AC9MFA01 · FOUNDATION · ALGEBRA

Patterns That Repeat

Recognise, copy and continue repeating patterns shown in different ways.

Patterns are everywhere a young child looks: the stripes on a beach towel, the tiles on a bathroom floor, the steady beat of a song, the days of the week coming round again. Learning to see these patterns, and to work with them, is the very first step on the long road toward algebra. Before letters and equations, there are circles and squares repeating in a row — and the thinking is exactly the same.

A repeating pattern is one where a small chunk says itself over and over. We call that chunk the unit (some teachers call it the core). In the pattern circle, square, circle, square, the unit is “circle, square” — just two things, repeated. In the pattern circle, circle, triangle, circle, circle, triangle, the unit is three things long. The single most useful skill in this whole topic is finding that unit. Once a child can point to the part that repeats, everything else follows.

The Australian Curriculum asks children to do three things with these patterns: recognise them, copy them, and continue them. Recognising means spotting that a row is a repeating pattern at all — and noticing that circle, square, green, yellow, seven is not one, because nothing repeats. Copying means building the same pattern yourself, unit by unit, beside the model. Continuing means looking at what is already there, working out the unit, and saying what must come next.

Continuing a pattern is really a small act of prediction, and it is where the algebra hides. To know what comes after circle, circle, triangle, circle, circle, a child has to hold the unit in mind and ask “where am I up to inside it?” That is the same reasoning that later lets a student predict the tenth term of a number pattern, or the hundredth. The row of shapes is training the mind to look for structure and use it to see ahead.

One of the deepest ideas in this topic is that a pattern is about its structure, not the particular things in it. The pattern A, B, B, A, B, B can be shown with shapes, or with two colours, or with two kinds of clap — a loud one and a soft one. They look and sound completely different, yet they are the same pattern, because the structure is the same. When a child sees that claps and shapes and colours can all carry one pattern, they have grasped something genuinely abstract — the first real taste of mathematical generalisation.

It helps to know where children most often stumble, so you can watch for it. Many will continue a pattern by simply repeating the last shape they see, rather than the whole unit — adding another circle after circle, circle, triangle instead of starting the unit again. Others copy the right shapes but lose the order, or stop the unit partway. The fix is always the same gentle question: “what is the part that repeats, and where are we up to inside it?” Saying the pattern aloud while pointing — circle, square, circle, square — turns a silent guess into clear reasoning.

None of this needs worksheets to begin. Threading coloured beads, stamping shapes, clapping a rhythm, or lining up toys all build the same sense. The five visualisations below let a child do it on the screen: mark the repeating unit, copy a pattern, predict what comes next, see one structure dressed three different ways, and set the unit on a striped scarf. Each one returns to the same quiet question — what is the part that repeats?

See it five ways

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