The Basic Pattern Idea

I like to have students choose their own ways of representing their patterns. But in my work where two patterns are going at once I have been using snap cubes lately to highlight a strategy of interpreting ratios, where there are two patterns with the same total cubes, but different patterns.



For example, for two against three, we need patterns that allow a length to be easily seen as two pieces or three pieces at the same time. If students are using snap cubes for patterns already (e.g., repeated 2s, 3s, 5, etc. etc.) then it seems to be straightforward that you can use two colors and make two threes or three twos. Hard without the pictures here, but: if B means blue cube, and R means red cube, then a cube train of two threes might be:

Whereas a cube train of three twos would be:

So next to each other they look like:


And I have the students count, either 123,123; or 12,12,12. and clap on the first of each color as they read off the counted cubes.


For 5 against 4,



One of the things I have been working on here at the forum is an interactive web-page so that students could color in cubes to make a pattern of sounds, and have it play back their pattern. Then I want to have classes around the world put together concerts of new compositions based on a call for certain types of pattern compositions to be submitted that they then select from.