Lesson objective: Understand that various strategies can be used to solve division problems and the choice of strategy does not affect the outcome or the relationships between the numbers involved.

Students bring prior knowledge of division solution strategies from 4.OA.A.3, 4.NBT.B.5, and 4.NBT.B.6. This prior knowledge is extended to analyzing the relationships between the numbers involved in a problem when various solution strategies are used as students solve multi-digit division problems using multiple strategies for the same problem. A conceptual challenge students may encounter is making connections between the strategies.

The concept is developed through work with the area model and partial quotients, which assists students in visually representing the connections between the strategies.

This work helps students deepen their understanding of number because they extend their understanding of the decomposition of numbers when choosing a solution strategy and examine the relationships of the numbers within the problem.

Students engage in Mathematical Practice #1, make sense of problems and persevere in solving them as they solve multi-digit, multi-step division problems using the area model and partial quotients. The complexity of the problems will encourage students to persevere in finding solutions using the strategies that are available to them. Students engage in Mathematical Practice #8, look for and express regularity in repeated reasoning as they work with multiple strategies to solve division problems and find the connections between the strategies.

**Key vocabulary:**

- area model
- decompose
- partial quotient
- place value
- properties of operations
- relationship