We did a model problem of a roof truss where they calculated the total lengths of wood. We discussed how the shape needs to be symmetrical and each triangle needs to have measurements that are mathematically sound. Other than that, the design was up to them. Here’s the model problem:

The Phantom Tollbooth is a classic. It is still my favorite accessible explanation of averages.

I have them write it in their class notebook. They try it independently first and then have an opportunity to share and workshop with a partner and then we come up with a class exemplar which they also write down. They can go back to reference these as notes.

After we wrap up an investigation task, I have students try to write their own one sentence summary of the big idea. For example: “Write one sentence to explain why the sine ratio for a reference angle like 30 degrees always has the same value even when the triangles have a different size.”

The two triangles made students think more deeply about WHY they had two different equations and yet came to the same solution. It kept the work simpler on the front end but then allowed them to draw the conclusion that they are in fact the same triangle.

They are also a great way to support MLL students with language development in math. I’ve seen a lot of impact from using them with those students.

This is super helpful! As an IM teacher I’m familiar with the MLR’s but I’ve never thought of associating them with specific parts of the lesson flow.