Illustrative Unit 7 Review

Positive and Negative Numbers

Inequalities

Coordinates

Factors and Multiples

Write and graph

Interpreting the Coordinate Plane

100

A whale is at the surface of the ocean to breathe. What is the whale’s elevation?
The whale swims down 300 feet to feed. What is the whale’s elevation now?
The whale swims down 150 more feet more. What is the whale’s elevation now?

0. (Sea level is 0 feet above or below sea level.)
-300 feet. (The whale is 300 feet below sea level.)
-450 feet. (The whale was 300 feet below sea level, and now it is an additional 150 feet below sea level.)

100

Given x = -3, mark and place these expressions on the same number line

x, -x, |5|, |-2.5|, - |-4|, -2.5 |-6|

100

In which quadrant is (-6, 5)?

Quadrant II

100

Select ALL the numbers that are common multiples of 6 and 8.

A. 1

B. 2

C. 6

D. 12

E. 24

F. 36

G. 48

E and G

6, 12, 18, 24, 30, 36, 42, 48

8, 16, 24, 32, 40, 48

100

A. Which temperature is COLDER, -3 degrees Celsius or -6 degrees Celsius?

B. Write an inequality to express the relationship between -3 and -6

C. Draw a number line and graph all the temperatures that are COLDER than -3 degrees Celsius.

A. - 6 degrees is COLDER

B. -6 < -3 OR -3 > -6

100

The graph below shows TIME on the X-AXIS and TEMPERATURE in degrees Celsius on the Y-AXIS.

Time: POSITIVE times are AFTER noon.

NEGATIVE times are BEFORE noon.

***What was the Temperature at Noon?

4 degrees Celsius

200

Order from least to greatest:

-1.5, 3/2, |−4/2|, −4/3

-1.5, -4/3, 3/2, |-4/2|

200

Insert the correct inequality symbol.

|-32| _____ |15|

200

Graph these points:
A=(3,3),
B=(3,-3),
C=(-3,3)
D=(-3,-3)
What is the perimeter of the shape formed? Area?

P = 24 units

A = 36 sq units

200

A school chorus has 90 sixth-grade students and 75 seventh-grade students. The music director wants to make groups of performers, with the same combination of sixth- and seventh-grade students in each group. She wants to form as many groups as possible.

What is the largest number of groups that could be formed?

15 groups. The greatest common factor of 75 and 90 is 15.

200

Two more students join Mr. Smith's math class after the fall semester. He can fit up to 30 desks in his classroom. How many students, s, attended Mr. Smith's math class before the end of fall semester?
Write and solve the inequality. Then graph.

s + 2 <= 30

s <= 28

Closed circle at 28, shaded to the left.

200

The graph below shows TIME on the X-AXIS and TEMPERATURE in degrees Celsius on the Y-AXIS.

Time: POSITIVE times are AFTER noon.

NEGATIVE times are BEFORE noon.

***What was the Temperature at 10:00 a.m.?

2 degrees Celsius

300

Select all of the statements that are equivalent to -8.7<-8.4

A: -8.7 is further to the right on the number line than -8.4.
B: -8.7 is further to the left on the number line than -8.4.
C: -8.7 is less than -8.4.
D: -8.7 is greater than -8.4.
E: -8.4 is less than -8.7.
F: -8.4 is greater than -8.7.

B, C, F

300

Match the statements with the mathematical statements.

A: The number -4 is a distance of 4 units away from 0 on the number line.
B: The number -63 is more than 4 units away from 0 on the number line.
C: The number 4 is greater than the number -4.
D: The numbers 4 and -4 are the same distance away from 0 on the number line.
E: The number -63 is less than the number 4.
F: The number -63 is further away from 0 than the number 4 on the number line.

|-63|>4
-63<4
|-63|>|4|
|-4|=4
4>-4
|4|=|-4|

A: 4
B: 1
C: 5
D: 6
E: 2
F: 3

300

The x-axis represents the number of hours before or after noon, and the y-axis represents the temperature in degrees Celsius.

At 9 a.m., it was below freezing. In what quadrant would this point be plotted?

Quadrant III

300

A red light blinks every 12 seconds and a blue light blinks every 9 seconds. When will both lights blink at the same time?

