Lesson objective: Understand that drawings and equations can be used to represent and solve problems involving multiplication and division. This lesson will extend the concept that multiplication and division are inverse operations, connect multiplication equations to division problems, and show that a drawing can represent both multiplication and division.

Students bring prior knowledge of quotients being equal groups or shares from Grade 3, Unit 1; 3.OA.A.2. This prior knowledge is extended to drawings and equations as students use them in multiplication to solve problems involving division. A conceptual challenge students may encounter is representing the wrong number of groups or total objects in a drawing or equation. They also may be confused at where the factors, products and quotients are represented in an equation.

The concept is developed through work with arrays, number lines, and equal groups, which helps link an equation to the drawing and shows how these strategies in multiplication can help solve division situations.

This work helps students deepen their understanding of operation because drawings and equations can visually show how multiplication and division are inverse operations.

Students engage in Mathematical Practice 1 (Make sense of problems and persevere in solving them) as they understand that they are making equal groups or parts and using division. They will recognize that they have solved problems like this before. They will persevere to find as many combinations as possible because they have been successful in the past tasks and units with similar problems.

Students engage in Mathematical Practice 7 (Look for and make use of structure) as they form distinguishable groups, rows or jumps in a drawing or representation. These can also help them make sense of how a multiplication and division equation can be used to represent the drawing or group of tiles or counters.

**Key vocabulary:**

- array
- divide
- equal groups
- equation
- quotient
- repeated subtraction
- representation

**Special materials needed:**

- base ten blocks to reason with, such as breaking apart numbers
- manipulatives such as square tiles, counters or cubes