Illustrative Mathematics Grade 7, Unit 3, Lesson 6: Estimating Areas

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Illustrative Math
Grade 7

Lesson 6: Estimating Areas

Let’s estimate the areas of weird shapes.

Illustrative Math Unit 7.3, Lesson 6 (printable worksheets)

Lesson 6 Summary

The following diagram shows how to calculate the area of a complicated shape by breaking it into shapes whose area I know how to calculate.

Lesson 6.1 Mental Calculations

Find a strategy to make each calculation mentally:

1. 599 + 87
   
2. 254 - 88
   
3. 99 · 75
   
   

• See Video for Whole Lesson

Lesson 6.2 House Floorplan

Here 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.

Lesson 6.3 Area of Nevada

Estimate the area of Nevada in square miles. Explain or show your reasoning.

Are you ready for more?

The two triangles are equilateral, and the three pink regions are identical. The blue equilateral triangle has the same area as the three pink regions taken together. What is the ratio of the sides of the two equilateral triangles?

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Lesson 6 Practice Problems

1. Find the area of the polygon.
   
2. a. Draw polygons on the map that could be used to approximate the area of Virginia.
   b. Which measurements would you need to know in order to calculate an approximation of the area of Virginia? Label the sides of the polygons whose measurements you would need. (Note: You aren’t being asked to calculate anything.)
   
3. Jada’s bike wheels have a diameter of 20 inches. How far does she travel if the wheels rotate 37 times?
   
4. The radius of the earth is approximately 6400 km. The equator is the circle around the earth dividing it into the northern and southern hemisphere. (The center of the earth is also the center of the equator.) What is the length of the equator?
   
5. Here are several recipes for sparkling lemonade. For each recipe describe how many tablespoons of lemonade mix it takes per cup of sparkling water.
   Recipe 1: 4 tablespoons lemonade mix and 12 cups of sparkling water
   Recipe 2: 4 tablespoons of lemonade mix and 6 cups of sparkling water
   Recipe 3: 3 tablespoons of lemonade mix and 5 cups of sparkling water
   Recipe 4: 1/2 tablespoon of lemonade mix and 3/4 cups of sparkling water
   

The Open Up Resources math curriculum is free to download from the Open Up Resources website and is also available from Illustrative Mathematics.

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