Mid-Module Assessment Review #2

1. Diamond used a number line to add. She started counting at 9, and then she counted until she was on the number −3 on the number line.

a. If Diamond is modeling addition, what number did she add to 9? Use the number line below to model your answer.

1. We are at positive 9 on the number line

2. If she is modeling addition, her equation has to include an addition sign

3. so 9 + a number

4. On your number line, you start at 0, go to 9 and then move to -3

5. how many spaces from 9 to -3?

6. 12 units to the left, meaning 12 is moving in a negative direction

7. Now combine and write the equation

8. 9 + (-12) = -3

video for reference:

• https://youtu.be/vhHl8mSOIi8?t=48

2. What value of 𝑎 will make the equation a true statement? Also, explain how you arrived at your solution.

-3 + 𝑎 = 0

𝑎 = 3

• For a number to equal a sum of zero:

  • you must add its additive inverse or its opposite

• The inverse/opposite of -3 is 3

​Watch this video for more information:

• https://youtu.be/p8OsA062OPY

​On a number line you go to the left of zero 3 spaces and then back right 3 spaces, landing back at zero.

​-3 + 3 = 0

3.The table below shows the temperature changes Monday morning in Bedford, New York over a 4-hour period after a cold front came through.

If the beginning temperature was −15°F at 5:00 a.m. What was the temperature at 9:00 a.m.?

Change in temperature
5:00 a.m. – 6:00 a.m.	-2°F
6:00 a.m. – 7:00 a.m.	−4°F
7:00 a.m. – 8:00 a.m.	−7°F
8:00 a.m. – 9:00 a.m.	7°F

1. The beginning temperature is -15 °F at 5am.

2. the table says that it drops (represented by negative) 2 degrees between 5am-6am = -15°F - 2°F= -17°F

3. Another drop of 4 degrees between 6am and 7am = -17°F - 4°F = -21°F

4. Another drop of 7 degrees between 7am - 8am = -21°F - 7°F = -28°F

5. A rise (represented by positive) of 7 degrees between 8am-9am = -28°F + 7°F = -21°F

6. Final temperature of -21°F at 9 am.

5. Every month, Ms. Thomas pays her car loan through automatic payments (withdrawals) from her savings account. She pays the same amount on her car loan each month. At the end of the year, her savings account balance changed by −$2,565 from payments made on her car loan.

​ _ 213.75___

12 |2,565.00

-24↓↓↓↓

-----------

16↓

-12↓

----------

45

-36

----------

90

-84↓

----------

60

-60

--------

0

​a. What is the change in Ms. Thomas’ savings account balance each month due to her car payment?

a.

2 2 4 3

213.75

x 6

-----------------------

1482.50

6. Michael’s father bought him a 16-foot board to cut into shelves for his bedroom.

• Michael plans to cut the board into 11 equal size lengths for his shelves.

  • After making his cuts, what will the exact length of each shelf be in inches? (hint: convert 16 feet into inches).

• ​He is trying to divide a 16-foot board into 11 equal lengths

• They want each length in inches, so convert feet to inches (16 feet x 12 inches per feet = 192 inches) so that you can solve for inches instead of feet.

• Although you can use a calculator, most of your points will be allocated to showing work in long division, so practice that.

__

__17.4545_

11 | 192.0000

- 11

____________

82

- 77

___________

50

- 44

________

60

- 55 _________

50

- 44

________

60

​Explanation:

It is a repeating decimal.

For a 16-foot board, each shelf piece will be approximately 17.45 inches long (rounding to the nearest hundredth.)

watch this video over long division if still struggling:

• https://youtu.be/yqP4Z99T6D0