Tuesday, April 15, 2014

Multi-Digit Multiplication: Choosing the BEST Strategy

Warning: this is a ginormous post, filled with student work. I am feeling just math-teacher-pride-nerdy enough to post it. You've been warned.

I mentioned how my students have learned many strategies for multi-digit multiplication this year. That, in itself, is terrific. But even better? They understand what types of numbers work best with certain strategies. This ability--to determine which strategy is most efficient in a given situation--shows that have an incredible array of mathematical knowledge in their tool boxes.

In the first several examples, students could choose from 20 multiplication expressions, selecting the problem that they thought was a good match for each of the strategies they've learned. They had to:
  1. choose an appropriate problem for the strategy
  2. solve the problem using that strategy
  3. explain why that strategy fit the problem
  4. double check their answer using a second strategy. 
It's important to note that when the year began, some students had zero strategies for multi-digit multiplication. We've come a LOOONNNGGGG way!!

I've added captions to a few examples near the end...stuff you mustn't miss. And then read on...there's more below!
    Strategy: Doubling & Halving
     Strategy: Over Strategy
     Strategy: Using Quarters


    Strategy: Four Partial Products
    Strategy: Ratio Table

    Strategy: Standard Algorithm
    Notice that this student deliberately chose more challenging numbers to use on this strategy.
    Cracks me up...I told them that the standard algorithm is the only strategy I was taught. Notice what this kiddo wrote in his explanation...

    After completing the strategy sheets, I compiled a list of the strategies and the problems chosen by students for each one. Students selected the identical expression on some problems (like 99x73 for the over strategy) and had different expressions for others. This led to a great discussion about which strategy was chosen for each, and why.
    Tips for Multi-Digit Multiplication Strategies
    After my students finished the strategy sheets, they made posters--TIPS--for using each strategy...

    I wish you could have heard the discussions that went with both the development and the presentation of these tip sheets. I couldn't believe the amount of higher-level thinking involved.

    Do these students "get" multi-digit multiplication, or what??? A parent told me that her student was about ready to bust a button when he proudly said, "I know TEN ways to solve problems."

    Awesome, awesome work!!!!!! (And thank you to Math Learning Center, Bridges Second Edition, Grade 5, for the strategies and core lessons.)

    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. Incredible. It makes my head split to see all of those options we never had "back in our day."

      1. Amazing, isn't it? Wish I'd been taught this way.


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