Lesson objective: Understand that we can represent problem situations with equations, understanding that the operations shown in the equation may not be the operation we use to solve the problem.

Students bring prior knowledge of being able to use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem from 3.OA.A.3. This prior knowledge is extended to representing problem situations with equations, understanding that the operations shown in the equation may not be the operation we use to solve the problem, as students solve a problem with multiple solutions. A conceptual challenge students may encounter is being confused by the meaning of a variable and are not sure how to relate it to the context of the problem. Through discussion and labeling, this unit will consistently relate the quantities in the equation to the problem’s context.

The concept is developed through work with a tape diagram, which allows students to determine what information is known and what information is unknown.

This work helps students deepen their understanding of operations because a word problem may translate into one operation, but another operation might be needed to actually solve the problem.

Students engage in Mathematical Practice 2 (Reason abstractly and quantitatively) as they take a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own. Also, students will create a representation of the problem at hand and then work with that representation to create another equation that gives the solution to the problem.

**Key vocabulary:**

- assortment
- decompose
- equation
- represent
- solution
- symbol
- tape diagram
- variable