Submarine Sandwiches

I taught this problem to several different classes – these are high school students that are in my class because of “number sense” difficulties and so we’re supposed to be working with them on elementary-level fraction skills. We only have a half hour for class, so there’s really only time to do the initial part of the task – the dividing the 4 sandwiches for 6 students. I teach in an online school, too, so I’ve adapted the lesson for use in the Blackboard Collaborate virtual classroom.

I noticed something rather interesting – that a lot of students start by cutting the 4 sandwiches in half on the provided diagrams. They give 1/2 to each person, but then get stuck with a sandwich left over. Students suggest things like giving the last one to the teacher, donating it to charity, returning it to the store, but most groups eventually realize they can split the last one into 6th and give 1/6th to each person.

One group didn’t ever figure out the 1/6th after getting stuck with the extra sandwich left over, but one student looked at the 4 and 6 in the problem and came up with 2/3rds and then had a team member draw that out on the provided diagrams. So someone who comes in with a bit more mathematical sophistication might actually solve it like a word problem and then from there see that their answer makes logical sense graphically.

They also tried to experiment with cutting the sandwiches into fourths, which could have made for an interesting problem – it works out to about 2.666 / 4 ths that way. They woudn’t figure out how many fourths to give each person, though, and we ran out of time before we could really dig into that. That could have been a major breakthrough. It wasn’t until I started doing CI tasks with other teachers in professional development that I realized it’s okay to put a decimal in a fraction – I always thought that was forbidden before, even though mathematicians study things like complex fractions – things like (1/2) / (3/4) all the time, so there’s really no reason not to put a decimal in a fraction other than convention.

At the end of class, someone said – do we only do one problem per class (implying that a math class should have multiple problems), and I said, well, it depends on who’s teaching, but when I’m teaching that’s very likely!