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Number System Chapter Questions
1. Explain what absolute value represents.
2. Create an owing money example for comparing two negative numbers.
3. What is the Cartesian (Coordinate) plane?
4. How is the Cartesian plane divided? 5. How are ordered pairs graphed?
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6th Grade Number System Chapter Problems Absolute Value Classwork
1. Find:
a. │-12│
b. │25│
c. │-47│
d. │13│
2. Which numbers have the number given as their absolute value?
a. 150
b. 75
c. 14
d. 1250
3. How would you explain to a new student how to find the absolute value of -10 and +10?
Homework
4. Find:
a. │32│
b. │-35│
c. │-55│
d. │3│
5. Which numbers have the number given as their absolute value?
a. 72
b. 28
c. 155
d. 2500
6. How would you explain to a new student how to find the absolute value of 27 and -27?
Comparing and Ordering Integers Classwork
7. Place the appropriate inequality symbol between the following pairs of integers:
a. 3 -7
b. -8 -10
c. 12 -11
d. 7 7
e. -4 0
f. 0 5
8. Draw a number line and mark and label points for these numbers: 4, -7, 5, 0, -2, 1, -4
9. Draw a number line and mark and label points for these numbers: -15, 0, 7, 4, -3, -1, 9
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10. If the temperature reading on a thermometer is 12°C, what will the new reading be if the
temperature:
a. Falls 15°
b. Rises 3°
c. Falls 12°
11. If the temperature reading on a thermometer is -7°C, what will the new reading be if the
temperature:
a. Falls 3°
b. Rises 5°
c. Rises 9°
Homework 12. Place the appropriate inequality symbol between the following pairs of integers:
a. 25 -25
b. -30 -30
c. -17 -15
d. -99 -100
e. -5 0
f. 0 -1
13. Draw a number line and mark and label points for these numbers: 15, -3, 0, 5, -9, 7, 11
14. Draw a number line and mark and label points for these numbers: -9, 1, 0, -3, 9, -1, -8
15. If the temperature reading on a thermometer is 5°C, what will the new reading be if the
temperature:
a. Falls 15°
b. Rises 3°
c. Falls 12°
16. If the temperature reading on a thermometer is -10°C, what will the new reading be if the
temperature:
a. Falls 3°
b. Rises 5°
c. Rises 9°
Comparing and Ordering Rational Numbers Classwork
17. Place the appropriate inequality symbol between the following pairs of integers:
a. 2
7 0.3
b. - 5
12 -0.42
c. 0.2 1
4
d. 2
5 -0.3
e. - 7
8 -0.8
f. -0.5 3
5
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18. Draw a number line and mark and label points for these numbers: 0, 3
4, -0.25, 1
3
4, -2.5
19. Draw a number line and mark and label points for these numbers: 0.26, - 2
7, -3.1,1
2
3, −2
7
8
Homework
20. Place the appropriate inequality symbol between the following pairs of integers:
a. 5
8 -0.6
b. -0.12 - 1
9
c. 2
7 -0.15
d. 1
2 0.55
e. -0.75 - 3
4
f. 0 0.36
21. Draw a number line and mark and label points for these numbers: 21
2, -5, 2.26, 0, -3
2
7, 8.1, -3.5
22. Draw a number line and mark and label points for these numbers: -0.73, 0, 2.53, 4.3, -0.39, -0.85
NJ Center for Teaching and Learning ~ 5 ~ www.njctl.org
-4 -3 -2 -1 1 2 3 4
-4
-3
-2
-1
1
2
3
4
-4 -3 -2 -1 1 2 3 4
-4
-3
-2
-1
1
2
3
4
x
y
B
D
A
CEE
E
F
-4 -3 -2 -1 1 2 3 4
-4
-3
-2
-1
1
2
3
4
Cartesian Plane Classwork
23. Label the quadrants, the origin, and the x-axis and y- axis.
24. In what quadrant or axis is each point located?
A ____ D ____
B ____ E ____
C ____ F ____
Homework 25. Label the quadrants, the origin, and the x-axis and y- axis.
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-4 -3 -2 -1 1 2 3 4
-4
-3
-2
-1
1
2
3
4
x
y
-4 -3 -2 -1 1 2 3 4
-4
-3
-2
-1
1
2
3
4
x
y
C
A
B
D
E
F
-4 -3 -2 -1 1 2 3 4
-4
-3
-2
-1
1
2
3
4
x
y
A
26. In what quadrant is each point located?
A ____ D ____ B ____ E ____ C ____ F ____
Graphing Ordered Pairs Classwork 27. Plot a point and label it with the letter in each location indicated.
