Name:Date:

School:Subject:

Part I (4 points each)

Find the sum

1) −? + (−??) =2) ? + (−???) =

Find the difference

3) −??−(−?) =4) ??−(−?) =

5) ?−(−?.?) =

Divide

6) −36 ÷ (−9) = 7) −50 ÷ 10 =

8) What is the decimal value of 4/11?

9) Write 3.0035 as a fraction

10) What is the rule for dividing two integers?Circle the correct choice.

A quotient is negative if the divisor and the dividend have the same oropposite signs.

PART II (10 points each)

11) Two 7th grade students, Monique and Matt, both solved the following math problem:

If the temperature drops from 7◦ F to −17◦ F, by how much did the temperature decrease?

The students came up with different answers. Monique said the answer is 24◦F, and Matt said the answer is 10◦F. Who is correct? Explain, and support your written response with the use of a formula or vertical number diagram.

12) Jake is hiking a trail that leads to the top of a canyon. The trail is ?.?miles long, and Jake plans to stop for lunch after he completes ?.?miles. How far from the top of the canyon will Jake be when he stops for lunch?

Represent each of the following problems using both a number line diagram and an equation

13) Create a real-life example that can be modeled by the expression −2×4, and then state the product

Part III (30 points):

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

Change in Temperature

5:00 am – 6:00 am / −3°F
6:00 am – 7:00 am / −2°F
7:00 am – 8:00 am / −6°F
8:00 am – 9:00 am / 7°F

a. If the beginning temperature was −13°F at 5:00 am, what was the temperature at 9:00 am?

b. The same cold front hit Hartford, Connecticut the next morning. The temperature dropped by 7°F each hour from 5:00 am – 9:00 am. What was the beginning temperature at 5:00 am if the temperature at 9:00 am was −10°F?

c. In answering part (b), Josiah and Kate used different methods. Josiah said his method involved multiplication, while Kate said she did not use multiplication. Both students arrived at the correct answer. How is this possible? Explain.

Grade 7 Unit 2

Alternative questions:

Part I

−? + (−??)

–??−(−?)

−20 ÷ (−5) =

Write the number ?/??as a decimal

What is the rule for dividing two integers? Circle the correct choice.

A quotient is positive if the divisor and the dividend have the same or oppositesigns.

Circle the integer with the greater absolute value. Decide whether the sum will be positive or negative without actually calculating the sum.

a. −?? + ??

b. ?? + (−?)

c. −? + ??

d. −???? +??

Part II

At the start of a trip, a car’s gas tank contains 12 gallons of gasoline. During the trip, the car consumes ???/?gallons of gasoline. How much gasoline is left in the tank? Create an equation and number line diagram to model your answer.

At the beginning of the summer, the water level of a pond is 2 feet below its normal level. After an unusually dry summer, the water level of the pond dropped another 11/3 feet.

Use a number line diagram to model the pond’s current water level in relation to its normal water level.

Which of these story problems describes the sum?? + (−??)? Check all that apply. Show your work to justify your answer.

______Jared’s dad paid him $?for raking the leaves from the yard on Wednesday. Jared spent $??at the movie theater on Friday. How much money does Jared have left?

______Jared owed his brother $??for raking the leaves while Jared was sick. Jared’s dad gave him $??for doing his chores for the week. How much money does Jared have now?

______Jared’s grandmother gave him $??for his birthday. He bought $?worth of candy and spent another $?on a new comic book. How much money does Jared have left over?

Write an equation to model the sum of the situation below.

A Hydrogen atom has a zero charge because it has one negatively charged electron and one positively charged proton.

Eric and four of his friends are taking a trip across the New York State Thruway. They decide to split the cost of tolls equally. If the total cost of tolls is $?, how much will each person have to pay?

Use one rational number to represent the following expression. Show your work.

3+(−0.2)−151/4

Diamond used a number line to add. She started counting at 10, and then she counted until she was on the number −4 on the number line.

a. If Diamond is modeling addition, what number did she add to 10? Use the number line below to model your answer.

b. Write a real-world story problem that would fit this situation.

c. Use absolute value to express the distance between 10 and −4.