Lesson objective: Understand that the choice of solution strategy for multiplication problems does not affect the answer or the relationships between the numbers involved.

Students bring prior knowledge of multiplication 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 multiplication 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 various decompositions of the factors, which assists students in visually representing the distributive property and understanding the connections between strategies.

This work helps students deepen their understanding of equivalence because they will decompose numbers in different ways, use different solution strategies and determine that these differences do not affect the outcome of the problem or the relationships between the numbers.

Students engage in Mathematical Practice #1, make sense of problems and persevere in solving them as they solve multi-digit, multi-step multiplication problems using the area model. 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 multiplication problems and find the connections between the strategies.

**Key vocabulary:**

- area model
- decompose
- distributive property
- partial product
- place value
- properties of operations
- relationship