Multiplying Fractions

I had a two-day week with my students this week, and while it was hard for me to go back for such a short week, it was a great couple of days. It was one of those weeks where I felt reasonably well-organized, but also where my lessons were going well. This was especially true in math where I started my unit on multiplying fractions.

Multiplying fractions is one of those topics that I was pretty nervous about teaching just because I think that it's conceptually challenging for students. The idea that multiplication can make a number smaller does not compute for a lot of kids (and even some teachers, e.g., myself a couple of years ago). Add to that the fact that none of the teaching resources for my grade level include any mention of multiplying fractions because they were all written and purchased pre-Common Core, and I worried this unit could be a disaster. As a result, I scavenged as many resources as I could find and cobbled together some lesson plans.

First, I purchased the Marilyn Burns book Lessons for Multiplying and Dividing Fractions from her Teaching Arithmetic series.

I'd used some of the previous fraction books in the series for the other fraction standards, and I'd found them really helpful. I figured this would be a good addition to my collection. While it doesn't have a lot for the fourth grade standard (it goes far beyond the scope of what's expected for fourth graders), the foundational lessons are excellent.

On Thursday, we did the first lesson in the book. In this lesson, students worked in small groups (4-5 students) to brainstorm as many factual statements as they could about multiplication. We reviewed the difference between facts and opinions, and I gave the students less than 10 minutes to make their lists. I was blown away by what they were able to come up with! In the end, they had almost all of the statements Marilyn suggested. (Notice how I called Marilyn Burns by her first name there? As if she and I are friends? HA!) They even had a few that she hadn't mentioned such as an even number times anything will be an even number or the various symbols that can be used for multiplication. In the end, we had this list (which is a slightly modified version of the one she suggested):

During this first day, we didn't discuss fractions at all -- it was entirely about whole numbers. We gave examples for each one, and that discussion plus a pre-test took up almost all of our instructional time. I was so impressed, though, that my students were able to come up with all of the statements from her book except for the one related to the distributive property. It made me feel like I'd really been productive in the fall.

Today, we revisited this anchor chart, and we talked again about each statement to see how it applied to multiplying fractions. I modeled doing multiplication as repeated addition of fractions (which they quickly understood), showed them how to use arrays with fraction multiplication, and spent a lot of time talking about the distributive property and breaking numbers apart. For example if you're multiplying 6 * 1/2, you could think of the 6 as being 2+2+2 so that you're solving 2 * 1/2 + 2 * 1/2 + 2 * 1/2 = 3. I really think it was the first time that the notion of breaking numbers apart like that ever made sense to some of them. Finally, we talked about #6 on the chart and how the product is smaller when you're working with a fraction that's less than 1.

Students worked on some problems independently after our lesson, and I can honestly say that every student had at least one strategy that they were able to use consistently to solve. Some students figured out the standard algorithm right away, while others took a lot of comfort in repeated addition for now. There are definitely some students who will need a bit more help next week, but we're much farther along in this process than I'd expected. I think they're getting the conceptual understanding, and that's clutch. I'm so excited!

Next week, we'll talk about estimating answers and connect multiplication to finding a fraction of a set.

What strategies are working best for you as you teach the new fraction standards in Common Core?

Have a great weekend!