Grade 7, Unit 4 Practice Problems - Open Up Resources

[Pages:30]Unit 4 Practice Problems

Lesson 1

Problem 1

A rectangle has a height to width ratio of be scaled versions of this rectangle.

. Give two examples of dimensions for rectangles that could

Solution

Answers vary. Sample response: A rectangle measuring 6 units by 9 units and a rectangle measuring 9 units by 13.5 units.

Problem 2

One rectangle measures 2 units by 7 units. A second rectangle measures 11 units by 37 units. Are these two figures scaled versions of each other? If so, find the scale factor. If not, briefly explain why.

Solution

No, these two figures are not scaled versions of each other. The 2 unit side is scaled by a factor of 5.5 to correspond to the 11 unit side, but 7 multiplied by 5.5 is 38.5, not 37.

Problem 3

(from Unit 2, Lesson 5)

Ants have 6 legs. Elena and Andre write equations showing the proportional relationship between the

number of ants, , to the number of ant legs . Elena writes

and Andre writes

. Do you

agree with either of the equations? Explain your reasoning.

Solution

Neither of them are correct. Although 6 and are the correct constants of proportionality, they are being multiplied by the wrong variables. For example, using Elena's equation, 1 leg is equal to 6 ants.

Problem 4

(from Unit 1, Lesson 4) On the grid, draw a scaled copy of quadrilateral ABCD with a scale factor .

Solution

Answers vary. Sample response on the right.

Problem 5

(from Unit 1, Lesson 5) Solve each equation mentally.

1. 2. 3.

Solution

1. 2. 3.

Problem 6

(from Unit 1, Lesson 11) Lin has a scale model of a modern train. The model is created at a scale of 1 to 48.

1. The height of the model train is 102 millimeters. What is the actual height of the train in meters? Explain your reasoning.

2. On the scale model, the distance between the wheels on the left and the wheels on the right is inches. The state of Wyoming has old railroad tracks that are 4.5 feet apart. Can the modern train travel on those tracks? Explain your reasoning.

Solution

1. 4.896 meters. Sample reasoning: The actual height is 48 times the scaled height.

. 4,896 mm is 4.896 m.

102 mm is 0.102 m. The actual train is 48 times 0.102 m.

.

2. No. Sample explanation: The modern train needs tracks that are 60 inches apart, because . The old tracks are only 54 inches, so they are not wide enough.

Lesson 2

Problem 1

A cyclist rode 3.75 miles in 0.3 hours. 1. How fast was she going in miles per hour? 2. At that rate, how long will it take her to go 4.5 miles?

Solution

1. 12.5 miles per hour 2. 0.36 hours or 21.6 minutes

Problem 2

A recipe for sparkling grape juice calls for

quarts of sparkling water and quart of grape juice.

1. How much sparkling water would you need to mix with 9 quarts of grape juice?

2. How much grape juice would you need to mix with quarts of sparkling water?

3. How much of each ingredient would you need to make 100 quarts of punch?

Solution

Notice that the ratio quarts of sparkling water to quarts of grape juice is equivalent to the ratio 2 quarts of sparkling water to 1 quart of grape juice. While not needed, this ratio with whole numbers can help answer all three questions.

1. 18 quarts

2. quarts or equivalent

3. quarts of sparking water and quarts of grape juice (or equivalent).

Problem 3

(from Unit 3, Lesson 10)

1. Draw a scaled copy of the circle using a scale factor of 2. 2. How does the circumference of the scaled copy compare to the circumference of the original circle? 3. How does the area of the scaled copy compare to the area of the original circle?

Solution

1. The outer circle is a scaled copy of the inner circle using scale factor 2.

2. The circumference of the scaled copy is twice the circumference of the original.

3. The area of the scaled copy is four times the area of the original.

Problem 4

At a deli counter,

Someone bought Someone bought Someone bought

pounds of ham for $14.50. pounds of turkey for $26.25. pounds of roast beef for $5.50.

Which meat is the least expensive per pound? Which meat is the most expensive per pound? Explain how you know.

Solution

Ham is the least expensive. It costs about $8.29 per pound, because

. Roast beef

is the most expensive. It costs about $14.67 per pound, because

. Turkey costs

about $10.50 per pound, because

. While these prices per pound are not exact, they are

far enough apart to put the costs in order with certainty.

Problem 5

(from Unit 1, Lesson 11) Jada has a scale map of Kansas that fits on a page in her book. The page is 5 inches by 8 inches. Kansas is about 210 miles by 410 miles. Select all scales that could be a scale of the map. (There are 2.54 centimeters in an inch.)

1. 1 in to 1 mi 2. 1 cm to 1 km 3. 1 in to 10 mi 4. 1 ft to 100 mi 5. 1 cm to 200 km 6. 1 in to 100 mi 7. 1 cm to 1000 km

Solution

E, F

Lesson 3

Problem 1

It takes an ant farm 3 days to consume of an apple. At that rate, in how many days will the ant farm consume 3 apples?

Solution

18 days

Problem 2

To make a shade of paint called jasper green, mix 4 quarts of green paint with cups of black paint. How much green paint should be mixed with 4 cups of black paint to make jasper green?

Solution

24 quarts

Problem 3

An airplane is flying from New York City to Los Angeles. The distance it travels in miles, , is related to the

time in seconds, , by the equation

.

1. How fast is it flying? Be sure to include the units.

2. How far will it travel in 30 seconds?

3. How long will it take to go 12.75 miles?

Solution

1. It is traveling at 0.15 miles per second.

2. It will travel 4.5 miles in 30 seconds.

3. It will take 85 seconds to travel 12.75 miles.

Problem 4

A grocer can buy strawberries for $1.38 per pound. 1. Write an equation relating , the cost, and , the pounds of strawberries.

2. A strawberry order cost $241.50. How many pounds did the grocer order?

Solution

1.

2. 175 pounds

Problem 5

(from Unit 3, Lesson 10) Crater Lake in Oregon is shaped like a circle with a diameter of about 5.5 miles.

1. How far is it around the perimeter of Crater Lake?

2. What is the area of the surface of Crater Lake?

Solution

1. About 17 miles ( )

2. About 24 square miles (

)

Problem 6

(from Unit 3, Lesson 8) A 50-centimeter piece of wire in bent into a circle. What is the area of this circle?

Solution

or about 199 cm2

Problem 7

(from Unit 1, Lesson 2) Suppose Quadrilaterals A and B are both squares. Are A and B necessarily scale copies of one another? Explain.

Solution

Yes. Since all four side lengths of a square are the same, whatever scale factor works to scale one edge of A to an edge of B takes all edges of A to all edges of B. Since scaling a square gives another square, B is a scaled copy of A.

Lesson 4

Problem 1

Match each situation with a diagram.

1. Diego drank ounces of juice. Lin drank less than that.

2. Lin ran miles. Diego ran more than that.

3. Diego bought pounds of almonds. Lin bought of that.

Solution

1. B 2. A 3. C

Problem 2

Elena walked 12 miles. Then she walked that distance. How far did she walk all together? Select all that apply.

1. 2. 3. 4. 5. 6.

Solution

C, D, F

Problem 3

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