"We worked on the SAT practice problems. The student began by asking some questions about the right triangles and Pythagorean Theorem. I selected problems on that topic for him to practice. I refreshed his memory by letting him writing down the Pythagorean Equation a^2 + b^2 = c^2. When two of the unknowns (a, b, c) are given, we can solve the third one by substitution and methods of solving equations. I emphasized that when he made a substitution, he MUST have this in his mind: ( )^2 + ( )^2 = ( )^2. I asked him to write the parenthesis first, in order to make sure that he carries the procedure correctly. It may take 30 seconds for him to write down the substitution, but that takes more than 30 seconds for him to check for errors if he doesn't write out this step but realize something is wrong later. I trained his carefulness and watched him do several problems on this. He got much better at the end. I introduced a problem-solving technology--set x for one unknown, write the other unknown in terms of x, and finally solve equations, on the Pythagorean Theorem problems, when he is given one side and the relationships of the two other sides. He got much better at the end. Then we moved to coordinate geometry. I introduced him the Midpoint Formula of the two points (averaging the x and y values) and the Distance Formula of the two points (take the square root of the sum of the squares of change in x and change in y). Before I taught him this, he was a little confused, but he strengthened his understanding much better after that. This is a crucial part on coordinate geometry. I also reviewed the rules of exponents for him because in the past sessions, I still saw that he was confused by this. I made him write down these rules so he could refer to them in the future. Then I gave him some problems on this topics and he gradually improved his understanding in this topic. Overall, his skills have improved because I always ask him to write down all the steps--again, it may take 30 seconds, but making a mistake and checking it again takes way more than 30 seconds."