Patterns • Topic 2 of 4

Shape Patterns

A shape pattern repeats a block of shapes again and again, and the trick to solving one is to spot that block -- the pattern core. In circle, square, circle, square, circle, square the core is just 'circle, square', a two-element AB pattern, so whatever comes after the last square must start the core again with a circle. Cores come in named flavours: AB (red, blue, red, blue), ABC (star, square, circle, repeated), AAB (red, red, blue), and so on. Find the core, count where the sequence is, and the next shape falls out. The second half of this topic is symmetry, which is a pattern in space rather than in a line. A shape has reflection symmetry when one half is the mirror image of the other -- the dividing line is the line of symmetry, and a butterfly or the letters A, H and M all have one. Rotational symmetry means the shape looks unchanged after a part-turn, like a windmill with identical blades. Translation symmetry is a motif that slides along a border without turning or flipping. At the primary level the teaching aim is simply to have children identify a core, extend it, and fold paper to discover a line of symmetry -- the formal vocabulary comes later.

✅ Solved examples

1. What comes next: circle, square, circle, square, circle, ___?
The repeating core is 'circle, square' (an AB pattern). The sequence ends on a circle, so the next shape completes the core: a square.
2. Identify the core: star, moon, sun, star, moon, sun, star, moon, sun. What is the 10th shape?
The core is 'star, moon, sun' (ABC), three shapes long. Nine shapes complete three full cores, so the 10th shape begins a new core: a star.
3. A child folds a paper butterfly down the middle and the two wings match exactly. Which kind of symmetry is this?
Reflection (mirror) symmetry. The fold line is the line of symmetry, and one half is the mirror image of the other.
4. What comes next: triangle, triangle, square, triangle, triangle, square, ___?
The core is 'triangle, triangle, square' (an AAB pattern). After a completed core the next shape restarts it, so the next shape is a triangle.

✏️ Practice — try these, take hints as needed

1. What comes next: heart, diamond, heart, diamond, heart, ___?
Find the smallest repeating block.
The core is two shapes long.
diamond (core: heart, diamond)
2. Name the type of symmetry in a windmill with four identical blades that looks the same after a quarter-turn.
Nothing is folded or mirrored.
It is a turn about a centre.
Rotational symmetry
3. What is the core of: A, B, B, A, B, B, A, B, B?
Look for the block that repeats.
It is three elements long.
A, B, B (an ABB pattern)
4. A border design repeats the same flower motif sliding along a line, never turning or flipping. Which symmetry is this?
The motif only moves sideways.
No mirror, no rotation.
Translation symmetry

📝 Topic test — 8 questions

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