Catherine likes to stump my husband and I with math questions. A couple of weeks ago it was, "Mom - x times x plus x times purple equals twelve."
She thought it was tough.
My husband and I talked about it, Catherine and I discussed it and over the course of a day and separate conversations this is what we came up with:
First, we limited the variables to positive whole integers.
Second, x times x could instead be x squared and x times purple could instead be expressed as xp.
Third, x squared has to be a square number smaller then 12.
After that it was easy and we came up with two solutions.
What really told me Catherine was doing okay though wasn't her original question. It was that whole, positive, integer, squared and condensing x times purple to xp were all things she understood. Not to mention notation, order of operation and the whole idea of variables. I looked back on it after and realized in that one question of hers and the subsequent conversations she'd demonstrated quite a bit of knowledge and more then that, could put it all to some use.
Most of the time it feels like we're stumbling through this homeschooling thing blind but every once in awhile I look up and see just how much territory we've put behind us and I'm amazed.