The Power of Match My Graph

I was checking out twitter last week and ran into this from Dan Meyer:

— Dan Meyer (@ddmeyer) February 19, 2015

and I had a concept coming up that I have always had a tough reaction to. I threw it out there.

To get students to be interested in it I wanted them to be “dying” to figure it out.

I thought about putting them in a place where they had to struggle— I wanted to open up the middle!
Michael Fenton has a series of Match my Parabola challenges and I thought of those. I modified his challenges a bit to include those examples from my tweet.

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Click to access Desmos page

The idea here was that they would be able to write most of the factored form equation since they were given the zeros, but have to figure out the “a” value that creates the matching equation.

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Struggling to fit an equation

There was a lot of trial and error….most groups, by trying different values got an “a” value very close. This allowed us to ask: How accurate are we? and is there a better way? They were hooked. They were ready to try a new method.

We discussed how knowing a point on the graph helps and how we can use the equation and the point to find the exact value of “a”. The best part is the self checking in Desmos! They can put the equation in and magically see it match!

They moved on to challenge 2 with this new method and felt a ton of success getting the correct equation with minimal struggle.
When we encountered the third they started right away which amazed me. I thought they would shutter at the exact value zeros….but no!

Exact roots

Exact roots

They went right into the same strategy….each group struggled a different steps depending on their comfort level multiplying radicals. We worked through it and came up with a “nice” a-value…..and Desmos confirmed our correct answer.

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The magic really happened when I suggested that we re-work the “ugly” equation with the roots and see if we can determine a nicer one. After simplifying and putting the “nice” equation in Desmos to see they were the same equation I heard “Wow, that is awesome” and “cool”. Great things to hear after a lesson.Screen Shot 2015-02-24 at 8.50.09 AM

Creating that initial struggle is so powerful. I think we underestimate this. If you haven’t tried Michael’s Match my Parabola …..go give it a try! Awesome stuff!

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