Last winter I became particularly attached to Full Sail Wassail beer, a delicious craft beer from Oregon. The kids became attached to it too, because Full Sail did a “12 days of Christmas” thing on the underside of the caps. Every night at dinner they fought to be the first one to look at my bottle cap and see whether we had gotten “5 golden ales” or “3 mash tuns.” We saved all the caps. Not sure why.
Today I pulled down the box of caps and spread them out on the table.
“I have a lot of questions about these caps,” I told Alex. “I want to know which number we have the most of, and which one we have the least of, and whether we have the same number of caps for any of them. What do you think would be the easiest way of figuring that out?”
She set out a pencil to mark a straight edge and then carefully began lining up bottle caps in neat rows. I made a couple of suggestions (“Do you think you should put them in order by number?”), but mostly Alex just got to it. Interestingly, she decided to put her X axis at the top.
Once she finished the graph, we were able to answer all of my questions. But what if we wanted to remember the distribution of the caps later, after the table had been cleared for dinner? What if we wanted to show it to someone else?
I picked up a sheet of graph paper and drew x and y axes. “Here, this up-and-down line can be like your pencil, and the other one can be a flat bottom. In graphs people usually put the flat line on the bottom instead of the top.”
She got it immediately. She counted the squares on the vertical axis to make sure there were enough spaces, and then started filling in. After the first three bars she asked me if they had to be colored in and was relieved to be told no.
She started numbering them along the top of each bar and then stopped. When she finished the graph, she asked me to number the rest of them for her, and instead I showed her that we could put them along the x axis. “…And then we should put some words there so people know what those numbers stand for.”
She studied it a little more. “It’s kind of hard to tell how many squares are covered up by those first bars.”
I nodded. “Also, people won’t know that each square stands for one bottle cap unless you tell them.” We labeled the y axis too. Then I cleaned up all the bottle caps and had Alex answer some questions using only the graph, not the real caps. She seemed delighted.
I am working on some data analysis projects this week for the family summer camp that we attend every year. While we’re waiting for Beast Academy 3C to come out, I’m going to have Alex do some more graphing with that data, and also have her work on reading some of the graphs I make. There’s just nothing like real data.
?
Beer bottle graphing – I love it! We could have used this post when we were at the cottage with my parents last month. Come to think of it, we could have also done a beer/lime vodka/Pinot Grigiot bottle graph. We’re willing to suffer like that for math’s sake too.
There’s a free graphing program on the internet that’s pretty fantastic, I forgot to mention: http://nces.ed.gov/nceskids/createagraph/default.aspx
Alex might get a kick out of entering the data and seeing it in different forms.
I am continually astounded by how brilliant your lessons can be.
The family I often write about with a child Alex’s age used to play a Concentration-like game with beer-bottle caps. Because you just start with a random handful out of the jar, you don’t know for sure if everything on the table has a match, so at any point a player can declare that everything left is a single, and this ends the game with a win (if the player’s right) or a loss (if the player’s wrong). Visiting aunties are at a disadvantage not knowing the little clues of recognising the top from the bottom.
They also play sorting games as you described.
I’m with Becky. This is completely brilliant. And you can feel so virtuous about all that beer you drank.
There was a brilliant dataset in the back of the statistics text I used in college: the M&Ms dataset.
He took a bag of M&Ms, and recorded color and weight (to four significant figures) for every candy in the bag. This let us do things like determine what color was most frequent in that sample, but answer questions like, “Are orange candies different in mass (in a statistically-significant amount) from blue candies?”
Bottlecaps are a good dataset too. Anything you have handy in large numbers that has at least two characteristics.
That stats textbook had a wonderful underlying sense of humor running through its footnotes and datasets, I love it.