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Chapter 4 Skills Practice • 489

Math FootballUsing Models to Understand Integers

Problem SetDetermine the ending position by adding and subtracting the indicated steps from each

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

Lesson 4.1 Skills Practice

Name ________________________________________________________ Date _________________________

490 • Chapter 4 Skills Practice

Lesson 4.1 Skills Practice page 2

Write a number sentence to describe each set of steps forward and backward.

Starting PositionSteps

BackwardSteps

ForwardNumber Sentence

11. 12 4 7 12 1 (24) 1 7 5 15

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

Calculate each sum.

21. 19 1 (24) 1 3 5 18

23. 16 1 (28) 1 5 5

25. 29 1 (21) 1 6 5

27. 0 1 (27) 1 9 5

29. 25 1 (23) 1 4 5

22. 22 1 (25) 1 8 5

24. 0 1 (22) 1 7 5

26. 13 1 (26) 1 5 5

28. 11 1 (21) 1 9 5

30. 23 1 (22) 1 8 5

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.

37. Your score starts at 0. You roll a red 6 and a black 1.

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.

Sampleanswers.

Starting ScoreRoll of the

Red Number Cube

Roll of the Black

Number CubeNumber 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

Name ________________________________________________________ Date _________________________

Walk the LineAdding Integers, Part I

Problem SetUse the number line to determine the number described by each statement. Explain your reasoning.

−15 −10 −5 0 10 155

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.

5. Determine the number that is 7 less than 3.

Use the number line to determine each sum.

9. 23 1 8 5 5 –15 –10 –5

0 10 155

3 1 (28) 5 25–15 –10 –5

0 10 155

23 1 (28) 5 211–15 –10 –5 0 10 155

3 1 8 5 11–15 –10 –5 0 10 155

Name ________________________________________________________ Date _________________________

10. 9 1 (22) 5 –15 –10 –5 0 10 155

29 1 2 5

–15 –10 –5 0 10 155

9 1 2 5

–15 –10 –5 0 10 155

29 1 (22) 5 –15 –10 –5 0 10 155

11. 24 1 10 5

–15 –10 –5 0 10 155

4 1 (210) 5

–15 –10 –5 0 10 155

24 1 (210) 5

–15 –10 –5 0 10 155

4 1 10 5

–15 –10 –5 0 10 155

12. 5 1 (27) 5

–15 –10 –5 0 10 155

25 1 7 5 –15 –10 –5 0 10 155

5 1 7 5

–15 –10 –5 0 10 155

25 1 (27) 5

–15 –10 –5 0 10 155

13. 6 1 (28) 5

–15 –10 –5 0 10 155

26 1 8 5

–15 –10 –5 0 10 155

6 1 8 5

–15 –10 –5 0 10 155

26 1 (28) 5

–15 –10 –5 0 10 155

Name ________________________________________________________ Date _________________________

14. 212 1 3 5

–15 –10 –5 0 10 155

12 1 (23) 5

–15 –10 –5 0 10 155

212 1 (23) 5

–15 –10 –5 0 10 155

12 1 3 5

–15 –10 –5 0 10 155

Write the absolute values for each pair of integers and explain what they mean.

15. |4| 5 4

|24| 5 4

Each integer is 4 units from 0.

17. |213| 5

|13| 5

19. |28| 5

16. |15| 5

|215| 5

18. |7| 5

|27| 5

20. |9| 5

|29| 5

Complete each number line model and then determine the unknown addend.

21. 15 1 27 5 8–15 –10 –5 0 10 155

22. 3 1 5 29–15 –10 –5 0 10 155

23. 24 1 5 5

–15 –10 –5 0 10 155

24. 21 1 5 211–15 –10 –5 0 10 155

25. 6 1 5 22

–15 –10 –5 0 10 155

26. 213 1 5 27–15 –10 –5 0 10 155

27. 8 1 5 23–15 –10 –5 0 10 155

28. 27 1 5 210

–15 –10 –5 0 10 155

Two-Color CountersAdding Integers, Part II

VocabularyDefine the term in your own words.

1. additive inverses

Problem SetDetermine each sum using the number line model or two-color counters.

1. 5 1 (25) 5 0

–15 –10 –5 0 10 155

2. (212) 1 12 5

–15 –10 –5 0 10 155

3. (22) 1 2 5

–15 –10 –5 0 10 155

Name ________________________________________________________ Date _________________________

4. 9 1 (29) 5

5. 4 1 (24) 5

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

−−

− + +

− −

Name ________________________________________________________ Date _________________________

− −

− − −

Draw a picture with two-color counters to represent and solve each number sentence. Cancel out the

pairs of counters to show the answer.

