A One-Branch Factoring Tree

Part of why I chose factoring for my semester topic is because there are so many ways it is used in high school math. In the previous unit I focused on factoring polynomials, which is a common application. This time I thought about factoring a number for the purpose of simplifying a square root. The way this is taught in Dexter Schools, the district where the majority of my students attend, is to do a full factor tree and look for repeating numbers (a pattern!). I watch students make mistakes with this strategy due to the complexity and number of steps. In addition, they often forget that two numbers in the tree become one number outside of the square root sign, due to the fact that you were supposed to have taken the square root of that number. I have zero belief that I came up with an entirely new way of simplifying square roots. I would bet lots of money that my “new” method from this unit’s creation is how it is taught in some school districts. However, my new method is new for my students. I think writing out the perfect squares is beneficial because they are sometimes hard to pull from memory. I think the visual aid is particularly supportive of learning this technique. I want to advocate for both strategies being taught. Seeing two different kinds of patterns - the repeating numbers in a factoring tree as well as divisibility by a perfect square - students are open to a better understanding of the topic. I created the pattern with the notecards for my video to emphasize how much simpler the “one branch tree” can be. I wasn’t going to add music to this video but I missed it after the last unit’s creation, so I added it in at the end. Now music is a pattern for my creations.