Can you explain why the multiplication method in the following video works? How about your upper-elementary or middle school students — can they explain it to you?
Pause the video at 4:30, before he gives the interpretation himself. After you have decided how you would explain it, hit “play” and listen to his explanation.
Multiplication with Rectangles
I liked that James Tanton didn’t use the standard pencil-and-paper method for multiplying numbers, but instead explained multiplication as a rectangle. Rectangles are a versatile model for multiplication, and the model will be even more useful when our students get to algebra.
Your students will have fun practicing rectangle multiplication with these sample pages from Beast Academy:
- Count up your rectangles: the lesson.
- Count up your rectangles: practice pages.
- Make perfect squares: the lesson.
- Make perfect squares: practice pages.
And be sure to check out the Beast Academy printable resources page for more fun math you can play.
Update: Another Multiplication Challenge
Mike added a second challenge on the Let’s Play Math Facebook page. Can your students explain the error in this video?
Denise Gaskins' Let's Play Math 
I pushed James Tanton’s explanation of line multiplication to counting problem of intersections of parallel lines to visualize multiplication of algebraic expressions in http://math4teaching.com/2012/06/03/line-multiplication-and-the-foil-method/
I love the second video. It’s a good teaching practice to teach by identifying errors.
This was very interesting. I had never seen this method before.
I really liked this. I’m excited to go back and try this the following
Humor is a valuable tool in reaching students. What a great way to lighten the air and gain everyone’s attention.
This Tanton Mathematics is something I have never seen in my life. So, it was very interesting to see that using these parallel lines can be used to multiply large numbers quickly.
I have used lattice multiplication, but the students found drawing the grids challenging. Line multiplication might work better. Neatness will definitely affect the outcome.
Thank you all for your encouraging comments!
If your students have trouble with neatness, I recommend focusing their attention on the rectangular area model of multiplication:
(1) Draw a rectangular box, which does not have to be “to scale”. Mark the length and width with the two numbers you want to multiply.
(2) Split the sides of your rectangle into easier numbers, which will usually be the tens and ones or something similar. For instance, James Tanton split 13 into 10+3 and 22 into 20+2.
(3) Draw lines to divide your whole rectangle into subsections based on how you split the sides.
(4) Figure out the area of each subsection of your rectangle, then add them all together.
Neatness doesn’t matter with this model, just careful thinking about how to make the numbers easier to work with. And the rectangle is a versatile model that will still work when your students get to algebraic multiplication and factoring.
I realize that this is an old blog post but someone just tweeted a link to it. I’m curious about the completing the square links that were shared. Those links are now Dead ends. Could you update and share those links?
Thanks for pointing out the bad links, Michael. All fixed now!
Things like that happen from time to time as people update their websites. Sometimes it makes resources disappear forever, but happily these pages just got moved to a new address.