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Archive for the 'classroomaction' Category

Great Sam Shah Action

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Sam Shah’s blog has been a veritable teaching clinic the last two weeks, more than filling his own installment of Great Classroom Action.

With Attacks and Counterattacks, Sam asked his students to define common shapes as best as they could – triangle, polygon, and circle, for instance. They traded definitions with each other and tried to poke holes in those definitions.

When the counter-attacks were presented, it was interesting how the discussions unfolded. The original group often wanted to defend their definition, and state why the counter-attack was incorrect.

Trade the definitions back, strengthen them, and repeat.

Sam created some very useful scaffolds for the very CCSS-y question, “If you have a shape and its image under a rotation, how can you quickly and easily find its center of rotation?”

This is an awesome exercise (inmyhumbleopinion) because it has kids use patty paper, it has them kinesthetically see the rotation, and it gives them immediate feedback on whether the point they thought was the center of rotation truly is the center of rotation. Simple, sweet, forces some thought.

Sam then pulls a move with a Post-It note that is a stunner, simultaneously useful for clarifying the concept of a variable and for finding the sum of recursive fractions:

Ready? READY? Flip. THAT FLIP IS THE COOLEST THING EVER FOR A MATH TEACHER. That flip was the single thing that made me want to blog about this.

Finally, Sam pulls a masterful move in the setup to his students’ realization that all the perpendicular bisectors of a triangle’s side meet in the same point. He has them first find those lines for pentagons (nothing special revealed) and quadrilaterals (nothing special revealed) before asking them to find them for triangles (something very special revealed).

There were gasps, and one student said, and I quite, “MIND BLOWN.”

Great Classroom Action

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

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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!

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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.

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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

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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.

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