Real-World Math: A Bit Of Trig And Hay For The Horses
Building a giant steel bale feeder is hard. Try it.
Problem No. 1: Unless you live in ranch country, you probably don't even know what it's supposed to look like — regardless of whether you can build one.
Problem No. 2: Arc welding is involved.
Problem No. 3: Getting it right requires some serious math.
The kids who take Jay Whaley's agriculture education class at Soroco High School in rural Oak Creek, Colo., have no trouble with No. 1. This is, indeed, ranch country. They know that the eight-sided steel structure in question looks like a flat-topped jungle gym. The hay goes inside, and steer, horses and pigs stick their heads through the zagging bars to eat. Easy.
Nor do they have much trouble with No. 2, either — they genuinely seem to enjoy welding and working with the shop's heavy-duty machinery.
The trouble, says Whaley, is the math. An octagonal feeder has a lot of angles. Get them wrong, and you waste a lot of steel. Many of his students aren't taking upper-level math classes, so Whaley asked Maggie Bruski for help.
Bruski teaches math at Soroco and thought this feeder would be a perfect way to reinforce the Common Core math standards she uses in class (and that teachers in more than 40 other states are using, too). The learning guidelines say, again and again, that a textbook understanding of key mathematical concepts isn't good enough. Take a look at this eighth-grade geometry standard:
"Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions."
But, Bruski says, finding those "real world" connections and making sense of them can be tricky — both for her as a teacher and for her students.
"It's way more rigorous now," she says. "Students need to be able to make these leaps that they might not have been asked to make 10, 13 years ago, and I think this project is a perfect example of one of those big leaps."
First, Getting The Angles Right
The Soroco High agriculture shop is massive — a warehouse full of old motorcycles, tractors, various machines, even a greenhouse. On the concrete floor is the start of the feeder: an octagon of blue tape, laid down with the utmost precision, using the Pythagorean theorem.
But getting those angles exactlyright was the hardest part of the project.
"Maybe somebody would not quite understand an equation," says student Bailey Singer. "Sometimes you have to go back and redo some equations, redo some math, trying to make sure every angle is right."
Sometimes, the pursuit of perfection led to spirited, mathematical debate.
"We all worked together pretty well but on some occasions we would somewhat argue — because one person would think something's right and then one person would think it's wrong," says Harrison Ashley.
Bruski says it's important for students, especially those who traditionally struggle in math, to "sort out those difficulties and hopefully really see — because they're able to touch the math, not just try to do the math on paper."
Though the project dovetailed with the kind of advanced work her upper-level students were doing, Bruski says Whaley's shop students, most of them freshmen, eagerly tackled the trigonometry.
"The math we were doing to calculate all this was way more advanced than what we're doing right now in class, so it was a whole new lesson we had to learn," says student Kendall Hood. "It's different to see how the math you are doing in class relates to real life. It definitely made it so there was a purpose in doing the math, not just to get numbers."
The entire project requires intense cooperation — from getting those early angles right to working the heavy machines that will cut and weld the steel pieces together. When construction begins, Whaley reminds his students to be as accurate as they can:
"Two feet, 10 and 3/4 inches, that's what you calculated, right? If you cut that the wrong way, you just wasted 2 feet of steel, right? And at $2.75 a foot."
The students level the shop's band saw. It's hard lining up the blade. After a few stops and starts to get it just right, the saw roars through the steel.
There are smiles all around when the first piece of cut steel clanks to the floor.
"Looks pretty good," says Hood.
It's projects like these, says Bailey Singer, that make her like math even more.
"I think math is one of the harder subjects for a lot of the kids. I think it's harder to understand," she says. "But once you see things like this, once you see how it comes into play with reality, it's pretty amazing when you think all the different ways that you can use math, every day. Just building this, it shows — you do need math, you do need it."
There's still a lot of work to be done: welding the bale feeder together, priming it, and painting it.
"But hey," says math teacher Bruski, "they're going to have something that they built, and that they can sell to the community!"
The bale feeder will go to the highest bidder at an auction later this year, using real-world math to make some real-world money for Soroco High.
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