36, 72, 108 . . . seconds, because these are common multiples of 15 and 9.

300

Marcus spent $117.89 from his savings account to buy a new bicycle. He still has more than $45 left in his account. How much money, m, was in his savings account before he bought the bicycle?

Write and solve the inequality. Then graph it.

m - 117.89 > 45

m > 162.89

Open circle at 162.89, shaded to the right.

300

The graph below shows TIME on the X-AXIS and TEMPERATURE in degrees Celsius on the Y-AXIS.

Time: POSITIVE times are AFTER noon.

NEGATIVE times are BEFORE noon.

A. At what time was the temperature - 1 degree Celsius?

B. Are the temperatures INCREASING or DECREASING from 10:00 a.m. to noon?

A. 8:00 a.m.

B. Increasing

400

Tina's rabbit weighs more than 5 pounds and less than 8 pounds.

Select ALL the inequalities that must be true if w is the weight of Tina's rabbit. Also, GRAPH your solution.

A. w >5

B. w <5

C. w>6

D. w<6

E. w>8

F. w<8

A and F are correct

400

Which inequality listed below matches the inequality graph?

A. 7 <= x

B. 7 >= x

C. 7 < x

D. 7 >x

B. 7 >= x because

x <= 7 but when you switch the number and the variable, you must also flip the inequality sign.

400

K is plotted at (-3, 4)

Name a point that could be 3 units away from it.

(-3,7)
(0, 4)
(-3,1)
(-6,4)

400

Cups are sold in packages of 8. Napkins are sold in packages of 12.

What is the fewest number of packages of cups and the fewest number of packages of napkins that can be purchased so there will be the same number of cups as napkins?

3 packages of cups (3⋅8=24) and 2 packages of napkins (2⋅12=24)

400

A teacher is passing out pencils to the students before a test. She wants each student to have at least two pencils. If she has 32 students in her class, how many pencils, p, will the teacher need?

Write and solve the inequality. Then graph it.

p/32 >= 2

p >= 64

Open circle at 64, shaded to the right.

400

The graph below shows TIME on the X-AXIS and TEMPERATURE in degrees Celsius on the Y-AXIS.

Time: POSITIVE times are AFTER noon.

NEGATIVE times are BEFORE noon.

A. What was the temperature at 7 a.m.?

B. At what time is the temperature -1.5 degrees Celsius?

A. about 1.5 degrees Celsius

B. 10:00 a.m.

500

The temperature at dawn is 6∘C away from 0. Select all the temperatures that are possible.

A: -12∘C
B: -6∘C
C: 0∘C
D: 6∘C
E: 12∘C

B, D

500

Kiran started his homework before 7:00 p.m. and finished his homework after 8:00 p.m. Let h represent the number of hours Kiran worked on his homework.

Decide if each statement is true or false.

1. True

2. False

500

The coordinates of a rectangle are(2,0), (2,−6), (−5,0)and(−5,−6)

a. Graph on the coordinate plane below.

b.What is the length and width of this rectangle?

L =6 units
w = 7 units

500

Mai, Clare, and Noah are making signs to advertise the school dance. It takes Mai 6 minutes to complete a sign, it takes Clare 8 minutes to complete a sign, and it takes Noah 5 minutes to complete a sign. They keep working at the same rate for a half hour.

Will Mai and Clare complete a sign at the same time?

Yes, they will both finish at 24 minutes, because 24 is a common multiple of 6 and 8.

500

The temperature in Anchorage, Alaska dropped more than 15 degrees F. over night. The temperature is now -13 degrees F. What was the temperature, t, the day before in Anchorage?

Write, solve, and graph the inequality.

t + 13 > 15

t > 2

Open circle at 2, shaded to the right.

500

The graph below shows TIME on the X-AXIS and TEMPERATURE in degrees Celsius on the Y-AXIS.

Time: POSITIVE times are AFTER noon.

NEGATIVE times are BEFORE noon.

A. Are the temperatures increasing or decreasing on this graph from morning to afternoon?

B. What is the temperature at 8:00 p.m.?

A. Decreasing

B. -6.5 degrees Celsius