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6.   Understanding Π (pi)
Comparing ratios using a spreadsheet

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	SREB Readiness Indicator Measure length with appropriate tools and find perimeter, area, surface area and volume use appropriate units, techniques, formulas and levels of accuracy > Additional indicators
	Skills Measure and calculate the perimeter of regular polygons Use rulers to measure Understand Π as the ratio of the circumference of a circle to its diameter
	Figure 1: Table of shape dimensions (Click to enlarge)

Overview

Students explore the number Π in the context of similar shapes by using a spreadsheet to record and compare the distance around shapes (perimeter/circumference) to the distance across those shapes (width/diameter). They measure the dimensions of five squares, five (other) rectangles, and five circles and enter data into a spreadsheet (Figure 1); then they write formulas and use the sort function to compare categories of shapes. In the process, they come to understand that there is a constant ratio between the distance around and the distance across a circle and that this ratio defines the number Π.

The Value of This Technology

The use of a spreadsheet instead of pencil and paper for this investigation enables students to quickly calculate ratios and manipulate a relatively large data set in a way that naturally reveals the connection between ratio and similarity. The ease of manipulation shifts the focus away from arithmetic skills and lets students focus on new concepts.

Look in the Classroom

During the first week of the school year, Mr. Pirie asks his students, "What is Π?"
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