CCSSM 4.NBT.5 reads:
Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. (CCSSI 2010)
As we begin to introduce multi-digit multiplication, the tendency is to dive right in to the standard algorithm. While the standard algorithm is an efficient strategy, it is very procedural and many kiddos mimic the steps without understanding the process. A great approach for building conceptual understanding is to begin with a combination of the partial products method and area model.
You can see from the examples below the similarities in the two methods. The area model is just a pictorial representation of the partial products method. Both capitalize on the student’s understanding of place value. The standard algorithm is actually a short-cut method of partial products. Once kiddos have had practice with partial products, the standard algorithm makes much more sense to them.
The partial products method really emphasizes place value. Students see that to multiply 324 x 6, they actually multiply 6 times the ones, 6 times the tens, and 6 times the hundreds. Of course this requires them to be able to work with multiples of 10 and 100. You might check out this blog post for an activity that builds fluency with multiples of 10 and 100. Another great activity is to have kids skip-count by multiples, so instead of counting 3, 6, 9, etc., they count 30, 60, 90, etc. That works great with this whole group Sparkle game.
I like to introduce the area model side-by-side with partial products, because it is a great visual model and I love the connection to area. We talk about finding the area of each of the smaller rectangles and then adding all the products together to find the area of the large rectangle.
Partial products gets a little cumbersome when you start multiplying by a 2-digit factor, but the area model is still very useful. When we move to 2-digit by 2-digit, I like to throw in a little problem solving. Hmmm, we’ve got two numbers that are both 2-digits now. I wonder how we’ll do that with our area model? Turn and talk to your neighbor and see if you can come up with a suggestion. They quickly decide that we need to add another row for the second digit. Works every time. 🙂
If you’re looking for a workstation activity to practice multiplication using the area model, take a look at my Area Model Multiplication Puzzlers. I threw in a little critical thinking for good measure.