In Lesson 6 of Patterns Everywhere, learners investigate 3D shapes, repeated structures and the ways solids can fit together in space. The lesson develops ideas from earlier work on symmetry, repetition and tessellation, but now in a three-dimensional setting.

Learners explore familiar solids, think about how surfaces and faces are arranged, and look at how repeated 3D forms can create larger structures and packing patterns.

This printable resource accompanies the free online lesson and brings the key ideas and activities together in one booklet.

This free download contains one combined PDF:

• Lesson 6 Handout & Activities — explanations, examples and activities for exploring patterns in three dimensions

Use alongside the free online lesson:

Patterns in 3D

Suitable for home education, enrichment, independent learning or exploring together with an adult.

The activities are designed for ages 7+ and allow learners to work at their own level of complexity.

Use it with the online lesson

This printable resource accompanies:

Patterns Everywhere — Lesson 6: Patterns in 3D

The online lesson brings together the ideas explored throughout the course and encourages learners to use mathematics creatively.

☕ Free to download

This resource is completely free.

If you find it useful and would like to support the creation of more free mathematics resources, you can support Sumthing Else on Ko-fi.

Lesson 6 of Patterns Everywhere

Patterns Everywhere is a six-lesson Beyond Curriculum course exploring patterns, tessellations, symmetry, transformations, patterns in art and nature, and mathematical design.

Ages 7+ · 6 lessons · No prerequisites

Look for the mathematics hiding in butterflies, leaves, buildings, pavements, artwork and everyday design.

In Lesson 5 of Patterns Everywhere,

learners become pattern detectives. They investigate how familiar mathematical ideas such as repetition, reflection, rotation, translation, tessellation and branching appear in the world around us.

The lesson also introduces an important distinction: mathematical patterns can be exact, while patterns in nature are often only approximately regular. Learners are encouraged to describe the rule they see rather than simply deciding that something “looks patterned”.

These printable resources accompany the online lesson and provide opportunities to record observations, identify pattern rules and continue exploring away from the screen.

This free download contains two separate PDF files:

• Lesson 5 Handout — key ideas, examples and vocabulary from the lesson
• Lesson 5 Activities — printable activities for investigating patterns in art, nature and design

Use it with the online lesson

This printable resource accompanies:

Patterns Everywhere — Lesson 5: Patterns in Art and Nature

The online lesson uses real-world images and visual investigations to connect mathematical ideas with the world around us.

☕ Free to download

This resource is completely free.

If you find it useful and would like to support the creation of more free mathematics resources, you can support Sumthing Else on Ko-fi.

Lesson 5 of Patterns Everywhere

Patterns Everywhere is a six-lesson Beyond Curriculum course exploring patterns, tessellations, symmetry, transformations, patterns in art and nature, and mathematical design.

Suitable for home education, enrichment, independent learning or exploring together with an adult.

Ages 7+ · 6 lessons · No prerequisites

A shape can move without changing its size or shape — but there are different ways to move it.

In Lesson 4 of Patterns Everywhere, learners explore transformations through slides, turns and flips, building intuition for translations, rotations and reflections.

They also discover that when two moves are combined, the order can matter.

In this resource

You’ll receive two printable PDFs:

Lesson 4 Handout

A guided companion to the online lesson, introducing the main transformation ideas and helping learners describe how shapes move.

Activities & Practice

A separate collection of activities for recognising, performing and combining transformations.

Learners will practise:

• recognising slides, turns and flips
• matching a shape to its transformed image
• describing a movement precisely
• identifying rotations and reflections
• combining transformations
• comparing the results of doing two moves in different orders
• creating transformation-based patterns

The activities are designed for ages 7+, with opportunities to investigate more sophisticated combinations of transformations.

Use it with the online lesson

This printable resource accompanies:

Patterns Everywhere — Lesson 4: Slide, Turn, Flip

The online lesson includes interactive transformation activities and animated examples showing why the order of moves can matter.

☕ Free to download

This resource is completely free.

If you find it useful and would like to support the creation of more free mathematics resources, you can support Sumthing Else on Ko-fi.

