Virginia SOL 6.MG.1.d
The Standard
Develop the formula for circumference using the relationship between diameter, radius, and pi.
Virginia Standards of Learning for Mathematics · The student will identify the characteristics of circles and solve problems, including those in context, involving circumference and area.
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students use measurements to find that the ratio of circumference to diameter is constant and represented by pi. They connect diameter and radius to build and use both circumference formulas.
What Mastery Looks Like
- Students measure several circles and recognize that circumference divided by diameter is always close to pi. They use diameter equals twice the radius to explain why both circumference formulas give the same result.
Common Misconceptions
- Students may confuse radius with diameter or use the area formula for circumference. Some think pi equals exactly 3.14 rather than viewing it as the constant ratio of circumference to diameter.
How to Assess It
- Give students a circle with radius 5 cm. Ask them to write both circumference formulas, explain why they are equivalent, and calculate the circumference in terms of pi.
Lesson moves
Ways to Teach It
Wrap string around circular objects, measure each diameter, then divide each string length by its diameter to estimate pi.
Ask students to explain in writing how replacing diameter with twice the radius changes one circumference formula into the other.
Play a formula match game using cards showing circles, radius or diameter measures, formulas, and matching circumferences.
Compare bicycle wheel sizes by calculating how far each wheel travels during one full rotation.
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Related Standards
- 6.MG.1.e
Solve problems, including those in context, involving circumference and area of a circle when given the length of the diameter or radius.
- 6.MG.1.c
Develop an approximation for pi (3.14) by gathering data and comparing the circumference to the diameter of various circles, using concrete manipulatives or tec...
- 6.MG.1.b.iii
Investigate and describe the relationship between diameter and circumference
- 6.MG.1.b.ii
Investigate and describe the relationship between radius and circumference
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