A Quadrant III B Quadrant I C Quadrant II D Quadrant IV E Origin F x – axis G y – axis
28. Write the coordinates of each point on the graph.
Label the point in quadrant I, A ____ Label the point in quadrant IV, B ____ Label the point in quadrant II, C ____ Label the point on the x – axis, D____ What is the point that is not labeled? ____
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-4 -3 -2 -1 1 2 3 4
-4
-3
-2
-1
1
2
3
4
x
y
B
D
A
CEE
E
F
-4 -3 -2 -1 1 2 3 4
-4
-3
-2
-1
1
2
3
4
29. Plot and label the following points:
A (2, 1.5) F (0, 4) B (1, 2) G (4, 0.25) C (-4, -2 1/2) H (-2, 0) D (-3, 1) I (0, - 3) E (5, -2) J (3, - 3) 30. Name the coordinates of each point.
A _____ D _______
B _____ E _______ C ______ F _______
31. Reflect each of the coordinates (in the previous problem) over the x and y axis. Write the new
coordinates below.
A _____ _____
B _____ _____
C _____ _____
D _____ _____
E _____ _____ F _____ _____
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-4 -3 -2 -1 1 2 3 4
-4
-3
-2
-1
1
2
3
4
x
y
-4 -3 -2 -1 1 2 3 4
-4
-3
-2
-1
1
2
3
4
x
y
-4 -3 -2 -1 1 2 3 4
-4
-3
-2
-1
1
2
3
4
Homework
32. Plot a point and label it with the letter in each location indicated.
A Quadrant I B Quadrant III C Quadrant IV D Quadrant II E Origin F y – axis G x - axis
33. Write the coordinates of each point on the graph.
Label the point in quadrant I, A ______
Label the points in quadrant IV, B & C ______ ______
Label the points in quadrant II, E & F
______ ______
Label the point in quadrant III, D ______
Label the origin, O ______
34. Plot and label the following points:
A (-2, 1.25) F (0, 1) B (2, 2) G (1, 0.5) C (4, -2 1/2) H (0, -3) D (3, -1) I (-3, 0) E (-5, -2) J (2, -2)
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-4 -3 -2 -1 1 2 3 4
-4
-3
-2
-1
1
2
3
4
x
y
A
B
C
D
E
F
35. Name the coordinates of each point.
A _____ D _______
B _____ E _______ C ______ F _______
36. Reflect each of the above coordinates (in the previous problem) over the x and y axis. Write the
new coordinates below.
A _____ _____ D _____ _____
B _____ _____ E _____ _____
C _____ _____ F _____ _____
Cartesian Plane Applications Classwork What is the distance between the two graphed points? 37.
Find the distance between each pair of points. 38. (20,-10), (20,6)
39. (-3,17), (15 1/4, 17)
40. (5,1), (5,-6.5)
41. (4,6), (4,-3)
42. (6,-3), (6,-7)
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Use the following map to answer questions the next three questions.
43. Each unit on the graph represents ¾ mile. What is the total distance driven, if Sebastian drives
from his house, to Ulysses’ house and then to Rodger’s house?
44. If the town library is at the map origin, describe the trip Tara would have to make to get to the
library.
45. What quadrant is Sebastian’s house in?
Homework What is the distance between the two graphed points? 46.
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Find the distance between each pair of points. 47. (6,2), (0,2)
48. (-3,-1), (-3,0.5)
49. (-2,3), (-2,7)
50. (-7 1/2, 8), (2,8)
51. (6,-2), (-8, -2)
Use the following map to answer the next three questions.
52. If each unit on the graph represents 2/3 mile, what is the distance from Cutler to Dixon?
53. Describe the trip a traveler would have to make to get from Edison to Brookdale.
54. When asked what quadrant Fischer Lake is in, Sammy says it is in Quadrant II. George says that
answer is not correct? Who do you agree with? Explain your answer.
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Number System Multiple Choice Problems
1. What is the opposite of -15?
a. 15
b. -15
c. 0
2. What is I-36I?
a. 36
b. -36
c. 0
3. What is I27I?
a. 27
b. -27
c. 0
4. -3 0
a. >
b. =
c. <
5. -5 -7
a. >
b. =
c. <
6. – 5
7 − 0.45
a. >
b. =
c. <
7. A point that lies on the y axis between quadrants I and II could have the following for the x
and y-coordinates:
a. (0, 5)
b. (5, 0)
c. (0, -5)
d. (-5, 0)
8. A point that lies on the x axis between quadrants I and IV could have the following for the x
and y-coordinates:
a. (0, 7)
b. (7, 0)
c. (0, -7)
d. (-7, 0)
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Use this Cartesian plane to identify the coordinates for each point for #9 - #11
9. Point A
a. (-2,2)
b. (0,2)
c. (2, 2)
d. (2,0)
10. Point B
a. (4, 3)
b. (-4, 3)
c. (4, -3)
d. (3, 4)
11. Point C
a. (3, 2)
b. (-3, -2)
c. (-3, 2)
d. (3, -2)
Find the distance between the two points for #12 - #13
12. (-5, 3.5) (-5, 7)
a. 4.5 units
b. 4 units
c. 3 units
d. 3.5 units
-4 -3 -2 -1 1 2 3 4
-4
-3
-2
-1
1
2
3
4
A
B C
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13. (-7, 5) (-7, -4)
