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## Tuesday, April 7, 2009

A simple idea: provide a structure for a skill the kids need to practice. Let them fill in the numbers to use through some randomization process (dice, playing cards, calculator random number generator...).

I find the idea appealing -
• it's a tad more engaging than a preprinted worksheet
• it saves paper
• sometimes it conveniently illustrates a larger concept, such as $\sqrt{ab}=\sqrt{a}\sqrt{b}$, and the commutative property of multiplication.
But using BYOW has consequences, and what I'd like to discuss is minimizing the undesirable consequences.

For example, these are my directions for BYOW: multiplying radical expressions.

I had them remove the face cards (which got me jokingly accused of being "facist" - ha ha), but leave the aces. They need a little experience with the fact that $\sqrt{1}=1$. You wouldn't think so, but it comes up in places like evaluating the quadratic formula.

I'd overall call this a "success", because the kids worked at it for a good 15 minutes without losing focus. Quick assessment at the end indicated that they knew meant "multiply", which was one of my goals.

The biggest issue is too many too-easy problems. Like, $\sqrt{1}\sqrt{9}(7)$. Or radicands that are already simplified. Or all black cards. Yes I want them to recognize when a radicand cannot be simplified, but I don't want 7 of these easy problems, and only 3 where they have to simplify the resulting radicand. You see?

So far the only idea I have is to keep the Queens in the deck, and say they are worth 12. Also, I could have them separate red and black, and always choose 2 of each.

Any other ideas?