The biggest part of the factoring lesson that I will incorporate into my classroom is the box method in reverse. It competely blew my mind the way the activity showed how to factor the example. I have struggled to show the kids ways to factor when <i>a</i> is a factorable coefficient. This activity I think will be very helpful for students who don't like manipulatives, but need some sort of visualization to solve the problems.
The biggest piece from the Algebraic Habits of Mind Diagram is the Abstracting from Computation. The reverse box method allows for some computational shortcuts while factoring. Also the concept of equivalent expressions is also addressed, because that is essentially what factoring is. Additionally, using the algeblocks to solve factoring problems (not discussed last month, but over the summer) allows students to calculate without computing.
When our curriculum covers multiplying and factoring polynomials, I plan to use our September lesson - building a garden with algebra tiles- to introduce the concept of multiplying and factoring polynomials. Our curriculum calls for using algebra tiles, but letting the students discover building a garden reinforces the concept of a rectangle, which leads to length times width, then to polynomial times polynomial. Ta da!
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