Here’s the original activity, from Illustrative Math’s 8th Grade curriculum:

I love the main task. I don’t really know what to do with that “Are You Ready For More?” extension, though.

It’s definitely challenging and interesting, but it’s not really connected deeply with the math that comes before it. And really solving that HANGER + HANGER + HANGER = ALGEBRA problem likely would require a bunch of time — where is that time coming from? Usually I don’t need something that’ll take kids ~15 minutes to solve, I need something interested a fast-finisher can think about for ~3 minutes.

Put it like this: I’m not sure it would be worthwhile (or even possible) to talk about that HANGER/ALGEBRA puzzle with the whole class, if only a couple students even got to it. But if I’m not going to be willing to honor those sorts of problems with airtime, why would a kid ever dig into it?

I don’t mean to give the Illustrative Math curriculum a hard time, as I’m a huge fan. I’m really thinking more about how to improve the problems I’ve prepared for students who finish quickly. How can I make it clear that they really are *part *of our class?

I’ve really been playing with these ideas this year. Here was my replacement for the HANGER/ALGEBRA puzzle:

The math is close enough to the task itself that I really felt like I could talk about these problems with everyone — even briefly — and it was valuable. Kids who try it will get some airtime. I’m trying to bring the extensions closer to the main task.

I’ve also been trying this with geometry, where I built an activity on top of some Don Steward practice problems:

Understandably, Illustrative Math doesn’t have extensions like these ready for every problem. But something like this is an easy way to make an activity more useful for a broader range of students (which also gives kids who need it more time).

But Illustrative Math is a free and openly licensed curriculum. They’re actively seeking user contributions to their curriculum — all this seems like a nice match for the sorts of revisions I’m talking about here.

How long would it take to write these things? How many could 20 teachers write in an afternoon? One for each 8th Grade task?

A teacher can dream!

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What’s the general number of questions, time given and max spare time?

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I should add I dislike on principle giving more of the same if you finish early. More != depth especially if mastery is demonstrated. But 3 minutes is barely enough time for anything of significance.

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I agree. If a kid finishes early, I come up with a more abstract problem using similar concepts that ups the difficulty significantly.

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I love to have the last question(s) be open ended. Not an extra if you’re done, which can make extra work feel like punishment for being done. Can you make an equation at least as complicated as Diego’s where the solution is x=4? Could you solve your own equation? How?

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