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"We began with a real-world scenario warm-up, which revisited long division of large numbers in context as a road trip problem from the student's address, extending across the US and ending in Los Angeles, CA. We then moved to the calculation of the area of a slightly irregular geometric shape laid onto a coordinate plane. The overall shape was "cut up" into 3 areas of simpler shapes of areas that could more easily be calculated. While I regularly utilize extensive inquiry during my lessons, she attempted 2 cuts into the figure, which I recognized as very good, interesting thoughts, though they did not achieve simplified geometric figures with basic, well known area formulas. To keep her engaged, I alluded to the fact that if she were to attempt a cut in a different direction which would result in a 90 degree angle with the top side of the figure (while showing her the cut direction with my pen) she might find a more familiar shape. She was then able to successfully complete all calculations, with guidance. I told her that I witnessed her solve problems that she would often tell me she "didn't know" how to do, after I pushed her to continue focusing, even after mistakes (and without giving away answers). Therefore, I knew she was capable, which she acknowledged. From there, we went back to reviewing algebra, solving for a single variable, which she was able to do with unprecedented focus and precision. I continued building complexity for her, and we began reviewing slope/intercept form (y=mx+b), isolating the "y" variable and graphing. She reacted that she scored poorly on previous quizzes in this subject, yet she was highly successful in accurately solving for "y" during multiple attempts. I highlighted this fact for her. She became so proficient at solving for variables and graphing, that I went deeper into the idea of equations of 2 variables, one "input" and another "output" variable, how they relate to "y=mx+b" and how they may be useful in business and other real-world applications, and finally invented a new problem for her involving the variables "p" and "star". She demonstrated the ability to recognize the input and output variable, and solve for the output. This came to the end of our session, so I asked her to complete the graphing of this equation for homework. I would say this was a very good session with near breakthroughs. If she continues gaining focus and confidence, she will become very successful in Algebra 2."