a. 1 unit
b. 9 units
c. 12 units
d. 3 units
14. Which of the following points would be located in the first quadrant?
a. (-3, -1)
b. (3, 1)
c. (3, -1)
d. (-3, 1)
15. Which of the following points would be located in the fourth quadrant?
a. (-4, 5)
b. (-4, -5)
c. (4, 5)
d. (4, -5)
16. A sunken ship is 150 feet below sea level. Which statement is expressed correctly?
a. 150 feet below sea level can be represented by the integer -150.
b. The depth of the sunken ship is -150 feet below sea level.
c. Both A & B
17. The temperature dropped by 10° F when the sun went down. Which statement is expressed
correctly?
a. The integer -10 represents the change in temperature in degrees Fahrenheit.
b. The temperature decreased by 10° F.
c. Both A & B
Number System Short Constructed Response Questions
1. Which numbers have 23 as their absolute value?
2. Put the following numbers in order on a number line: -31
3, 4.7, 0, -2.58,
7
8, -5.2
3. Explain how to plot (-3 ½ , -6) on the coordinate plane.
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-4 -3 -2 -1 1 2 3 4
-4
-3
-2
-1
1
2
3
4
-4 -3 -2 -1 1 2 3 4
-4
-3
-2
-1
1
2
3
4
4. Label the quadrants, x-axis, y-axis, and origin.
5. Plot the following points on the coordinate grid: A (0, 4)
B (2 1/4, -3)
C (-4, 0)
D (-2, -3.25)
E (-4, 4)
F (1.5, -2)
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-4 -3 -2 -1 1 2 3 4
-4
-3
-2
-1
1
2
3
4
Number System Extended Constructed Response Questions
1. Each unit on the coordinate grid represents 1 kilometer.
a. Plot the following cities on the county map: Smithville (-3.5, 2), Horton (4, -1.5),
Marina (2, 2), Fair Hills (-3, -1 1/2).
b. What is the distance in kilometers from Smithville to Marina?
c. What is the distance in kilometers from Horton to Fair Hills?
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2. Below is a map of Lake County. Use the map to answer the following questions.
a. If each unit on the graph represents 1/3 mile, what is the distance from Cutler to Dixon?
b. Describe the trip a traveler would have to make to get from Brookdale to Edison.
c. Marcus thinks that the train tracks are in Quadrant IV. Is he correct? Explain your answer.
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3. It is well known that Antartica has freezing temperatures. The chart below shows the average
monthly temperature from 1958-1020, at Vostok Station in Antartica.
Month Jan Feb Mar April May June July Aug Sept Oct Nov Dec
Average Temp F (rounded to nearest
½ number.)
-26 -48 -72 -85 -86 -85 -88 -90 -87 -71 -45 -25
a. Plot these temperatures on a number line.
b. Hannah wrote the inequality -72 > -85 to compare the average temperatures for
March and April. Explain what this comparison means about the temperatures for
these two dates.
4. A scuba diver is on an expedition to view whales in their natural habitat. The diver begins his
journey on a boat, at 10 feet above the surface of the water. He spots his first whale at 100
feet below the surface.
a. Write an integer to represent the diver’s depth.
b. Draw and plot these points on a number line to show the distance from the diver’s
position on the boat to the location where he spots his first whale.
c. The diver views a school of fish on his way back to the surface, 30 feet above the
spot where he viewed his first whale. What integer represents the diver’s depth
during this sighting? Add this location to the number line.
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Answer Key
1.
a. 12
b. 25
c. 47
d. 13
2.
a. -150, 150
b. -75, 75
c. -14, 14
d. -1250, 1250
3. Absolute value is the distance from zero on the number line, regardless of direction. -10 and 10
are both 10 units from zero, so │-10│=10 and │10│=10.
4.
a. 32
b. 35
c. 55
d. 3
5.
a. -72, 72
b. -28, 28
c. -155, 155
d. -2500, 2500
6. Absolute value is the distance from zero on the number line, regardless of direction. -27 and 27
are both 27 units from zero, so │-27│=27 and │27│=27.
