measuring up....

I love it when a project crosses curriculum boundaries, and connects the dots among different areas of study -- say, Social Studies and Math. I am also looking for ways to go deeper into concepts that sometimes seem self-evident: concepts like “rural” and “urban.”

I live and teach in a town of 6,000 people, and it’s the biggest town for thousands of square kilometres in this part of the world. The nearest city is 200 km away, and it’s not that big (approximately 55,000 people). The nearest city of any size is 500 km away. Most of my kiddos have been there, but their experience of big cities is still fairly sketchy. To say that cities are “big” and towns like ours are “small” may not be enough. What means “big”? And what means “small”?

So I set up a provocation. I drew a simplistic city skyline on paper on one table, and a “small town” on another table of similar size. I set out Numicon shapes and pencils and pencil crayons.

(Numicon is a set of manipulatives that teach early numeracy concepts in a multi-sensory way. Sturdy plastic shapes with holes in them represent each of the numbers to 10. They are sized and weighted so that kids can discover equivalencies in a number of ways. And best of all, they can pick them up, turn them around, put their fingers or pegs in the holes, immerse them in sand, press them into play dough, and so much more.)

I challenged the kids to find out how many people could live in the buildings I had drawn. I showed them how to trace the Numicon shapes to fill in the building shapes. Every hole would be like a window one person could look out of. So essentially, we would measure the area/capacity of the buildings using Numicon shapes/numbers.

Over the course of a few weeks, they worked at it and coloured the two skylines mostly in. Was it flawless? No. Was it enough to create an understanding of what “bigger” means when you are talking about cities? Yes, I think so.

So then came the tricky part: how to count up the numbers, clearly much bigger than what my Grade Ones could be expected to know? Fortunately, they had had some experience with constructing “100” in recent weeks.

Can 100 people fit in our "small town"?

The bucket on the left has 100 in it. The bucket on the right will hold the shapes
that fill the buildings in the "small town" in the background.

We started with the “small town.” I asked the kids to predict whether we could fit 100 people in our town; a rudimentary way of estimating. We put 10 "tens" in one bucket of a balance scale. We matched Numicon shapes to the ones that had been drawn and coloured on the buildings; then moved them all into the other bucket of the balance scale. We found out that there were fewer than 100 people living in our "small town." Next, we removed tens from the first basket until it was lighter than the shapes from the town. We added "ones" to that bucket until the two buckets were balanced — and therefore equal. Using tens and ones made them easy to count; and also served as an illustration of how place value works. In this way, we were able to determine that our “small town” would accommodate 72 residents.

Estimating the population of our "big city".

With that information and experience, I asked the kids if they thought our “city” could accommodate 100 people. Everybody thought so; so I asked them to estimate how many hundreds they thought could fit in it. I recorded their estimates, and we began to count.

Adding shapes to the balance scale that match the ones on the drawing.

It's a long process....

For the big city, we decided to count 100 at a time. We put 10 “tens” in one bucket of the balance scale. Then we looked at the shapes that we had coloured inside the skyline buildings one at a time. For each drawn shape, we put the matching plastic shape in the second bucket of the balance. As we did so, I tagged the shapes we had counted with sticky notes so we wouldn’t count them twice or miss any of them. As our two buckets achieved equilibrium we counted it as 100, and put a sticky note on the side of the paper noting 100 more each time.

We use sticky notes to cover the shapes we had already counted.

Periodically, we reviewed our estimates. After counting three hundreds, for example, I asked them if they thought there would be one hundred more. Two hundreds? Three?

Here, the "living space" for 300 people is covered up. Time to revise
some of our initial estimates.

It was a long process, but in the end we determined that the “city” could accommodate 743 people. And interestingly, the very first estimate of “700” was the closest to the final answer.

What we learned is that a city is not only bigger in the sense of the buildings being taller and wider. It also accommodates more people —  a LOT more people — in the same amount of space. In addition, the spaces between the buildings are fewer and smaller; adding to density of the population (not that I used that terminology with the kids).

And that’s a more sophisticated and complex understanding of what “bigger” means.