Lesson 19

Distinguishing Circumference and Area

Lesson Narrative

Students have spent several lessons investigating circumference, and then several lessons investigating area, separately. In this lesson, both types of problems are mixed together so students have to distinguish which measurement is called for in each problem situation (MP 1 and 2). Also, in previous lessons students were always given one measurement of each circle, but in this lesson they must rely on their own estimations to solve the problems (MP 6). Students continue working with answers expressed in terms of \(\pi\), which was introduced in the previous lesson.

Teacher Notes for IM 6–8 Accelerated
Use this optional lesson any time after lesson 16.

Learning Goals

Teacher Facing

  • Critique (orally and in writing) claims about the radius, diameter, circumference, or area of a circle in a real-world situation.
  • Decide whether to calculate the circumference or area of a circle to solve a problem in a real-world situation, and justify (orally) the decision.
  • Estimate measurements of a circle in a real-world situation, and explain (orally and in writing) the estimation strategy.

Student Facing

Let’s contrast circumference and area.

Required Preparation

You will need the Card Sort: Circle Problems blackline master for this lesson. Prepare and cut one copy for every 2 students. These can be reused from one class to the next. If possible, copy each complete set of cards on a different color of paper, so that a stray card can quickly be put back.

Be prepared to explain or show images of any of the examples of circles in the sorting activity that may be unfamiliar to your students.

Learning Targets

Student Facing

  • I can decide whether a situation about a circle has to do with area or circumference.
  • I can use formulas for circumference and area of a circle to solve problems.

CCSS Standards


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