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Session Summaries by Algebra Tutors

The student recently finished learning substitution and elimination in his Algebra I class, and is now focusing on real-life application of those concepts using story problems. Our session focused on a homework set of 12 story problems. In the beginning, he was unsure how to approach the questions and turn the given information into algebraic expressions. However, after going through a problem together, he learned how to set up expressions and was able to set up expressions on his own. For extra practice, he will complete the remaining questions in his homework set using the previously completed problems for guidance. There is still room for improvement in solving the systems of equations, specifically he should continue practicing basic algebraic rules (i.e. moving terms from one side of the equation to the other, simplification, etc.). It is clear that he knows the concepts well.
Tonight was our first meeting for the new semester. The student informed me that she made an A for her first semester average in algebra, and so far for the second semester, she is maintaining an A. We looked at examples of solving systems of equations by graphing and reviewed recent graded homework to correct mistakes. This week she is beginning to look at expressions and fractions containing variables with exponents, and is learning the simplification methods using subtraction and multiplication of exponents. After reviewing her recent class notes, she became excited to practice using unassigned problems from her homework. She is off to a great start for this spring.
The student and I reviewed his class notes on exponent rules using multiplication. We also practiced problems related to exponents on his homework. I reviewed the math terminology associated with exponents including base, coefficients, variables, and combining like terms. We worked on writing problems in expanded and in simplified forms. I reinforced the importance of checking for similar bases when combining values with exponents in simplified form and understanding how parentheses/bracket placement can alter the base number, variable or expression associated with an exponent. We also reviewed the following exponent rules: 1) When multiplying common bases, their exponents can be added to calculate the final exponent in the answer, and 2) when exponents are written as power to power, they can be multiplied to calculate the final exponent in the answer. He was able to independently and accurately work through the final problems on his homework. We also reviewed the extra credit problems involving perimeter, area and volume using exponent rules and expanded and simplified forms. His mother also requested that he receive additional practice on solving systems of equations in word problems, so we will review practice problems during our next session. He was very cooperative and motivated throughout the session. He seemed to have a very good grasp of the material as our session came to a close.
Student K worked on her homework which was a series of word problems that involved systems of equations (two numbers, their sum is 12, their difference is 4). She seemed to need help with translating the written situation to math equations at first so we worked on this translation. She also struggles with basic division, but that is a problem solved with practice. Once she started understanding why the math equations and word problems were equivalent, she smiled after every question. Even if math isn't intuitive yet, as long as she can enjoy it she can master it. Student D also brought his homework which was graphing work. I taught him how to draw graphs of simple functions he's never seen before, and then how to draw more complicated functions as their simpler counterparts just shifted or scaled up. He finished his homework and started practicing more problems. Many times in the session he said he needed help. When I asked him what he needed help with, he couldn't come up with anything specific. Math should be learned like a foreign language because it's way easier to do math if you can think in math. He just needs more exposure to math notation and concepts. On the plus side this kid has tenacity. He started reviewing his material on his own, no prompt needed. I've never seen someone so determined to graph things.
We covered solving then graphing linear inequalities. The student is able to solve the inequalities and set up the graph. To avoid mistakes when graphing the inequalities, I suggested that she test her solution before she graphs it. We also worked on setting up ratios and proportions and using cross multiplication to find the unknown variable.
We covered the FOIL method using radicals, and rationalizing radical fractions. The student's upcoming quiz covers both of these subjects. We also reviewed simplifying polynomials, identifying polynomials by name and degree, as well as multiplying complex polynomials. I had the student complete the other have the chapter review quiz we worked on last week, and she answered every question correctly.