CCSS.Math.Content.7.G.B.4
The standard
Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle.
Common Core State Standards for Mathematics · Geometry
What this standard means
Students need to know and use the circle formulas for circumference and area. They should choose the right formula, identify radius or diameter from a diagram or word problem, use pi correctly, and label units.
Mastery means students can solve straightforward and real-world circle problems, including finding missing radius or diameter from area or circumference. They can also explain why area relates to circumference, often by cutting a circle into sectors and rearranging them. Common stuck points are mixing up radius and diameter, using square units for circumference, and forgetting to square the radius.
Ways to teach it
- Have students cut paper circles into equal wedges, rearrange them into a near-rectangle, then connect its base and height to circumference and radius.
- Prompt students to explain why circumference uses linear units but area uses square units, using one labeled circle diagram.
- Give a 5-minute exit ticket with one circumference problem, one area problem, and one question asking students to circle the radius.
- Ask students to find the area of a round pizza and compare cost per square inch for two menu sizes.
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Related standards
- CCSS.Math.Content.HSG-C.A
Understand and apply theorems about circles
- CCSS.Math.Content.HSG-GMD.A.1
Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone.
- CCSS.Math.Content.8.G.C.9
Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.
- CCSS.Math.Content.4.MD.A.3
Apply the area and perimeter formulas for rectangles in real world and mathematical problems.