"This was my first session with this student. We discussed the placement exam, which she is preparing to take to get into private high school. To prepare for the exam, we discussed challenging areas and focused on those sections in her review book.
We began by discussing charts, graphs, and problems with tabular data. Since calculators are not permitted on the exam, I emphasized to the student to try to see relationships in numbers, especially when doing percentages or fractions. For example, identifying numbers that are half or double of another part within the whole will help her to see the relationship of one portion to another. When presented with a graph or chart, I advised her to first visually scan the data for important information like outliers or averages.
Next, we moved to order of operations. She struggled a bit with order of operations when it came to multiplication and division. I emphasized that these can be thought of as inverse operations, and should be treated as one step, working from left to right. The same is applied to addition and subtraction; these operations are performed in the order they appear from left to right. She wanted extra practice on this concept so I created some problems for her on the spot. I have prepared a worksheet with further problems for more detailed study which we will go through next time.
After order of operations, we moved on to geometric concepts, including perimeter, area, and volume of basic polygons, and identifying different types of triangles. We went through examples in the book and solved some of these geometric problems together. After the session, I suggested to the student to memorize the perimeter, area, and volume equations for various geometries. After repeated practice from memory, these equations will become more intuitive and second nature."