# Sticks and Dots, Compensation and more!

Yesterday I posted last week’s (or at least the LAST week that we were in school’s) math warm-ups.  I mentioned that there’d be more about the strategies on which we’ve been focusing.  Well, that time is now.  Hope this makes sense and gives some insight into the work we’ve been doing for the last few months.  Well all quarter, really…but I digress.  Here we go. 🙂

One thing I wanted to do was to be able to SHOW how these strategies work, and even better, have KIDDOS involved in that work.  So, just before we left for our break, many of them volunteered to help me with a project.   I have a Tweep (that’s a friend you know from Twitter, for those who might not know) named Shannon in Alabama who was interested, too, so this is for you and your friends, lady! 🙂

Ok…so here are some videos of our Rm. 202 kiddos explaining more about how to add 2-digit numbers using place value strategies!  (I will mention, though, that they are a little rough, so ignore the bumpy parts and see the big ideas, ok? THANK YOU!! 🙂 )

Sticks and Dots

Splitting 10s/1s

Keeping 1 Number Whole

(This one’s a little long, and shows more than 1 strategy, so be prepared for that!)

Compensation

Hope this helps–and WAY TO GO, RM. 202 KIDDOS!!  You are ROCKING mathematicians!! 🙂

# Rethinking Multiplication Strategies

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.

District Math Rubric for Multiplication

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):

Classroom anchor chart for multiplication strategies

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:

Math Warm-Up for October 14

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!