Problem Solving

“I Can Solve Problems” Stepladders LEVEL E
Stepladders
Ismael is painting the walls and ceilings in a house and is using a
ladder to help.
The ladder has ten rungs.
Ismael can step up either one or two rungs at a time.
He cannot step up more than two rungs at a time because he knows
this would be dangerous.
To stand on the second rung he could
a. go up taking one at a time, i.e. 1, 1 or
b. go up taking two at a time, i.e. 2.
So there are two different ways for Ismael to go up to the second rung.
The problems
Ismael wants to stand on the tenth rung to paint the ceiling.
How many different ways can he climb to the tenth rung?
Pupil Worksheet 1
Task 1
With a partner discuss what strategies you could use that would help you solve the problem.
Task 2
If the ladder had only three rungs how many different ways could Ismael go up the ladder?
Task 3
If the ladder had only four rungs how many different ways could Ismael go up the ladder?
Task 4
Now attempt to solve the problem of the ladder with ten rungs.
You can use the worksheet attached to help you if you wish.
Extension
What if there were 100 steps and you could jump 1 or 2 or 3 steps at a time? How many
different ways could you climb the ladders?
p r o b l e m s o l v i n g A N D E N Q U I R Y 178