15. 29 1 3 5 26

− − −

16. 23 1 9 5

17. 29 1 (23) 5

18. 2 1 (25) 5

19. 5 1 (22) 5

20. 2 1 5 5

Name ________________________________________________________ Date _________________________

21. 211 1 7 5

22. 27 1 11 5

23. 211 1 (27) 5

24. 25 1 12 5

Complete each model and determine the unknown addend. Circle all of the zero pair counters to show

the answer.

25. 8 1 22 5 6

−−

26. 24 1 5 3

−−

27. 210 1 5 22

−−

− −

28. 13 1 5 6

Name ________________________________________________________ Date _________________________

29. 23 1 5 28

30. 25 1 5 0

− −

Determine each sum.

31. 242 1 79 5 37

33. 29 1 (238) 5

35. 286 1 51 5

37. 237 1 (264) 5

32. 219 1 19 5

34. 117 1 (299) 5

36. 243 1 80 5

38. 2106 1 78 5

Determine each unknown addend.

39. 259 1 41 5 218

41. 262 1 5 9

43. 16 1 5 233

45. 1 25 5 13

40. 256 1 5 284

42. 30 1 5 230

44. 1 (214) 5 21

46. 249 1 5 217

Name ________________________________________________________ Date _________________________

What’s the Difference?Subtracting Integers

VocabularyDefine the term in your own words.

1. zero pair

Problem SetDraw two other models to represent each integer.

++ + −−− −

− −

−−− +

−−

−−−

−−

Complete the two-color counter model for each subtraction problem. Circle the subtracted portion and

write the difference.

7. 23 2 6 5 29

−−

8. 23 2 (26) 5

9. 9 2 (25) 5

10. 29 2 5 5

−−

Name ________________________________________________________ Date _________________________

11. 7 2 (22) 5

12. 27 2 2 5

−−

13. 4 2 8 5

14. 4 2 (28) 5

Name ________________________________________________________ Date _________________________

Draw a number line model to solve each subtraction problem.

15. 25 2 7 5 212

–15 –10 –5 0 10 155

–(+7)

16. 25 2 (27) 5

–15 –10 –5 0 10 155

17. 5 2 7 5

–15 –10 –5 0 10 155

18. 5 2 (27) 5

–15 –10 –5 0 10 155

19. 3 2 (211) 5

–15 –10 –5 0 10 155

20. 3 2 11 5

–15 –10 –5 0 10 155

21. 23 2 11 5

–15 –10 –5 0 10 155

22. 23 2 (211) 5

–15 –10 –5 0 10 155

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 1 5

25. 31 2 17 5 1 5

26. 210 2 (28) 5 1 5

27. 5 2 (216) 5 1 5

28. 14 2 23 5 1 5

29. 220 2 (232) 5 1 5

30. 22 2 19 5 1 5

Determine the unknown integer in each number sentence.

31. 21 2 (26) 5 27 32. 1 (26) 5 27

33. 2 6 5 227 34. 4 2 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

What Do We Do Now?Adding and Subtracting Rational Numbers

Problem SetCalculate each sum.

1. 2 3 __ 8 1 5 1 __

2 3 __ 8

1 5 1 __ 4 5 7 5 __

2 3 __ 8 5 2 3 __

15 1 __ 4 5 5 2 __

7 5 __ 8

3. 12 2 __ 5 1 ( 23 1 __

2. 7 1 __ 6

1 4 2 __ 3

4. 5.3 1 (27.45) 5

Name ________________________________________________________ Date _________________________

5. 2 5 __ 8 1 8 3 __

7. 23 2 __ 5

1 ( 22 3 __ 5 ) 5

9. 14 1 __ 4

1 ( 25 2 __ 3

6. 29.21 1 10.39 5

8. 218.76 1 (211.23) 5

10. 220.245 115.12 5

Name ________________________________________________________ Date _________________________

Calculate each difference.

11. 2 3 __ 8 2 5 1 __

4 5 12. 28.38 211.29 5

13. 7 2 __ 3 2 ( 24 1 __

4 ) 5 14. 32.85 2 (210.65) 5

15. 24 5 __ 6 2 6 2 __

3 5 16. 219.01 2 10.91 5

17. 23 1 __ 5

2 ( 25 1 ___ 10

) 5 18. 26.2 2 (23.82) 5

19. 10 5 __ 6 2 ( 22 1 __

3 ) 5 20. 217.538 2 12.371 5

Name ________________________________________________________ Date _________________________

Add or subtract using your algorithms.

21. 4.76 2 (22.91) 5 7.67 22. 2 3 __ 8

1 ( 2 5 __ 6 ) 5

23. 20.108 2 (24.3) 5 24. 2719 2 (2698) 5

25. 22 4 __ 7

2 1 1 __ 4

5 26. 2824 1 970 5

27. 3.862 1 (27.4) 5 28. 4 7 ___ 11

2 6 2 __ 3 5

29. 25.5 1 18.002 5 30. 13 ___ 15

1 ( 2 7 __ 9

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