## IM Commentary

This task is intended to help build understanding as students work toward deriving a general formula for the area of any triangle. The purpose of this task is for students to use what they know about area and express regularity in repeated reasoning (MP.8) to generate a formula for area of a *right* triangle.

This task is intended to be used before students know that the area of a triangle can be expressed with bh/2. So, in part (c), they should be reasoning using geometric methods (surround and subtract, composing and decomposing, counting unit squares, etc.). They are not expected to use a formula in part (c), because they are not expected to know a formula yet.

It would be appropriate to make grid paper, straight edges, and even scissors available to students who want to think about area in terms of counting square units. In part (c), this tactic will become more difficult, nudging students to think more abstractly.

Students thinking very concretely about the number of unit squares may struggle with parts of (c). For these students, it may be helpful to assist drawing pictures of all four part (c) triangles with leg lengths labeled. Even though it is difficult to count unit squares, students can still reason that the right triangle is half of an associated rectangle, and compute half the area of the rectangle. Generalizing this process will help them respond to parts (d) and (e).

Still other students may simply need support multiplying fractions.