Lesson objective: Understand that we can find unknown measurements if we know the area and sufficient information about the figure.

Students bring prior knowledge of finding the area from 6.G.A.1. This prior knowledge is extended to finding missing dimensions as students seek to determine appropriate dimensions for a dog pen that meets a parent’s requirements. A conceptual challenge students may encounter is thinking backwards.

The concept is developed through work with a detailed drawing using "guess and check" and/or solving equations, which helps students see how to determine appropriate measures.

This work helps students deepen their understanding of operations because they are able to see the relationship between what is happening with the shape and what is happening in the equation.

Students engage in Mathematical Practice 1 (Make sense of problems and persevere in solving them) as they work to discover two different dog pens that will meet the area and perimeter restrictions.

**Key vocabulary:**

- area
- base
- height
- perimeter