Oct 18, 2026 · @MrPurdyMath Display a picture, like of a roll of cardboard on the board and ask, "What do you notice?" Within a minute, hands go up all over the room, including from students who rarely talk in math class. That's the power of Notice and Wonder: every student has something to say, and no answer is wrong. This routine comes from the National Council of Teachers of Mathematics (NCTM), whose Notice and Wonder lesson plans pair a striking photo with real math. Their cardboard lesson (grades 6–8) is a great example. Its first part works as a five-minute warm-up in almost any lesson. When you have more time, the second part turns it into a full lesson on circles and cylinders. The 4 steps Here's the whole warm-up, using NCTM's photo of a rolled-up sheet of corrugated cardboard. The sample responses come straight from the lesson. Look silently for one minute. Show the image and say, "Take a minute to carefully look over the image." No hands y...