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
3.
15
2
4
4.
0
5
8
5.
24
3
7
6.
11
7
9
7.
26
1
5
8.
22
5
6
9.
8
3
1
10.
29
2
4
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
13.
16
9
4
14.
14
6
1
15.
25
2
9
16.
0
5
3
17.
23
1
4
18.
28
2
6
19.
0
8
2
20.
19
7
8
Number Sentence
12 1 (24) 1 7 5 15
21. 19 1 (24) 1 3 5 18
22. 22 1 (25) 1 8 5
23. 16 1 (28) 1 5 5
24. 0 1 (22) 1 7 5
25. 29 1 (21) 1 6 5
26. 13 1 (26) 1 5 5
27. 0 1 (27) 1 9 5
28. 11 1 (21) 1 9 5
29. 25 1 (23) 1 4 5
30. 23 1 (22) 1 8 5
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.
33. Your score is 22. You roll a red 4 and a black 1.
34. Your score is 7. You roll a red 6 and a black 2.
35. Your score is 25. You roll a red 2 and a black 4.
© 2011 Carnegie Learning
36. Your score is 1. You roll a red 5 and a black 3.
37. Your score starts at 0. You roll a red 6 and a black 1.
38. Your score is 23. You roll a red 1 and a black 5.
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
41.
15
42.
19
43.
112
44.
16
45.
114
46.
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.
3. Determine the number that is 12 more than 28.
© 2011 Carnegie Learning
4. Determine the number that is 10 more than 21.
5. Determine the number that is 7 less than 3.
Chapter 4 Skills Practice • 493
Lesson 4.2 Skills Practice
page 2
6. Determine the number that is 13 less than 6.
7. Determine the number that is 10 less than 2.
8. Determine the number that is 4 less than 1.
Use the number line to determine each sum.
–3
9. 23 1 8 5
8
5 –15
–10
–5
0
5
10
15
–15
–10
–5
0
5
10
15
–15
–10
–5
0
5
10
15
–15
–10
–5
0
5
10
15
3 1 (28) 5
3185
494 • Chapter 4 Skills Practice
© 2011 Carnegie Learning
23 1 (28) 5
Lesson 4.2 Skills Practice
page 3
Name_________________________________________________________ Date__________________________
10. 9 1 (22) 5
–15
–10
–5
0
5
10
15
–15
–10
–5
0
5
10
15
–15
–10
–5
0
5
10
15
–15
–10
–5
0
5
10
15
–15
–10
–5
0
5
10
15
–15
–10
–5
0
5
10
15
–15
–10
–5
0
5
10
15
–15
–10
–5
0
5
10
15
29 1 2 5
9125
29 1 (22) 5
11. 24 1 10 5
© 2011 Carnegie Learning
4 1 (210) 5
24 1 (210) 5
4 1 10 5
Chapter 4 Skills Practice • 495
Lesson 4.2 Skills Practice
page 4
12. 5 1 (27) 5
–15
–10
–5
0
5
10
15
–15
–10
–5
0
5
10
15
–15
–10
–5
0
5
10
15
–15
–10
–5
0
5
10
15
–15
–10
–5
0
5
10
15
–15
–10
–5
0
5
10
15
–15
–10
–5
0
5
10
15
–15
–10
–5
0
5
10
15
25 1 7 5
5175
25 1 (27) 5
13. 6 1 (28) 5
26 1 8 5
26 1 (28) 5
496 • Chapter 4 Skills Practice
© 2011 Carnegie Learning
6185
Lesson 4.2 Skills Practice
page 5
Name_________________________________________________________ Date__________________________
14. 212 1 3 5
–15
–10
–5
0
5
10
15
–15
–10
–5
0
5
10
15
–15
–10
–5
0
5
10
15
–15
–10
–5
0
5
10
15
12 1 (23) 5
212 1 (23) 5
12 1 3 5
Write the absolute values for each pair of integers and explain what they mean.
15. |4| 5
|24| 5
16. |15| 5
4
4
|215| 5
© 2011 Carnegie Learning
Each integer is 4 units from 0.
17. |213| 5
18. |7| 5
|13| 5
|27| 5
19. |28| 5
20. |9| 5
|8| 5
|29| 5
Chapter 4 Skills Practice • 497
Lesson 4.2 Skills Practice
page 6
Complete each number line model and then determine the unknown addend.
