Embed Size (px)
Citation preview
Chapter 4 Skills Practice • 489
© 2
011
Car
negi
e Le
arni
ng
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
© 2
011
Car
negi
e Le
arni
ng
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
Chapter 4 Skills Practice • 491
© 2
011
Car
negi
e Le
arni
ng
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.
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.
492 • Chapter 4 Skills Practice
© 2
011
Car
negi
e Le
arni
ng
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.
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
Chapter 4 Skills Practice • 493
© 2
011
Car
negi
e Le
arni
ng
Lesson 4.2 Skills Practice
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.
2. Determine the number that is 9 more than 24.
3. Determine the number that is 12 more than 28.
4. Determine the number that is 10 more than 21.
5. Determine the number that is 7 less than 3.
494 • Chapter 4 Skills Practice
© 2
011
Car
negi
e Le
arni
ng
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.
9. 23 1 8 5 5 –15 –10 –5
–3
0 10 155
8
3 1 (28) 5 25–15 –10 –5
3
0 10 155
–8
23 1 (28) 5 211–15 –10 –5 0 10 155
–8
–3
3 1 8 5 11–15 –10 –5 0 10 155
8
3
Chapter 4 Skills Practice • 495
© 2
011
Car
negi
e Le
arni
ng
Lesson 4.2 Skills Practice page 3
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
496 • Chapter 4 Skills Practice
© 2
011
Car
negi
e Le
arni
ng
Lesson 4.2 Skills Practice page 4
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
Chapter 4 Skills Practice • 497
© 2
011
Car
negi
e Le
arni
ng
Lesson 4.2 Skills Practice page 5
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
|8| 5
16. |15| 5
|215| 5
18. |7| 5
|27| 5
20. |9| 5
|29| 5
498 • Chapter 4 Skills Practice
© 2
011
Car
negi
e Le
arni
ng
Lesson 4.2 Skills Practice page 6
Complete each number line model and then determine the unknown addend.
21. 15 1 27 5 8–15 –10 –5 0 10 155
15
–7
22. 3 1 5 29–15 –10 –5 0 10 155
3
23. 24 1 5 5
–15 –10 –5 0 10 155
–4
24. 21 1 5 211–15 –10 –5 0 10 155
–1
25. 6 1 5 22
–15 –10 –5 0 10 155
6
26. 213 1 5 27–15 –10 –5 0 10 155
–13
27. 8 1 5 23–15 –10 –5 0 10 155
8
28. 27 1 5 210
–15 –10 –5 0 10 155
–7
Chapter 4 Skills Practice • 499
© 2
011
Car
negi
e Le
arni
ng
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
5
–5
2. (212) 1 12 5
–15 –10 –5 0 10 155
3. (22) 1 2 5
–15 –10 –5 0 10 155
Lesson 4.3 Skills Practice
Name ________________________________________________________ Date _________________________
500 • Chapter 4 Skills Practice
© 2
011
Car
negi
e Le
arni
ng
4. 9 1 (29) 5
5. 4 1 (24) 5
Lesson 4.3 Skills Practice page 2
Chapter 4 Skills Practice • 501
© 2
011
Car
negi
e Le
arni
ng
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.
+
+
+
+
+
−
502 • Chapter 4 Skills Practice
© 2
011
Car
negi
e Le
arni
ng
Lesson 4.3 Skills Practice page 4
9.
+
+
++
−
−
−−
−
−−
−
10.
−−
− + +
+
11.
+ +
+ + +
+ +
− −
−
− −
12.
+
+
+
+ +
+
Chapter 4 Skills Practice • 503
© 2
011
Car
negi
e Le
arni
ng
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.
15. 29 1 3 5 26
− − −
− − −
− − −
+
+
+
16. 23 1 9 5
504 • Chapter 4 Skills Practice
© 2
011
Car
negi
e Le
arni
ng
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
Chapter 4 Skills Practice • 505
© 2
011
Car
negi
e Le
arni
ng
Lesson 4.3 Skills Practice page 7
Name ________________________________________________________ Date _________________________
21. 211 1 7 5
22. 27 1 11 5
23. 211 1 (27) 5
24. 25 1 12 5
506 • Chapter 4 Skills Practice
© 2
011
Car
negi
e Le
arni
ng
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.
