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 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.

 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.

 3

Symmetry detectives

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

 4

Slide, turn, flip

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

 5

Patterns in art, nature and design

Spot mathematical rules in nature and architecture, then use symmetry, transformations and tessellation to create an artwork of your own.

 6
More advanced

Patterns in 3D

Explore planes of symmetry, Platonic solids, shapes that fill space and why balls always leave gaps when packed together.

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.