Math Monday...on Thursday

I am joining Mandy at Enjoy and Embrace Learning for Math Monday. Franki has resolved to join Alyson Beecher's Nonfiction Book Challenge in order to stretch herself to read more nonfiction. I'm going to stretch myself in a different direction and try to focus on what's working (or not working) in my 5th grade math workshop.

This week (in between a snow day and a windchill day) we began working towards a deep understanding of division. Our standards in 5th grade do not require students to be able to do long division with the algorithm. We will be exploring multiple strategies for division.

Mandy wrote this week about the importance of play. What I discovered was the importance of manipulatives...even for fifth graders.

Students were in groups of 4 or 5 on the floor in the meeting area. Each group had different manipulatives (beans, dominoes, pattern blocks, tiles). We modeled what addition looks like (combining groups) and what subtraction looks like (starting with a big group and taking some away from it).

Then we moved to modeling multiplication, which was surprisingly hard for them. After I gave them a problem to model (3x4), they realized/remembered that they needed to make equal groups or an array. We spent a lot of time thinking about what a multiplication problem SAYS -- "Three TIMES" tells you will be repeating a process three times, or making three groups.

Modeling division was as challenging as modeling multiplication. We started with a problem that they could easily solve with mental math so that they could check to make sure their model made sense (22 ÷ 2). Knowing that partial products is one of the first strategies we'll work on once we move to paper-pencil, I also gave them problems like 68 ÷ 5 so we could talk about efficient ways to share 68 into 5 equal groups rather than counting one by one. (Starting with 10 in each of the five groups, for example, and then sharing the leftover 18 into the 5 groups.)

Our math block is cut 10-15 minutes short by related arts, which we have actually come to love, because we can come back to our work and share, or students can complete an exit ticket or formative assessment that will inform my instruction for the next day. I gave each student a sheet of notebook paper and asked them to draw a model for 19 ÷ 3 and then write three things they know about division. What an eye opener! I've got a group of 5-6 who modeled 19 x 3, and another 4 or so who modeled 19 ÷ 3, but didn't demonstrate complete understanding by giving an answer. There were students who could model, but not write anything they know about division, and there were students who could write three things about division but not model.

So, now it's time for differentiation. I need to get some students to that deep understanding of what division means (modeling), and I need to move others along to applying that understanding to various strategies! This is the tricky part! This is the FUN part!