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Finding the area of a circle

Finding the area of a circle. Parts of a circle. A circle is the set of all points in a plane that are the same distance from a given point (i.e., the center of the circle) The radius is the distance from the center of the circle to any point on the circle

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Finding the area of a circle

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  1. Finding the area of a circle

  2. Parts of a circle • A circle is the set of all points in a plane that are the same distance from a given point (i.e., the center of the circle) • The radius is the distance from the center of the circle to any point on the circle • The diameter is the distance from one point to another point on the circle crossing through the center of the circle • The circumference of a circle is the distance around the entire circle radius diameter circumference The contents of this content module were developed by special educator Bethany Smith, PhD and validated by content expert Drew Polly, PhD at University of North Carolina at Charlotte under a grant from the Department of Education (PR/Award #: H373X100002, Project Officer, Susan.Weigert@Ed.gov). However, the contents do not necessarily represent the policy of the Department of Education and no assumption of endorsement by the Federal government should be made

  3. Area of a circle • The formula for finding the area of a circle is A=πr2 • When discussing the formula, the teacher may want to talk about the value for πand that it is a constant. This means the value of πis always the same which equals approximately3.14. The contents of this content module were developed by special educator Bethany Smith, PhD and validated by content expert Drew Polly, PhD at University of North Carolina at Charlotte under a grant from the Department of Education (PR/Award #: H373X100002, Project Officer, Susan.Weigert@Ed.gov). However, the contents do not necessarily represent the policy of the Department of Education and no assumption of endorsement by the Federal government should be made

  4. Finding Area • Students should begin calculating the area of a circle when the radius is provided. • For example, what is the area of a circle with a radius of 4. • Step 1: Plug numbers into an equation template A= π(4)2 Helpful Hint: Remember to review order of operations. Students must square r before they multiply by π 4 The contents of this content module were developed by special educator Bethany Smith, PhD and validated by content expert Drew Polly, PhD at University of North Carolina at Charlotte under a grant from the Department of Education (PR/Award #: H373X100002, Project Officer, Susan.Weigert@Ed.gov). However, the contents do not necessarily represent the policy of the Department of Education and no assumption of endorsement by the Federal government should be made

  5. Finding Area • Step 2: Use a calculator to solve for area • A=π(16) • A≈ 50.24 cm2 • Once students can successfully solve when the radius is provided, begin to give problems where the diameter is provided. • In this case the first step becomes dividing the diameter in half to find the radius Don’t forget to label the units Note the change in symbol to communicate an approximation The contents of this content module were developed by special educator Bethany Smith, PhD and validated by content expert Drew Polly, PhD at University of North Carolina at Charlotte under a grant from the Department of Education (PR/Award #: H373X100002, Project Officer, Susan.Weigert@Ed.gov). However, the contents do not necessarily represent the policy of the Department of Education and no assumption of endorsement by the Federal government should be made

  6. Ideas for application • Compare the radius and area of various circles. Which one has more area? Does it make it a better price? • Small and large pizzas • Focus on as radius increases, so does the area of the circle • How much bigger is the area of a large pizza compared to a small The contents of this content module were developed by special educator Bethany Smith, PhD and validated by content expert Drew Polly, PhD at University of North Carolina at Charlotte under a grant from the Department of Education (PR/Award #: H373X100002, Project Officer, Susan.Weigert@Ed.gov). However, the contents do not necessarily represent the policy of the Department of Education and no assumption of endorsement by the Federal government should be made

  7. Making Connections • Finding the area of a circle addresses the following 7th and 8th grade Core Content Connectors • 7-8.NO.3c1 Use the rules for mathematical operations to verify the results when more than one operation is required to solve a problem • 7.ME.2d1 Apply formula to measure area and circumference of circles • 7-8.NO.3c5 Explain each step to solve a problem • 8.NO.1k1 Identify πas an irrational number The contents of this content module were developed by special educator Bethany Smith, PhD and validated by content expert Drew Polly, PhD at University of North Carolina at Charlotte under a grant from the Department of Education (PR/Award #: H373X100002, Project Officer, Susan.Weigert@Ed.gov). However, the contents do not necessarily represent the policy of the Department of Education and no assumption of endorsement by the Federal government should be made

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