Lesson 12

In this lesson, students discover that there is a proportional relationship between the diameter and circumference of a circle. They use their knowledge from the previous unit on proportionality to estimate the constant of proportionality. Then they use the constant to compute the diameter given the circumference (and vice versa) for different circles. We define \(\pi\) as the value of the constant and discuss various commonly used approximations. In the next lesson, students use various approximations for pi to do computations. Also, relating the circumference to the radius is saved for the next lesson.

Determining that the relationship between the circumference and diameter of circles is proportional is an example of looking for and making use of structure (MP7).

The lesson narrative refers to “knowledge from the previous unit on proportionality.” In IM 6–8 Math Accelerated, that learning is from a previous section of this unit.

Household items: collect circular or cylindrical objects of different sizes, with diameters from 3 cm to 25 cm. Each group needs 3 items of relatively different sizes. Examples include food cans, hockey pucks, paper towel tubes, paper plates, CD’s. Record the diameter and circumference of the objects for your reference during student work time.

The empty toilet paper roll is for optional use during the warm-up as a demonstration tool.

You will need one measuring tape per group of 2--4 students. Alternatively, you could use rulers and string.