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.
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.
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...
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.
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.
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.