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The student continued working on unit 10 on statistics in the K-12 home school curriculum. Lesson 8 presented mean absolute deviation, a measure of how far data points are from the mean. He first needed to recall the difference between mean and median. He fully understands that mean is an average, found by adding all the numbers and dividing by how many were in the data set. The lesson checkpoint quiz score was 100%, where he understood each step and performed the calculations with minimal support. He scored 84% on a 6-question mid-unit assessment, showing his understanding of stem and leaf plots and stem and whisker plots. Lesson 10 on outliers began with a skills update, which reviewed angles, on which he scored 100% independently. He understands complementary, supplementary and straight angles. He knows to subtract to find missing angle measures. He then scored 80% on the lesson checkpoint, showing good comprehension of how an outlier makes the mean less useful than the median to represent the data. He is able to find the interquartile range in a box and whisker plot. In considering how an outlier will change mean and median, he made the calculations with minimal prompting and some review. Finally, lesson 11 on sampling and bias was completed. Here, he demonstrated exceptional prior knowledge of the meanings of population, representative sample and bias. He firmly grasped the lesson and scored 100% on both the skills update quiz and the lesson checkpoint quiz.

We continued to cover rules of exponents and how to simplify problems with exponents and multiple variables. I emphasized taking the problems step by step and focusing on one set of like values at a time.

The Geometry that we covered was not at all in the arena of traditional Euclidean Geometry. It dealt exclusively with coordinate geometry, using higher levels of advanced algebra. I was very happy that this was the case because I am personally very proficient in this type of mathematics and have developed all sorts of techniques that help students manage the elements of what they are being asked to do. This session, we worked primarily with quadratic equations, their solutions and their parabolic graphs. This involved finding the vertex, axis of symmetry, direction of opening, and actual creation of the parabola that is created from a given quadratic equation using a formula and a sequential process. We also worked with the quadratic equation and the discriminant, and I was able to help her see the importance of and correct use of these mathematical elements. She seemed almost relieved that the methods I was able to teach her made it all seem much more manageable and understandable for her. She even made comments that it was so much easier for her now. We both seemed to look forward to meeting again in two weeks so that she could get further answers and become more proficient in dealing with what is required of her. I left her with many notes and problem solving samples.

We reviewed conversions of fractions, decimals, and percents from a homework sheet. Then we began discussing solving for unknowns in one- and two-step problems. We discussed how to calm the mind and focus attention.

We reviewed over the concepts of limits, substitution involving interchanging x and u terms, separating integrals, and solve limits with L'Hopital.

We covered proofs using theorems concerning parallel lines. The student had difficulty with definitions/terminology. We will meet again tomorrow, so I am having her memorize/familiarize herself with all the theorems so we can go over them easily tomorrow and work on applying them correctly.

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Session Summaries by Tutors