Unit 3, Lesson 6: Estimating Areas

6.1: Mental Calculations (5 minutes)

Setup: Display one problem at a time. 1 minute of quiet think time per problem, followed by a whole-class discussion.

Lesson GoalsCalculate areas of polygons.Find area of a complex shape by decomposing into polygons of known areas.

Required Materialsgeometry toolkits

Student task statementFind a strategy to make each calculation mentally:

1.

2.

3.

Possible responses

1. 686

2. 166

3. 7,425

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•

GRADE 7 MATHEMATICS

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Unit 3: Measuring Circles, Lesson 6: Estimating Areas 1

6.2: House Floorplan (15 minutes)

Setup: 4–5 minutes of quiet work time followed by whole-class discussion

Student task statementHere is a floor plan of a house. Approximate lengths of the walls are given.

What is the approximate area of the home, including the balcony? Explain or show your reasoning.

Possible responses

About 1,080 ft2

Anticipated misconceptions

If students struggle getting startedfinding the area of the floor plan,consider suggesting that they usecomposition and decomposition tobreak the floor plan up into familiarshapes whose area can be calculated.

GRADE 7 MATHEMATICS

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Unit 3: Measuring Circles, Lesson 6: Estimating Areas 2

6.3: Area of Nevada (15 minutes)

Setup:

Students in groups of 2. Notice and wonder about the unlabelled map. Reveal dimensions. 5 minutes of quiet work time followed bypartner and whole-class discussion.

Student task statementEstimate the area of Nevada in square miles. Explain or show your reasoning.

Possible responses

Approximately 110,000 sq mi

Anticipated misconceptions

If students decompose the image of thestate into a rectangle and triangle, theymay use the 270 miles for a side lengthof the rectangle instead of finding thedifference of the 490 miles on theopposite side and 270 miles. Ask themto check their answer with a partnerand reevaluate their calculations.

GRADE 7 MATHEMATICS

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Unit 3: Measuring Circles, Lesson 6: Estimating Areas 3

Lesson Synthesis (5 minutes)How can we use triangles and rectangles to calculate or estimate the area of a complex shape?

Are you ready for more?The two triangles are equilateral, and the three pink regions are identical. The blue equilateral triangle has thesame area as the three pink regions taken together. What is the ratio of the sides of the two equilateraltriangles?

Possible Responses

or . Since both triangles areequilateral, the three pink regions areidentical, and the pink regions have thesame area as the blue region, theymust fit inside as shown.

GRADE 7 MATHEMATICS

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Unit 3: Measuring Circles, Lesson 6: Estimating Areas 4

6.4: The Area of Alberta (Cool-down, 5 minutes)

Setup: None.

Student task statementEstimate the area of Alberta in square miles. Show your reasoning.

Possible responses

About 250,000 square miles

GRADE 7 MATHEMATICS

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Unit 3: Measuring Circles, Lesson 6: Estimating Areas 5