Number Talks: Division

We've been doing a lot of division lately and I began to notice that the preferred method is the traditional algorithm, mainly because that’s what parents are more comfortable with at home when helping with homework.  Because of this, I was noticing that if students made a mistake in following the steps, they really didn't notice they were making a mistake, let alone that their answer was not reasonable.  So, I decided to encourage more mental math.  We did this through some number talks and the use of slates.  In previous Number Talks, I didn't allow my students to write anything down to force them to do work mentally, however, for the division number talks (at least at first) I allowed them to write down their thinking on slates so they wouldn't confuse themselves.  The only stipulation was that they weren't allowed to divide the “normal way.”  No “houses!”  

We started with smaller, simpler numbers: 25 ÷ 4.  Here is a picture of their thinking:

Molly began by saying, "I know that 4 x 5 = 20 , and that was too small, so I added another group of 4 to get to 24.  Then, I knew I just had to add one more to get to 25.  So I had 6 groups of 4 with one left over."

Once some students saw how others were using basic facts to help them, they began to catch on.  More and more students began volunteering their thinking.  This is something we will continue to build a knowledge base of.  My hope is that this will lead my students to a greater understanding of division and answers that are reasonable.

Blake is one of my students that has an amazing sense of numbers: he does almost all of his calculations mentally.  I always try to see what he is thinking to guide the other students.  

This was a great example of two students building from something they already knew: multiples of ten.  I love how one counted up from ten and the other counted down from 20!

Jillian wasn't afraid to say she started with a fact that was too low and built her way from there!  I always encourage them to admit when they make a mistake and tell us how they found it and fixed it!  Chances are, they aren't the only one making that mistake!

We are really improving and they are finally telling me how much they love math!

  

Number Talks

As previously mentioned, our district has the fortunate opportunity to train teachers on the CCSS.  In addition to discussing RICH problems and how they can be used in our own classrooms, we conduct Number Talks.  We use the book Number Talks: Helping Children Build Mental Math and Computation Strategies, Grades K-5, by Sherry Parrish as a resource.  Number Talks were designed to improve students' mental computation skills and number sense.  Inside Mathematics is another fantastic resource that shows how different teachers in varying grade levels apply Number Talks to their lessons.  In fact, this is a wonderful website that allows you to see teachers in action applying the Common Core Practice Standards! Woo! 

Anyway, we have been doing our best to introduce these talks into our classroom.  In my room, students sit together right in front of the board.  I tell them to summon their inner Kindergartner, which they giggle at.  We have only had time for a couple "formal" Number Talks, but we are beginning to apply it in all aspects of our day when answering questions verbally.  Here is an example of how my students were able to solve a basic addition problem using mental math and their process for doing so: 

Are they stellar?  Probably not.  My students were looking at me like I was a crazy person that day.  They didn't quite understand why understanding how to compose and decompose numbers is so important.  Many said, "I put them on top of each other and added.  I also carried the one." My point was that I wanted them to know what "carrying the one" actually meant.  As we do more, they do improve, and I can see it translating in other areas of math.  They are really starting to think about the VALUE of the numbers.  

I plan on doing more complex problems as we go and seeing how they improve.  I told them I would keep their original posters so we can compare them to how they are doing in a few months.  They have already drastically improved!  If you don't do Number Talks in your classroom, I highly recommend you look into incorporating them every now and then, especially in younger classrooms!