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Age 5 to 7
Challenge Level
The Tall Tower
You have been imprisoned at the top of the Tall Tower by the Wicked Magician!
You can get out by climbing down the ladders. As you come down you collect useful spells.
You can go down the ladders and through the doorways into an adjoining room, but you cannot go into the same room twice, nor climb up the ladders.
The numbers in the rooms show how many spells there are in each one.
Which way should you go to collect the most spells?
And which way to collect as few as possible?
Can you find a route that collects exactly 35 spells?
By clicking below, you can read how some other children started this problem.
I thought that if I want to get the highest number of spells I need to visit as many rooms as possible.
Hiromi says:
I wondered whether it was possible to visit all of the rooms in counting order.
Fay says:
I chose a route and then added up how many spells I had collected.
”‹Did you start the problem in the same way as any of these children?
Why do this problem?
By offering three different ways into the problem, you can capture pupils' curiosity. By focusing on different approaches to a task, learners' attention is on the mathematical journey rather than just the answer.
Possible approach
Set pairs off on finding the route which collects the most spells (this sheet might be useful for recording) but, if possible, do not give them time to find the solution. Instead, offer the three starting points from the problem, characterised by Krishan's, Hiromi's and Fay's methods, and ask learners to try to understand them. (You may wish to print off this sheet to give out, which contains the problem and the three approaches.)
After a suitable length of time, bring everyone together again to facilitate a discussion about possible ways of starting this problem. Did any pair use one of the approaches on the sheet? What do they like about each one? What are they less keen on? Why?
Give time for pairs to continue to work on the problem, but invite them to choose one of the approaches they have heard about, if they so wish. In the plenary, you could ask a couple of pairs to explain why they changed their approach, or not, and/or you could share ways of working on the two other parts of the task.
Key questions
Possible extension
Children could find how many different ways there are to go down the tower. Is it possible to collect all the different numbers of spells between the highest and lowest? Alternatively, learners could create their own version of the task by adding numbers of their choosing to these images of the tower.Possible support
If arithmetic is a barrier to tackling this task, counters could be used to represent the spells on this large picture of the tower.
NRICH is part of the family of activities in the Millennium Mathematics Project.