In this article we are going to code an app to find the area or circumference of a circle. The focus is grade eight numeracy for Ontario but can easily be adjusted for different shapes and polygons. I have found the retention of the formula is a bi-product of this process.

Let us begin with the curriculum expectations:

Overall Expectations

• determine the relationships among units and measurable attributes, including the area of
  a circle and the volume of a cylinder.

Specific Expecations

• solve problems that require conversions involving metric units of area, volume, and capacity;
• determine, through investigation using a variety of tools (e.g., cans and string, dynamic geometry software) and strategies, the relationships for calculating the circumference and the area of a circle, and generalize to develop the formulas;
• determine, through investigation using a variety of tools and strategies (e.g., generalizing from the volume relationship for right prisms, and verifying using the capacity of thin-walled cylindrical containers), the relationship between the area of the base and height and the volume of a cylinder, and generalize to develop the formula

Before you begin, please familiarize yourself with the video below:

Not only can you directly assess the expectations above from a student product, you are able to observe and converse the learning process as outlined in Growing Success.

This task could be extended to include having a student app that:

• works backwards to give diameter/radius from area/circumference
• finds area given circumference or vice versa (deconstructing the formula)
• draws a circle from specified user input of radius or diameter
• outputs a labelled circled with appropriate terms (eg: arc, chord)
• explains the relationship between the distance across and the distance around a circle

There is also room for natural differentiated instruction or scaffolding which may include having a student app that only:

• determines the relationship between radius and diameter
• shows Pi to the nth decimal value

As stated above, the idea behind this lesson is completely applicable to triangles, rectangles, squares or trapezoids from different grade levels.