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

Students bring their prior knowledge of solving problems arithmetically and solving equations. This prior knowledge is extended to solving problems both with arithmetic and algebraically. A conceptual challenge students may encounter is why they are asked to write and solve an equation for a problem they could more easily solve with arithmetic. This lessons highlights the connection between those methods so that students see that writing and solving an equation is just another way to represent their problem solving process, not as a completely different way to solve problems.

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 may 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 reason abstractly and quantitatively (Mathematical Practice 2) as they use numbers, variables, and operations across different problem solving approaches.

**Key vocabulary:**

- algebraic approach
- arithmetic approach
- variable