Repeating patterns lead easily into ideas of skip counting, multiplication and division, and odd and even numbers.
Exploration of repeating patterns can form an easy introduction to some of the fundamental ideas of early mathematics.
Here is a very simple repeating pattern made from coloured blocks. It is called a 'train'.
By talking about this pattern, students can come up with the following ideas.
- The number of blocks is 1, 2, 3; 4, 5, 6; 7, 8, 9; 10, 11, 12 (rhythmic counting).
- The number of blocks is 3, 6, 9, 12 (skip counting).
- There are 4 lots of 3 blocks, making 12 blocks in all.
- Each unit of repeat is a quarter of the whole object.
After exploring many other similar trains, students could reach some more general ideas.
- To find the number of blocks in a train, you multiply the number of blocks in the unit of repeat by the number of repetitions.
- To find the number of repetitions needed to make a train of a given size, you divide the total number of blocks by the number of blocks in the unit of repeat.
- A number is even if you can make a train with that number of blocks using a unit of repeat consisting of two blocks. If not, the number is odd.
Can you see any other general ideas here?
