This is a step-by-step guide on how to teach multi-digit multiplication to 3rd and 4th grade. In this blog we will focus on multiplying 2 and 3-digit numbers by a 1-digit number. Moving from concrete, to representational (pictorial), to abstract is key! And making connections between the progressions is absolutely crucial!
The first thing we are going to have students do is practice building multiplication problems using base-10 blocks. A word of caution, be careful with the problems you choose for this or you’ll end up doing 859 x 8 and no one wants to count out 72 unit cubes… Keep it simple!
From there, we are going to have students transfer that skill to paper. Instead of physical base-10 blocks, we are going to draw those blocks. Be sure to show this to students side-by-side. They need to understand it is the exact same thing! Just now, we are representing the problem pictorially. Again, be careful about the problems you choose…because the only thing worse than counting out 72 unit cubes is drawing 72 unit cubes…
A note on drawing base-10 blocks: This is something that needs to be explicitly taught and modeled. However you want students drawing these, show them and have them do it that way. We don’t need grid lines all over our hundreds blocks and our unit cubes don’t need to be 3D cubes. I always tell my students “this is about representing the problem, not an art contest.”
Students may start to realize that getting out base-10 blocks or drawing them is kind of time consuming. Which is why we may want a more efficient strategy. Side note…we discuss how each strategy gets us the same answer. One isn’t necessarily “better” than the other. Some are simply more efficient!
We are going to take what we have learned from our model so far and transfer that to an area model. When I first introduce this, I do make them write what we are multiplying in each box (as shown in the picture above). We don’t do that forever, but we do at first so they can show me they know where the number in the box came from. It also helps with keeping track of how many zeros each section should have.
Have students discuss or write what they notice is the same and what is different between the different strategies. Connections, connections, connections!
You can click the link below to download the worksheet I use as our guided practice when introducing this skill.
Multiplying by 1 digit Arrays and Area Models
Here’s part 2 for connecting area models to expanded algorithm and standard algorithm.
