While walking in the woods, Fred the frog fell into a hole that was 10 meters deep. Each day, Fred would jump 3 meters up the side of the hole. Each night, he would slid down 2 meters. How many days did it take Fred to get out of the hole?
Generalize the problem to the case where the hole is x meters deep, while Fred jumps y meters up the hole's side each day and slides down z meters each night. How many days does it take Fred to get out of this "general" hole?
Hint: Draw a diagram or construct a table to model the situation.
Solution Commentary: You should get an answer of 8 days....Right?
Now, what patterns did you discover that will help you solve the general case? If you did not see any patterns, relook at a table that models the situation.
How could you extend the problem further? Suppose that Fred jumps up 3+(n-1/2) meters each day where n is the number of days (Fred is getting desperate) and falls back 2-(n+1/2) meters each night. Then...and on with other generalizations your creative mind can dream up.