I have seen other people use the prompt “What is the same? What is different?” around Twitter (Check out #samediffmath), but I’d never formally used it in my classroom. I have asked those questions before on the fly, but I’d never created something to put in front of my students where those questions were the main focus.

As I was driving to school Friday and was thinking about what I was teaching that day, I had this thought to create one for function notation. Function notation is something that some students struggle with, and it sort of surprises me every year because it is so similar to things they’ve already done. Here’s what I came up with.

I printed these out on half sheets of paper and had my students do a Stand and Talk with them.

Here are some of the responses I got for “What is the same?”

- Both have an answer of 57
- The last 5 rows are the same.
- Both replace the x with 4.
- Both have 3x^2 + 2x + 1

For “What is different?” we talked about how on the right it has f(x) and asks to find f(4), and on the left instead it says “evaluate…for x = 4”

We talked about how so much of the problems are the same, but if I just gave my students the top row, they would know how to do the left one, but would feel completely lost with the right one.

In my second class, I explained how these questions are asking something very, very similar but the notation is different. I thought of the example of in elementary school if they were given 5 × 3, they would know exactly what to do. However, if they were given 5 • 3, they wouldn’t, even though it is asking the same thing. As I was explaining that, I could see some students making the connection to the two problems we were looking at.

I LOVED using these prompts intentionally in my classroom, and I’m looking forward to finding more ways to incorporate this into my classes.

(Here are some of the other things I’ve done with function notation.)