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 *exactly *right 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."

**Big Machines**

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.

ROBERT SIEGEL, HOST:

We're going to learn now what real-world can mean when it comes to understanding math. The phrase real-world shows up many times in the official explanation of the Common Core math standards. Those are academic goals for kids from kindergarten through high school that are used around the country. So for example, when it comes to things like the Pythagorean theorem, students need more than a textbook understanding. They need to be able to solve real-world problems. From Colorado Public Radio, Jenny Brundin has the story of two teachers and hands-on math.

JENNY BRUNDIN, BYLINE: Jay Whaley had an idea. He teaches everything from horticulture and animal science to welding at Soroco High in Oak Creek, a tiny rural town in western Colorado. Whaley's idea was something his introductory shop class could build.

JAY WHALEY: It's an octagon round bale feeder.

BRUNDIN: Translation - an eight-sided steel structure that's open at the top. It lets steer, horses and pigs stick their heads through the bars to eat hay.

WHALEY: It's a really simple thing but...

BRUNDIN: But it's complicated to build. Whaley knew how to guesstimate angles...

WHALEY: ...But to explain to the kids why the angle is that - that's what I needed help to do.

BRUNDIN: So he went to math teacher Maggie Bruski.

MAGGIE BRUSKI: I like to call myself the guide on the side instead of the sage on the stage.

BRUNDIN: Bruski is almost never at the front of her class saying...

BRUSKI: OK, guys, this is how you cross multiply. No-no.

BRUNDIN: Students work in teams to discover solutions on their own. And Bruski searches for real-world applications - part of the goals of the Common Core standards.

BRUSKI: It's way more rigorous. I think that 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.

BAILEY SINGER: We built a square first of all.

BRUNDIN: Talking about these first steps in the project is freshman Bailey Singer. She's pointing down to an outline of an octagon taped to the floor. Most of the kids in introductory shop class are freshmen so the trigonometry was new to them, but they jumped right in.

BRUSKI: A squared plus B squared equals C squared, so what is that?

KENDALL HOOD: So that's the Pythagorean theorem.

BRUNDIN: Here's Kendall Hood.

KENDALL: It's just to help you find the hypotenuse which is the...

BRUNDIN: For those who don't remember, the Pythagorean theorem helps you figure out the length of a side of a right triangle. Harrison Ashley says if you don't do that, you'll end up with...

HARRISON ASHLEY: A lopsided feeder.

BRUNDIN: After doing the math on paper, the students get to operate the heavy-duty machines that will help them cut and weld pieces of steel together for the hay bale feeder.

BAILEY: All right, this is our plasma cutter. This is kind of what we use to cut thin sheet metal like this.

BRUNDIN: You can tell these kids, like Bailey, love the hands-on stuff.

BAILEY: And the air pressure forces out a little bit of a UV light.

BRUNDIN: They're excited to show someone what they know. Then comes the real exciting part, cutting steel at precise angles and lengths. We go to the band saw. There are smiles all around when they've cut the first piece of steel. It's projects like these that have made 15-year-old Bailey Singer like math even more.

BAILEY: It's pretty amazing how many different ways you wouldn't think of that you use math every day. Even just building this, it really shows you that you do need math. You do need it.

BRUNDIN: There's still a lot of work to be done - welding, priming and painting - but once it's done, the feeder will be auctioned off and make some real-world money for the school's AG program. For NPR News, I'm Jenny Brundin in Oak Creek, Colo. Transcript provided by NPR, Copyright NPR.