Why do this problem?
is designed to create a challenge that is completely new to pupils so they will not have practised particular ways to approach situations like it. They will therefore have to use their initiative and draw on potentially useful problem-solving skills. This task also provides an excellent opportunity for a discussion about different
approaches that have been used once children have had chance to tackle it in their own way.
Show the group the four pictures of the cottage and the tower, and invite them to talk to a partner about anything they notice. Share some ideas amongst the whole class. It is likely that they will notice the different size of the tower in each picture so you can explain that in fact these pictures show the same cottage and tower. (If you prefer, you could use the pictures
in the Hint
as an initial stimulus.)
Encourage them to make suggestions as to what has happened to create these pictures. Explain that you're not expecting them to know necessarily straight away how to do it so give them plenty of time to work on ideas in pairs or small groups. Pupils may also be encouraged to validate their suggestions, for example by using two items of their choice to position and compare.
Just as valuable as having a go at this activity is the discussion which should then follow. Bring everyone together and invite pairs/groups to explain how they went about the problem. You may like to jot a few notes on the board so by the time everyone has contributed, there is a record of the different approaches to which subsequent discussion can refer. What
are the advantages and disadvantages of each? Which approach might individuals use if they were having a go at a similar task? Why?
How do you think the pictures were created?
Could you make something similar?
What do you think about others' ideas?
Pupils could create a similar set of pictures for others to understand. They could then progress to using more than two objects in the picture.
Some pupils may need to have this presented in 'real time' with the teacher using a camera and projecting the image directly onto a screen. It may also be useful to use the images which appear in the Hint
and to have the two towers made.