25. 8 1 22 5 6
−−
++
++
++
++
26. 24 1 5 3
−−
−−
27. 210 1 5 22
−−
−
−
−−
− −
− −
28. 13 1 5 6
++
++
++
++
+
+
+
+
+
Chapter 4 Skills Practice • 507
© 2
011
Car
negi
e Le
arni
ng
Lesson 4.3 Skills Practice page 9
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
508 • Chapter 4 Skills Practice
© 2
011
Car
negi
e Le
arni
ng
Chapter 4 Skills Practice • 509
© 2
011
Car
negi
e Le
arni
ng
Lesson 4.4 Skills Practice
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.
1. 23
++ + −−− −
− −
−−− +
+
−−
−
−−
2. 4
++++
510 • Chapter 4 Skills Practice
© 2
011
Car
negi
e Le
arni
ng
Lesson 4.4 Skills Practice page 2
3. 2
++
4. 25
−−−
−−
5. 1
+
6. 0
Chapter 4 Skills Practice • 511
© 2
011
Car
negi
e Le
arni
ng
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
−
−
−
−
−−
−
−
−
Lesson 4.4 Skills Practice page 3
Name ________________________________________________________ Date _________________________
512 • Chapter 4 Skills Practice
© 2
011
Car
negi
e Le
arni
ng
11. 7 2 (22) 5
+
+
+
++
+
+
12. 27 2 2 5
−
−
−
−−
−
−
13. 4 2 8 5
+
+
+
+
14. 4 2 (28) 5
+
+
+
+
Lesson 4.4 Skills Practice page 4
Chapter 4 Skills Practice • 513
© 2
011
Car
negi
e Le
arni
ng
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
–15 –10 –5 0 10 155
–(+7)
–5
–12
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
514 • Chapter 4 Skills Practice
© 2
011
Car
negi
e Le
arni
ng
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
Lesson 4.4 Skills Practice page 6
Chapter 4 Skills Practice • 515
© 2
011
Car
negi
e Le
arni
ng
What Do We Do Now?Adding and Subtracting Rational Numbers
Problem SetCalculate each sum.
1. 2 3 __ 8 1 5 1 __
4 5
2 3 __ 8
1 5 1 __ 4 5 7 5 __
8
2 3 __ 8 5 2 3 __
8
15 1 __ 4 5 5 2 __
8
7 5 __ 8
3. 12 2 __ 5 1 ( 23 1 __
4 ) 5
2. 7 1 __ 6
1 4 2 __ 3
5
4. 5.3 1 (27.45) 5
Lesson 4.5 Skills Practice
Name ________________________________________________________ Date _________________________
516 • Chapter 4 Skills Practice
© 2
011
Car
negi
e Le
arni
ng
5. 2 5 __ 8 1 8 3 __
8 5
7. 23 2 __ 5
1 ( 22 3 __ 5 ) 5
9. 14 1 __ 4
1 ( 25 2 __ 3
) 5
6. 29.21 1 10.39 5
8. 218.76 1 (211.23) 5
1
10. 220.245 115.12 5
Lesson 4.5 Skills Practice page 2
Chapter 4 Skills Practice • 517
© 2
011
Car
negi
e Le
arni
ng
Lesson 4.5 Skills Practice page 3
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
518 • Chapter 4 Skills Practice
© 2
011
Car
negi
e Le
arni
ng
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
Lesson 4.5 Skills Practice page 4
Chapter 4 Skills Practice • 519
© 2
011
Car
negi
e Le
arni
ng
Lesson 4.5 Skills Practice page 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
520 • Chapter 4 Skills Practice
© 2
011
Car
negi
e Le
arni
ng
Lesson 4.5 Skills Practice page 6
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
) 5
