Geometry

Lesson 9

Objective

Solve real-world and mathematical problems using the relationship between the area of a circle and its radius.

Common Core Standards

Core Standards

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  • 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.

Criteria for Success

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  1. Know the formula that relates the area and radius of a circle: $${{A=\pi r^2}}$$.
  2. Use the formula $${{A=\pi r^2}}$$ to solve problems.

Tips for Teachers

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Lessons 8 and 9 focus on the relationship between a circle’s area and its radius. In Lesson 9, students will solve real-world and mathematical problems involving area. Students will solve more problems involving all measurements of circles in Lessons 10 and 11.

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Anchor Problems

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Problem 1

Suzanne is making a circular table of out a square piece of wood. The diameter of the circle she is cutting is 6 feet. How much waste will she have for this project? Express your answer to the nearest square foot.

Guiding Questions

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References

EngageNY Mathematics Grade 7 Mathematics > Module 3 > Topic C > Lesson 17Example 3

Grade 7 Mathematics > Module 3 > Topic C > Lesson 17 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..

Modified by The Match Foundation, Inc.

Problem 2

Recall the image below from Lesson 7, composed of a square and two semi-circles. Find the area of the figure. 

Guiding Questions

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Problem 3

A 12 ft. rope is attached to the wall of a garage. A dog’s collar is attached to the end of the rope to allow him to safely stay outside. What is the area of the space the dog has outside?

Guiding Questions

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Problem Set

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With Fishtank Plus, you can download a complete problem set and answer key for this lesson. Download Sample

The following resources include problems and activities aligned to the objective of the lesson that can be used to create your own problem set.

  • Include problems with composite shapes including simple quadrilaterals, triangle, and circles or semi-circles.
  • Include problems where students determine the percent increase in area from one circle to another; for example, a medium pizza has a diameter of 14 inches and a large pizza has a diameter of 16 inches. By what percent is the area of the large pizza greater than the medium pizza?

Target Task

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A circular platter fits exactly into a box. The base of the box is a square with side lengths 24 cm. 

What is the area of the circular platter? 

Mastery Response

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