M has been proud of his ability to use a number line to estimate sums, but differences were too difficult, and getting “wrong answers,” on his work sheets were very trying for him.

We switched venues by drawing a long number-line on the sidewalk. (This also gave little sister a chance to run around outside!) M practiced adding and subtracting numbers, hopping by twos, and such things. I had to draw a new one today, because Tuesdays has gotten so scuffed. We included negative numbers of course, that makes M feel so grown up.

He solved one of his on-going irritations: he figured out why he often made the “off by one.” mistake. When he was adding a number to another on the number line, he began counting with that first step onto number-line, not the first step in the direction he was going. He also wasn't counting zero as a place on the number-line. When I told him that computers often made that mistake too, he laughed and said, “oh, if the computers make it all the time, of course I make it all the time.”

M has a wonderful grasp of doubling, in fact, the way he used to count was, “one, two, one and two, two and two, two and two and one, Mommy, I can't count that high.” Then he switched to, “One, two, three, two and two, five, three and three, seven, four and four...” Just as I thought he'd tired excessively of number-line hopping, he announced that he did know some differences! If he subtracted 3 from “three and three” he'd land on three. He patiently stepped it out, and was delighted to be correct. He also did it with ten to five and four to two.

Sometimes I think I am teaching calmness as much as I'm teaching mathematics: but then I don't set him a good example of anti-perfectionism by being annoyed that he is not perfectly relaxed!