Math: Multiplication Algorithms

Updated: Nov 29, 2019

I recently had a conversation with a 5th grade teacher (thanks Cheryl!) about how students aren't ready for multiplication and division algorithms. Many students can't follow all the steps and end up making mistakes based on place value.


In my Progression of Multiplication and Division course, I spend an hour just talking about how to help students move from the concrete to the abstract algorithm for multiplication. Many times we make the jump from manipulatives straight to teaching the steps in the algorithm. Some teachers even do Concrete manipulatives, Pictorial representations using the area model, and then try the Abstract algorithm.


All of these are great strategies, but what do we do if we have a student who still is unable to do it? We provide scaffolds to make a bridge between representations.



I like to use the following progression:

Concrete Materials with Base Ten Materials

Place Value and Expanded Form

Area Models that rely on Expanded Form

Partial Products

Standard Algorithm


I build anchor charts with each of these methods and ask students to compare them. Where do you see each product? What's the same about this method? What's different? What method makes the most sense to you? The goal is for students to scrutinize each method and see how they are developed.


If you use Common Core standards, fourth graders are to multiply using strategies based on place value and properties. That means fourth graders can be working in these other representations: place value, area models and partial products. They don't need to be doing the standard algorithm until 5th grade. Hearing this, takes some of the pressure off and allows me to focus on meaning instead of steps.


Of course, we want to always continue to push our students to the standard algorithm. What I often do is encourage students to solve in 2 or 3 ways. I have students solve in the way that seems most comfortable to them and then encourage them to try another way.


I know these look like a lot of steps and a lot of work, but that's what algorithms are- short cuts! Students really can't appreciate the short cut until they have realized all the work and steps that go into creating it!


If you would like to find out more information and get over 250 pages of centers and resources, check out my online course of the Progression of Multiplication and Division. Discounts are available for multiple accounts. Also check out my Understanding Multiplication and Division Bundle for lots of activities for students to practice!



Finally, be on the lookout for my fluency webinar and activities coming soon! I'm hoping to post these next week and am so excited!




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