This semester we have covered many aspects of Algebra. Whether it be graphing functions, learning how to utilize the FOIL method, or even learning the basics of Logarithms and Natural Logarithms. As for all of the skills that we have learned, I will be displaying one that I feel I have perfected, as well as demonstrating one Habit of a Mathematician that I try to implement into my math work every day.

I have learned many skills throughout the course of this semester, and until now I had yet to consider one of those skills to be 'mastered'. I feel that I have mastered the FOIL method, or First Outside Inside Last. This method comes into play when dealing with binomials and trinomials, and allows one to easily simplify an equation. This idea was first introduced to me in 8th grade, and at that time I found it to seem confusing, yet as time went on and my understanding of binomials and trinomials deepened, I soon realize the simplicity of applying the method. We have been using the FOIL method a lot recently, particularly in explorations (mini math worksheets that we complete as homework). Below you see two explorations where we utilized the FOIL method, and not only were these little challenge to complete, but my understanding allowed me to help classmates during the seminars we held on these explorations.

**CONTENT SKILL:**I have learned many skills throughout the course of this semester, and until now I had yet to consider one of those skills to be 'mastered'. I feel that I have mastered the FOIL method, or First Outside Inside Last. This method comes into play when dealing with binomials and trinomials, and allows one to easily simplify an equation. This idea was first introduced to me in 8th grade, and at that time I found it to seem confusing, yet as time went on and my understanding of binomials and trinomials deepened, I soon realize the simplicity of applying the method. We have been using the FOIL method a lot recently, particularly in explorations (mini math worksheets that we complete as homework). Below you see two explorations where we utilized the FOIL method, and not only were these little challenge to complete, but my understanding allowed me to help classmates during the seminars we held on these explorations.

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This work shows that I have mastered the skill given that not only are all of the problems involving FOIL correct, yet I demonstrate and show my steps, proving my comfort in this area. The true mastery, however, I feel comes from the actual physical demonstration that I was able to show with my peers on both seminars held for both explorations. I was able to communicate clearly how the method would work and clear confusion with two different classmates. The exercise that I used to increase my mastery of the skill was actually just sitting down and solving the problems, and through trial and error finding the correct answer. I also applied other Algebra skills (like creating rules for equations) using this method, and so I find that, in all actuality, that the FOIL method is more useful than it is accredited for.

**HABIT OF A MATHEMATICIAN:**

The most important Habit of a Mathematician in my eyes is formulating plans. In math, it is easy to get caught up in overthinking a problem or a worksheet, and so by creating a plan, and showing steps I personally feel that solving a problem becomes ten times easier. In a POW (problem of the week) that we completed recently, I was able to utilize the section where we are supposed to include our process and steps and actually solve the problem. It was the first time that I actually felt confident that writing out steps and creating a plan had helped me significantly. | |

Above you you see two sections of two different POWs that allowed me to write out each step and plan the solution. Both of these problems had proven to be a particular challenge before hand given that I had been absent and missed content that could have been extremely beneficial, yet I still felt that with the math skills that I already had I could solve them both. That's where formulating a plan helped me. I was lost on where to go, and so I planned out my steps and actually ended up getting the correct answers. Since that time I have never underestimated the power of planning ones steps.