I have always found laundry to be one of the more education household chores.
Of course laundry helps with colors. Please hand me that green washcloth. Put these orange pants in your sisters pile please. The black socks are always Daddy's.
Shapes are easy to teach when folding towels. Washcloths are usually square, fold them in half to make a rectangle, and again to make a square. Place on pile and repeat. (count when you are done to see how many you had to fold)
Dishtowels and hand towels are nice rectangles. I fold mine in thirds, then in half. Fraction practice for slightly older kids, shapes for younger ones.
My bath towels are usually a little to big for kids in need of shapes to fold, but we also have a collection of towels that have lost their 'edging' and become smallish kid towels. We get to experiment with them to see how they can be folded to fit in the kid pile. All different starting sizes, makes for all different folding before you get the proper sized rectangle. (roughly). I memorized which towel needs what pattern, but the kids get lots of fun trying different methods. I figure if nothing else it should help them fold maps when they are older.
All the kids get practice in size comparison as we fold. Mommy's jeans are big, Princess' are small, but not as small as Baby Girl's. Dude's socks are bigger than Little Man's. We put the big shirts in Daddy's pile.
For that matter we can compare piles, 'who has more laundry to put away'?
We have also been known to have a race divide the work into equal piles, or measure who did the most before it was all done. If you have to get work done, you might as well have fun with it. We could use a stopwatch and add up all the time we all spent folding. At the end we might count how many towels each team folded, or measure the tallest pile.
When they are old enough to actually deal with the washer and dryer they get practice in sorting dirty into piles of light, or dark. This is oddly enough good practice for the whole world not being 'black' or 'white'. Plenty of items are good enough in either pile. And plenty would be sorted differently by Mommy than by Daddy. (I tend to fudge to make a whole load). And fractions again with the measuring soap. We make our own, and we use a collection of different lids to measure. Partly because we keep losing them, so we can't just say 'one of these'. Some things are 1/4 cup (use 2) others are 1/2 use one, others are bigger 'fill half way' or 'fill two thirds'.
Of course through all that we also learn the basic 'how to deal with laundry' Home Ec lessons.
Oh and I promised a very cute story about Baby Girl. Yesterday she wanted to 'do maf' so I took a sheet of her notebook and drew an equilateral triangle. She told me it was an A. Huh, well I showed her the difference, then I drew an obtuse triangle. She said it was a 'tine-gle' Which is about as close as she gets. One of these days I will get her to learn to talk.
Then after I drew a few more triangles she excitedly pointed behind my head on the couch. 'an das a tine-gle!'. I checked there was nothing but a washcloth that someone forgot to put away. Since she was so insistant, I turned fully around to view the washcloth sure enough one corner was folded back making a triangle against the rest of the washcloth!
See a slightly messy house isn't all bad.
Awesome Baby Girl!!! So many kids (not yours or mine) have trouble taking math into the world and she can do it at 2!
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