Another Math Tutoring Update

My current student's penultimate Math test for the school year happened last week, on the topic of 3D Geometry (surface area and volume of boxes and prisms). This was a section that I couldn't get him terribly interested in, but we still plowed through the material as best we could. His test result was quite respectable (87%) but didn't beat the average across the grade (86%) by very much at all. This seems to indicate that it was a fairly easy test that he could've done better on, but you're going to have that sort of outcome if the student doesn't get into the material at all, I suppose.

The only section left is Equations, for which the test is this Monday coming up. I've had him doing Algebra problems much more complicated than the ones taught in Grade 7, but unfortunately he's now discovered that his teacher expects many more details in the answer than I've been requiring of him. To see what I mean, here's a sample question done in both styles:

Style # 1:

4m + 5 = 21
4m = 16
m = 4

(then he would check his answer by mentally substituting it back into the original equation)


Style # 2:

4m + 5 = 21
4m + 5 - 5 = 21 - 5
4m = 16
4m/4 = 16/4
m = 4

Left Side
= 4m + 5
= 4(4) + 5
= 16 + 5
= 21

Right Side
= 21

So the question won't be, Can he get the right answer each time? but rather, Will he remember to solve each equation that way? He did ask me why everyone wouldn't simply get 100% on the test, since the second style requires that you prove that your answer is correct. I said that it might be the case that some students wouldn't be able to finish the test in time (depending on how many equations there are, and how quickly each person can do all of those steps), or that they might get the wrong answer, see that it didn't work out, but not be able to find their mistake.

What had looked like a slam dunk for him has now become somewhat interesting!