Geometry

Lesson 11

Objective

Solve problems involving area and circumference of two-dimensional figures (Part 2).

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.

  • 7.G.B.6 — Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.

Foundational Standards

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  • 6.G.A.1

  • 7.G.A.1

Criteria for Success

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  1. Know and use the formulas for area and circumference of a circle.
  2. Use a scale to find the actual area and perimeter/circumference from scale drawings. 
  3. Find the area and perimeter/circumference of composite shapes and shaded regions, including shapes composed of circles, semi-circles, quadrilaterals, and triangles.

Tips for Teachers

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  • Lessons 10 and 11 engage students in finding area and circumference/perimeter measurements of different geometric shapes including circles, quadrilaterals, and triangles. The Problem Set Guidance includes a variety of problems that range in difficulty and time required.
  • Students engage in MP.1 and MP.7 as they make sense of complex geometric figures, looking for significance of shapes and measurements within the structure of the diagram, and looking for entry points to solve the problem. Support students by asking questions about what they observe in the diagrams and what initial strategy ideas they have.

Remote Learning Guidance

If you need to adapt or shorten this lesson for remote learning, we suggest prioritizing Anchor Problem 2 (benefits from worked example). Find more guidance on adapting our math curriculum for remote learning here.

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Anchor Problems

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Problem 1

The figure below is composed of eight circles, seven small circles and one large circle containing them all. Neighboring circles only share one point, and two regions between the smaller circles have been shaded. Each small circle has a radius of 5 cm.

Calculate:

  1. The area of the large circle.
  2. The area of the shaded part of the figure.

 

 

 

 

Guiding Questions

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References

Illustrative Mathematics Eight Circles

Eight Circles, accessed on June 2, 2017, 11:46 a.m., is licensed by Illustrative Mathematics under either the CC BY 4.0 or CC BY-NC-SA 4.0. For further information, contact Illustrative Mathematics.

Problem 2

A circular mirror is placed in a square wooden frame, as shown in the scale drawing below. The scale of the drawing is 1 inch to 6 inches.

  1. What is the actual perimeter of the wooden frame?
  2. What is the actual area of the circular mirror?

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.

Target Task

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A circle is divided into 4 equal sections and placed within a square with side lengths 15 cm, as shown below. What is the area of the region that is shaded in the middle of the square?

Mastery Response

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