Here is an activity I forgot to write about. My students were learning how to write linear equations when given two ordered pairs. I wanted to help them make the connection between the algorithm and what was happening graphically. On some index cards, I wrote an ordered pair, laminated them, cut hole in them, and put a string in them to make them necklaces. I also wrote a letter in the bottom corner of each index card.
As the students walked into the room, I handed them a necklace, and asked them to wear it. The students were then instructed to work with a partner to write the equation of the line that passed through both of their points. They also needed to record the letter of the person they were working with (this is pointless, but I did it so the students thought I had an answer key). Once they had their equation, they found another partner and repeated the process.
It all seems rather straightforward and very much like a worksheet. But what happens as they keep changing partners blows their minds. THEY KEEP GETTING THE SAME EQUATION. And not only that, everyone in the room is getting the same equation. Every. Single. Time.
They begin to wonder what is going on. Of course I don't tell them. One student finally spoke up and said that if we were to plot all of the points, they would fall on the same line. So we did.