(  )
9  ​ 
1  ​  ​5 23​ __
1 ​ 1 5​ ___
1  ​ 5 1​ ___
1 ​ 2 ​ 25​ ___
23​ __
5 (
5
10 )
10
10
1 ​ 2 ​25​ ___
1  ​  ​5
17. 23​ __
5
10
1  ​ 5 4​ ___
11 ​ 
5​ ___
10
10
1  ​5 3​ ___
2  ​ 
23​ __
5
10
page 4
18. 26.2 2 (23.82) 5
26.2 2 (23.82) 5 26.2 1 3.82 5 22.38
6.2
23.82
2.38
9  ​ 
1​ ___
10
(  )
5 ​ 1 2​ __
5 ​ 2 ​ 22​ __
1 ​   ​5 10​ __
1 ​ 5 13​ __
1 ​ 
10​ __
6 (
3)
6
3
6
5  ​2 ​22​ __
1 ​   ​5 19. 10​ __
6
3
5 ​ 5 10​ __
5 ​ 
10​ __
6
6
1 ​  5 2​ __
2 ​ 
12​ __
6
3
20. 217.538 2 12.371 5
217.538 2 12.371 5 229.909
17.538
112.371
29.909
© 2011 Carnegie Learning
7  ​5 13 ​ __
1 ​ 
12​ __
6
6
518 • Chapter 4 Skills Practice
Lesson 4.5 Skills Practice
page 5
Name_________________________________________________________ Date__________________________
Add or subtract using your algorithms.
3 ​ 1 ​2​ __
5 ​  ​5 21 ​  5  ​
22. 2​ __
24
8
6
23. 20.108 2 (24.3) 5 4.192 24. 2719 2 (2698) 5 221 ___ 
4 ​ 2 1​ __
1 ​ 5 23 ​ 23  ​
25. 22​ __
7
4 28
© 2011 Carnegie Learning
(  ) ___ 
20   ​​5 2​ ___
9   ​1 ​ 2​ ___
29  ​ 
2​ ___
24 ( 24 )
24
5 21​___
  5  ​ 
24
21. 4.76 2 (22.91) 5 7.67 26. 2824 1 970 5 146 16  ​
4  ​5 2​ ___
2​ __
7
28
1  ​5 1​ ___
7  ​ 
11​ __
4
28
23 ​ 
3​ ___
28
Chapter 4 Skills Practice • 519
Lesson 4.5 Skills Practice
27. 3.862 1 (27.4) 5 23.538 page 6
___ 
7  ​ 2 6​ __
2 ​  5 22 ​  1  ​
28. 4​ ___
3
11
33
 22  ​
6​__
 2 ​5 6​___
3
33
7  ​ 5 4​___
24​ ___
 21  ​
11
33
2​___
  1  ​ 
33
29. 25.5 1 18.002 5 12.502 (  )
___ 
13 ​ 1 ​ __
​  4  ​
30.​ ___
2​ 7  ​ ​5 45
9
15
___  ( 
) ___ 
© 2011 Carnegie Learning
35
​ 39  ​1 ​ 2___
​    ​ ​5 ​  4  ​
45
45
45
520 • Chapter 4 Skills Practice