Why do this problem?
The original version of this problem uses only a 4x4 grid, but reducing the size makes this investigation
accessible to younger children too. Doing this problem is an excellent way to work at problem solving with learners. The problem lends itself to small group work, and provides an engaging context for
pupils to use the skills of trial and error, and working systematically.
No matter how old the children, it would be advisable to have objects to represent the teddies and houses as an introduction to the activity. These can be, for example, coloured counters and coloured squares if there are no plastic teddies available (or you could print these teddies
). Coloured magnets would
be ideal for use on a whiteboard as a demonstration. If you prefer, click on the following links to download word documents of the different coloured houses which you could print, laminate and cut out: yellow
, red, blue
, green, purple
It would be worth clarifying the very first instruction. Work out the four different combinations together with the children, using teddies and houses of two different colours.
Throughout all of this investigation, encourage the children to explain their thinking orally. This may be to each other, or to the class as a whole. Either way, it is vital in allowing them to clarify their own ideas, reflect critically on their work and so move themselves forward.
How can we make sure they are all different?
Is there a way to go about making the combinations so we don't leave any out?
Talk about being methodical and systematic i.e. planning and checking.
Some children might find it easier to work out all the possible combinations of houses and teddies before putting them onto the grid - others might prefer to put all of the houses onto the grid first and then put the teddies on afterwards. If pupils are finding it difficult to check their solutions, they might benefit from using a checking mechanism for the first grid:
Encourage pupils to solve each problem again, while also making sure that the diagonals follow the same rules as the rows and columns. Children might like to have a go at Tea Cups
, which is a similar activity.