Catherine was doing work with decimals yesterday. She had to work through addition, subtraction and multiplication problems, keeping in mind what she had to do with the decimal. It didn't go so well. The first time through she moved the decimal as you do in multiplication on every single question, subtractions and addition included. I pointed out her mistake, erased all the wrong answers and asked her to do it again. She did and got most of them right but still didn't have a firm idea of what to do.
I thought about it for a minute and drew a snake to represent how decimals moved in the answer to a multiplication question:
I couldn't come up with an image for addition and subtraction so I gave Catherine some paper and 15 minutes to come up with as many pictures as she could that would represent what to do with the decimal in different operations. Here is some of what she came up with:
I was surprised by the different images and the cleverness of some of them. The dolphin is definitely my favourite.
Right after she had left the room to draw those pictures I came up with an image for decimals in adding and subtracting:
Catherine's drawing went into her math book and mine went on a poster I'm making of math symbols and ideas:
(Would anyone be interested if I did up some PDF's of our math visuals?)
Catherine now knows what to do with the decimal in different operations. She still doesn't get the why of this however. The pictures help her remember what to do but not the reasons for doing it. We'll conquer that later.