This is a grade five homework of my son, can you help me solve?

1. Show how the shapes can be used to from a larger similar figure using 4 shapes.

  2. You are planning to build a birdhouse as shown. You are going to cut the pieces from a board that is 12 inches wide. How long should the board be?

Marina,

For problem 1 I think you are to make 3 copies of the rectangular shape (so that you have 4 in total) and put them together to form a figure that is similar to the original rectangle but larger.

For problem 2 you need to cut seven pieces, the front, the back, two sides, the bottom and two pieces for the roof. Each piece is 12 inches wide so it will fit on the 12 inch wide board. What is the total length you need?

Harley

Marina wrote back

Thank you again,
My son manage to solve this problem and am not sure if it is correct. Pls see attached
Marina

Marina,

Your son's answer is fascinating, and I would give him full credit, but it's not the answer I would have given. He gives four small triangles he calls the side roof to finish the peak at the front and back. (I shaded them so that you would see what I mean.) I would have cut the front and back 12 inches long and cut off and discarded the triangles to make the peak. I would then need 4 more inches in length than your son. My solution gives pieces that are easier to put together but I ended up wasting 4 inches of the board.

Contrary to what many people believe, in mathematics there is not always only one correct answer.

Harley