MATH: Unit 4's "Last Problem"

On the test review for Unit 4, the last problem (#12), which will be similar to the "Open Response" question on the test, asks students to find the difference between two multiplication problems without doing any multiplication.

That's tricky.

I wanted to show a strategy for how to do this with an array. We used this strategy in an example problem today. So here's a similar problem we'll use for our example:

Mrs. Smith told her class that they could calculate the difference between 11x6 and 11x7 without doing any multiplication. Make sure to include the answer to the problem in your explanation.

Here is what a student might draw/write/record to receive a strong score on this problem:

In the image above, you can see how drawing an array for 11x6, and then adding a row to create 11x7, can show the "difference" between the two problems. The difference is just one row of eleven.

After doing several of these types of problems, students may see a pattern. Like, if I asked what the difference is between 4x13 and 5x13, they might start to see the answer would just be 13, which is right. However, it is still important that students be able to show or explain how to get the difference. And you know how much we like arrays in third grade!

This array strategy certainly isn't the only route to get to a correct answer and explanation, but it is definitely an option for students to use.