Reflection: Complex Tasks Circle Designs: Finding the Area and Perimeter of Shapes Composed of Arcs and Line Segments - Section 2: Problem Solving


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.

  Making Sense!
  Complex Tasks: Making Sense!
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Circle Designs: Finding the Area and Perimeter of Shapes Composed of Arcs and Line Segments

Unit 6: Geometry
Lesson 12 of 37

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

Big Idea: These shapes look really cool.

  Print Lesson
Math, volume (3-D Geom), Geometry, circumference (Determining Measurements), area and perimeter (circles), composite shapes, 7th grade
  50 minutes
a circle design
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