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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?

1. I have a background in programming, so all kinds of ideas pop into my head about writing "random problem" programs so that students could practice a particular skill with problems created "on the fly". You'd be surprised (or maybe not!) how challenging it is to make something as simple as a fraction arithmetic quizzer that has just the right mix of problem types. What ranges should the fractions be from? Should they be "improper" or "mixed-numeral", or both? If both, in what ratio? Do we want to throw integers into the mix? Everyone's needs would be different, and it throws lots of variables into the equation, so to speak.

So I don't really have any ideas for your card worksheet (which is a pretty cool idea), I just wanted to share in the frustration!

2. If they draw a red card, that and the next card concatenate (join) to make a two digit number under the radical. This would then count as 1 'card'...
I.E - The student draws a B3, then R5. The B3 just becomes a 3, but since the other is R5, they must draw a next card to finish the radicand. Suppose it is B4. This is ok, just connect the 5 and 4 together. They should have 3rad(54) so far. Then keep going until they have 4 pieces total.

3. I haven't done enough to have some of my classes work as independently as this requires, but when I love the make your own practice.

I just did the whole unit on fractions with my Precalc class using the X-pression deck I discovered at I Love Math. We decided on the template first (add, subtract, multiply, divide, etc.) and drew cards. Not quite as fun as a traditional deck, but still fun.

4. Kate
I love this deck of cards thing. It is pretty limitless as to the type of "worksheets" one could create. Thanks for the post.

5. This is a great idea Kate! I will use it for sure next term. I think I would leave out the black aces and use the queens as you suggested. I wonder what other topics in Maths you could apply this too? Fractions, Integers and Pythagoras come to mind.

6. Thanks for all the ideas!

I've also used this idea successfully for operations on integers, fractions, and fractional exponents/logs. Sometimes I have them use the RandInt() calculator function.

7. Matt,

Actually, the programming aspect of this isn't too difficult. It's the algorithm problem. A competent program could take those arguments into consideration in a simple configuration file. I think you hit the nail on the head when you said one size won't fit all, but why should we be limited to one size?

Kate (hah, I get to call you that now),

Why not use what the students have on them? Those kids (especially the freshmen!) are lugging around enormous amounts of junk with them. Tell them one of the numbers comes from the number of pages in the first book they pull out of their bag. Another number is the number of contacts in their cell phone. Another number is the grade they got on their last quiz. Another number is the number of pencils they have with them. Chaotic? Of course. But sometimes a class needs a little chaos to remove the boring monotony of a simple lecture or ditto.