In this lesson, students use the equation \(C=\pi d\) to solve problems in a variety of contexts. They compute the circumference of circles and parts of circles given diameter or radius, and vice versa. Students develop flexibility using the relationships between diameter, radius, and circumference rather than memorizing a variety of formulas. Understanding the equation \(C = 2 \pi r\) will help with the transition to the study of area in future lessons.
Students think strategically about how to decompose and recompose complex shapes (MP7) and need to choose an appropriate level of precision for \(\pi\) and for their final calculations (MP6).
- Apply understanding of circumference to calculate the perimeter of a shape that includes circular parts, and explain (orally and in writing) the solution method.
- Compare and contrast (orally) values for the same measurements that were calculated using different approximations for $\pi$.
- Explain (orally) how to calculate the radius, diameter, or circumference of a circle, given one of these three measurements.
Let’s use \(\pi\) to solve problems.
- I can choose an approximation for $\pi$ based on the situation or problem.
- If I know the radius, diameter, or circumference of a circle, I can find the other two.
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