Well,Well!

The Problem

Freddo has had a nice swim in the bottom of the well and decides that now is the time to get out. Freddo climbs 3m up the wall of the well and then rests. But the wall is slippery and he then slips down 1m. He is so tired he goes to sleep for the rest of the day. The next day he does the same thing.  He climbs up 3m, slips back 1m, and goes to sleep. In fact he does this every day until he gets out of the well.

Now the well is 13m deep. How long does it take Freddo to climb out of the well?

Lesson Sequence

1. Use Freddo to share his problem with the class.
2. Ask the students to think of ways that they might solve the problem.  For beginning problem solvers you may get them to act out the problem (with Freddo) on the board.
3. Remind the students to keep track of what they are doing as they solve the problem.
4. Students solve the problems.
   As you circulate encourage the students to identify the leaps and slips that Freddo makes. Check to see if they are looking for patterns in the numbers that they are recording.
5. Sharing of answers & then solutions
   For those who give 7 as the answer get them to think about where Freddo was before he went to sleep the night before.

Extension to the problem

Freddo has a brother who likes climbing trees. Each day he climbs 5m and them slips back 2m each night. How many days does it take him to reach the top of a 20m tree?

Other contexts for the problem

A koala climbing a tree
A snail climbing a wall

Solution

We suppose that this is a bit of a trick question. The thing to think about is how high Freddo gets each day and not where he ends up before he goes to sleep. So each day in turn he reaches the 3m mark, the 5m mark, 7m, 9m, 11m, 13m. Freddo climbs out after 6 days! (A picture will show you all this quite quickly.)

Solution to the Extension:

Here the sequence of numbers is 5, 8, 11, 14, 17, 20.  So it takes 6 days for Freddo's brother to climb the 20m tree.