Bad at Fractions

I just about always wear a collared shirt with buttons to school, so several kids noticed when I showed up in a T-shirt today. "I don't think I've ever seen you in a half-sleeve T-shirt," one fourth-grade girl commented. "I have," a classmate said proudly. "Really?" I asked. "Here at school?" "No," he said. "In a restaurant."

There was a reason for the shirt. The third and fourth graders are working on fractions, and the shirt's message is, well, fractional. It proclaims:

5 out of 4 people are bad at fractions.

I used the shirt's message as a very informal way of checking students' understanding of fractions and fractional thinking. My hope was that they'd lodge a complaint, and fortunately I was right.

"Your shirt's wrong," one student stated flatly after she read it. "It should be '4 out of 5 people are bad at fractions,' not 5 out of 4."

"Yeah," a classmate agreed. "It doesn't make sense this way. If there are only 4 people, you can't take 5."

"It can't be more than the whole," someone in another class pointed out. "It's 1 and one fourth, but that doesn't make sense when you're talking about people."

"The shirt is bad at fractions," somebody said. "It's a bad-fraction shirt. It's complaining about people being bad at fractions, but the person who made it is the one that's bad at fractions."

"They're trying to disguise the fact that they're bad at fractions," noted a fourth grader.

"So I guess I should take it back to the store and exchange it for a shirt that's mathematically correct," I said. "What do you think?"

A few nodded slowly, but the bulk of them shook their heads. "It's a joke," someone explained. "People will see the shirt in the store and say, 'Oh, that's wrong!' and then they'll buy the shirt to make other people confused."

That settled, we moved on to the rest of the lesson.

There's a lot more to fractions, obviously, than determining what's wrong with a T-shirt statement. Still, it's kind of fun to use something as mundane as a T-shirt to do a brief informal assessment--and nice to know that the kids could see the error, and even, perhaps, the irony.

Photo credit to Rhiannon P. in Jan's class.