How Children Understand Tessellations With Art
Look closely at a honeycomb, a tiled bathroom floor, or a checkerboard — every one of them is covered edge to edge with repeating shapes and not a single gap in sight. That is a tessellation, and it turns out to be one of the most satisfying math concepts for children to explore with a crayon.
How Art Reveals a Child's Understanding of Tessellations
A tessellation is a pattern made of one or more shapes that fit together perfectly on a flat surface, covering it completely with no gaps and no overlaps. Certain shapes tessellate beautifully on their own: squares, equilateral triangles, and regular hexagons all tile a surface without leaving any empty space, which is exactly why hexagons show up naturally in honeycombs. Other shapes, like regular pentagons, cannot tessellate alone — there's always an awkward gap left over, no matter how they're arranged.
When children draw and color tessellating patterns, they are directly testing this idea: does the shape fit snugly against its neighbors, or does it leave gaps? Discovering which shapes work and which don't through hands-on drawing builds a much deeper understanding than simply being told the rule.
A Simple Activity to Try
- Grid tessellation — draw a grid of squares or triangles and color them in a repeating pattern to see how neatly they tile the page.
- Hexagon honeycomb — draw a cluster of hexagons fitting together, just like a honeycomb, and color each one differently.
- Try drawing regular pentagons next to each other and see the gaps that appear, comparing the result to a hexagon tessellation.
- Tessellations grow naturally out of repeating patterns — revisit our pattern drawing activities as a warm-up.
Tips for Parents and Teachers
- Start with squares or triangles on graph paper, since their straight, equal sides make tessellating easy to see and draw.
- Let children test different shapes and discover through trial and error which ones tessellate and which leave gaps.
- Introduce the artist M.C. Escher's tessellation artwork as inspiration for older children interested in more creative, animal-shaped tessellations.
- Use color to highlight the repeating unit within a tessellation, making the underlying structure easier to spot.
Frequently Asked Questions
Which shapes tessellate on their own?
Squares, equilateral triangles, and regular hexagons are the three regular shapes that can tessellate a flat surface entirely on their own, without needing to be combined with any other shape.
Why don't regular pentagons tessellate?
The angles inside a regular pentagon don't divide evenly around a point the way squares, triangles, and hexagons do, which always leaves small gaps when pentagons are placed edge to edge.
Is tessellation art or math?
It's genuinely both. Tessellations rely on precise geometric properties like angle and side length, but they also produce visually striking patterns, making them a natural bridge between art class and math class.
Conclusion
Tessellations let children discover a real geometric rule simply by drawing, coloring, and noticing which shapes fit together perfectly. Grid paper and a few crayons are really all it takes to get started.