Award-Winning Test Prep & Academic Tutoring in Weber State University, UT

We went over the chapter to review for her upcoming test. I explained a few concepts to her which she grasped quickly. We went over similar triangles and showing similarity by SSS and AAA. We also went over a few questions she had.

The student and I began this session by going over his chapter 11 test. For the test corrections that he had problems with, I wrote more practice problems. We spent some time solidifying his understanding of rational vs. irrational numbers, and a good 20 minutes working on converting decimals that have a repeating pattern into fraction form. We had a bit of time at the end to work on another practice worksheet that he had been assigned, which reviewed ch. 10-11 concepts.

We finished up division word problems today. These were 3-digit numbers divided by 1-digit numbers and the final problems had no remainders. He did really well with these! We then moved on to division of 4-digit numbers by 1-digit numbers. He has got the steps of the process down (which is impressive as they are lengthy) and it seems his biggest difficulty was the actual calculations. So we took a break from this today and created a multiplication table for 1-9. He was very happy with the result and how helpful it was during subsequent division problems. Although the table is in my handwriting, he gave me all the numbers to fill in!

We started reviewing logical reasoning as presented in his book: introduction to if (hypothesis) then (conclusion). He also went through his homework, and for each question he gave his answer and the ones he was in doubt or got wrong we analyzed together to reach the right answer. After that, we advanced to the next week's class through the study of simple proofs. He practice 4 proofs by himself and he did it very well. He told me he understood everything and he seemed to be more confident with the material given in class. Overall the wins from this session is that the student had a better understanding of the proofs and he is ready to keep moving forward.

We covered the squeeze theorem and how that applies to limits going to zero. The student didn't seem to have any problem with that and was learning it fine. We then moved on to a more difficult part of differential calculus which is implicit differentiation. He actually understood this better than I had anticipated and he was able to solve related rates questions very well and efficiently. We spent a short time on Euler's identity involving complex exponentials and how it relates to sine and cosine. We then went on to talk a little more about the limit definition of the derivative, and how there are two different definitions that both give you the same result. I showed him how one definition is better than another in some contexts, Overall, the student has a very good grasp of calculus so far.

The student continues to improve at such an incredible rate! His fluency is increasing dramatically, and he is gaining confidence in reading aloud. We are now focusing almost entirely on reading comprehension, with a review of flashcards at the beginning of each session. He really needs to focus on sequencing -i.e. figuring out what happened at the beginning, middle, and end of a story. He can typically recall what's happened at the beginning, but the middle and end can get a little confusing for him. Asking him to recall what happened at the beginning, middle, and end of the story after reading is a great activity to do at home!