Since last month's problem didn't spark any discussion, I hope this one does.    This problem uses area models to arrive at a solution.  This is a great strategy to get the brain engaged and to help learners to think visually about mathematics, which is the approach that Dr. Jo Boaler, author of Mathematical Mindsets , recommends most for improving math understanding.

Mathematical modeling picture

source:  here is a link to the problem to print out:  http://bit.ly/2B6d420

Let's discuss what do you notice and wonder, FIRST about this problem and not just the solution.

Images: 
Mathematical modeling picture

Comments (4)

S Jones's picture

I went straight to the picture and recognized "area model -- this times that equals that"  in their spaces, and wondered if that's obvious to students.   Thinking we would need some concrete examples first.... 

Then I looked at where I had both things to multiply, did that, and went from there.   I'm a part-whole learner...

ecappleton's picture

I'm going against my better instincts here since I tend to hate holiday-themed math problems (sorry for being a scrooge), but the area model puzzle is a cool idea. We explored something similar in a math teachers circle meeting a few months back. I agree that students would need some preparation before working on a puzzle like this, but I think looking at the area model for multiplication is time well spent.

Here's a process for moving from a concrete area model to an abstract area model (based heavily on Connie Rivera and Amy Vickers' webinar).

And here's a way of writing area model puzzles (based on Benjamin Dickman's idea). Students can create their own puzzles and quiz each other.

(notes from math teachers' circle meeting on factors)

 

Eric

 

 

 

BrookeIstas's picture

Thank you, Eric, for sharing your work!  I hope this will encourage more practitioners to share what they are doing in their classrooms!  I like the  idea of having learners create their own problems.  My learners really like this method of multiplying binomials - so much so, that they do not like the FOIL method (distributive property) that is traditionally taught in our program/school.

Image result for area model of multiplication of binomials

BrookeIstas's picture

Thank you, both for participating in this discussion.  I find that I learn so much from other instructors when I brainstorm and strive to understand a different way to "see" or to "do" a math concept.  So thank you both for helping me to grow.  I want to encourage others to jump in and tell us what you see or think - that way we all can benefit from the support of this type of learning activity.