A frog climbs up the side of a well from the bottom and slides partially back down when it rests. Every hour the frog climbs 5 meters. It then rests for an hour. Each time the frog rests, it slides back down 3 meters. It then starts again, climbing one hour and resting one hour. The well is 11 meters deep. How long will it take the frog to get out of the well? Explain how you got this answer.
The frog will take 7 hours to get out of the well. I drew a number line and made jumps alternating between 5 units and -3 units, respectively. Then, I counted how many jumps I made.
Let’s take it a step further: We can ask a variety of generalizing questions (such as “what if….”) of this problem. Suggest some in the comments. What part of algebraic thinking do you see exhibited in your questions and solution? What algebraic tools are needed to express the solution?