128 divided by 8. I chose this problem because my class was in a unit on division and I had already done a few number talks where I was hoping students would use multiples of 10 times the divisor to help them solve it.  You know, problems like 186 divided by 6 where it’s just begging you to think about 6 x 30.  They were getting more proficient at that way of thinking, so I wanted to use a dividend that wasn’t so close to a multiple of ten of the divisor.

Here’s what my students came up with:

division talk

There’s almost always someone who wants to do the standard algorithm, so instead of fight it, I just slap it up on the board as they walk me through it and then move on by saying, “Did anyone think about it another way?”

Every now and then, there is also someone who arrives at the right answer, but their strategy doesn’t make sense mathematically and wouldn’t work if tried with other numbers.  (See the one in red at the bottom) I ask the students what they think and if they have any questions for the one who explained the strategy.  They asked things like: “Why did you round to 100?” and “Why did you add 4 to 96?” Sometimes they are not sure if it would work with other numbers and want to try it out.  I love that they are genuinely thinking about each other’s strategies and trying to follow the line of thinking of a classmate!

I totally dig the two strategies in the middle of the board!  (The ones written in black and green) These students were thinking multiplication and using facts they are comfortable with to build up to 128.  What is written in red on the two middle strategies came out of me asking clarifying questions so the rest of the class could more easily see the thinking that led to the quotient.

I want to give them more experience with these types of problems for a few more days, but then I want to move into two digit divisors and problems with remainders to see what they think up!

I am crazy if I number talk to myself?

Do you ever number talk to yourself?