Tracy Rains
Material Type:
Lesson Plan
High School
9, 10, 11, 12
  • Algebraic Expressions
  • Foundations of Algebra
  • Numerical Expressions
  • License:
    Creative Commons Attribution Non-Commercial
    Media Formats:
    Downloadable docs, Interactive, Text/HTML, Video

    Variables, Expressions, & Combining Like Terms

    Variables, Expressions, & Combining Like Terms


    In this seminar, you will learn about variables and how they are used in mathematical expressions. You will also learn what it means to be a like term and how to combine like terms.  You will pull variables, expressions, and like terms together so that you can apply them moving forward.



    Interpret the structure of expressions to represent a quantity in terms of its context.


    Write expressions in equivalent forms to solve problems.


    Introductory warm-up activity.

    Your neighbor has asked you to take care of their lawn next summer. They said they would pay you $8.00/hour at the end of each month. What would be a way you can plan for how much you will make each month regardless the numbers of hours you work? Remember, some months may have more rain than others, so your time spent each month will most likely vary. Take a minute to think about this and try to write a mathematical way to figure out how much you will make. Then next summer you can use this to make sure you are paid correctly!


    Read or watch the resources to learn about this concept, then do the practice activity.




    In this reading assignment you will be focusing on “variable”, “expressions”, and “like terms.” First, read the definition of a variable here to remind yourself of the meaning of this term.

    Next, read the article “Writing Algebraic Expressions,” to review how to use variables in expressions being careful to make sure you understand how to write the expressions. Complete all the practice problems at the end of the reading and take notes on all your correctly solved problems.

    It is also important that you understand how to combine like terms.

    Now that you’ve read about variables and expressions, watch this video to make sure you fully understand the concepts.  

    You have heard the terms Numeric Expression and Algebraic Expression - watch this short video to make sure you have a clear understanding of each.

    Now let’s make sure you understand how to write expressions.  This video will help you understand how to do translate from words to mathematical symbols.  This second video is a little more practice writing expressions - it is recommended that you pause the video, write the expression, then start the video and see how you did!

    Finally, let’s review what like terms are and how you combine them by watching this video.

    It’s your turn to practice these concepts - remember to review any of the readings or videos if you are still a bit confused!

    To practice writing expressions, please try this quizlet.

    To practice identifying and combining like terms, please try these three activities:

    1. Combining Like Terms

    2. Combining Like Terms with Distribution

    3. Combining Like Terms Quiz

    How did you do?  Please review as needed or seek your instructor’s assistance.



    Discuss your ideas / opinions / understandings.

    4n - 20

    With a partner, consider the expression above. Use complete sentences in your answers to the following.

    • Write a scenario that this expressions could apply to in the real-world.

    • Change the scenario slightly, and explain how it would change the expression and why.

    • Pick 4 different numbers to fill into the scenario and evaluate the expression at those numbers.

    • Can you think of a way you could add like terms into your scenario and the expression?


    Now it is time to self-check how much you have learned about the this topic.  If you do not know as much as you thought, go back to the “Explore” section of this seminar and reread, rewatch, or redo the activities listed.  See your facilitator if you have questions.

    Click here to take the quiz online. You do not have to log into the quiz site in order to take this quiz. If a window pops up asking you to sign up for the quiz site, just close the sign-up window and start your quiz.


    This is a task or project where you can show what you know.

    Pretend you are creating a presentation for younger students on like terms. HINT: You may want to use pictures! Include an introduction that includes basic terminology, create at least 5 examples to complete together (2 very basic, 2 average difficulty, 1 challenging), and then 5 problems for them to try on their own. You may choose to create a video, powerpoint, or other method to complete this assignment. It is worth 30 points.



    Complete this wrap-up activity where you reflect on your learning.  

    Write a brief summary of what writing expressions means to you, i.e. how it’s done, what you look for, etc.  What do you still find challenging about this lesson? What can you do to overcome that challenge?