Grade 6, Unit 3 - Practice Problems (2024)

A sandwich shop serves 4 ounces of meat and 3 ounces of cheese on each sandwich. After making sandwiches for an hour, the shop ownerhasused 91 combined ounces of meat and cheese.

1. How many combined ounces of meat and cheese are used on each sandwich?

2. How many sandwiches were made in the hour?
3. How many ounces of meat were used?
4. How many ounces of cheese were used?

Here is a flower made up of yellow hexagons, red trapezoids, and green triangles.

Match each quantity in the first list with an appropriate unit of measurement from the second list.

Select the unit from the list that you would use to measure each object.

When this pet hamster is placed on a digital scale, the scale reads 1.5.

Circle the larger unit of measure. Then, determine if the unit measures distance, volume, or weight (mass).

Lin bought 3 hats for \$22.50. At this rate, how many hats could she buy with \$60.00? If you get stuck, try using the table.

Decide if each is a measurement of length, area, volume, or weight (or mass).

1. How many centimeters across a handprint
2. How many square inches of paper needed to wrap a box
3. How many gallons of water in a fish tank
4. How many pounds in a bag of potatoes
5. How many feet across a swimming pool
6. How many ounces in a bag of grapes
7. How many liters in a punch bowl
8. How many square feet of grass in a lawn

Tyler’s height is 57 inches. Whatcould be his height in centimeters? Explain your reasoning.

1. 22.4
2. 57
3. 144.8

4. 3,551

A large soup pot holds 20 quarts. What could be its volume in liters?

1. 7.57
2. 19
3. 21
4. 75.7

Clare wants to mail a package that weighs $4\frac12$ pounds. What could this weight be in kilograms?

1. 2.04
2. 4.5
3. 9.92
4. 4,500

Noah bought 15 baseball cards for \$9.00. Assumingeach baseball card costs the same amount, answer the following questions.

1. At this rate, how much will 30 baseball cards cost? Explain your reasoning.
2. At this rate, how much will 12 baseball cards cost? Explain your reasoning.
3. Do you think this information would be better represented using a table or a double number line? Explain your reasoning.

Jada traveled 135 miles in 3 hours. Andre traveled 228 miles in 6 hours. Both Jada and Andre traveled at a constant speed.

1. How far did Jada travel in 1 hour?
2. How far did Andre travel in 1 hour?
3. Who traveled faster? Explain or show your reasoning.

Priya’s family exchanged 250 dollars for 4,250 pesos. Priya bought a sweater for 510 pesos. How many dollars did the sweater cost?

There are 3,785 milliliters in 1 gallon, and there are 4 quarts in 1 gallon. For each question, explain or show your reasoning.

1. How many milliliters are in 3 gallons?
2. How many milliliters are in 1 quart?

Lin knows that there are 4 quarts in a gallon. She wants to convert 6 quarts to gallons, but cannot decide if she should multiply 6 by 4 or divide 6 by 4 to find her answer. What should she do? Explain or show your reasoning. If you get stuck, consider drawing a double number line or using a table.

Identify whether each unit measures length, volume, or weight (or mass).

An ant can travel at a constant speed of 980 inches every 5 minutes.

1. How far does the ant travel in 1 minute?
2. At this rate, how far can the ant travel in 7 minutes?

Here are the prices for cans of juice that are the same brand and the same size at different stores. Which store offers the best deal? Explain your reasoning.

Costs of homes can be very different indifferent parts of the United States.

1. A 450-square-foot apartment in New York Citycosts \$540,000. What is the price per square foot?Explain or show your reasoning.
2. A 2,100-square-foot home in Cheyenne, Wyoming, costs \$110 per square foot. How much does this home cost?Explain or show your reasoning.

There are 33.8 fluidounces in a liter. There are 128 fluidounces in a gallon. About how manyliters arein a gallon?

1. 2
2. 3
3. 4
4. 5

Is your estimate larger or smaller than the actual number of liters in a gallon? Explain how you know.

Name an object that could be about the same length as each measurement.

A pink paint mixture uses 4 cups of white paint for every 3 cups of red paint.

A farm lets you pick 3 pints of raspberries for \$12.00.

1. What is the cost per pint?
2. How many pints do you get per dollar?
3. At this rate, how many pints can you afford for \$20.00?
4. At this rate, how much will 8 pints of raspberries cost?

Han and Tyler are following a polenta recipe that uses 5 cups of water for every 2 cups of cornmeal.

