First of all, I know. It’s been forever. Man, I’ve been saying that a lot lately. All I can do is apologize, though, and ask that you’ll kindly keep reading. Life is nuts these days. 🙂
So…we are just about at the end of a study of multiplication and this year I’m asking my friends to think in a different way about the word efficient when it comes to multiplying.
Based on our district rubrics, which have recently been rewritten based on work related to Common Core and an updated curriculum, the standard for 5th grade has changed. Instead of just being able to use the traditional algorithm, students are expected to be able to fluently use a variety of strategies. But get this: the strategy they choose to use should be based on the numbers in the problem, rather than personal preference or the strategy they know best. WHAT??!! I seriously have some friends whose heads might explode.
But it’s not really their fault, I guess, because for years the algorithm was the goal. And once they learned how to use it, that’s what they stuck with and used every time. For years, we (or they) saw the other strategies as lower-level–ones used by friends who didn’t yet “get” how the algorithm worked.
Now we’re thinking more about how mathematicians should be able to be flexible with their thinking, to use place value correctly and to explain their reasoning based on what they know about numbers. This doesn’t mean that the algorithm isn’t something kids should know how to do, but that it’s not the only thing they should know how to do. I mean think about it in the real world: there are times when you have to be able to do math in your head, in an efficient way–without paper. The algorithm doesn’t really fit into that model.
So what does this look like in our room?
First of all, here’s an anchor chart that now hangs in our room (made based on our knowledge of how to solve multiplication problems):
While I don’t have any pictures of the math warm-ups we’re doing right now, this is where many of our opportunities come to try out this thinking. The problem today, for example looked like this:
There are obviously (based on the chart) multiple ways to do this problem. But based on the numbers (which were chosen on purpose), the strategy that makes the most sense is to either use splitting or a close 10 to solve the problem. That way, you can solve 75 X 20 and 75 X 3 and then add them together, which can easily be done in your head–without paper. If you chose to use the algorithm (which most would do–even most adults!) you’d have to do 5 X 3, then 70 X 3, 5 X 2 and then 70 X 2 and add it all together–many more steps than the other strategy.
So while this is still a little tricky for some friends, it will get easier with time. We just need some more practice. 🙂
What strategy would you have used to solve 75 X 23? Do you know more than one strategy to multiply? Is the traditional algorithm your “go to” strategy? I know my 5th grade mathematicians would love to hear your answers!