5.3: Calculating Circumference

This is the third section of "Chapter 5: Measurement of Circles". We skipped section 5.2, since we covered all the relevant material when we did section 5.1, "Exploring Circles".

Relationships Between Circumference, Diameter and Radius

There are three relationships that students can use to solve problems.

  • The diameter is twice the radius: $latex d = 2r$
  • The circumference is pi times the diameter: $latex C = \pi d$ and
  • The circumference is 2 times pi times the radius: $latex C = 2 \pi r$.

What Makes a Good Answer?

An important part of developing a rigorous mathematical mind is learning how to structure our thinking. One way to do that in math is to use labels. We did two support questions together to help identify what makes a good answer. We found four things:

  • Drawing a diagram (stating what we know)
  • Labelling our steps
  • Stating the formula we're going to use
  • Ending the problem with a "therefore" statement

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Support Questions

Students identified what they felt were the most important support questions for this section. On pages 158-159, they chose numbers 6, 7, 10, 11, 13, 14, 15, 16, 19, 20 and 21. On page 161, the identified numbers 3, 4, 5 and 6. We will have enough time in class that students will be able to complete these exercises if they are focused and work hard. Students should only have homework if they are either aren't working well in class, or have difficulty with certain questions.

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