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Great Classroom Action

Classrooms are back in session in the United States, which means lots of classroom action, lots of it great.


The blogger at Simplify With Me posts two interesting activities with dice, one involving blank dice, and the other involving space battles:

Once you have your ships, place one die on the engine, one on the shield, and the other two on each weapon. Which die on which part you ask. That’s the magic of this activity. Each person gets to decide for themselves.

Kathryn Belmonte posts five more uses for dice in her math classroom.

Kate Nowak set the tone for her school year with debate about a set of shapes:

Then I said, okay, so here’s a little secret: what we think of as mathematics is just the result of what everyone has agreed on. We could take our definition of “the same” and run with it. In geometry there’s a special word “congruent” where specific things, that everyone agrees to like a secret pact, are okay and not okay. Then, I erased “the same” and replaced it with “congruent,” and made any adjustments to the definition to make it correct. They had heard the word congruent before, and had the perfectly reasonable middle school understanding that congruent means “same size and shape.” I said that that was great in middle school, but in high school geometry we’re going to be more precise and formal in our language.

Hannah Schuchhardt isn’t happy with how her game of Transformation Telephone worked but I thought the premise was great:

I love this activity because it gives kids a way to practice together as a group and self-assess as they go through. Kids are competitive and want their transformations to work out in the end!

Featured Comments

Mary Dooms:

Kate does a great job connecting all the dots by focusing on the learning target at the end of the lesson. It appears all great classroom action positions the learning target there. Now to convince our administrators.


Christina Tondevold teaches her first three-act math task. There’s a lovely and surprising result at the end, when her students realize that with modeling the calculated answer doesn’t always match the world’s answer exactly.

After they all had taken the 24 bags x 26 in each bag, every kid in that room was so confident and proud that they had gotten the answer of 624, however … the answer is not 624! Why do you think our answers might be off?

John Golden creates and implements a math game around decimal addition called Burger Time with some fifth graders:

Roll five dice to get ingredients for your burger. The numbers correspond to how many mm tall each part is.

Matthew Jones creates a Would You Rather? activity and one of his “defiant” students makes an effective justification of a counterintuitive choice:

He blurted out “I want to paint Choice C.” I told them at the beginning that there was no right/wrong answer, they just had to justify it. I was lucky enough that he thought of the reason why you’d want to paint the larger one. The only reason you’d want to paint the largest wall is because you are paid by the hour. It was really interesting watching him come to that conclusion. And to take pride and ownership in the way that he did.

Jennifer Wilson describes one of NCSM’s “Great Tasks” and shows how she gathers and sorts student work with a TI-NSpire.

Students are asked to create a fair method for cutting any triangular pizza into 3 equal-sized pieces of pizzas. I asked students to work alone for a few minutes before they started sharing what they were doing with others on their team. I walked around and watched.

Great Classroom Action


Joe Schwartz hosts a pie-eating contest:

The game consists of two circles (the pies) and a set of Angle Race cards. Partners take turns drawing a card and then using a protractor to measure off the right sized piece. Keep going until you’ve eaten your entire pie. Whoever finishes the pie first is the winner!

Joe improvises his lesson plan in two very interesting ways and he explains his thinking. That’s great blogging.

Matthew Jones gives us a nice picture of modeling in the elementary grades when he asks his students to help him put a new roof on the school gym:

Will any of them have to do this in the “real-world?” Who knows? Maybe, maybe not. But the pictures and slides set into motion a new enthusiasm about solving it because it was their school, it was their gym. It was something they know like the back of their hand. Maybe next time they’ll look up at the ceiling and remember how they figured out the area.

Kaleb Allinson and Sarah Hagan offer different but useful approaches to probability.

Here’s Sarah:

My students instantly wanted to play again. I had anticipated this, hence the double-sided bingo cards. Based on our first round of bingo, my students set out to create a better bingo card. One of my students decided to calculate the probability like I had. She accidentally left the BB combination off of her card. She was not happy about this!

And Kaleb:

I will have students make their own boards using geometric shapes that will convince someone to think they can win but that odds are still in the game owners favor. As an extension students can include winning different amounts of money depending on where you land so a player is more enticed to play.

David Cox:

I’m noticing that more kids are gaining confidence in looking for patterns, forming hypotheses and then seeing if they can make the hypothesis fail. The phrase that seems to be gaining ground when it comes to hypothesis testing is “wreck it” – as in, “Oh, you think you have a rule? See if you can wreck it.”

There are two things I love about this:

  1. The phrase “see if you can wreck it,” and the toddler-knocking-down-a-tower-of-blocks spirit of destruction it conveys.
  2. The fact that you are supposed to wreck your own conjecture. Your conjecture isn’t something you’re supposed to protect from your peers and your teacher as though it were an extension of your ego. It’s supposed to get wrecked. That’s okay! In fact, you’re supposed to wreck it.

BTW. When David Cox finds a free moment to blog, he makes it count. Now he’s linked up this spherical Voronoi diagram that shows every airport in the world and the regions of points that are closer to them than every other airport. “Instead of having to teach things like perpendicular bisectors and systems of equations,” he says, “I just wish we could do things like this.”

Of course you need perpendicular bisectors to make a Voronoi diagram, so David’s in luck.

Great Classroom Action


Mitzi Hasegawa links up a clever game called Entrapment that helps student understand these reflections, translations, and rotations that (I’m told) now constitute the entirety of K-12 mathematics:

One table debated the transformation highlighted in today’s picture. Is the figure on the grid a reflection of the figure or a rotation?

Federico Chialvo asks his students “How safe is a Tesla?

Jonathan Claydon poses the deceptively simple challenge to spin a measuring tape handle at exactly one mile per hour:

Most students experience miles per hour in a car. The challenge would imply “I should spin pretty slow.” Yet, the handle isn’t very long. And there’s the curiosity. What does 1 mph look like at this small scale? So they spun.

Mary Bourassa repurposes a classic party game for the sake of learning features of quadratic equations:

They would ask “Is my h value positive?” but then either interpret the answer incorrectly or not be sure whether the person they had asked truly understood what a positive h value meant. They all figured out their equations and had fun doing so. And they want to play again next week when the whole class is there. I’ll be happy to oblige.

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