Progression
This lesson will ultimately just be one lesson in a series of lessons on factoring quadratic polynomials. The goal of the series would be to introduce the connection between the distributive property and factoring (or the undistributive property). After establishing this connection, we would introducing pulling out the GCF from a set of terms, then factoring when A=1, followed by the Tix-Tac/Box Method, splitting the middle term and how it relates to the Box Method, and then special cases (e.g. difference of squares, perfect square trinomials). After receiving efficient techniques on factoring, students will then learn how to solve quadratic equations using these techniques.
Misconceptions
Seeing as how the Tic-Tac and Box methods both rely on a similar structure (they both uses boxes), students may get confused with the placement of the numbers. Students may also get confused with the placements because of the word “quadrants”. It’s important that when this lesson is being taught, that the teacher reminds students of the four quadrants when that term is used and that the teacher makes sure to properly distinguish the differences between the two methods: Tic-Tac is just a tool to facilitate the Box Method.
Assessments
The worksheets, Factoring 1 and Factoring 2, are taken from Kutasoftware.com and are used as the main practice problems for factoring, whether as a bellringer to assess if they understood the previous lesson or as group classwork so that students can discuss amongst themselves and teach each other as need be. The worksheets, factoring handout 1, factoring handout 2, and factoring handout 3, are used to introduce the Tic-Tac Method. There is an emphasis on group work and discussion as I find that peer learning is quite effective at both engaging students and making sure they properly digest the material. The class discussions allow to informally assess the class as a whole and emphasize any key ideas while also addressing any misconceptions. I would be sure to emphasize clear instructions during the lesson so that students don’t fall for misconceptions, but if they still struggle with any then we could go back to when they first started struggling and talk about it as a class. However, for this to be effective, I would need to have already fostered a healthy classroom atmosphere where students feel free and open to talk about any issues they have with the lesson and that learning is team based, so we can all learn from one anot