End of School -- Start of Summer

Today is the start of Summer in the Northern Hemisphere. And it's also the last day of school for our daughter.

She had trouble with math this year. She was supposed to be placed in the advanced math program, but someone messed up, and she was put in the regular math program. After a few days, things got straightened out, and she got put into the advanced class, but by then she was already behind. And each few days that she was out sick, she fell behind more.

We decided to have her take the regular math program next year. Half of the material will be review for her. I want to make sure she gains math skill over the summer or at least not lose anything. So I've decided to give her Daily Math Problems, which, if she solves them correctly, will get her excused from scooping out the four litter boxes.

The first problem is to identify the quadratic expressions (from a group of ten) that factor into squares like this:

(x + a)(x + a)

She's actually pretty good at factoring since it's algorithmic. But the trick here is to do it efficiently. I want her to realize that she doesn't have to factor all ten expressions. Instead, she should realize that only the expressions with a constant a * a need to be tested.