Lesson objective: Understand that arithmetic and algebraic approaches to problem solving are related and use the same operations.

Students bring their prior knowledge of solving problems arithmetically and solving equations. This prior knowledge is extended to solving problems algebraically by using variables, numbers, and operations to set up relationships between the quantities as students translate word problems into algebraic sentences. A conceptual challenge students may encounter is reasoning abstactly and making the connections between the context of the situation and the relationship between the variables and numbers.

The concept is developed through work with translating situations into algebraic equations and solving them, which illustrates the concept that arithmetic and algebraic approaches are very similar and use the same operations.

This work helps students deepen their understanding of operations because both approaches use the same operations to solve problems.

Students engage in Mathematical Practice 7 (Look for and make use of structure) as they write algebraic equations and compare an arithmetic approach to problem solving with the algebraic approach. Students will identify the same operations that are used in both approaches to reinforce the concept that the two approaches are similar.

**Key vocabulary:**

- algebraic approach
- arithmetic approach
- variable