Friday, April 11, 2014

Multiple Strategies for Multi-Digit Multiplication

For the record, I was cheated. As a child, I learned ONE WAY to calculate multi-digit multiplication: the "standard" or "traditional" algorithm. As an adult, I was shocked to learn that the "standard" method is NOT standard in all parts the world, and neither is it always the easiest or most efficient way to solve a problem.

This past school year, my students have learned many strategies for multi-digit multiplication. I am astounded by their ability to think flexibly and find the best strategy to fit a particular problem. They can compute so much faster and with greater ease and efficiency than I was ever able to do with only one multi-digit multiplication tool. Many times, they can compute mentally because the right strategy makes multiplication easy. This week, we reviewed using 25 x 96. Take a look.

(The sheet below comes from Bridges Grade 5 Second Edition and is used by permission.)

Doubling & Halving

Ratio Table
 Over Strategy

Using Quarters

Partial Products

Standard Algorithm

After the review, I gave them a sheet of multi-digit multiplication expressions and let them choose a different problem to illustrate each of the six strategies. They organized their work on these Strategy Support Sheets (questions/ideas modified from Bridges Second Edition) where they had to:

1. show their work using the strategy
2. explain why that strategy was well-suited for that particular problem
3. prove their answer correct by solving with a second strategy.

I heard kids exclaim, "this is FUN!" and saw example after example of high-level mathematical thinking. They GET which strategies are the most efficient for different types of problems. The sheets will be used as reference pages in their math notebooks.

I can't begin to describe how proud I am!

The articles in this 3-part series on Teaching Multi-Digit Multiplication include:
1. Multiple Strategies for Multi-Digit Multiplication (introduction)
2. Choosing the BEST Strategy
3. Student Video Tutorials


  1. I love this. This is very helpful. And, yes, I was only taught one way to do it as well.

  2. This is fantastic. You are a real gem. Thank you for sharing.


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