MOUNT VERNON CITY SCHOOL DISTRICT

“Children of Promise”

Math 6

Mid-Winter Recess

Student Name: ___________________________________________________

School Name: ___________________________________________________

Teacher: ___________________________________________________

Score: ___________________________________________________

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Module 1: Ratios and Unit Rates

1. Jasmine has taken an online boating safety course and is now completing her end of course

exam. As she answers each question, the progress bar at the bottom of the screen shows

what portion of the test she has finished. She has just completed question 16 and the

progress bar shows she is 20% complete. How many total questions are on the test? Use a

table, diagram, or equation to justify your answer.

2. Alisa hopes to play beach volleyball in the Olympics someday. She has convinced her

parents to allow her to set up a beach volleyball court in their back yard. A standard beach

volleyball court is approximately 26 feet by 52 feet. She figures that she will need the sand

to be one foot deep. She goes to the hardware store to shop for sand and sees the following

signs on pallets containing bags of sand.

a. What is the rate that Brand A is selling for? Give the rate and then specify the unit rate.

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b. Which brand is offering the better value? Explain your answer.

c. Alisa uses her cell phone to search how many pounds of sand is required to fill 1 cubic

foot and finds the answer is 100 pounds. Choose one of the brands and compute how

much it will cost Alisa to purchase enough sand to fill the court. Identify which brand

was chosen as part of your answer.

3. Loren and Julie have different part time jobs after school. They are both paid at a constant

rate of dollars per hour. The tables below show Loren and Julie’s total income (amount

earned) for working a given amount of time.

Loren

Hours 2 4 6 8 10 12 14 16 18

Dollars 18 36 54 72 90 108 162

Julie

Hours 3 6 9 12 15 18 21 24 27

Dollars 36 108 144 180 216 288 324

a. Find the missing values in the two tables above.

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b. Who makes more per hour? Justify your answer.

c. Write how much Julie makes as a rate. What is the unit rate?

d. How much money would Julie earn for working 16 hours?

e. What is the ratio between how much Loren makes per hour and how much Julie makes

per hour?

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f. Julie works 1

12 hours/dollar. Write a one or two-sentence explanation of what this rate

means. Use this rate to find how long it takes for Julie to earn $228.

4. Your mother takes you to your grandparents’ house for dinner. She drives 60 minutes at a

constant speed of 40 miles per hour. She reaches the highway and quickly speeds up and

drives for another 30 minutes at constant speed of 70 miles per hour.

a. How far did you and your mother travel altogether?

b. How long did the trip take?

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c. Your older brother drove to your grandparents’ house in a different car, but left from the

same location at the same time. If he traveled at a constant speed of 60 miles per hour,

explain why he would reach your grandparents house first. Use words, diagrams, or

numbers to explain your reasoning.

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Module 2: Arithmetic Operations Including Dividing by a Fraction

1. L.B. Johnson Middle School held a track and field event during the school year. The chess

club sold various drink and snack items for the participants and the audience. All together

they sold 486 items that totaled $2,673.

a. If the chess club sold each item for the same price, calculate the price of each item.

b. Explain the value of each digit in your answer to 1(a) using place value terms.

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2. The long jump pit was recently rebuilt to make it level with the runway. Volunteers provided

pieces of wood to frame the pit. Each piece of wood provided measured 6 feet, which is

approximately 1.8287 meters.

a. Determine the amount of wood, in meters, needed to rebuild the frame.

b. How many boards did the volunteers supply? Round your calculations to the nearest

thousandth and then provide the whole number of boards supplied.

9.54 meters

2.75 meters

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3. Andy ran 436.8 meters in 62.08 seconds.

a. If Andy ran at a constant speed, how far did he run in one second? Give your answer to

the nearest tenth of a second.

b. Use place value, multiplication with powers of 10, or equivalent fractions to explain

what is happening mathematically to the decimal points in the divisor and dividend

before dividing.

c. In the following expression, place a decimal point in the divisor and the dividend to

create a new problem with the same answer as in 3(a). Then explain how you know the

answer will be the same.

4 3 6 8 ÷ 6 2 0 8

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4. The PTA created a cross-country trail for the meet.

a. The PTA placed a trail marker in the ground every four hundred yards. Every nine

hundred yards the PTA set up a water station. What is the shortest distance a runner will

have to run to see both a water station and trail marker at the same location?

