I got to spend time with my 3rd grade tutorial group this afternoon (LOVE Mondays and Thursdays), and we were working on 2-digit by 1-digit multiplication. They have been struggling with not only the computational aspect (the algorithm), but also the conceptual understanding of what multiplication means. I used a very simple SMART Notebook file to connect the representational stage (drawing) to the abstract stage (algorithm).

So before we even got to the model drawing, we had to establish that 45 x 4 means 4 groups of 45 (or 45 groups of 4, but we decided that would be too hard to draw!). What you see below is a picture of the SMART Notebook page and how we worked through each problem. I’ll take you through it step by step.

- Verbalize that 45 x 4 is 4 groups of 45 (or 45 groups of 4).
- Draw 4 groups and draw the base-10 block representation of 45 in each group.
- Show the multiplication using the partial products method (left side of the picture). I kept referring back to the model to make sure they connected the number sentence for multiplying the 1s with the model and then the same thing with the 10s. Side note here–we worked a LOT on seeing that 4 x 40 is really 4 x 4 adjusted for place value. I tell them to look for the “little fact they know” and then adjust for the extra zeros. They thought this was uber cool!!
- Show the multiplication using the traditional algorithm, connecting it back to both the partial products method and the model.

While the 3rd grade objective is only 2-digit by 1-digit, I took it to a 3-digit by 1-digit problem just so the kiddos could see that it’s the same process no matter how many digits are on top. They always get excited when I tell them that I’m showing them a skill from the next grade level! (Sssshhhh, we even did a 4-digit by 1-digit problem…). :))

We just started 1 digit times 2 digits yesterday. We started with multiples of ten. The students seemed very exicted about learn “4th grade” math. We have have 4 weeks left of school with several events planned so I am anxious to see how far we can get with this.

I just wanted to state that your math blog is one of the best resources online!! I appreciate that you also periodically review academic literature that is very helpful and that offers more in-depth analysis of the concepts you discuss here. Keep up the great work!!

Thank you so much for the thoughtful comment! I love sharing my passion. 🙂