Lesson objective: Understand that the meaning of division is the same regardless of the strategy being used.

Students bring prior knowledge of division from 4.NBT.B.6. This prior knowledge is extended to the meaning of division as students work to understand that mathematically, division always means the same thing. A conceptual challenge students may encounter is thinking that different strategies or division problems require different mathematical calculations.

The concept is developed through work with partial quotients using area models and a vertical notation method, which students compare to arrive at the conclusion that despite the strategy or representation, division always means the same thing.

This work helps students deepen their understanding of division because they are required to justify that, mathematically, division does not change even if the strategy or situation does.

Students engage in Mathematical Practice 3 (Construct a viable argument) as they justify why the meaning of division does not change, even if the strategy or type of problem does.

**Key vocabulary:**

- area model
- dividend
- division
- divisor
- partial quotients
- quotient