In Algebra I, we’re having some fun with order of operations and also still getting to know one another (via some nice problems). As students finished a quiz the other day, I put the numbers 1 to 10 on the board and told students to see if they can use four 4’s and any operation they like to get each value. Sure enough, as kids finished the quiz, they would saunter up to the board and write down a solution. A few values started to gather multiple approaches.
An audible “ohhhhh” could be heard around the room. Then,
Student: Is he allowed to do that? Is using 44 against the rules?
Teacher: I don’t know. It’s pretty cool, right?
Teacher: Yea, I’m not sure. I didn’t make up this game. But, it feels like a good solution. So I see no reason to deny it.
Sometimes the students are too hung up on rules (or unstated potential rules) to get creative and think outside the box. I say, take a shot. Worst thing that can happen is that you are wrong and have determined an extreme case that doesn’t work.