Patterns Everywhere

Beyond Curriculum · Mathematics

Tiles, Symmetry & Shapes

Look. Play. Notice. Create.

Patterns are hiding all around us — on floors, in flowers, on animals, in pictures and in the shapes we draw. In this course you’ll make patterns, hunt for symmetry, cover surfaces with shapes, slide and turn pictures, explore patterns in art and nature, and finally create a mathematical artwork of your own.

Ages 7+ 6 lessons No prerequisites
See it first. Play with it. Describe what you notice. Then learn the mathematical name.

Lessons

1

What makes a pattern?

Continue patterns, find mistakes, predict what comes next and discover that more than one rule can be happening at the same time.

Explore pattern rules →
2

Can every shape tile a floor?

Try fitting shapes together, discover gaps and overlaps, and meet the idea of a tessellation only after you’ve experimented.

Explore tessellations →
3

Symmetry detectives

Use mirror lines, complete half-images and investigate symmetry in shapes and natural objects.

Explore symmetry →
4

Slide, turn, flip

Move shapes without changing them. Older learners can optionally meet translation, rotation and reflection.

Explore transformations →
5

Patterns in art and nature

Investigate shells, crystals, plants, animal markings, mosaics and patterns in movement. Ask: what rule is creating the pattern?

Explore patterns in art & nature →
6

Design your own mathematical artwork

Choose a motif, invent a repetition rule, use symmetry or transformations, colour it and explain the mathematics behind your design.

Create mathematical art →

How to use this course

This course is designed to be explored by looking, drawing, moving things around, experimenting and talking about what you notice.

Whenever possible, try the activity before reading the mathematical vocabulary. Questions such as “What do you notice?”, “What stays the same?” and “What do you think will happen next?” are often more useful than being told the answer.

Each lesson has a core activity designed to be accessible from around age 7. Optional Go further sections offer extra depth for older or more confident learners.

There is no need to finish a whole lesson in one sitting. Stopping because you have found something interesting to investigate is a perfectly good place to stop.