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"This was our final session before the student takes the placement exam. At the request of his parents, I have been focusing on math. In this lesson, I tried to condense and reinforce all the concepts we have covered, and I told him that I would send him some videos to cover concepts like translations and reflections of shapes in the coordinate plane, the properties of circles, and a video that reviews the properties of all essential shapes for the exam, and the concept of volume. At the conclusion of this lesson, I gave him part of lower level exam to maintain his progress over his winter break ( I emailed his mother the answer key to the different sections), and I also emailed him the complete answer key to the review sheet we worked on during this session. His abilities and familiarity with exam vocabulary have improved much since we began working together. His confidence with the material reflects his earned knowledge of the vocabulary encoding many of the questions.
In this lesson the student correctly identified the greatest common factor of two odd numbers, solved a mathematical problem asking for the mean, median, range, and mode of a data set, decoded the increment in a number pattern and predicted the last number in the pattern, combined positive and negative numbers with subtraction, multiplied, added, and divided fractions. He was also able to identify two forms of the same mixed number, one written with a fraction, the other with a decimal. However, he did not correctly identify two equivalent numbers: one in fraction form the other in decimal form; when we reviewed the problem, he identified the correct answer. He also correctly plotted and labeled four points on a graph, and connected the points to form a parallelogram. When asked to complete a problem that required knowledge of the order of operations, he correctly computed a squared negative number as a positive integer. However, he followed a literal interpretation of order of operations and attempted to multiply to numbers when, moving from left to right, division should have preceded multiplication. We reviewed the operation steps and the importance of moving from left to right when calculating the answers.
He and I reviewed a shorthand method for metric conversions when he initially failed to compute m to cm. I told him the "King Henry Drinks Ucky Dark Chocolate Milk"ù and wrote the letters of each word, scrawling meter, gram, and liter under the U. He correctly converted the number.
In this lesson, we spent a fair amount of time reviewing proportions: a central concept to the placement exam. He asked me how to do a rate problem. We worked together to set up the proportion; he understood why I placed each number in its position. I left him to complete the calculation independently (the answer, in detail, was written on the answer key I emailed his parents). I also showed him how to approach various percent problems with a simple formula: N/100 = is/of. The student and I worked through two percent problems (one with a given percent, the other with the of value missing); he calculated the correct answers. I showed him how to check his work by affirming that the two fractions is/of = n/100 are equal: you can simply both fractions to the same fraction in simplest terms, or the cross products should be equal."