This lesson features two creative twists on the standard lesson of having students measure several circles to discover that the ratio of the circumference to the diameter seems always to be a little more than 3.  This lesson starts with squares, so students can first identify a simpler constant ratio (4) of perimeter to length of a side, before moving to the more difficult case of the circle. The second good idea is to measure with a variety of units, so students can more readily see that the ratio of the measurements remains constant, not only across different sizes of figures, but even for the same figure with different measurements.

This lesson features two creative twists on the standard lesson of having students measure several circles to discover that the ratio of the circumference to the diameter seems always to be a little more than 3.  This lesson starts with squares, so students can first identify a simpler constant ratio (4) of perimeter to length of a side, before moving to the more difficult case of the circle. The second good idea is to measure with a variety of units, so students can more readily see that the ratio of the measurements remains constant, not only across different sizes of figures, but even for the same figure with different measurements. An activity sheet, overheads, discussion questions, lesson extensions, suggestions for assessment, and prompts for teacher reflection are included. (sw)