Combining Like Terms w/ Desmos

For the first 3 weeks of the school year, the math coaches are stationed at the District Office.  This being the 3rd and final week, we’re transitioning from the DO to working at our respective sites.  On Monday, I sent out a reminder email and asked how could I be of service prior to my arrival.

The following 2 emails ignited a chain reaction which resulted in this post.

Email #1:  Mrs. A asked if I could help her come up with a way to use Desmos with her students

Email #2: Mr. J inquired about a sorting activity on the topic of linear solutions: Infinite, no solution or 1.


Wednesday August 19, 2015 – Morning

I’m a part of 4 member middle level coaching team.  So for our last days together before heading off to our respective sites, we batted around ideas for the sort. One idea:  Write 2 expressions on a card with the instructions to graph both on Desmos.  Our 8th graders have not discussed slope yet, therefore we wanted them to notice patterns with the coefficients and constants.  If the 2 expressions have:

  1.  The same coefficient of x and same constant = Single line and infinite solutions

Screen Shot 2015-08-19 at 8.32.06 PM

2.  The same coefficient of x but different constants = Parallel lines & no solution.

Screen Shot 2015-08-19 at 8.24.21 PMScreen Shot 2015-08-19 at 8.13.31 PM

3. Different coefficients of x = Intersecting lines and 1 solution

Screen Shot 2015-08-19 at 8.38.16 PM  Screen Shot 2015-08-19 at 8.40.38 PM


Wednesday August 19, 2015 – After Lunch

After lunch, I met with Mr. J and refined the sorting activity to his liking. He liked the Desmos piece :).  I then walked across the courtyard to Mrs. A’s room.

  • Me:  Hi Mrs. A …. You emailed asking how to integrate Desmos.  What concept are you working on?
  • Mrs. A:  My students are struggling with combining like terms.  Can Desmos help with that?
  • Me:  (chills running up my arms)  YES!

I was just discussing that connection when working on the sorting activity! Boom!  If the described series of events didn’t occur, I’m not sure how I would have answered Mrs. A’s question, for I had never thought of using Desmos as a tool to formatively assess combining like terms prior to that day.  Now the challenge was to alter the lesson to fit her needs.

                          Our General Plan to incorporate Desmos when                                                            Combining Like Terms

(because we only had enough time for the initial brainstorming session):

Activity 1:

  1. Give students an expression to simplify
  2. Enter the full expression into Desmos
  3. Discuss the connection to the line
  4. Ask students to simplify the expression
  5. Have them enter their simplified expression
  6. Compare the graph
  7. If a second line shows up, then they made a mistake.
  8. If the line changes color, then they simplified correctly.
  9. It’s immediate feedback!
  10. Repeat as necessary

Activity 2:

  1. Give the students a simplified expression
  2. Enter the expression into Desmos
  3. Ask students to deconstruct the expression.  Break it down into 3, 4 or 5 separate terms.
  4. Graph the deconstructed expression
  5. Compare
  6. If a second line shows up, then they made a mistake.
  7. If the line changes color, then they deconstructed correctly.
  8. Again … Immediate feedback!
  9. Every student in the room could have a different deconstructed expression.


At TMC15 (Twitter Math Camp), I spent three mornings in the Desmos session.  The middle school group leader, Michael Fenton, shared this thought, which I tweeted.

Screen Shot 2015-08-19 at 9.32.00 PM

My planning meeting with Mrs. A exemplifies Michael’s message.  If the plan works, then I’ve leveraged Desmos to help her students learn how to combine like terms – A challenging concept for her kiddos.

What I presented in this blog is a general outline.  A level of refinement will take place prior to teaching but I’m looking forward to testing out the idea. I’ve worked with this group of students last year and I’m excited to observe their reaction to the lesson. I’ll keep you posted…

For more Desmos related activities and posts:


About jgvadnais

Instructional Technology Coach. Desmos Fellow. Google Level 1 Certified. SoCal transplant. New Englander at heart. Lover of yoga, dogs, green smoothies and coffee creamer
This entry was posted in combining like terms, desmos, equations, expressions, math, Math Education and tagged , , , , , . Bookmark the permalink.

2 Responses to Combining Like Terms w/ Desmos

  1. Pingback: Desmos Activity Builder – Intro to Unit Rate | Communicating Mathematically

  2. Pingback: Dance Dance Transversal – A Guide | Communicating Mathematically

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