## Thursday, February 20, 2014

### Old School

It felt really retro on Monday when Rich and I spent some time at the chalkboard trying to give the kids some options for multiplying mixed numbers.  I thought we might play around with the partial products algorithm.

 Rich started out by reminding them how we organized multi-digit multiplication by breaking the numbers into tens and ones, finding the partial products, and then adding them up.

 We tried it with mixed numbers.
 It worked!
Then something really interesting happened.  Flashback: about a week ago, Rich and I had spent some time at his back table playing around with the fraction tiles, seeing if they could be put to practical use in a fraction multiplication "area model".

 We turned the tiles on their sides.  We started with 1/2 X 1/3.

 We defined the whole.

 We built it out.  I liked the way it divided the whole into six 1/2 by 1/3 rectangles.  But it wasn't so practical.  The tiles kept toppling over.

 So Rich copied frames that measured 1 square unit bar and he put them  in plastic protectors.

 The tiles could be used to measure off the halves and thirds...
 ...and then the whole could be divided into 1/3 by 1/2 rectangles.
 1/3 x 1/2 = 1/6
We tried it with mixed numbers.

 2  1/2 x 2  1/3

 5  5/6.  See it?  I wasn't sold on the idea.  The bell was about to ring.  We decided to revisit it later.

Flash forward: So, after we had used the partial-products box for multiplying mixed numbers, a boy raised his hand and asked if he could come up to the board and draw something.  "I overheard Mr.Schwartz and Mr. Whalen talking about this last week," he said.  "I watched them work with the tiles.  Those boxes reminded me of that."

 Rich and I looked at each other.  Who knew he had been paying attention?

After that, a student piped up:  "What about lattice?  Would that work?"

 We tried it out.  Instead of "tens and ones" we used "whole numbers and fractions".  The kids went wild.
Another student volunteered to come up to the board.  At this point the chalk dust was really flying.

 The old "turn the mixed numbers into improper fractions, multiply, and then convert back into a mixed number" method. .
We asked the kids to work on some problems and try out some of the different strategies.

Still a work in progress.  But I hadn't been covered in so much chalk dust since...well, since Eddie Shore laced up his skates.

 "Old time hockey! Like Eddie Shore!"