7th Grade Math : Unit #6 - Geometry : Lesson #12

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

Objective: SWBAT find the area and perimeter of shapes composed of arcs and line segments
Standards: 7.G.B.4 MP1 MP3 MP4
Subject(s): Math
60 minutes
2 Problem Solving - 25 minutes

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? 

Making Sense!
Complex Tasks

Here is a re-creation of the discussions around the blue figure.  The blue figure is composed of two circles and a square.  The square occupies 1/4 each circle.  It took a lot of questioning to get some students to see this.  

I asked in order:

1) What shapes do you see?

2) What fraction of each circle is taken up by the square?  How do you know?

The "how do you know" part was challenging for students.  I might have to ask them what is the angle for the square? [a right angle] How many degrees is a full circle? [360]  What fraction of a complete circle is a right angle?  [1/4]

For some students, I had them refer back to the fraction circles that we looked at in the opening of the lesson.  

Find the actual area and perimeter seemed to be easier than making sense of the shapes!  In other words, once students made sense of the shapes, they did not have much difficulty find the area and perimeter.

3 Summary - 15 minutes

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).