"We began this session by handing out two math sections for Student B and Student P, who went and completed them independently while Student A and I worked one-on-one.
With Student A, we first started by going over a vocabulary section from his full length practice test, and we created more vocabulary index cards together for about 10 minutes. Then worked on the math section that the four of us had gone over the previous day. I don't know if he was really trying when he did the problem set initially, because he selected answers which were wrong, even for the very first question, which involved addition only. We went through and re-did problems that I had selected. The two largest topics that we worked on were the addition and multiplication of fractions, and the idea of substituting in values into an equation. For instance if you had an equation of two variables, say 3x = 5y and you knew one of the variables, say y = 15, it was difficult for Alex to see that we were just writing 15 instead of writing y (because we knew that y and 15 are the same thing) in order to get 3x =5*15. Questions like these took us to the end of our 60 minute interval. I assigned him a math practice section to complete for the following day.
Next, I spent time with Student P. We started by thumbing through the practice math section we completed yesterday together and we went over why he got certain questions wrong. We worked on questions which involved the manipulation of equations, something that he does reasonably well, but still makes mistakes in occasionally. Once we were through going over the questions he got wrong, we continued by learning more about lines and slope. He said that in his school he learned that slope is rise over run and I told him that this was true and we did an example of how you use counting to determine the rise and run. I then said to him however, what if he wasn't able to count, or what if he had to count fractions? I then showed him how to calculate the slope by using delta y over delta x. We talked about how delta anything is equal to the final state minus the initial state. We then did an example together about two points connected by a line and we found the slope of the line. We did many more examples like this one while incorporating more ideas about the line equation, such as plugging in the slope you calculated into your line equation, and then plugging a point on the line into the equation in order to find b. We finished our 60 minute portion by talking about the slope of lines which are perpendicular to other lines. We reviewed that the slope is the negative inverse of the previous slope.
Student B was next and we also started by going straight to the math section and reviewing why she got certain questions wrong. One topic that we went over for a little while was a question involving finding the area of a shaded region (the area between a circle and a square. Her main problem in math is that she hasn't, up to this point in her math career, written out information to help herself find the answer. I told her that she MUST do this to find the answer to more complex questions, otherwise she is going to end up guessing and she will not get the right answer. We wrote down area of the square minus the area of the circle, and then we re-wrote the area of the square as length times length, and the area of the circle as pi r squared. Then we plugged in the values and found the answer.
This session was very productive for each student and allowed them to learn where they are instead of where an average of the three are."