15
21. 15 1
–7
27 58
–15
–10
–5
0
5
10
15
0
5
10
15
0
5
10
15
5
10
15
0
5
10
15
0
5
10
15
0
5
10
15
0
5
10
15
3
22. 3 1
5 29
–15
–10
–5
–4
23. 24 1
55
–15
–10
–5
–1
24. 21 1
5 211
–15
–10
–5
0
6
25. 6 1
5 22
–15
–10
–5
–13
5 27
–15
–10
–5
8
27. 8 1
5 23
–15
–10
–5
–7
28. 27 1
5 210
–15
498 • Chapter 4 Skills Practice
–10
–5
© 2011 Carnegie Learning
26. 213 1
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
Problem Set
Determine each sum using the number line model or two-color counters.
1. 5 1 (25) 5
0
5
–5
–15
–10
–5
0
5
10
15
–15
–10
–5
0
5
10
15
–15
–10
–5
0
5
10
15
© 2011 Carnegie Learning
2. (212) 1 12 5
3. (22) 1 2 5
Chapter 4 Skills Practice • 499
Lesson 4.3 Skills Practice
page 2
4. 9 1 (29) 5
© 2011 Carnegie Learning
5. 4 1 (24) 5
500 • Chapter 4 Skills Practice
Lesson 4.3 Skills Practice
page 3
Name_________________________________________________________ Date__________________________
6. (26) 1 6 5
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.
−
−
+
© 2011 Carnegie Learning
+
−
−
−
+
+
−
−
+
−
+
−
+
−
Chapter 4 Skills Practice • 501
Lesson 4.3 Skills Practice
10.
+
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9.
page 4
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11.
12.
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+
© 2011 Carnegie Learning
502 • Chapter 4 Skills Practice
Lesson 4.3 Skills Practice
page 5
Name_________________________________________________________ Date__________________________
13.
14.
−
−
−
−
−
−
+
−
−
+
+
−
−
−
+
+
+
−
−
−
+
+
+
+
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
16. 23 1 9 5
26 −
−
−
+
−
−
−
+
−
−
−
+
Chapter 4 Skills Practice • 503
Lesson 4.3 Skills Practice
page 6
17. 29 1 (23) 5
18. 2 1 (25) 5
19. 5 1 (22) 5
20. 2 1 5 5
© 2011 Carnegie Learning
504 • Chapter 4 Skills Practice
Lesson 4.3 Skills Practice
page 7
Name_________________________________________________________ Date__________________________
21. 211 1 7 5
22. 27 1 11 5
© 2011 Carnegie Learning
23. 211 1 (27) 5
24. 25 1 12 5
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.
+
+
+
+
+
+
+
+
−
5 22
−
−
−
−
−
−
−
−
−
−
53
−
27. 210 1
26. 24 1
56
22 506 • Chapter 4 Skills Practice
−
−
−
−
28. 13 1
56
+
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+
© 2011 Carnegie Learning
25. 8 1
Lesson 4.3 Skills Practice
page 9
Name_________________________________________________________ Date__________________________
29. 23 1
5 28
30. 25 1
50
−
−
−
−
−
−
−
−
Determine each sum.
31. 242 1 79 5
37 32. 219 1 19 5
33. 29 1 (238) 5
34. 117 1 (299) 5
35. 286 1 51 5
36. 243 1 80 5
37. 237 1 (264) 5
38. 2106 1 78 5
© 2011 Carnegie Learning
Determine each unknown addend.
39.
259 41. 262 1
43. 16 1
45.
1 41 5 218
59
5 233
1 25 5 13
40. 256 1
42. 30 1
44.
46. 249 1
5 284
5 230
1 (214) 5 21
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
Problem Set
Draw two other models to represent each integer.
1. 23
−
−
−
−
−
−
+
−
+
−
−
+
−
+
−
−
+
−
−
+
+
+
+
© 2011 Carnegie Learning
2. 4
Chapter 4 Skills Practice • 509
Lesson 4.4 Skills Practice
page 2
3. 2
+
+
−
−
4. 25
−
−
−
5. 1
+
© 2011 Carnegie Learning
6. 0
510 • Chapter 4 Skills Practice
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
−
+
−
−
+
+
−
−
+
+
−
+
−
−
−
8. 23 2 (26) 5
29 −
−
−
9. 9 2 (25) 5
+
+
10. 29 2 5 5
+
−
+
−
+
© 2011 Carnegie Learning
+
+
−
+
−
+
−
−
−
−
−
Chapter 4 Skills Practice • 511
Lesson 4.4 Skills Practice
+
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13. 4 2 8 5
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−
12. 27 2 2 5
−
11. 7 2 (22) 5
page 4
14. 4 2 (28) 5
+
+
+
+
+
+
+
+
© 2011 Carnegie Learning
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
–5
212
–(+7)
–15
–12 –10
–5
0
5
10
15
–15
–10
–5
0
5
10
15
–15
–10
–5
0
5
10
15
–15
–10
–5
0
5
10
15
–15
–10
–5
0
5
10
15
–15
–10
–5
0
5
10
15
–10
–5
0
5
10
15
–10
–5
0
5
10
15
16. 25 2 (27) 5
17. 5 2 7 5
18. 5 2 (27) 5
19. 3 2 (211) 5
20. 3 2 11 5
© 2011 Carnegie Learning
21. 23 2 11 5
–15
22. 23 2 (211) 5
–15
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 9 1
24. 222 2 15 5
1
25. 31 2 17 5
5
1
26. 210 2 (28) 5
5
1
27. 5 2 (216) 5
1
28. 14 2 23 5
29. 220 2 (232) 5
5
5
1
5
1
30. 22 2 19 5
22 5
1
5
5
Determine the unknown integer in each number sentence.
