This week my second grade students have been exploring multiplication strategies. We started off early in the year looking at arrays and using doubling strategies. Then we moved to helper facts. These are still used to this day, but we introduced a new tool this week. Enter the area model. Hello!
Students transitioned from arrays to squares, but didn’t sit at that spot long. Through the area model, students take apart numbers and partition (yes, we say partition at second grade) the rectangle into parts. Each part is a partial product.
I’m fortunate in my position to see this strategy used at multiple grade levels. The rectangle evolves over time. As students progress, I find that place value and advanced decomposing strategies become more prevalent. You can learn quite a bit about a student’s understanding by checking out their math work with an area model. How they split up the numbers can also tell a story. Why did they split up the rectangle that way?
I find quite a bit of value in using this strategy. For one, it doesn’t immediately move students towards the standard algorithm and it helps build/show conceptual understandings. My 2-6th grade math students use it in a variety of capacities. My 5th grade crew has recently been using them to multiply fractions. Short story: It makes an appearance at every grade level. It’s also a a fairly smooth transition to using the partial-products strategy.
Even though it’s a useful resource, I find there are a a couple things that irk me about using this tool. Sometimes organization skills can hamper the effectiveness of drawing and organizing. I’ve had more than a handful of students draw boxes that overlap or numbers that might not be decomposed correctly. Also, it’s not to scale, but that’s not a game changer for me.
As students progress through elementary school they encounter a variety of math tools and strategies. Manipulatives are generally used to help students build a better understanding of math concepts. The CRA model is often emphasized at this level. Many tools are brought out to help fill gaps and others are continually used. At some point, I’m assuming the my students will rely on the standard algorithm to quickly multiply numbers (if they don’t have a calculator handy). They probably won’t understand why the algorithm works, but it just does. The area model shows multiplication in a concrete way. Don’t get me started on lattice.