Number System Chapter Questions
1. What is an integer?
2. Explain what absolute value represents.
3. Create an owing money example for comparing two negative numbers.
4. What is the Cartesian (Coordinate) plane?
5. How is the Cartesian plane divided?
6. How are ordered pairs graphed?
6th Grade Number System Chapter Problems
Integers
Classwork
1. Name 5 integers.
2. Name 5 numbers that are not integers.
3. What is the opposite of 20?
4. What is the opposite of -13?
5. Write an integer to represent each situation:
a. The temperature falls 5 degrees.
b. The team gains 25 yards.
c. You deposit $100 in your savings account.
d. You withdraw $75 dollars from your savings account.
e. The mountain is 1,500 feet above sea level.
f. A company loses $200,000.
g. You owe your dad $15.
h. The scuba diver is 35 feet below sea level.
6. Using the scoring system in the game of Jeopardy (you earn points for correct responses and lose points for incorrect responses) what would be the final score after the following 5 responses:
a. Player 1 answers a 200 point question correct, a 150 point question wrong, a 50 point question correct, a 150 point question wrong, and 100 point question correct.
b. Player 2 answers a 100 point question wrong, a 50 point question correct, a 100 point question correct, a 150 point question correct and 200 point question wrong.
c. Player 3 gets a 200 point question correct, a 200 point question wrong, a 50 point question wrong, a 150 point question correct and a 200 point question correct.
7. Use the Jeopardy scoring system and create a sequence of 5 answers that would give you a score of:
a. 300 points
b. -50 points
c. 0 points
Homework
8. What is the opposite of -50?
9. What is the opposite of 11?
10. What is the opposite of 2?
11. What is the opposite of -7?
12. Write an integer to represent each situation:
a. The temperature rises 11 degrees.
b. The submarine dives 125 feet below sea level.
c. The team loses 15 yards.
d. You earn $35 babysitting.
e. A company loses $12,000 in a month.
f. A fee of $2.50 is charged.
g. You deposit $100 in your bank account.
h. Sea level.
13. Using the scoring system in the game of Jeopardy (you earn points for correct responses and lose points for incorrect responses) what would be the final score after the following 5 responses:
a. Player 1 answers a 200 point question correct, a 50 point question wrong, a 250 point question correct, a 50 point question wrong, and 150 point question correct.
b. Player 2 answers a 200 point question wrong, a 100 point question correct, a 100 point question wrong, a 100 point question wrong and 50 point question correct.
c. Player 3 gets a 150 point question correct, a 100 point question wrong, a 50 point question wrong, a 100 point question correct and a 250 point question correct.
14. Use the Jeopardy scoring system and create a sequence of 5 answers that would give you a score of:
a. -150 points
b. 400 points
c. 0 points
Absolute Value
Classwork
15. Find:
a. │-12│
b. │25│
c. │-47│
d. │13│
16. Which numbers have the number given as their absolute value?
a. 150
b. 75
c. 14
d. 1250
17. How would you explain to a new student how to find the absolute value of -10 and +10?
Homework
18. Find:
a. │32│
b. │-35│
c. │-55│
d. │3│
19. Which numbers have the number given as their absolute value?
a. 72
b. 28
c. 155
d. 2500
20. How would you explain to a new student how to find the absolute value of 27 and -27?
Comparing and Ordering Integers
Classwork
21. 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
22. Draw a number line and mark and label points for these numbers: 4, -7, 5, 0, -2, 1, -4
23. Draw a number line and mark and label points for these numbers: -15, 0, 7, 4, -3, -1, 9
24. 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°
25. 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
26. 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
27. Draw a number line and mark and label points for these numbers: 15, -3, 0, 5, -9, 7, 11
28. Draw a number line and mark and label points for these numbers: -9, 1, 0, -3, 9, -1, -8
29. 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°
30. 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
31. Place the appropriate inequality symbol between the following pairs of integers:
a. 27 0.3
b. - 512 -0.42
c. 0.2 14
d. 25 -0.3
e. - 78 -0.8
f. -0.5 35
32. Draw a number line and mark and label points for these numbers: 0, 34, -0.25, 134, -2.5
33. Draw a number line and mark and label points for these numbers: 0.26, - 27, -3.1,1 23, -278
Homework
34. Place the appropriate inequality symbol between the following pairs of integers:
a. 58 -0.6
b. -0.12 - 19
c. 27 -0.15
d. 12 0.55
e. -0.75 - 34
f. 0 0.36
35. Draw a number line and mark and label points for these numbers: 212, -5, 2.26, 0, -327, 8.1, -3.5
36. Draw a number line and mark and label points for these numbers: -0.73, 0, 2.53, 4.3, -0.39, -0.85
Cartesian Plane
Classwork
37.Label the quadrants, the origin, and the
x-axis and y- axis
38. In what quadrant or axis is each point located?
A ____ D ____
B ____ E ____
C ____ F ____
Homework
39.Label the quadrants, the origin, and the x-axis and y- axis
40. In what quadrant is each point located?
A ____ D ____
B ____ E ____
C ____ F ____
Graphing Ordered Pairs
Classwork
41. 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
42. 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? ____
43. 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)
44. Name the coordinates of each point
A _____ D ______
B _____ E ______
C ______F ______
45. Reflect each of the above coordinates over the x and y axis. Write the new coordinates below.
A ______
B ______
C ______
D ______
E ______
F ______
Homework
46. 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
47. 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 ______
48. 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)
49. Name the coordinates of each point
A _____ D ______
B _____ E ______
C ______F ______
50. Reflect each of the above coordinates over the x and y axis. Write the new coordinates below.
A ______B ______
C ______D ______
E ______F ______
Cartesian Plane Applications
Classwork
What is the distance between the two graphed points?
51.
Find the distance between each pair of points.
52. (20,-10), (20,6)
53. (-3,17), (15 1/4, 17)
54. (5,1), (5,-6.5)
55. (4,6), (4,-3)
56. (6,-3), (6,-7)
Use the following map to answer questions 57-59.
57. 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?
58. If the town library is at the map origin, describe the trip Tara would have to make to get to the library.
59. What quadrant is Sebastian’s house in?
Homework
What is the distance between the two graphed points?
60.
Find the distance between each pair of points.
61. (6,2), (0,2)
62. (-3,-1), (-3,0.5)
63. (-2,3), (-2,7)
64. (-7 1/2, 8), (2,8)
65. (6,-2), (-8, -2)
Use the following map to answer questions 66-68.
66. If each unit on the graph represents 2/3 mile, what is the distance from Cutler to Dixon?
67. Describe the trip a traveler would have to make to get from Edison to Brookdale.
68. 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.
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. – 57 -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)
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
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: -313, 4.7, 0, -2.58, 78, -5.2
3. Explain how to plot (-3 ½ , -6) on the coordinate plane.
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)
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?
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.
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 / DecAverage 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.