This is a good opportunity to explore aspects of generality in
three dimensions and for pupils to discuss images and possible
solutions, and find convincing arguments for the unique solution.
For some this may be a hard problem to visualise, which is not
always made easier by diagrams.
Suggestion for introducing the
Invite the class to imagine a 3 x 3 square grid.
How many small squares are there?
How are they arranged?
Ask the group to draw a 3 x 3 grid.
Now, ask them, in their mind's eye, to colour one of their nine
squares and ask for a volunteer to describe to the rest of the
class where it is. When the person has described their square ask
everyone to fill in that square on their grid. Repeat this activity
several times with the aim of identifying some notation that fully
describes the position of squares on the grid.
Repeat the activity but this time describe lines of three squares,
like the winning lines in "Noughts and Crosses".
How many lines are there?
Suggestions for the main part of the
Ask the group to imagine that they have a 3 x 3 x 3 cube made up
from 27 unit cubes.
Can they devise a notation for describing positions of little cubes
and lines of cubes within this cube (as if they were playing 3D
Noughts and Crosses)?
Tell the group that a marble is placed in the unit cube found at
middle-middle-top. Another is placed at middle-middle-middle. Where
should the third marble be placed to make a winning line of three
marbles? Try some other examples with the group.
Ask students to come up with examples of their own.
The interactivity can be used to give feedback to students.
How about trying
to play Noughts and Crosses without paper?