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Filling and Wrapping: Three-Dimensional Measurement Name: ______________________ Per: _____

Investigation 3: Area and Circumference in Circles

Date Learning Target/s Classwork

Homework

Self-Assess Your Learning

Thurs, Mar. 31

Find the circumference of a circle from the diameter or radius.

Pg. 2: FW 3.1 – Circumference

Pg. 3: Piano Player Puzzle (use ruler)

Fri, Apr. 1 Find the area of a circle by estimating and squaring a circle.

Pg. 4-5: FW3.2 and 3.3 – Area of Circles

Pg. 6: FW 3.2 and 3.3 – Complete and Correct with Zaption

Mon, Apr. 4

Find the area of a circle by connecting to the area of a parallelogram.

Pg. 7-8: FW 3.4 – Connecting Circumference and Area

Pg. 9: Title of Picture Puzzle

Tues, Apr. 5

Review unit learning targets. Pg. 10-11: Airline Puzzle

Unit Review (separate)

Weds, Apr. 6

Review unit learning targets. Correct Unit Review

Google Doc Review

Thurs, Apr. 7

Assess understanding of unit learning targets.

Filling and Wrapping Unit Test

Pg. 12: SBAC Review 3 – Complete and Correct with Zaption

Inv. 3 CCSS.MATH.CONTENT.7.G.B.4:

Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle.

Parent/Guardian Signature: ________________________________ Due: Friday, April 8

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FW 3.1: Circumference

A. Label the diameter and radius of the circle.

1. How can you find the diameter if you know the radius?

2. How can you find the radius if you know the diameter?

B. What is circumference?

1. What is pi?

2. How can you find the circumference of a circle if you know its diameter?

3. How can you find the radius of a circle if you know its circumference?

C. Practice finding circumference. Write and solve an equation for each problem. Use 3.14 as an estimate for

pi. Round to the nearest tenth.

1. What is the circumference of a circle with a diameter of 6 meters?

2. What is the circumference of a circle with a radius of 3 meters?

3. What is the circumference of a circle with a diameter of 7.2 inches?

4. What is the circumference of a circle with a radius of 18 centimeters?

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FW 3.2: Connecting Area, Diameter, and Radius

A pizzeria plans to sell three sizes of its new pizza with cheese in the crust. A small pizza will be 9 inches in

diameter, a medium will be 12 inches in diameter, and a large will be 15 inches in diameter.

The owner surveyed her lunch customers to find out what they would be willing to pay for a small pizza. She found

that $6 was a fair price for a 9-inch pizza with one topping. Based on this price, the owner wants to find fair prices

for 12-and 15-inch pizzas with one topping.

One of the cooks suggests making the

difference in prices match the

difference in pizza diameters, but the

owner disagrees. She says that area is

the best measurement to use to set the

prices. She also says that comparing

areas would suggest different prices

from comparing diameters.

What is the relationship, if any,

between the diameter or radius of a

circle and its area?

To answer this question, the owner uses

scale models of the different size pizzas:

A. Record each pizza’s diameter, radius, and your estimate of its area based on the scale models above.

Size Diameter (in) Radius (in) Area (in2)

Small

Medium

Large

B. Examine the data in the table.

1. Describe the pattern relating area to diameter or radius.

2. What would you be your best estimate for the area of a circle with diameter 18 inches?

C. Based on your area estimations, what would be fair prices for medium and large pizzas? Explain your

reasoning.

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FW 3.3: Connecting Area, Diameter, and Radius

How is the area of a circle related to the area of a square?

In the drawing below, a shaded square covers a portion of each circle. The length of a side fo the shaded square is

the same length as the radius of the circle. You call such a square a “radius square”.

A. For each circle, record the radius, area of the “radius square”, area of the circle, and number of “radius

squares” needed to cover each circle.

Circle Radius of circle (units) Area of Radius Square (square units)

Area of Circle (square units)

Number of Radius Squares Needed

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2

3

B. Describe any patterns and relationships you see

in the table that will allow you to predict the

area of the circle from its “radius square”.

C. How can you find the area of a circle if you know

its radius?

D. How can you find the radius of a circle if you

know its area?

E. What would you be your best estimate for the

area of a circle with a radius of 8 units?

F. What is the formula for finding the area of a circle?

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FW 3.2 and 3.3 Homework – Complete and correct with Zaption

1. What is the formula for circumference of a circle?

2. A juice can is about 2.5 inches in diameter. What is its circumference?

3. What is the formula for area of a circle?

4. A juice can is about 2.5 inches in diameter. What is its area?

5. A pizzeria sells three different sizes of pizza. The small size has a radius of 4 inches, the medium size has a

radius of 5 inches, and the large size has a radius of 6 inches.

a. Complete the table:

Pizza Size Diameter (in) Radius (in)

Circumference (in) Write and solve an equation. Round to the nearest tenth. Use 3.14 as an estimate for pi.

Area (in2) Write and solve an equation. Round to the nearest tenth. Use 3.14 as an estimate for pi.

Small

Medium

Large

6. Describe the two-dimensional figure formed by each type of slice of the square prism.

a. Vertical slice

b. Horizontal slice

c. Slanted slice

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FW 3.4: Connecting Circumference and Area

A. The radius of the circular pizza is 6 inches. What are its circumference and area? Show your calculations.

B. The shape made by re-arranging the pizza slices looks like a parallelogram.

1. Estimate the height and base of the parallelogram. Explain your reasoning.

2. What is the approximate area of the parallelogram?

3. How does the approximate area of the parallelogram compare to the exact area of the circular pizza?

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C. The connection between the area of the circular pizza and the area of the near-parallelogram formed when

the pizza slices are rearranged is only an approximation.

Sara thinks about the parallelogram and says that the area of a circle is A = ½ (Πd)(r).

Evan thinks about covering the circle with radius squares and says the area is A = Πr2.

1. Do these formulas give the same area for radius 6 centimeters? Explain your reasoning.

2. Would both formulas work for all values of r? Why or why not?

3. How would the accuracy of the approximation change if you cut the pizza into more slices?

D. Suppose that you have 12 meters of fencing and want to make a pen for your pet dog. Which shape, a

square or a circle, would give more area? Explain.

E. A rectangular lawn has a perimeter of 36 meters and a circular exercise run has a circumference of 36

meters. Which shape will give Rico’s dog more area to run? Explain.

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Note: Show all of your calculations.

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Note: Show all of your calculations.

Puzzle continues on the next page…

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SBAC Practice Test – Part 3 Score: ___ / 4

? Question and Answer Correct Answer

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