21 33.
2 (26) 5 27
32.
2 6 5 227
34. 4 2
1 (26) 5 27
5 31
35. 4 2
5 231
36. 28 1
5 238
37. 8 2
5 238
38. 28 1
5 38
39.
1 (212) 5 50
40.
2 (212) 5 50
Determine each absolute value.
41. |5 2 9| 5
4 42. |25 2 9| 5
43. |5 2 (29)| 5
44. |25 2 (29)| 5
45. |27 2 15| 5
46. |7 2 (215)| 5
47. |27 2 (215)| 5
48. |7 2 15| 5
514 • Chapter 4 Skills Practice
© 2011 Carnegie Learning
31.
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
3  ​1 5​ __
5 ​ 
1 ​ 5 7​ __
2​ __
4
8
8
3 ​ 5 2​ __
3 ​ 
2​ __
8
8
1  ​5 5​ __
2 ​ 
15​ __
4
8
5 ​ 
7​ __
8
( 
)
4. 5.3 1 (27.45) 5
© 2011 Carnegie Learning
1 ​  ​5
2  ​1 ​23​ __
3. 12​ __
5
4
Chapter 4 Skills Practice • 515
Lesson 4.5 Skills Practice
5
3 ​ 5
5. 2​ __ ​ 1 8​ __
8
8
(  )
2 ​ 1 ​22​ __
3 ​   ​5
7. 23​ __
5
5
page 2
6. 29.21 1 10.39 5
8. 218.76 1 (211.23) 5
(  )
2 ​   ​5
1 ​ 1 ​25​ __
9. 14​ __
4
3
516 • Chapter 4 Skills Practice
10. 220.245 115.12 5
© 2011 Carnegie Learning
1
Lesson 4.5 Skills Practice
page 3
Name_________________________________________________________ Date__________________________
Calculate each difference.
​ 3 ​2 5__
​ 1 ​5 11. 2__
8
4
© 2011 Carnegie Learning
(  )
12. 28.38 211.29 5
​ 2 ​2 ​24__
​ 1 ​ ​5
13. 7__
3
4
14. 32.85 2 (210.65) 5
5  ​2 6​ __
2 ​ 5
15. 24​ __
6
3
16. 219.01 2 10.91 5
Chapter 4 Skills Practice • 517
Lesson 4.5 Skills Practice
( 
)
1 ​ 2 ​25​ ___
1  ​  ​5
17. 23​ __
5
10
(  )
18. 26.2 2 (23.82) 5
20. 217.538 2 12.371 5
© 2011 Carnegie Learning
5  ​2 ​22​ __
1 ​   ​5 19. 10​ __
6
3
page 4
518 • Chapter 4 Skills Practice
Lesson 4.5 Skills Practice
page 5
Name_________________________________________________________ Date__________________________
Add or subtract using your algorithms.
21. 4.76 2 (22.91) 5
7.67
(  )
3 ​ 1 ​2​ __
5 ​  ​5
22. 2​ __
8
6
24. 2719 2 (2698) 5
4 ​ 2 1​ __
1 ​ 5
25. 22​ __
7
4
26. 2824 1 970 5
© 2011 Carnegie Learning
23. 20.108 2 (24.3) 5
Chapter 4 Skills Practice • 519
Lesson 4.5 Skills Practice
page 6
27. 3.862 1 (27.4) 5
7  ​ 2 6​ __
2 ​  5
28. 4​ ___
3
11
29. 25.5 1 18.002 5
13 ​ 1 ​ __
30.​ ___
2​ 7  ​ ​5
9
15
© 2011 Carnegie Learning
(  )
520 • Chapter 4 Skills Practice