Whoa! At first I thought it was a classic confusion of multiplication with other functions, and my prescription was to take all the algebra 1 books in the world and make them use multiplication dots instead of writing things next to each other for multiplication.

But then I saw that subtraction lurking and realized that even if it were multiplication here, this “cancellation” is still no good. My own feeble attempt at getting kids to be less likely to make that kind of mistake has been to require a mathematical word along with those lines drawn through things that “cancel” — so here they would have to write “divides out” at the least, which gives them one last chance to notice that what they’re doing on the top and bottom of the fraction is not, in fact, division.

I’m happy that their first response to the prompt is to start with the more complicated-looking side and start substituting sin/cos in place of tan. I would be happier if they had written sin(a) / cos(a) instead, though.

I like the idea of having students write what they are doing to make terms ‘cancel’ – I tutor a student who writes the number/term underneath what she wants to move and crosses them out *before* she decides why that’s a valid algebraic maneuver. That step might help.