Virginia SOL 6.MG.1.b.ii
The Standard
Investigate and describe the relationship between radius and circumference
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 measure or calculate the radius and circumference of circles, then compare the values. They recognize that circumference is about 6.28 times the radius and express the relationship as C = 2πr.
What Mastery Looks Like
- Students find that circumference divided by radius is always about 6.28, or 2π. They use C = 2πr to calculate circumference and explain that doubling the radius doubles the circumference.
Common Misconceptions
- Students may use πr instead of 2πr because they confuse the radius with the diameter. They may use the area formula, πr², or think circumference grows by a fixed amount rather than in direct proportion to radius.
How to Assess It
- Exit ticket: A circle has a radius of 5 cm. Find its circumference using 3.14 for π, then explain how circumference changes if the radius doubles.
Lesson moves
Ways to Teach It
Give pairs string, rulers, and circular objects to measure each radius and circumference, then calculate and compare circumference divided by radius.
Ask students to write why a circle with twice the radius has twice the circumference, using a formula, table, or diagram.
Play a matching game with cards showing radii, circumference expressions, approximate circumferences, and graphs of the relationship.
Compare bicycle wheel sizes by calculating how far each wheel travels in one full rotation.
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Printable 6.MG.1.b.ii Worksheet
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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.d
Develop the formula for circumference using the relationship between diameter, radius, and pi.
- 6.MG.1.b.i
Investigate and describe the relationship between diameter and radius
- 6.MG.1.b.iii
Investigate and describe the relationship between diameter and circumference
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