Algebraic Expressions Teaching Resources

Explore the world of algebraic expressions in math class this year with the help of Teach Starter! This collection of printable and digital math resources was created by teachers for teachers like you.

Teach students how to read expressions with letters standing in for numbers, explore the parts of an expression and more this school year with the help of activities and games aligned with both TEKS and the Common Core math curriculum. This resource collection includes everything you need to plan lessons for fifth, sixth and seventh grade algebra classes!

Is this your first year teaching upper elementary or middle school math? Looking for a handy guide? Read on for a primer from our teacher team!

What Is an Expression in Math? A Kid-Friendly Definition

The term expression has a very specific meaning in math, so it helps to clarify for your students what you mean when you say "expression." Here's a definition that you can use with students:

An expression is a math statement that's made up of numbers and operation symbols. It does not include an equal sign and can include variables.

What Is an Algebraic Expression? A Kid-Friendly Definition

So, if that's the definition of expression, what happens when you add the word "algebraic" at the front?

An algebraic expression is a math statement that's composed of numbers, operations and variables.

These are also sometimes called variable expressions.

How to Evaluate an Algebraic Expression

A core skill of working with algebraic expressions is evaluating these math statements.

Evaluating is how we find the value of the expression when a given number replaces the variable. So how does it work? Let's walk through evaluating an expression step-by-step.

1. Identify the Variables. In the first step, your students need to look for the letters — such as x, y, or a — that are standing in as variables in the expression.
2. Determine the Value of Each Variable. Using the provided information for the problem, determine the value for each variable used in the expression. There could be multiple variables used in a single expression!
3. Substitute the Values — Once the values of each variable is known, replace the variables in the expression with their corresponding values.
4. Complete the Operation(s) — Students then follow the order of operations rules to complete any whole number operations that are represented in the expression until you have simplified the expression down to a single numerical value.

Equivalent Expressions – A How-To Guide

Identifying and generating equivalent expressions is another skill your students will likely come across during their algebraic expressions unit. Equivalent expressions are numerical statements that have the same value, but may look different. An example of two equivalent expressions are 3(8+5x) and 24 + 15x. Even though the expressions look different, they would equal the same number if evaluated with the same value for x.

So, what are some ways to make equivalent expressions? Here's a quick guide for creating expressions with the same value.

1. Use the Distributive Property

The distributive property can be used to create equivalent expressions. This math rule tells us that if you multiply a number by the sum or difference of two other numbers, you will be able to distribute the multiplication to each term within the parentheses. Finally, you can add or subtract the results.

For example, let's say you have the expression 2(x + 9) - 7. If you use the distributive property, you can create the expression 2x + 18 - 7. After subtracting 18 and 7, this simplifies to 2x + 11. These two expressions are equivalent.

2. Combine Like Terms

Another way to create an equivalent expression is to combine terms with the same variables and exponents.

For example, in the expression 6x + 2x, you can combine the "6x" and "2x" terms to get "8x."

3. Combine Constants

Constants are the numbers without variables in the expression. Combining these numbers will create an expression that is the same value as the first.

For example, in the expression 4x + 2 + 3, you can combine "2" and "3" to get "5," resulting in 4x + 5.