Georgia 7.GSR.5.4
The Standard
Explore and describe the relationship between pi, radius, diameter, circumference, and area of a circle to derive the formulas for the circumference and area of a circle.
Georgia's K-12 Mathematics Standards · Solve practical problems involving angle measurement, circles, area of circles, surface area of prisms and cylinders, and volume of cylinders and prisms composed of cubes and right prisms.
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students measure several circles and compare each circumference with its diameter to identify the constant ratio π. They connect radius and diameter, then use diagrams or cut sectors to justify the circumference and area formulas.
What Mastery Looks Like
- A student can use measurements to show that circumference divided by diameter stays close to π. They can explain C = πd = 2πr and reconstruct A = πr² by rearranging circle sectors. They use correct linear and square units.
Common Misconceptions
- Students often swap radius and diameter, especially when a diagram labels only one measure. Some use πr² for circumference or 2πr for area. Others think doubling the radius doubles the area instead of making it four times as large.
How to Assess It
- Exit ticket: A circle has a diameter of 12 centimeters. Find its circumference and area, then explain why the units differ.
Lesson moves
Ways to Teach It
Give pairs string, rulers, and circular lids; have them measure circumference and diameter, then record circumference divided by diameter for five lids.
Have students write a diagram-based response to: “Why does doubling a circle’s radius double circumference but multiply area by four?”
Run a card match where teams pair radius, diameter, circumference, and area cards, then explain one match before keeping it.
Compare two pizza sizes by calculating area per dollar, then decide which menu option gives more pizza for the price.
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Printable 7.GSR.5.4 Worksheet
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