Wyoming Math 7.G.4b
The Standard
Investigate the concept of circles. Understand that π is defined by the constant of proportionality between the circumference and diameter.
2023 Wyoming Mathematics Content and Performance Standards · Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students measure the distance around circles and across their centers. They divide each circumference by its diameter and find that the ratio is always close to pi.
What Mastery Looks Like
- Given measurements for several circles, students calculate circumference divided by diameter and explain why the results are nearly equal. They use that relationship to find a missing circumference or diameter.
Common Misconceptions
- Students may divide diameter by circumference or measure across a circle without passing through its center. They may think pi is exactly 3.14, or that small measurement differences mean the ratio changes.
How to Assess It
- Exit ticket: Two circles have diameters of 4 cm and 10 cm and circumferences of 12.6 cm and 31.4 cm. Find each circumference-to-diameter ratio and explain why they are close but not identical.
Lesson moves
Ways to Teach It
Wrap string around a jar lid and a paper plate, measure each string and diameter with a ruler, then compare the ratios.
Ask students to explain why a circle with twice the diameter has twice the circumference, using their measurements as evidence.
Give pairs cards showing diameters and rounded circumferences; have them match the cards and check each match by dividing.
Measure a bike wheel's diameter, predict how far one full turn travels, then roll it along a tape measure to check.
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Printable 7.G.4b Worksheet
A ready-to-print activity worksheet aligned to 7.G.4b, with an answer key for the teacher on its own page. No account needed.
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