Similarity and Area

I’ve been working with a colleague brainstorming ideas for exploring similarity using pattern blocks. We can make similar shapes quite nicely, and prove they are similar because the angles are the same and the side lengths are proportional. We can see that when the side length changes by a factor of 3 the area changes by a factor of 9 etc. My colleague took pictures from his class to show what they did. Students noticed that there was a quadratic pattern in the area, since the change was changing by a consistent amount (the 2nd differences are the same).

We can do this with other shapes too. This was from my brainstorming.

and this was from my colleagues class. They found creative ways to grow the shapes.

I’m thinking now about how these same pictures could be used later when fractions are discussed.

Students said they enjoyed the task and liked working with the blocks ro show their learning.