Wearing many hats, Part II

Continuing from yesterday, we are looking at our many hats. How can math help us understand what we have accumulated?

I think we might want to sort through the hats and classify (divide) them into sets today. So my wife sorted through the ball caps and here's what we found. We have this many CAPS of these COLORS.

Is the visual representation clear enough for you? If so, then that's enough of ball caps; we'll move on.

We have hats with these different FUNCTIONS - 5 mesh, 6 rain-proof, 6 winter, 3 driving, 2 helmets.

Helmets? Are helmets hats? We say yes; helmets cover the head. They go in the hat count.

I also noticed a visor or two. Are visors hats? We say no; they shade the eyes but don't cover the head. They don't get counted.

Are caps hats? They shade the eyes AND cover the head. We say yes. Why not?

Do you see where this is taking us? Suddenly we need a new term for these head things. Let's call them head gear. We need the right vocabulary to CLASSIFY and SORT head gear. Here's one way we could do it, with graphics:

Sadly, it gets a little difficult to show how many hats have light blue fabric and are intended for winter use, and contrast them with caps that are dark blue and aimed at summer use. What if we made a grid that would allow us to see two sets of characteristics at once? Then we could classify our head gear a bit more conveniently.

This could easily be turned into a pretty graph. But I think you get the idea. Math is a language that allows us to count, to classify and sort information.

This is how we teach it to kids (and adults). We introduce words that precisely describe a set of items. We distinguish one set from another. We find ways to clearly share our findings with others. We look at the data and try to learn from it. What can you learn from the chart above?

First, I don't need any more dark gray or black caps! Second, I need to decide how to spell gray (grey).