Lesson 4 of Patterns Everywhere

Patterns Everywhere is a six-lesson Beyond Curriculum course exploring patterns, tessellations, symmetry, transformations, patterns in art and nature, and mathematical design.

Ages 7+ · 6 lessons · No prerequisites

Symmetry appears in shapes, designs, nature and art — but how can we describe it mathematically?

In Lesson 3 of Patterns Everywhere, learners investigate reflection symmetry, search for mirror lines and explore how one half of a design determines the other.

In this resource

You’ll receive a printable PDF:

Lesson 3 Handout and Activities

A guided companion to the online lesson, helping learners identify and describe symmetrical objects and designs accompanied by an extensive collection of activities for drawing, testing and creating symmetrical patterns.

Learners will practise:

• recognising reflection symmetry
• identifying lines of symmetry
• completing symmetrical designs
• reflecting shapes across a mirror line
• deciding whether a design is symmetrical
• comparing shapes with different numbers of symmetry lines
• creating their own symmetrical designs

The activities are designed for ages 7+, with opportunities to investigate more complex symmetry for confident learners.

Use it with the online lesson

This printable resource accompanies:

Patterns Everywhere — Lesson 3: Symmetry Detectives

The online lesson includes visual investigations, interactive symmetry activities and a practical snowflake activity. The printables can be used alongside the lesson or afterwards.

☕ Free to download

This resource is completely free.

If you find it useful and would like to support the creation of more free mathematics resources, you can support Sumthing Else on Ko-fi.

Lesson 3 of Patterns Everywhere

Patterns Everywhere is a six-lesson Beyond Curriculum course exploring patterns, tessellations, symmetry, transformations, patterns in art and nature, and mathematical design.

Ages 7+ · 6 lessons · No prerequisites

Why do some shapes fit together perfectly while others leave gaps?

In Lesson 2 of Patterns Everywhere, learners investigate tessellations: repeating arrangements of shapes that cover a surface without gaps or overlaps.

They experiment with familiar shapes, look for structure in tiling patterns and begin to explain why some arrangements work.

In this resource

You’ll receive two printable PDFs:

Lesson 2 Handout

A guided companion to the online lesson, helping learners record observations, test shapes and explain what they notice.

Activities & Practice

A separate collection of activities for practising tessellations and exploring new tiling arrangements.

Learners will practise:

• recognising tessellations
• identifying gaps and overlaps
• testing whether a shape can tile
• spotting repeating units
• comparing different tiling arrangements
• explaining why some shapes tessellate
• designing their own tessellating patterns

The activities are designed for ages 7+, with opportunities to explore more deeply for older or more confident learners.

Use it with the online lesson

This printable resource accompanies:

Patterns Everywhere — Lesson 2: Can Every Shape Tile a Floor?

The online lesson includes visual investigations and interactive exploration. The printables can be used alongside the lesson or afterwards for extra practice.

☕ Free to download

This resource is completely free.

If you find it useful and would like to support the creation of more free mathematics resources, you can support Sumthing Else on Ko-fi.

Lesson 2 of Patterns Everywhere

Patterns Everywhere is a six-lesson Beyond Curriculum course exploring patterns, tessellations, symmetry, transformations, patterns in art and nature, and mathematical design.

Ages 7+ · 6 lessons · No prerequisites

Explore tessellations by cutting, turning, fitting and reasoning. The pack includes hands-on puzzles for younger learners and deeper geometric questions for older children.

Inside the pack:

• Every triangle tessellates — discover why by pairing copies into a parallelogram.
• The wonky quadrilateral puzzle — test an irregular four-sided shape.
• Regular polygon investigation — which regular shapes can meet perfectly around a point?
• Penrose kite-and-dart activity — explore a non-repeating tessellation.
• Escher-inspired tessellation activity — cut, move and transform a tile into mathematical artwork.

The pack accompanies Lesson 2: Can every shape tile a floor?

Free download.

If you’d like to support Sumthing Else: this resource is completely free, but you can help us create more lessons and printables by supporting us on Ko-fi ☕.