This is the first entry in my ePortfolio. Attached is the first lesson plan I made for EDN550 Transition to Teaching, the initial intensive unit of the Graduate Diploma in Education at Murdoch University in 2018. The lesson evaluation section is completed, but this is not the revised lesson plan (a later post).
This Year 8 (Australia) lesson is about finding 𝜋 (pi) and the formulae for circumference and area of a circle. I have found that students are often already familiar with the concept of 𝜋, a mathematical constant for circles. What they lack, however, is an intuitive understanding of the diameter–circumference ratio and the formulae. This activity has students cutting up circles into sectors and rearranging them into rectangles, which can be measured to obtain 𝜋 and analysed to derive the formulae for circumference and area of the circle (given that they already know circumference and area of a rectangle).
In a variation of this activity, students are given three rectangles of different width to length ratios which they cut into thin triangles and arrange into circles. The shortest rectangle does not make a complete circle. The longest rectangle makes a complete circle and then some. The middle rectangle makes a circle exactly (because its dimensions were made with the ratio 𝜋).