Using the area model as a tool to teach polynomial multiplication is a great way for students to visualize the process. I would use the tool when teaching factoring and figuring out if the boxes are fill, what would the terms on the outside of the box be. It reinforces what the concept of multiplying and helps the visual learner. In addition, I use colored pencils/markers to show the students how to multiply polynomials and that also helps them to see the multiplication and organization of the terms. Currently we are on inequalties, but I would use this in the future.
Maria, I really like your suggestion regarding using different colored pencils/markers to help the students organize their thoughts. I remember using this tool when I taught and it definitely assisted both me and my students with the teaching and learning of this concept.
I agree with Maria. Also, I have used Algebra tiles to model the area which has been a great visual tool for multiplying and factoring expressions.
I definitely agree that this tool would be an excellent way to introduce, reinforce, and help students master polynomial division. It could also be used to help students factor polynomials from various levels of difficulty. I would definitely be willing to utilize this tool in the future.
This tool would be a great way to differentiate for students that need a visual representation when learning how to multiply or divide polynomials. I also like Maria's idea to fill the boxes with the information and have the students determine what polynomials were multiplied together to reach the information in the chart. Great idea!