Alternate Strategies for Multi-Digit Multiplication - Math Coach's Corner
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# Alternate Strategies for Multi-Digit Multiplication

### Written by Donna Boucher

Donna has been a teacher, math instructional coach, interventionist, and curriculum coordinator. A frequent speaker at state and national conferences, she shares her love for math with a worldwide audience through her website, Math Coach’s Corner. Donna is also the co-author of Guided Math Workshop.
##### Grades 3-5 | Operations

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.

1. Great idea to lead into the standard algorithm. When I teach area model, I have the students put the addition sign between the numbers to show it is the expanded form. Then I have them draw the lines down from the addition sign to help create the boxes at the signs. What are your thoughts on the use of the addition signs?

• I’ve seen it done that way, too, and I think it’s a great idea!

2. Amazing post! Students need to be more exposed to the conceptual understanding rather strictly focusing on the procedural methods and this is a terrific way to show it with multiplication. Pinning for when we start multiplication in a few weeks! Thanks 🙂
Elizabeth
Fun in Room 4B

3. It is so important for kids to have a solid understanding of area models and partial products before introducing the standard algorithm. In my school, we talk about and use the area model and partial products in grades 3 and 4 and do not introduce the standard algorithm until grade 5. It took us a while to convince teachers and parents that this was the way to go but we now have much better conceptual understanding in our students. When we introduced the algorithm earlier it became the only strategy. Students would still use the procedure even for problems such as 43X12 which are very simple to do mentally if you have a good understanding of multiplication and its properties.

Tara
The Math Maniac

• I totally agree, Tara! The understanding is so much deeper when kiddos are exposed to these strategies first. You also make a great point that it’s often the teachers and parents who are the hardest sell!!

4. Thank you for explaining partial products so clearly!
-Lisa

• Thanks, Lisa! Glad it was clear. 🙂

5. Love this! I have a handful who are still really struggling with multiple digit multiplication, and the rest of my 6th graders could use a refresher too! Thank you:).

• Glad to hear it! It will be helpful for those kiddos who aren’t successful with the traditional algorithm. Once they see the connection and make meaning of it, I’ll bet they’ll understand the traditional process in no time!

6. Thanks for this post. I will begin teaching this next week.