## illustrative_mathematics_1512.pdf - Section 2: Problem Solving

*illustrative_mathematics_1512.pdf*

*illustrative_mathematics_1512.pdf*

# Circle Designs: Finding the Area and Perimeter of Shapes Composed of Arcs and Line Segments

Lesson 12 of 37

## Objective: SWBAT find the area and perimeter of shapes composed of arcs and line segments

*50 minutes*

#### Problem Solving

*25 min*

I will remind students to show work as they solve and be prepared to discuss their solutions. As noted in the comments section of the task, there will be some discussion and perhaps confusion over finding the perimeter of the green and red shapes. I think it will be simplest just to have students find the total distance of the border around the shaded regions including the holes.

When students struggle, I will ask questions like the opener: What fraction of a circle is present? What fraction of the square is shaded or not shaded?

#### Resources

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#### Summary

*15 min*

We will share out our findings. I will call on groups to present their solutions. I will try to make time to discuss at least two different solution methods per problem. Here is an opportunity for students to critique the reasoning of others or construct a viable argument for their solutions (**MP3**).

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##### Similar Lessons

Environment: Urban

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###### Old and New Knowledge of Circles

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Environment: Urban

- LESSON 1: Explore Perimeter and Area of Composite Shapes
- LESSON 2: Perimeter of Irregular Rectilinear Shapes
- LESSON 3: Area of Composite Shapes Using a Grid
- LESSON 4: Area of Composite Shapes
- LESSON 5: Area of Regions Formed by Inscribed Shapes
- LESSON 6: CORNERSTONE:Circle Ratios: Diameter to Radius; Circumference to Diameter
- LESSON 7: CORNERSTONE: Circumference Formula
- LESSON 8: Area of a Circle
- LESSON 9: Circumference & Area Fluency Practice
- LESSON 10: Finding the Radius From a Given Circumference or Area
- LESSON 11: Circumference from Area / Area from Circumference
- LESSON 12: Circle Designs: Finding the Area and Perimeter of Shapes Composed of Arcs and Line Segments
- LESSON 13: Assessment_Area and Perimeter (Circumference) of Composite Shapes and Circles
- LESSON 14: Drawing Prisms & Pyramids
- LESSON 15: Describe Prisms and Pyramids Using Algebra
- LESSON 16: Using Nets to Find the Surface Area of Prisms
- LESSON 17: Using a Formula to Find the Surface Area of Prisms
- LESSON 18: Finding the surface area of triangular prisms using a net
- LESSON 19: Finding the Surface Area of a Triangular Prism Using A Formula
- LESSON 20: Discovering the Formula for the Surface Area of A Cylinder
- LESSON 21: Finding the Surface Area of Cylinders Using a Formula
- LESSON 22: Practice Day: Surface Area of Prisms & Cylinders
- LESSON 23: Surface Area of Prisms and Cylinders Assessment
- LESSON 24: Finding the Surface Area of Pyramids Using Nets
- LESSON 25: Finding the Surface Area of Pyramids Using a Formula
- LESSON 26: Surface Area of Composite Shapes
- LESSON 27: Surface Area of Composite Shapes With Holes
- LESSON 28: Surface Area Assessment
- LESSON 29: 3-D Models from 2-D Views
- LESSON 30: Exploring Volume and Surface Area with Unifix Cubes
- LESSON 31: Explore Volume of Rectangular Prisms
- LESSON 32: Find the Volume of Prisms Using a Formula
- LESSON 33: Volume Of Cylinders Using a Formula
- LESSON 34: Volume of Composite Shapes
- LESSON 35: Volume and Surface Area - Accelerated Math Fluency Day
- LESSON 36: Volume of Pyramids
- LESSON 37: Surface Area and Volume Final Assessment