Multiplying Signed Numbers: Velocity and Hot Wheels

Today I decided to take a risk in my middle school math classes.

And it wasn’t bad! or wild! or necessarily great! But I’m glad I tried. I’m so proud of my young mathematicians… and me!

MY FIRST YEAR teaching Open Up Resources 6-8 Math, a problem-based curriculum promoting student investigation and active learning, was all about survival. I had days where I wanted to facepalm and/or cry, days that can only be described as “meh,” and others that had me figuratively walking on sunshine. (But none of those days were without a stack of formative Cool Downs in tow. That’s beside the point.)

I remember my very first time teaching the skill: multiply signed numbers (lesson link). The Open Up Resources 6-8 Math curriculum tackled it with the context of velocity.

Lesson 8 Learning Targets:

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Lesson 9 Learning Targets:

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And even though I’d studied the lessons and syntheses for too much time and put pencil-to-paper myself, my first class (bless them all) was a disaster-in-all-caps. I panicked.

I ran to the library, made double-sided copies of a red car on cardstock paper, and attached magnets to the wheels. I drew a number line across my white board, similar to the line from the lesson plan. And I guided the lesson. There wasn’t productive investigation. There was total direct instruction. I fell back into the pattern of how I was taught: these are the rules, they always work, take my word for it, mmk? Bleh. It didn’t feel good or student-centered.


IN YEAR TWO, after learning more deeply about the 7th grade content presented in this curriculum (after failing so many times and picking myself up again, putzing to the freezer and downing a pint of ice cream), I made more progress. I gave my students time to grapple and struggle with the context, and I modeled the context with the same red car. And I invited students up to the board too! They proved their thinking and synthesized the learning. They made mistakes and learned from them collectively. We all struggled. We synthesized. We all learned.

*If I could take you all in a time machine to Year 2+ with this curriculum, I would, though all of the learning in Year 1 made me a better, more reflective teacher with a deeper understanding of this content.

ROUND THREE *ding, ding ding! This year, Year 3, as I was playing Hot Wheels with my two boys as I approached the same skill, multiplying rational numbers. I thought, Why am I doing all of the leg work during this lesson? Could my students handle working with these Hot Wheels as a math tool? I talked to my colleagues and family, and it was determined that this was surely a terrible idea. Middle school students couldn’t handle it.

But I couldn’t shake the idea. How could I possibly get all 25 students using my torn-up red car during a class period to independently investigate and grapple with this new learning? That would be virtually impossible. This is an age group of hands-on learners, and my modeling was fine, but I was still taking charge of the synthesis and content. I wanted my students to take ownership. My young sons agreed to let me take the cars to school… as long as I didn’t take the Batmobile. Fine.

I provided each student a slip of paper as their highway number line (link, page 1). I made a Parking Lot (link, page 2) for when the students didn’t need the cars, to keep some sort of classroom management, for when the students couldn’t handle these new, unconventional “math tools.” And I let them know that the Hot Wheels would be towed if they couldn’t handle them. Those were the only directions they really needed.

Parking Lot

My students were engaged in quiet work time. They asked lots of questions as we moved their cars across the number line. And they helped each other out, sharing their learning and understanding. I wish I had a clip of their working, collaboration, and active learning.

Did today go perfectly? Nope. Not in the slightest. I polled my class, and most (not all) thought that the Hot Wheels were a helpful tool. Some found them distracting, though the number was surprisingly very low. And my class average for correct answers out of 8 total true/false questions on the formative Cool Down was right at 84.6% after the second lesson (lesson link) about the multiplying signed numbers skill.

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After the formative one student exclaimed, “I’m excited! I actually get this!” Another said, “I told my team that if we did a pop quiz right now, I’d ace it!”

Not a single car was towed. Taking chances is a good thing. It’s not always a perfect result, as proven in these reflections. BUT I had a great day. My students took ownership of their learning and voiced it to their peers as they investigated, engaged in productive struggle, and synthesized this new math content. I’m so proud of them… and me! Solid curricula, like Open Up Resources 6-8 Math, provide a wonderful foundation for active and deeper learning; teachers taking risks or bringing in personal style, flair, and enthusiasm, make it magical for young mathematicians.


And of course, I have to include these cuties:


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