This past week, we studied congruency and symmetry. Congruency tends to be relatively simple for the kids. Same size, same shape. That's pretty easy to remember. What often throws them is when the shapes are rotated. Especially when the shapes are triangles.
But symmetry really throws them for a loop. When I would draw a shape and ask how many lines of symmetry it had, several of them would just count the sides and give me that answer. Several would always say 2 (vertical and horizontal). And several would find lines that weren't symmetrical at all.
Diagonal lines are especially hard for the kids to judge. Though I've emphasized to them that they can and should TURN their paper, to make the line look vertical, they usually don't. Also, they confuse it with congruency, so if the two sides of the line are the same size and same shape, they go with symmetry. Even if the two sides aren't mirror images. For instance, the diagonal line of a rectangle DOES split the rectangle into two congruent triangles. However, this line is not a line of symmetry, because folding the shape on the line would not yield a perfect matchup.
Friday's test results weren't too bad, but there is clearly still a lot of work to be done, especially in some dire cases. (Where kids still don't even know their basic shapes.)
At least I haven't had anyone yet this year call it a "line of cemetery."