When I was in 4th grade, I really began to hate math. I struggled to memorize the multiplication tables, I didn’t understand division, and I just wanted to put my head down on my desk and cry. My feelings that I wasn’t good at math continued all throughout my education and stopped me from pursuing some science classes I was really interested in taking.
Now here I am teaching 4th grade and my class tells me how much they love math! When I switch screens from screen sharing, back to being able to see their faces (virtual teaching in a pandemic…right?), their cameras are on and they’re smiling. Smiling at long division! I would have been crying as a kid.
The big difference between my experience as a student and my students’ experience is in the strategies. When I was in elementary school, we learned one way to solve a division problem. If you didn’t understand that method, oh well. And the language wasn’t very precise. I remember saying “How many times does 4 go into 36?'“ and not really understanding what that meant. Now we say “How many times does 4 divide into 36?”, but that’s also backed up in my classroom with lots of concrete, hands-on representation.
When I began our division unit this year, I had all my students bring counters to our virtual class. Some brought dried beans or macaroni noodles, some brought crayons or small toys, and one student tore a sheet of paper into small pieces for their counters. Whatever works works for me! I used mini-erasers (Thank you Target Dollar Spot!) and modeled the dividend and how to break the dividend up by the divisor. We practiced making groups and finding how many in a group, then we practiced using the amount in each group as our divisor and finding how many groups.
Anything can be used as a counter for division. Having kids physically move objects into groups helped grow their understanding of division so much!
I spent a solid 2-3 days just having my students practice dividing with their counters, working with dividends 40 and under, and without remainders. Then, we moved into the abstract of solving long division problems using partial quotients. (I skipped the representation stage of the Concrete-Representation-Abstract [CRA] method. I felt this class was ready to go right into the Abstract after our practice with concrete.)
I modeled the Partial Quotients strategy with smaller dividends and single-digit divisors first, then had students practice. I also color-coded the partial quotients, to help students better understand what we were doing and how we were doing it.
Their understanding of division just took off! They had that concrete understanding as a solid base, and that they could go back to as needed, and it made a huge difference. My class was telling me they LIKE math and that they were having FUN! What?! I don’t think I ever said those things about math as a kid!! (Which is a huge motivator for me to make sure my students do understand that there are multiple strategies that can be used in math.)
If you’re looking for a division resource to save you time in your planning, be sure to check out my Division Using Partial Products Bundle on TPT. It includes step-by-step example problems, so you can teach your students the strategy with confidence. There are also student practice problems (including word problems) with a fully solved answer key-perfect for the I Do, We Do, You Do model, as well as great for sub plans, independent practice, or review.
