Got some sidewalk chalk lying around? Tired of watching your kids draw the same old flowers and rainbows and such? Get mathy with that chalk!
Recently I drew a timeline on the ground. Not the usual kind of timeline, though. I drew 5 long lines parallel to each other on the ground and labelled them 1, 2, 3, 4, and 5. I had some idea in my head of teaching a preschool class about zero with this timeline, but it became so much more.
I asked the group of 10 5-year-olds to stand on the line that represented their age. They all crowded onto the 5. Except for one little boy who shyly hovered off the line.
“I’m four and a half,” he said.
Ooh! Here was an opportunity!
“I am so glad you are four and half! Now we get to draw another line just for you! But where should it go?”
We agreed the new line, in a new color, should be drawn between lines 4 and 5. We could have spent more time on the idea of “half”, but, well, there were 10 preschoolers and we were on a roll. (“Half” reappeared later when the kids were drawing with their own chalk, and one child called me over to see how she took a circle and cut it in half with a line.)
Of course, as soon as we drew the line for 4.5, three children told me they were actually 5.5 years old. So, we figured out where their line should be and added it in. Just to be sure, I asked if anyone was five and three-quarters. I got no response. Blank stares. So I left that fraction for another day.
Then we made a game of it. I asked the kids to step back in time…one year, two years, etc. until we were back to the year in which they were born. But we didn’t have a line or a label for that. So we drew it. And we called it zero. (Here we also got into a little conversation about what zero actually is. We agreed it meant nothing. We also noted that it can make other numbers much more than they were. Jaws dropped when I mentioned that it took mathematicians centuries to come up with zero…long after we came up with counting numbers.)
Next, I asked the kids to step back to the year before they were born. We drew the line. And then we wondered what we were going to label it. What comes before zero?? Oh, that was a challenge. The kids came up with some great names for that line…lots of potty-talk involved…but, finally, I suggested that because it was one step away from zero, we should label it 1, and because we already had a 1, we should give this one a small symbol in front of it so it looked a little bit different. And that’s how we came up with -1.
Then I handed each kid their own piece of chalk and set them to work drawing their own numbers all over the ground. The ground quickly became colorful and numerical! And as you can see in the photo above, we didn’t stick to just one numeral system.
(Mathematically…there are so many kinds of numbers. Counting, Whole, Integers, Fractions, Rational, Real, Imaginary. Before many of these numbers were discovered, there were many different kinds of numerals (symbols for numbers.) Before your child encounters all these numbers in a formal school classroom, why not get to know some of them in a creative comfortable setting? Playing with sidewalk chalk is a way to draw your child in to activity and conversation. What does it mean to be between two whole numbers? What does it look like to write that kind of number? What happens before the beginning? Who invented numbers? These conversations can be deeply mathematical, deeply philosophical, AND accessible to a very young child whose imagination is full of energy.)