• Han says, “I am using 3 cups of water. I will need $1\frac15$ cups of cornmeal.”
• Tyler says, “I am using 3 cups of cornmeal. I will need $7\frac12$ cups of water.”

Do you agree with eitherof them? Explain your reasoning.

A large art project requires enough paint to cover 1,750 square feet. Each gallon of paint can cover 350 square feet. Each square foot requires $\frac{1}{350}$ of a gallon of paint.

Andre thinks he should use the rate $\frac{1}{350}$ gallons of paint per square foot to find how much paint they need. Do you agree with Andre? Explain or show your reasoning.

A soccer field is 100 meters long. What could be its length in yards?

1. 33.3
2. 91
3. 100
4. 109

A car travels 55 miles per hour for 2 hours. Complete the table.

The table shows the amounts of onions and tomatoes in different-sizedbatches of a salsa recipe.

A restaurant is offering 2 specials: 10 burritos for \$12,or 6burritos for \$7.50. Noah needs 60 burritos for his party. Should he buy 6 orders of the 10-burrito special or 10 orders of the 6-burrito special? Explain your reasoning.

Complete the table so that the cost per banana remains the same.

A car has 15 gallons of gas in its tank. The car travels35 miles per gallon of gas.It uses $\frac{1}{35}$ of a gallon of gas to go 1 mile.

A kangaroo hops 2 kilometers in 3 minutes.At this rate:

At 10:00 a.m., Han and Tyler both started running toward each other from opposite ends of a 10-mile path along a river. Han runs at a pace of 12 minutes per mile. Tyler runs at a pace of 15 minutes per mile.

1. How far does Han run after a half hour? After an hour?
2. Do Han and Tyler meet on the path within 1 hour? Explain or show your reasoning.

Two larger cubes are made out of unit cubes. Cube A is 2 by 2 by 2. Cube B is 4 by 4 by 4.The side length of Cube B is twice that of Cube A.

This package of sliced cheese costs \$2.97.

A copy machine can print 480 copies every 4 minutes. For each question, explain or show your reasoning.

Order these objects from heaviest to lightest.(Note: 1 pound = 16 ounces, 1kilogram $\approx$ 2.2 pounds, and 1 ton = 2,000 pounds)

Andre sometimes mows lawns on the weekend to make extra money. Two weeks ago, he mowed a neighbor’slawnfor$\frac{1}{2}$ hour and earned \$10. Last week, he mowed his uncle’s lawn for $\frac{3}{2}$ hours and earned \$30. This week, he mowed thelawn of a community centerfor 2 hours and earned \$30.

Which jobs paid better than others? Explain your reasoning.

Calculate and express your answer in decimal form.

1. Decompose this polygon so that its area can be calculated. All measurements are in centimeters.

What percentage of a dollar is the value of each coin combination?

1. 4 dimes
2. 1 nickel and 3 pennies
3. 5 quarters and 1 dime

1. List three different combinations of coins, each with a value of 30% of a dollar.

2. List two different combinations of coins, each with a value of 140% of a dollar.

The United States government used to make coins of many different values. For each coin, state its worth as a percentage of \$1.

Complete the double number to line showpercentages of \$50.

Elena bought 8 tokens for \$4.40. At this rate:

1. How many tokens could she buy with \$6.05?
2. How much do 19 tokens cost?

A snail travels 10 cm in 4 minutes. At this rate:

1. How long will it take the snail to travel 24 cm?
2. How far does the snail travel in 6 minutes?

1. 3 tacos cost \$18. Complete the table to show the cost of 4, 5, and 6 tacos at the same rate.

   	number oftacos	costin dollars	ratein dollarspertaco
   row 1	3	18
   row 2	4
   row 3	5
   row 4	6

   b. If you buy $t$ tacos for $c$ dollars, what is the unit rate?

Solve each problem. If you get stuck, consider using the double number lines.

1. During a basketball practice, Mai attempted 40 free throws and was successful on 25% of them. How many successful free throws did she make?

   

2. Yesterday, Priya successfully made 12 free throws. Today, she made 150% as many. How many successful free throws did Priya make today?

   

A 16-ounce bottle of orange juice says it contains 200 milligrams of vitamin C, which is 250% of the daily recommended allowance of vitamin C for adults. What is 100% of the daily recommended allowance of vitamin C for adults?

At a school, 40% of the sixth-grade studentssaid that hip-hop is their favorite kind of music. If 100 sixth-grade studentsprefer hip hop music, how many sixth-grade students are at the school? Explain or show your reasoning.

