Around the time we finish curve sketching in AB Calculus, I have an activity where kids go on a little scavenger hunt for graphs. I have 14 sets of graphs and they start at the graph of the second derivative. From there, they have to find their first derivative and original function. I stick all the sets on some lockers in the hallway outside my room. The second derivatives, first derivatives, and originals are all grouped together.
How do students know they’re correct? Each card features a code word on it. As they progress they gather three code words. The words are loosely associated with one another. When they think they have the three correct words, they first confirm with me that their set belongs together. If approved, they face the Wall of Prizes. To unlock their prize, they have to figure out the correct fourth word that goes with their other three. The words are from the Remote Associates Test. They were developed as puzzles in studies related to creativity. There are lots of lists out there. As an example, given LIGHT, BIRTHDAY, and STICK the fourth associated word is CANDLE. Should a student correctly guess candle, they receive a prize.
The graphs I use for this task are created to be very similar looking to avoid making it too easy. They are sets of 5th, 4th, and 3rd degree functions.