Maryland Math 7.GR.B.3
The Standard
Apply the formulas for the area and circumference of a circle to solve problems in context. Use informal reasoning and visual models to explain the relationship between the circumference and area of a circle.
Maryland College and Career Ready Standards for Mathematics (2025) · REASON WITH AND ABOUT GEOMETRIC FORMULAS TO SOLVE PROBLEMS AND JUSTIFY SOLUTIONS IN CONTEXT.
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students use a radius or diameter to calculate the distance around a circle and the area inside it. They use a sketch of rearranged circle wedges to explain why the area is half the circumference times the radius.
What Mastery Looks Like
- For a garden with a 4-meter radius, students find 8π meters of edging and 16π square meters of ground cover. They label the length of a rearranged wedge sketch as half the circumference and its height as the radius.
Common Misconceptions
- Students may use the diameter as the radius when finding area, or forget to double the radius when finding circumference. Some use square units for circumference or think area only doubles when the radius doubles.
How to Assess It
- Exit ticket: A circular flower bed has a radius of 3 meters. Find its edging length and planting area, then sketch rearranged wedges to explain how the two measurements are related.
Lesson moves
Ways to Teach It
Cut paper circles into wedges, alternate them into near rectangles, and label each rectangle's length C/2 and height r.
Ask: If a circular garden's radius doubles, how do its edging length and planting area change? Explain with a sketch.
Give pairs radius cards and circumference and area cards; have them match values, check units, and explain one mismatch.
Draw a 6-foot-wide circular flower bed, then calculate the edging length and the area that mulch must cover.
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Related Standards
- 7.GR.B.4
Solve mathematical problems with and without context involving area, surface area, and volume of two- and three-dimensional objects.
- 7.GR.B.4.c
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- 4.GR.A.4
Relate the area of a triangle to the area of a rectangle using decomposition and visual models. Derive and apply the formula to solve problems in contexts invol...
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