# Lesson 23

Applications of Expressions

### Lesson Narrative

In this culminating lesson, students look at several real-world situations that can be represented by an expression with a variable. In the warm-up, students decide whether each of four expressions is equivalent to a given expression, recalling what it means for expressions to be equivalent and relevant terminology. In the following activity, students write expressions corresponding to two ways of doing a real-world calculation, and explain why the two ways are equivalent. Finally, students are presented with two coupons to a store (a 20% off coupon and a \\$30 off coupon), and use their skills to decide in which order the coupons should be applied to save more money on a purchase. In this lesson, students write expressions to represent calculation methods, which allows them to use familiar properties to decide whether two methods are equivalent. This is an example of decontextualizing and recontextualizing (MP2) and creating a mathematical model to understand a situation (MP4).

### Learning Goals

Teacher Facing

• Determine which order for applying multiple coupons gives the better discount and explain (orally and in writing) the reasoning.
• Justify (orally, in writing, and using other representations) that two different sequences of calculations give the same result.

### Student Facing

• Let’s use expressions to solve problems.

### Student Facing

• I can write algebraic expressions to understand and justify a choice between two options.

Building On