# Expressions and Equations / Building Expressions in Two Variables

Activity 10 of 18
In this lesson students gain more practice creating equivalent expressions using the properties of multiplication and addition. Students are able to build more complex expressions for the purpose of demonstrating expressions of the second and third degree.

## Planning and Resources

Objectives
Students should be able to identify equivalent expressions involving rational numbers and explain why they are equivalent using properties of multiplication and addition

Vocabulary
expression
equivalent expressions
rational numbers
integers
distributive property of multiplication over addition

Standard:

## Lesson Snapshot

#### Understanding

Students develop an understanding of the properties of operations and how to use them to create different but equivalent expressions .

### What to look for

This activity can be used to serve two different levels of learning. First to develop flexibility using negative number in simple linear expressions, and second to prepare students for factoring or expanding polynomials. Care should be taken not to overreach with the first level.

### Sample Assessment

Find the value of $$p$$ so that the expression $$\frac{5}{6} - \frac{1}{3^n}$$ is equivalent to $$p(5-2n)$$.

Answer: $$\frac{1}{6}$$

#### The Big Idea

Proper use of the properties of multiplication and addition helps to identify and create equivalent expressions involving rational numbers and explain why they are equivalent.

### What are the students doing?

Students create equivalent expressions in two variables and explain why two expressions are equivalent.

### What is the teacher doing?

Engage students in reasoning about the values produced by an expression in two variables and in looking for patterns that can be used in creating equivalent expressions.