Recent Tutoring Session Reviews
"We continued working through volume problems, this time focusing entirely on spheres and hemispheres. He has a good grasp of the concept, but required help in properly inputting values into his calculator (I showed him how it is important to use parenthesis for fractions and for terms being cubed). We also worked on problems that required getting from circumference or areas, to values of radius, in order to find the volume. When finished, we reviewed Tuesday's homework problems about volumes of prisms and cylinders."
"Today we focused on Geometry; the student's class is a combination of Geometry & Algebra 2. He had a challenging homework assignment dealing with finding the lateral area, total surface area, and volume of many different 3D shapes, including prisms, pyramids, cylinders, and complex figures. In order to answer many of these questions, the student had to employ his prior knowledge of finding the area of regular polygons using the formula half x apothem x perimeter. These regular polygons also required him to recall his prior knowledge of Pythagorean theorem and special right triangles. So there were many different topics all combined in several problems, but as usual, the student was up for the challenge, working very quickly and efficiently, but also carefully. His ability to perform tough mental math calculations is strong and impressive. He handled this challenging assignment really well, remaining focused and persistent right to the end of each problem. After reviewing this assignment, we went back to some prior chapters in his geometry textbook and reviewed them, thereby beginning to prepare for his final exam, as well as clearing up any confusions or lingering questions that were revealed. We focused on the many different theorems and properties that exist with circles, including secants, chords, and angles. We will continue reviewing past topics next time to be sure the student fully understands everything he is responsible to know."
"Today the student and I worked on a worksheet for her geometry class that covered finding the volume and surface area of cones and pyramids. Given the formulas, she was able to find the appropriate information and plug it into the equations to find the correct answer. She knew how to apply the appropriate formulas and only made occasional minor mistakes where she used the wrong number for a given part of the equation. She was quickly able to realize her mistakes and change them, which showed that she understood the underlying concepts. She and I then worked on another worksheet that required her to be able to visualize a 3D structure and identify the front, back, left, right, and top views. This was challenging as some students cannot easily visualize 3D structures in their heads. Towards the end of the worksheet, it became much easier for her to visualize these structures in her head which is a huge accomplishment. She has a makeup test on Monday that will cover finding the area of polygons, finding arc length, and finding arc area. I emailed her eight worksheets with answers that she can use as practice."
"Today, the student and I reviewed what she is learning in class right now, which is 3-dimensional solids and how to find the area and volume of solids. She did the problems correctly and without any trouble. I think she does excellently when she is able to visualize the concept properly and analyze the problem one step at a time rather than looking at the problem as a whole. I thought she also did great with the proofs we worked. She was able to do a complicated proof, and that helped her in dealing with less complicated proofs. She is very bright and always shows enthusiasm and an eagerness to learn. Today was no exception, and I look forward to our next session."
"The student and I spent a few minutes reviewing how to know when a word problem requires a permutation vs. a combination using keywords and determining whether order matters or not in a problem. We practiced with several word problems; after the first couple, the student demonstrated mastery of the concept. We then finished our review of quadrilaterals, mediums and midpoints, tackling a tough problem in his textbook. I have been coaching him to spend more time marking up pictures with the information he knows. We reviewed some principles and then solved a few problems in the textbook. Next session, we will continue reviewing circles, practice a few problems from the unit on quadrilaterals, and then move onto a tougher unit: solids."
"Today, the student and I worked on his newest class material and homework assignment. This focused on finding volumes of geometrical prisms, pyramids, and cones. For the prisms, I wanted him to focus on thinking how to find their volumes rather than reverting back to the formula equations to do so. This will really help him learn how to find the volumes of all prisms and will help him prepare for his upcoming test, as well. He finds it more difficult to do it this way, but his math critical thinking skills are definitely improving. He understood this material quite well, and was able to think through the more difficult problems mostly on his own, which is great. As for wins, he had a quiz recently and received one of the highest grades in the class on it. This is a testament to how much he has improved! He has been doing so well on this past chapter in particular. During our next session, we will prepare for his upcoming test."