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The first thing that we went over in the lesson was long division. The student was able to do the steps to complete a division problem, but he was also able to use a shortcut by using his times tables and subtracting the remainder. I reminded him to show his work if it is asked for. We then went on to circle graphs and modeling fractions. He seemed to understand that fractions represent parts of a circle but may need additional work in drawing circle graphs. We then worked on multiplying fractions. He needed to be reminded of the procedure but completed the problem afterwards and did an excellent job reducing it. We also worked on adding and subtracting fractions. He does a good job in finding the common denominator. He also needs more review on mixed numbers and improper fractions. I will be sending step-by-step guides for how to add fractions, change mixed numbers, and change improper fractions.

Today we reviewed basic math, division, multiplication, addition/subtraction, powers, roots, and logs. We are working to help the student refresh on the basic math functions and arithmetic before we begin working on the calculus topics. He is doing a good job in understanding the basic concepts, and we should be able to finish our review in one more session.

We reviewed circles and using interior angles to find the arc length of a segment of the circumference. We also practiced converting between degrees and radians for angle measurements and found how the radius of a circle is related to the arclength marked by a certain interior angle. We also reviewed angles in the context of triangles and intersecting lines. The student only had papers from the current topic, so we focused mainly on new material rather than earlier concepts. We plan on going over earlier topics, particularly old quizzes or tests, as well as reviewing what she's learning about circles now. The student did well applying concepts about angles in general, to the current ideas about interior angles of a circle.

Today, the student covered 6 pages of his summer math preparation packet. He has about seven pages left which he should be able to cover since a couple of pages are repeated. We covered rounding numbers and inequalities explicitly today. He struggled a little today with knowing where to round numbers to. So, we took a five minute break that allowed him to recuperate and then jump back in. And from there on he was much better. The next session could possibly be the last one depending on how much we cover in that time period.

The student was excellent and engaged with the material. We were able to pinpoint where she was having difficulty with the problem (mostly the imaginary roots) and to find a polynomial that fit the required parameters. She also looked at how multiplying by additional factors changes the graph of a polynomial function.

During yesterday's session, the student and I worked on several topics. He had already finished his spelling homework when I arrived, so he began with his math homework - his class is working on performing mathematical operations with numbers expressed in scientific notation. Some of his word problems involved very large numbers, and building on information from previous problems. I showed him how sometimes when there are lots of large numbers we're dealing with, it can be useful to make diagrams to keep track of what is being asked in the word problem. Overall, he demonstrated an excellent grasp of scientific notation. He then moved on to his French homework. His assignment was to study the verb courir (to run) and to answer a series of questions in his textbook using the pronoun "y," to take the place of a previously-specified location in a sentence. One skillset I would love to see the student begin to practice more is getting in the habit of asking clarifying questions if he doesn't understand a topic, rather than doing guesswork or being hesitant to bring up that he may be unsure about how to approach a problem-set or certain content. I look forward to continuing to work on French with him, because it seems that he may not have been taught many effective techniques in class for how to practice and develop mastery of important language topics. We concluded our session with working on a draft of a model high school essay question. The prompt was "Describe a challenging event you have had to overcome, and how it affected you." I gave him a couple of pointers to think about heading into the essay (he had already chosen what he was going to write about), and then he wrote freely and I made some grammatical suggestions and minor technical tweaks at the end. I was very impressed and appreciative of his openness when writing about (and accepting help on the assignment) personal events that he's had to overcome in the past. He deserves huge kudos for this, and I really look forward to continuing to working on these essays with him. I made him a "high school essay pointers sheet" with tips to keep in mind, mostly surrounding what admissions professionals are generally looking for when they read these essays. Overall it was a very productive session, and I appreciate the student's willingness to work with me on these items. Great work!