Circumference of a Circle & the Meaning of Pi

This Sticky Math Lesson examines the circumference of a circle conceptually by exploring the meaning of pi. This lesson can introduce vocabulary through the drawings, offers an opportunity for students to use precise vocabulary (MP6), and acts as a formative assessment of academic vocabulary. 7.G.B.4

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Any connection students make throughout the lesson should be valued and acknowledged to build students’ mathematical agency, authority and identity; however, the idea for this stage in the lesson is to realize:

The left sticky, the three lines are congruent.

The two lines outside the circle are congruent to the diameter inside the circle.

Three diameters and little more from the left sticky make up the circumference of the circles.

The point of this Sticky Math Pair is to make connections to the abstract, symbolic representation of the relationship found in the previous pair and to define pi conceptually:

From the right sticky, three diameters and a little more are equivalent to the circumference.

If the circumference is equivalent to three diameters and a little more, then pi must be equal to a little more than three.

This Sticky Math Pair helps define the circumference of a circle in terms of the radius.

Pi must still be a little more than three.

The diameter has been replaced with two radii.

The circumference is equivalent to a little more than three groups of two radii.

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