Answer: hundred yards

b. There are 1,760 yards in one mile. About how many miles will a runner have to run

before seeing both a water station and trail marker at the same location? Calculate the

answer to the nearest hundredth of a mile.

c. The PTA wants to cover the wet areas of the trail with wood chips. They find that one

bag of wood chips covers a 3 1

2 yards section of the trail. If there is a wet section of the

trail that is approximately 501

4 yards long, how many bags of wood chips are needed to

cover the wet section of the trail?

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5. The Art Club wants to paint a rectangle-shaped mural to celebrate the winners of the track

and field meet. They designed a checkerboard background for the mural where they will

write the winners’ names. The rectangle measures 432 inches in length and 360 inches in

width. What is the side length of the largest square they can use to fill the checkerboard

pattern completely without overlap or gaps?

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Module 3: Rational Number

1. Mr. Kindle invested some money in the stock market. He tracks his gains and losses using a

computer program. Mr. Kindle receives a daily email that updates him on all his transactions

from the previous day. This morning, his email read as follows:

Good morning, Mr. Kindle,

Yesterday’s investment activity included a loss of $800, a gain of $960, and another

gain of $230. Log in now to see your current balance.

a. Write an integer to represent each gain and loss.

Description Integer Representation

Loss of $800

Gain of $960

Gain of $230

b. Mr. Kindle noticed that an error had been made on his account. The “loss of $800”

should have been a “gain of $800.” Locate and label both points that represent “a loss

of $800” and “a gain of $800” on the number line below. Describe the relationship of

these two numbers, when zero represents no change (gain or loss).

c. Mr. Kindle wanted to correct the error, so he entered −(−$800) into the program. He

made a note that read, “The opposite of the opposite of $800 is $800.” Is his reasoning

correct? Explain.

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2. At 6:00 a.m., Buffalo, NY had a temperature of 10℉. At noon, the temperature was −10℉,

and at midnight it was −20℉.

a. Write a statement comparing −10℉ and −20℉.

b. Write an inequality statement that shows the relationship between the three recorded

temperatures. Which temperature is the warmest?

c. Explain how to use absolute value to find the number of degrees below zero the

temperature was at noon.

d. In Peekskill, NY, the temperature at 6:00 a.m. was −12℉. At noon, the temperature

was the exact opposite of Buffalo’s temperature at 6:00 a.m. At midnight, a

meteorologist recorded the temperature as −6℉ in Peekskill. He concluded that, “For

temperatures below zero, as the temperature increases, the absolute value of the

temperature decreases.” Is his conclusion valid? Explain and use a vertical number line

to support your answer.

6:00 a.m. Midnight Noon

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3. Choose an integer between 0 and −5 on a number line, and label the point 𝑃. Locate and

label each of the following points and their values on the number line.

a. Label point 𝐴: the opposite of 𝑃.

b. Label point 𝐵: a number less than 𝑃.

c. Label point 𝐶: a number greater than 𝑃.

d. Label point 𝐷: a number half way between 𝑃 and the integer to the right of 𝑃.

4. Julia is learning about elevation in math class. She decided to research some facts about

New York State to better understand the concept. Here are some facts that she found.

Mount Marcy is the highest point in New York State. It is 5,343 feet above sea level.

Lake Erie is 210 feet below sea level.

The elevation of Niagara Falls, NY is 614 feet above sea level.

The lobby of the Empire State Building is 50 feet above sea level.

New York State borders the Atlantic Coast, which is at sea level.

The lowest point of Cayuga Lake is 435 feet below sea level.

a. Write an integer that represents each location in relationship to sea level.

Mount Marcy

Lake Erie

Niagara Falls, NY

Empire State

Building

Atlantic Coast

Cayuga Lake

b. Explain what negative and positive numbers tell Julia about elevation.

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c. Order the elevations from least to greatest, and then state their absolute values. Use the

chart below to record your work.

Elevations Absolute Values of

Elevations

d. Circle the row in the table that represents sea level. Describe how the order of the

elevations below sea level compares to the order of their absolute values. Describe how

the order of the elevations above sea level compares to the order of their absolute values.

