Lesson plan

6. Understand how to find a circle's area (C)

teaches Common Core State Standards CCSS.Math.Content.7.EE.B.4a http://corestandards.org/Math/Content/7/EE/B/4/a
teaches Common Core State Standards CCSS.Math.Content.7.G.B.4 http://corestandards.org/Math/Content/7/G/B/4
teaches Common Core State Standards CCSS.Math.Practice.MP2 http://corestandards.org/Math/Practice/MP2
teaches Common Core State Standards CCSS.Math.Practice.MP5 http://corestandards.org/Math/Practice/MP5
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Lesson objective: Extend understanding of area for rectangles and parallelograms to circles.

Students bring prior knowledge of the area of two dimensionsal shapes from grade 4 (4.MDA.3). This prior knowledge is extended to circles as students decompose a circle to determine the formula for the area of a circle. A conceptual challenge students may encounter is how to break up the circle into shapes that can be reassembled into a parallelogram. 

The concept is developed through work with a circle drawing or other circle model that students experiment with in order to find the area formula.

This work helps students deepen their understanding of equivalence because the area of the two shapes (a circle and a parallelogram) are equivalent (and so the area of the circle can be calculated).

Students engage in Mathematical Practice 2 (Reason abstractly and quantitatively) as they explore the relationships between measures of circles and parallelograms while not knowing exact measures. Students also use tools strategically and appropriately (SMP5) as they work with decomposing circles into different shapes, discovering which is the best to reassemble into a parallelogram.

Key vocabulary:

  • area
  • circle
  • diameter
  • radius

Special materials needed:

  • paper circles (either paper cut outs or flattened coffee filters)
  • scissors
  • tape (optional, but may help to create parallelograms)