Tabitha (9 years old) is keenly attuned to the temperatures these days, as subzero air temperatures or wind chills mean indoor recess. Being a child of great physical energy, indoor recess is not ideal.

We have an indoor/outdoor thermometer on our kitchen table, which she checks several times a day. Yesterday evening before doing the dishes together, she checks the thermometer.

Tabitha(9 years old): It’s 1 below.

Me:What was it this morning? Five degrees?

T: Four

Me:Crazy. So it’s colder now.

T: Yeah.

Me:How much colder?

T: Five below

Me:How do you know? Is it because 4 + 1, or did you count?

T: Neither.

Me:Oh! Now Ihaveto hear it!

T: Well…Four minus four is zero, then it’s one less, so it’s five.

Me:So one more than four less…er…one less than four….no….[we laugh]

T: It’s one more because it’s one less!

## So what do we learn?

This conversation reminded me very much of a game I used to play with Griffin (who is now 12 years old) on cold winter mornings. In both cases, the children naturally developed a strategy using zero as a stopping point in making comparisons.

The thing I especially love about this story is that Tabitha expresses a complicated relationship that is crystal clear to her: “One more because it’s one less.” Expanded out, she’s saying that “The difference between -1 and 4 is bigger than the difference between 0 and 4—the difference is bigger by 1 because -1 is one unit further from 4 than 0 is.”

She can express this complicated idea because it is her own.

If I tried to *tell* her that this is how subtraction with negative numbers works, she would definitely pronounce my ideas confusing—whether they were expressed in the language of 9-year-olds or the language of mathematicians.

I cannot tell her these things and have them be meaningful. What I can do is ask how much colder it is now than it was this morning.

## Starting the conversation

Move to Minnesota.

I’m kidding.

You can buy a Celsius thermometer, though.

You can make comparisons more generally, both asking your child how she knows, and talking about how you think about it. How many more full cups in the muffin tin than empty ones? How many more fork than spoons? How many more adults on the bus than children (or vice versa)? How many more quarters than dimes in the change bowl?