Posted in classroomaction on May 27th, 2014 2 Comments »

**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.

Posted in classroomaction on April 22nd, 2014 2 Comments »

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.

Posted in classroomaction on April 4th, 2014 4 Comments »

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:

- The phrase “see if you can wreck it,” and the toddler-knocking-down-a-tower-of-blocks spirit of destruction it conveys.
- 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.

Posted in classroomaction on November 11th, 2013 No Comments »

**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.

Posted in classroomaction on October 25th, 2013 No Comments »

**Cathy Yenca** gives Graphing Stories a go and the going gets tough (and interesting) when she runs into Christopher Danielson’s step-function:

The last video we tried today was Ponies in Frame. I heard the most awesome muttering as soon as the video began. “Oh! I get it. This one’s discrete.” [..] It wasn’t all lollipops and rainbows. A comment laced with negativity that resonated with Lauren and me was an outburst that “graphing used to be so easy, and this just made it hard.” How would *you* take a comment like that? What does that comment say about the student’s true level of understanding?

**Jonathan Newman** has his students analyze parametric motion by creating stop-motion videos.

**Nicora Placa** reminds us that the one of the best ways to assess a student’s understanding of direct proportions is to give her an indirect proportion and see if she treats it directly.

At a workshop last week, the following task caused a bit of confusion. “If a small gear has 8 teeth and the big gear has 12 teeth and the small gear turns 96 times, how many times will the big gear turn?” Several participants were convinced it was 144.

**Megan Schmidt** uses one of the Visual Pattern tasks and surprises us (me, at least) with all the different interesting equivalent ways there are to express the pattern algebraically:

They came up with the following pre-simplified expressions for the nth step:

2n(n+1) + 3

1 + (n^{2} +n^{2}) + (n+1) + (n+1)

2[n(n+1)] + 3

2n(n+1) + 3

3 + [(n+1)n] + [(n+1)n]

3+2(n+1) + 2[(n+1)(n-1)]

2n^{2} + 2n + 3

For each of these, I had the student put the expression on the board. I then had different students explain the thinking of the student who came up with the expression and relate it to the pictured pattern. I saw a real improvement here from when I had them do this activity the first time last week. I had many more students volunteer to explain the thinking of their cohorts and much less hesitation to work out what the terms in the expressions represented.