A Good Day

When in the course of human events, teachers will sometimes adopt curriculum.

The best days happen outside of it.

Gremlins, Speed Dating, and Monomial Cubes

Before we go further, I should describe what we call “Monster Equations” in my school.

"Ach! Gross!"


The above equation is a Monster. It has several steps, uses multiple operations, and is terrifying to an 8th grade RSP student. Luckily, we have tools to fight such monsters.

Monster instructions

Our notes for this week.

The acronym DCMAM stands for Don’t Call Me A Monster.
It also stands for the steps needed (in order) to whittle a “Monster” down to a 2-step equation (with which, the students are modestly comfortable).

Got it? That’s a Monster Equation and why we call it that. Onward:


Last week, I taught Monster Equations and it bombed. Students didn’t know how to combine like terms, distribute properly, mirror operations on both sides of the equal sign “wall”, or even add two numbers with different signs.

This isn’t surprising; those are all skills covered in 7th grade, and our adopted curriculum assumes they remember everything.

The same way that my wife assumes hot dogs are good for you, you just have to eat enough of them.

So, my class is going back to those basics, and today was “Gremlin Equations”.

Surprisingly, about 1/3 of each class had seen the movie.

Surprisingly, about 1/3 of each class had seen the 30-year-old movie.

A “Gremlin” equation isn’t quite a Monster, but still requires delicate handling, because if you break the rules…


…they get ugly.

Here enters our activity for today:

“Each of you has an expression glued to the bottom of your paper, it’s half of a Gremlin Equation. You and your partner will combine your two expressions to make a Gremlin and solve it together. When you’re done, you both stand and find new partners.”

As I described it to my department head, I realized what it actually was:

Equation Speed Dating.

"I see you checking out my coefficients, baby."

“I see you checking out my coefficients, baby.”

In the first classes, one student would fill both sides of the worksheet with about 10 minutes left and proclaim, “I’m done.” At that point, I killed the music, returned students to their seats, and opened up the Pan Balance from NCTM. They dove right into it and burned the last few minutes.

AutoCrat, a Foldable, and Impromptu Estimation

After about three hours of attempting to synthesize Google Drive with my district firewall, I was met with a failure sandwich on toasted frustration bread. My digital team-mates–John and Karl–did the best they could to troubleshoot unique solutions:

Well, 6th period arrived before IT support did, so I pulled a quick foldable from Sarah’s blog and followed it with my bag full of monomial cubes, planning to do some random practice.

Photo Feb 04, 2 55 59 PM

I held up the bag and immediately a student called, “How many dice are in the bag?”

Oh. I thought. This just got much more interesting.
“What do you think?” I asked.

A couple students call out guesses before someone yells, “Can we see one of them?”

Photo Feb 04, 2 56 21 PM

We pull a few guesses (where the median is about 65) and start counting them together.

Photo Feb 04, 2 46 17 PM

“Is there an easier way to arrange them for counting? This is confusing me.”

Photo Feb 04, 2 49 38 PM

“Okay, five by five… so we’ve got three 25s plus one… so… ”
Student: 76! I was close!
“What if this was on a planet where humans had 4 fingers on each hand instead of 5?”

Students paused. Thought for a little bit. Then…

Photo Feb 04, 2 53 59 PM

Hey! Five 16s with 4 missing! That’s also 76!

So, yeah. It was a good day.

Tomorrow, students will finish up their Monster Posters with this cut-and-paste Monster Equation activity.

~Matt “The Expression Matchmaker” Vaudrey


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4 responses to “A Good Day

  1. Wait…so 3\cdot5^{2}+1=5\cdot4^{2}-6? I wonder if we can replace those bases with the same number and get a true equation? Now I want to solve 3\cdot x^{2}+1=5\cdot x^{2}-6.

    Is it going to be between 4 and 5?

  2. Mr Vaudrey

    Love it ! I shared this blog post with my middle school team and my Algebra I team. I also posted a link on my own Virtual Filing Cabinet

    Thanks for sharing

  3. LOL…in my class we call those “ugly” problems “releasing the Kracken” and show pictures of Pirates of the Caribbean. But I LOVE your idea of Gremlins. Will steal this if you don’t mind. Have a group of freshmen who are struggling with “Gremlin” level problems!

  4. What’s most impressive about this is how seamlessly you are able to adjust your lesson to what your students are prepared to learn. Next year I am teaching 7th grade for the first time in about six years so this is gold for me. Thank you.

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