7.
a. 3 > -7
b. -8 > -10
c. 12 > -11
d. 7 = 7
e. -4 < 0
f. 0 < 5
8. Order on number line: -7, -4, -2, 0, 1, 4, 5
9. Order on number line: -15, -3, -1, 0, 4, 7, 9
10.
a. -3°C
b. 15°C
c. 0°C
11.
a. -10°C
b. -2°C
c. 2°C
12.
a. 25 > -25
b. -30 = -30
c. -17 < -15
d. -99 > -100
e. -5 < 0
f. 0 > -1
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origin -4 -3 -2 -1 1 2 3 4
-4
-3
-2
-1
1
2
3
4
I II
III IV
y-axis
x-axis
13. Order on number line:
-9, -3, 0, 5, 7, 11, 15
14. Order on number line: -9, -8, -3, -1, 0, 1, 9
15.
a. -10°C
b. 8°C
c. -7°C
16.
a. -13°C
b. -5°C
c. -1°C
17.
a. 2
7 < 0.3
b. - 5
12 > -0.42
c. 0.2 < 1
4
d. 2
5 < -0.3
e. - 7
8 < -0.8
f. -0.5 3
5
18. Order on number line: -2.5, -0.25, 0, 3
4, 1
3
4
19. Order on number line: -3.1, - 27
8, -
2
7, 0.26, 1
2
3
20.
a. 5
8 > -0.6
b. -0.12 < - 1
9
c. 2
7 > -0.15
d. 1
2 < 0.55
e. -0.75 = - 3
4
f. 0 < 0.36
21. Order on number line: -5, -3.5, -32
7, 0, 2.26, 2
1
2, 8.1
22. Order on number line: -0.85, -0.73, -0.39, 0, 2.53, 4.3
23.
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origin -4 -3 -2 -1 1 2 3 4
-4
-3
-2
-1
1
2
3
4
I II
III IV
y-axis
x-axis
24.
a. III
b. y-axis
c. II
d. IV
e. I
f. IV
25.
26.
a. I
b. II
c. III
d. III
e. IV
f. IV
27. a. A(-3,-2)
b. B(2,2) c. C(-3,2) d. D(2,-2) e. E(0,0) f. F(2,0) g. G(0,2)
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-4 -3 -2 -1 1 2 3 4
-4
-3
-2
-1
1
2
3
4
28. The origin is not labeled.
29.
30.
a. (-4, -5)
b. (0, 3)
c. (-2, 1)
d. (1, -2)
e. (5, 3)
f. (5, -4)
31.
a. (-4, 5) (4, -5) (4, 5)
b. (0, -3)
c. (-2, -1) (2, 1) (2, -1)
d. (1, 2) (-1, -2) (-1, 2)
e. (5, -3) (-5, 3) (-5, -3)
f. (5, 4) (-5, -4) (-5, 4)
A B
C
D
E
F
G
H
I J
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32. Answers will vary.
33. a. A(5,2)
b. B (2, -1)
c. C (3, -4)
d. D(3, -2)
e. E(-3,1)
f. F(-1, 3)
g. O(0,0)
34.
35.
a. (-2, 3)
b. (-4, 0)
c. (0, -2)
d. (1, 4)
e. (3, -2)
f. (-1, -4)
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-4 -3 -2 -1 1 2 3 4
-4
-3
-2
-1
1
2
3
4
I II
III IV
y-axis
x-axis origin
36.
a. (-2, -3) (2, 3) (2, -3)
b. (4, 0)
c. (0, 2)
d. (1, -4) (-1, 4) (-1, -4)
e. (3, 2) (-3, -2) (-3, 2)
f. (-1, 4) (1, -4) (1, 4)
37. 3
38. 16
39. 18 ¼
40. 7.5
41. 9
42. 4
43. 10 ½ miles
44. She would have to travel 4 units (or 3 miles) down.
45. Quadrant II
46. 4
47. 6
48. 1.5
49. 4
50. 9 ½
51. 14
52. 2 2/3 miles
53. A traveler would have to travel 3 units (or 2 miles) up and 5 units (or 3 1/3 miles) to the left, in
either order.
54. George is correct, because Fischer Lake is in all four quadrants.
Number System Multiple Choice Questions
1. a 2. a 3. a 4. c 5. a 6. c
7. a 8. b 9. c 10. c 11. b 12. d
13. b 14, b 15. d 16. a 17. c
Number System Short Constructed Response
1. 23, -23
2. Order on the number line: -5.2, -3 1
3, -2.58, 0,
7
8, 4.7
3. Start at the origin and go left to -3 ½ on the x axis, then go down 6 from that position. 4.
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5.
Number System Extended Constructed Response 1.
a. see grid below.
b. 5.5 kilometers
c. 7 kilometers
2.
a. 1 1/3 miles
b. A traveler would have to travel 2 ½ units (or 5/6 of a mile) and 5 units (or 1 2/3 miles)
to the right, in either order.
c. His answer is not complete. The train tracks are in quadrants III and IV.
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3. a.
b. It means that the average temperature for March (-72) is warmer than the average
temperature for April (-85).
4.
a. -100
b and c.
c. -70