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5. For centuries, a mysterious sea serpent has been rumored to live at the bottom of Seneca

Lake, the longest of the Finger Lakes. A team of historians used a computer program to plot

the last five positions of the sightings.

a. Locate and label the locations of the last four sightings: 𝐴 (−91

2, 0), 𝐵 (−3, −4.75),

𝐶 (9, 2), and 𝐷 (8, −2.5).

b. Over time, most of the sightings occurred in Quadrant III. Write the coordinates of a

point that lies in Quadrant III.

c. What is the distance between point 𝐴 and the point (91

2, 0)? Show your work to

support your answer.

d. What are the coordinates of point 𝐸 on the coordinate plane?

e. Point 𝐹 is related to point 𝐸. Its 𝑥-coordinate is the same as point 𝐸’s, but its 𝑦-

coordinate is the opposite of point 𝐸’s. Locate and label point 𝐹. What are the

coordinates? How far apart are points 𝐸 and 𝐹? Explain how you arrived at your

answer

.

E

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Module 4: Expressions and Equations

6. Gertrude is deciding which cell phone plan is the best deal for her to buy. Super Cell charges

a monthly fee of $10 and also charges $0.15 per call. She makes a note that the equation is

𝑀 = 0.15 𝐶 + 10, where 𝑀 is the monthly charge and 𝐶 is the number of calls placed. Global

Cellular has a plan with no monthly fee, but charges $0.25 per call. She makes a note that the

equation is 𝑀 = 0.25 𝐶, where 𝑀 is the monthly charge and 𝐶 is the number of calls placed.

Both companies offer unlimited text messages.

a. Make a table for both companies showing the cost of service, 𝑀, for making from 0 to

200 calls per month. Use multiples of 20.

Number of

Calls, 𝐶

Super Cell 𝑀 = 0.15𝐶 + 10

Global Cellular 𝑀 = 0.25𝐶

b. Construct a graph for the two equations on the same graph. Use the number of calls, 𝐶,

as the independent variable, and the monthly charge, 𝑀, as the dependent variable.

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c. Which cell phone plan is the best deal for Gertrude? Defend your answer with specific

examples.

7. Sadie is saving her money to buy a new pony, which costs $600. She has already saved $75.

She earns $50 per week working at the stables and wonders how many weeks it will take to

earn enough for a pony of her own.

a. Make a table showing the week number, w, and total savings, 𝑆, in Sadie’s savings

account.

Number of

Weeks(w)

Total

Savings(S)

b. Write an equation for the total amount Sadie has saved (S), if given the number of weeks

Sadie has worked (w).

c. How many weeks will Sadie have to work to earn enough to buy the pony? Justify your

answer.

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8. The elevator at the local mall has a weight limit of 1,800 pounds and requires that the

maximum person allowance be no more than nine people.

a. Let 𝑥 represent the number of people. Write an inequality to describe the maximum

allowance of people allowed in the elevator at one time.

b. Draw a number line diagram to represent all possible solutions to part (a).

c. Let 𝑤 represent the amount of weight. Write an inequality to describe the maximum

weight allowance in the elevator at one time.

d. Draw a number line diagram to represent all possible solutions to part (c).

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9. Devin’s football team carpools for practice every week. This week is his parents’ turn to

pick up team members and take them to the football field. While still staying on the roads,

Devin’s parents always take the shortest route in order to save gasoline. Below is a map of

their travels. Each gridline represents a road and the same distance.

Devin’s father checks his mileage and notices that he drove 18 miles between his house and

Stop 3.

a. Create an equation that can be used to determine the amount of miles that each gridline

represents. Let g represent the number of miles each gridline represents.

b. Using this information, determine how many total miles Devin’s father will travel from

home to the football field, assuming he made every stop. Explain how you determined

the answer.

c. At the end of practice, Devin’s father dropped off team members at each stop and went

back home. How many miles did Devin’s father travel altogether?

Stop 4 Stop 3 Stop 2

Stop 1

Devin’s House Football Field

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10. For a science experiment, Kenneth reflects a beam off a mirror. He is measuring the missing

angle created when the light reflects off the mirror. (Note: figure is not drawn to scale.)

Use an equation to determine the missing angle, labeled 𝑥 in the diagram.

Laser

beam

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51

X

Mirror