# 3. Discover Pi (C)

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.MP8 http://corestandards.org/Math/Practice/MP8

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Lesson objective: Understand that the ratio of the circumference of a circle to its diameter is a constant and it is represented by the symbol π.

Students bring prior knowledge of perimeter from fourth grade (4.MDA.3). This prior knowledge is extended to circles as students discover the relationship between the circumference and the diameter. A conceptual challenge students may encounter is understanding that this ratio always results in a constant, which we call Pi (π).

The concept is developed through work with examples of circles from real life, which are used as examples to measure and then the ratios (c/d) as compared.

This work helps students deepen their understanding of equivalence because understanding that the ratio Pi represents is true for all circles is key to moving forward in the examination of circles in two and three dimensions.

Students engage in Mathematical Practice #7 (Look for and make use of structure) as they measure circles of different sizes and discover that the same value (π) repeatedly comes up.

Key vocabulary:

• circumference
• diameter

Special materials needed:

• string, rulers, and a copy of task worksheet or other circle items to measure
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