Recent Tutoring Session Reviews
"The student had a long list of figures for which the class is to learn the area calculations. Not knowing how far they may have gotten, we pressed as far as area for circle sector before stopping. Figures included regular polygons, rhombus, trapezoid, and kites along with figures she would have studied previously. She was able to successfully complete at least one example calculation for all figures that we discussed. She reported that she currently has a 95 average in geometry, which is great! However, it came out in working examples that she could use some fractions review as she had difficulty with 1/2 x 1/2, also had difficulty multiplying 1/4 by 2 and reducing result to 1/2. I will include some fractions reviews as we meet."
"The majority of our work today was on straight-line functions of the form y=mx+b. We practiced various ways of finding m and b given different sets of data. Then, we went through problems finding the functions and plot points of lines parallel and perpendicular to straight lines. This involved a lot of graphing, which allowed us to visualize properties of lines, including, for example, why the slope of a perpendicular line is -1/m of the other. We then went on to explore how rhombi relate to straight line functions; specifically, that the diagonals of a rhombus are 90 degrees, even though its angles may not be, and that you can determine all the possible locations of two opposite points of a rhombus if you know two other points. The student was attentive and insightful throughout these discussions. We then went into some extra difficult problems in the textbook, including the graphing of functions which contain both abs(x) and abs(y). We will continue to work on writing out proofs in notation that is clear for the teacher to read. (For example, the student needs to better distinguish his s's and 5's, and keep his calculations along a clear left margin.) At our next lesson, we will double check his project on pi, continue to discuss and review the worksheets he has been given in class, and look at more extra-challenging problems in the textbook. The student is doing excellently and learning a lot in a short period of time!"
"The student and I worked on deriving information about regular polygons (side length, radius, area, perimeter, and apothem given one datum). We discussed generalizing her understanding, through formulae, of various concepts of geometric regularity. We ended the session discussing the intersection of logic and geometry (why manhole covers are round, the Sherlock Holmes riddle, etc.)."
"We met to go over the student's homework which expanded on the trigonometry concepts she's been working on for the past week--specifically angles of elevation and depression. She understood the ideas conceptually and didn't have too much trouble doing the problems. The hardest part for her is to visualize the diagrams at times but we worked through it."
"We reviewed the three missed questions on her recent test. We discussed why using the pi symbol is exact, and 3.14 is approximate. We discussed where the formula for the area of a trapezoid comes from. We discussed how to find the arc length of a section of a circle, as well as the area for a given section of a circle."
"Covered Chapter 11: Spatial Reasoning; Section 11.1: Solid Geometry; Handout Sect. 2: Representation of 3 Dimensional Figures; Handout Sect. 3: Formulas in 3 Dimensions; Handout Sect. 4: Surface Area of Prisms and Cylinders; Handout Sect. 5: Surface Areas of Pyramids and Cones; for Handout Sect. 5, did problems #1 - #11."