Unusual Baker

Today I was in a grade 9 math class while they worked through the unusual baker task from building thinking classrooms. There’s a baker who cuts cakes in unusual ways. If each cake has a total price of $10, what is the price of each piece.

The class was using their reasoning skills and their fraction sense to split up the cake and split up the price. Once groups were done with one cake, they got the next more challenging cake to try.

I was working with a group that were unsure of how to approach the question. The visual representation was too abstract, so I brought it back to the concrete. Sometimes that will help.

we looked at the entire cake, and one by one cut it up. We agreed that the 2 thin rectangles make up 1/2 of the cake, so they are each $2.50, and then with a bit more cutting and rearranging we could see that the big triangle was also half of half of the cake, so it is also $2.50. The tricky part was the 2 smaller triangles. If you cut the 2 smaller triangles in half, then rearrange them they are equal in area despite being different dimensions, so they are each $1.25

The concrete representation helped these students understand that 1/4 can look quite different, it could be a square, a rectangle or a triangle.