When are two patterns the same?
Give each student (or group of students) 12 coloured cubes — 8 of one colour and 4 of another.
Then ask students to use their cubes to make a train which shows a repeating pattern with a unit of repeat that is 3 cubes long.
Now put all the constructions together and ask students to sort them into groups that are the same pattern.
It may take students some time to accept that patterns can be the same even though they are made with different colours (e.g. red-blue-blue gives the same pattern as green-yellow-yellow and even blue-red-red).
If necessary, align the various constructions to show how they match. Call this type of pattern an ABB pattern.
Students will be able to make three different types of pattern which can be symbolised as ABB, AAB and ABA.
However, some students may argue that ABB is the same pattern as AAB (e.g. red-blue-blue is the same pattern as blue-blue-red) on the grounds that the train can always be turned around or looked at from the other side.
Repeat the exercise allowing students a free choice of colours and unit of repeat. Challenge them to find as many different patterns as they can.