Algebraic Expressions

By the time students are in algebra, they should have experience with algebraic expressions. I never feel comfortable enough with this fact, so I always start the year with a refresher. Expressions are the building blocks of algebra, so it’s better to cover this topic and make sure students have a good foundation before heading into solving equations.

As I begin the year, I like to review operations with integers and rational numbers, order of operations, expressions and terminology. Terminology is key. Students must know what you are talking about when you use words such as like terms, coefficients, variables, distribute and constants. Also, never assume students know things like a fraction is really a division problem and all numbers have exponents of 1 when no other exponent is visible. Get all of this taken care of in the beginning and you will find out really quickly who has these foundational skills and who doesn’t. I will not get the calculator out until after all of this material has been covered.

Here’s the content that I like to make sure to cover during the expression lesson:

  • Setting up expressions from phrases like: five less than twice a number
  • Evaluating expressions by plugging in a number for a variable. It’s important to review order of operations at this point.
  • Simplifying expressions using combining like terms and distributive property.
  • Using applications with expressions.

If students are able to do the 4 items above, they will be in a good position for success when moving to solving equations. I will probably take a week to practice expressions, but I feel like this is time well spent.

My lesson plan will look something like this – (I’m on a block schedule, so I see my students 80 minutes two days and 50 minutes on Friday.)

Day 1:

  • Bell Ringer – Operations with Integers
  • Math Terminology
  • Expression Opener
  • Setting Up Expressions
  • Evaluating Expressions

Day 2:

  • Bell Ringer – Operations with Rational Numbers
  • Simplifying Expressions
  • Practice Writing, Evaluating and Simplifying with a Partner
  • Application with Expressions – Digital Practice

Day 3:

  • Quizizz Activity – (I have a Quizizz Activity that practices the skills used in the application activity.)
  • Quiz – Short quiz that will let me know how well the students understand the concept.

I have a resource that covers all of this material. The expressions lesson that I created has a PowerPoint that goes through the terminology and example problems. I like students taking notes and following along, so I have note pages that follow the PowerPoint.

Expression PowerPoint
Note Page Example

The lesson comes with a practice page that contains 12 problems covering the three categories: writing expressions, evaluating expressions and simplifying expressions. The quiz has a section where students fill in terminology and the rest of the problems are multiple choice for quick grading.

The application part of this activity is a Google Slides where students show that they understand what an expression is versus equations or inequalities. Students then see some perimeter problems where the dimensions are expressions. Students solve the problems two ways. There is a video tutorial that walks students through simplifying some expressions with the distributive method.

Expressions are the foundation of Algebra. Students start learning expressions early in their math classes, but variables are an abstract concept and tend to be something difficult for them. The more we expose our students to understanding the purpose of a variable, the better they will grasp it. Give your classes lots of examples of how expressions might be used and keep checking for understanding. See if they can come up with their own examples. If they can create their own expressions and tie it to a real-life concept, then you know they have made the leap to understanding this idea.

If you’d like to look further into my Expression Lesson, I have linked it to the picture below. Thank you for going through this thought process with me and good luck with your students.