Pattern generation

What: A multicoloured pattern, similar to some wrapping paper designs.

Shapes going diagonally to the right, coloured squares going diagonally to the left. A maths and art activity.


  • We took an A3(ish) sheet of drawing paper and folded it into a strip, then folded the strip into a small square. When we unfolded it, there was a grid of creases in the paper.
  • In the first square we drew something small, an easily repeated shape, with a coloured marker from a tuned set of six. We then counted across one square and down one square and drew the same shape again, and repeated til we had a diagonal line that went down to the bottom of the page.
  • We then went to the second square, and drew a new shape in a new colour, and repeated this down the diagonal line. There was a little bit of fiddly explanation to show how the line “wrapped” around from the right hand side of the paper to keep going on the left – Kid 6 took this as a random nonsensical instruction and followed it meticulously, eventually beginning to get a glimmer of why, and Kid 4 (who is very pattern oriented) grasped the idea immediately but had difficulty with implementation. Both kids worked out pretty quickly that moving one over and one down always put you on the right of the drawing you did before.
  • We kept going until every square had a shape in it. This is where Kid 4 ran out of patience / thought their pattern was complete / decided they were Done, and where I encouraged them to stop.
  • Then, we took a new colour of marker from the set and coloured the right-most-top square’s background, and went one over-left and one down to make a new diagonal line. I took some care to try and pick a colour that wasn’t going to turn up in the shapes we were colouring around. Eventually Kid 6 worked out for themself that there was a repeating pattern in the shapes they were colouring around – e.g. orange, brown, blue, orange, brown, blue – and that some of the colours weren’t in each line at all. The idea was to keep the background colours wrapping around as well, but Kid 6 lost track of this and decided to do their lines in a symmetrical colour pattern (green – purple – blue – purple – green) instead of wrapping (green – purple – blue – green – purple – blue).
Kid 4’s pattern, with just the shapes and no background to make it simpler/quicker. Kid 4 also made each diagonal its own pattern, with shapes rotating or growing or changing in size. They are a bit obsessed with patterns and I was OK with them playing with the idea of nesting patterns inside other patterns.

The whole thing took us quite some time, it was meticulous work, and a reasonable way to fill in part of an afternoon when it was too warm to go outside. I actually did this activity with each of the kids separately, having thought that kid 4 wouldn’t be up to that much drawing / colouring (which they hate) but that kid 6 would like the time working quietly with me and talking, and was quite able / needing to deal with 2D patterns instead of linear ones. However, kid 4 is competitive (they both are) and didn’t want to miss out on having a pattern on their gallery wall if kid 6 had one.

Kid 6’s finished pattern, which they were very pleased with the appearance of. Tuned colour sets do help with the final result. 

Extras: In theory, if we used butcher paper instead of good drawing paper this could become our own wrapping paper. I suspect if it was a good enough piece I could probably digitise it and find somewhere online that prints wrapping paper too (Spoonflower?). We could do something like this again but with stamping and gluing paper squares instead of drawing and colouring, which would speed it up / make it a little easier on the non-drawing child (it’s a long time to grip a marker).  Spending more conscious time on the idea of nesting patterns would be interesting, to see how the results then changed across the whole grid. A related activity would be to tape paper around a cylinder of some sort, get them to draw lines around the cylinder and then untape it to see how the wrapping had mapped back to flat.


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