Determine the relationship between the area and radius of a circle and use it to solve problems.
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Lessons 8 and 9 focus on the relationship between a circle’s area and its radius. In Lesson 8, students determine this relationship and the formula that represents it. In Lesson 9, students will solve real-world and mathematical problems involving area.
If you need to adapt or shorten this lesson for remote learning, we suggest prioritizing Anchor Problem 2 (benefits from discussion) and Anchor Problem 3 (benefits from worked example). Students can use the interactive Academo applet (linked to the right) to explore finding the area of a circle and then discuss As a discovery problem, if live discussion or reflection of the problem were possible, it would allow for students to arrive at the conclusion on their own. Find more guidance on adapting our math curriculum for remote learning here.
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Use the centimeter grid to find an approximate area of the circle. Explain why your approximation is reasonable.
Use this applet from Academo, Area of a circle (Rearrangement Method) to informally derive the relationship between the area of a circle and its circumference
Start with a small number of sectors or wedges of the circle and then slowly increase the number. Click “rearrange” after each number. Ask:
Area of a Circle (Rearrangement Method) is made available by Academo. © Academo.org 2016. Accessed March 10, 2018, 11:26 a.m..
Use the relationship between area and radius to solve the two problems below.
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The following resources include problems and activities aligned to the objective of the lesson that can be used to create your own problem set.
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A circle is divided into 16 equal wedges, as shown below. Explain or show how you can rearrange the pieces to determine the area of the circle.
Find the area of a circle that has a radius of 5 inches.
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