Diego has a skateboard, scooter, bike, and go-cart. He wants to know which vehicle is the fastest. A friend records how far Diego travels on each vehicle in5 seconds. For each vehicle, Diegotravels as fast as he can along a straight, level path.

It takes10 pounds of potatoes to make 15 pounds of mashed potatoes. At this rate:

Here is a tape diagram that shows how far two students walked.

1. What percentage of Priya’s distance did Tyler walk?
2. What percentage of Tyler’s distance did Priya walk?

There are 70 students in the school band. 40% of them are sixth graders, 20% are seventh graders, and the rest are eighth graders.

1. How many band members are sixth graders?
2. How many band members are seventh graders?
3. What percentage of the band members are eighth graders? Explain your reasoning.

An athlete runs 8 miles in 50 minutes on a treadmill. At this rate:

1. How long will it take the athlete to run 9 miles?
2. How far can the athlete run in 1 hour?

1. How can you find 50% of a number quickly in your head?

2. Andre lives 1.6 km from school. What is 50% of 1.6 km?

3. Diego lives $\frac 1 2$ mile from school. What is 50% of $\frac 1 2$ mile?

There is a 10% off sale on laptop computers. If someone saves \$35 on a laptop, what was its original cost? If you get stuck, consider using the table.

Explain how to calculate these mentally.

1. 15 is what percentage of 30?
2. 3 is what percentage of 12?
3. 6 is what percentage of 10?

Noah says that to find 20% of a number he divides the number by 5. For example, 20% of 60 is 12, because $60 \div 5 = 12$. Does Noah’s method always work? Explain why or why not.

Lin and Andre start walking toward each other at the same time from opposite ends of 22-mile walking trail. Lin walks at a speed of 2.5 miles per hour. Andre walks at a speed of 3 miles per hour.

Here is a table showing the distances traveledand how far apart Lin and Andrewere over time. Use the table to findhow much time passes before they meet.

For each problem, explain or show your reasoning.

1. 160 is what percentage of 40?
2. 40 is 160% of what number?
3. What number is 40% of 160?

Select all the expressions whose value islarger than 100.

1. 120% of 100
2. 50% of 150
3. 150% of 50
4. 20% of 800
5. 200% of 30
6. 500% of 400
7. 1% of 1,000

An ant travels at a constant rate of 30 cm every 2 minutes.

1. At what pace does the ant travel per centimeter?
2. At what speed does the ant travel per minute?

Name a unit of measurement that is about the same size as each object.

1. The distance of a doorknob from the floor is about 1 _____________.

2. The thickness of a fingernail is about 1 _____________.

3. The volume of a drop of honey is about 1 _____________.

4. The weight or mass of a pineapple is about 1 _____________.

5. The thickness of a picture book is about 1 _____________.

6. The weight or mass of a buffalo is about 1 _____________.

7. The volume of a flower vase is about 1 _____________.

8. The weight or mass of 20 staples is about 1 _____________.

9. The volume of a melon is about 1 _____________.

10. The length of a piece of printer paper is about 1 _____________.

1. To find 40% of 75, Priya calculates $\frac{2}{5} \boldcdot 75$. Does hercalculationgive the correct value for 40% of 75? Explain or show how you know.
2. If $x$ represents a number, does $\frac{2}{5} \boldcdot x$ always represent 40% of that number? Explain your reasoning.

Han spent 75 minutes practicing the piano over the weekend. For each question, explain or show your reasoning.

Last Sunday 1,575 people visited the amusem*nt park. 56% of the visitors were adults, 16% were teenagers, and 28% were children ages 12 and under. Find the number of adults, teenagers, and children that visited the park.

Order from greatest to least:

• 55% of 180
• 300% of 26
• 12% of 700

Complete each statement.

On a field trip, there are 3 chaperones for every 20 students. There are 92 people on the trip. Answer these questions. If you get stuck, consider using a tape diagram.

1. How many chaperones are there?
2. How many children are there?

A sign in front of a roller coaster says "You must be 40 inches tall to ride." What percentage of this height is:

1. 34 inches?
2. 54 inches?

The sale price of every item in a store is 85% of its usual price.

1. The usual price of a backpack is \$30, what is its sale price?
2. The usual price of a sweatshirt is \$18, what is its sale price?
3. The usual price of a soccer ball is \$24.80, what is its sale price?

Elena is 56 inches tall.

1. What is her height in centimeters? (Note: 100 inches = 254 centimeters)

2. What is her height in meters?