MathsFreePrintable

Tessellation Pattern Exploration

A free maths worksheet ready for your classroom. Open in Kuraplan to grab the print-ready PDF, customize it for your students, or generate a fresh version in seconds.

Download now

Name:Date:

Tessellation Pattern Exploration

Hana and Ari are planning a tiled floor for an aquarium viewing area. A tessellation covers a flat surface with shapes that fit together without gaps or overlaps. Use the clues below to investigate which designs will work. Show calculations where needed.

Investigate the pattern

Use angle totals and ratios to decide whether shapes can meet neatly around a point.

1.Which statement best defines a tessellation?

Shapes overlap to make a thicker pattern.
Shapes cover a surface with no gaps or overlaps.
Only one type of shape is allowed.
Shapes must be arranged in a circle.

2.At any point where tiles meet, the angles around that point must add to 360°. A regular hexagon has an interior angle of 120°. How many regular hexagons can meet at one point?

3.A regular pentagon has an interior angle of 108°. Explain why regular pentagons cannot tessellate on their own. Include the angle total and the size of any leftover gap.

4.At one vertex in a tile design, two regular hexagons and two equilateral triangles meet. Their interior angles are 120° and 60°. Calculate the angle total and decide whether the tiles fit without a gap or overlap.

5.Ari uses 18 hexagonal tiles and 12 triangular tiles in a sample panel. Write the ratio of hexagons to triangles in simplest form, then state what the ratio means.

6.Hana wants to scale up the sample panel while keeping the hexagon-to-triangle ratio unchanged. If the larger panel has 45 hexagons, how many triangles are needed?

7.A square tile has four 90° corners meeting at a point. Use a calculation to show why squares tessellate.

8.The aquarium's rectangular feature panel is 2.4 m wide and 1.8 m high. Find the ratio of width to height in simplest whole-number form.

9.True or false? A tessellation can use translations, rotations, or reflections to repeat its shapes. Explain your choice with one example of a transformation.

10.Design a small tessellation using at least two different shapes. Sketch at least 8 tiles, mark one point where the shapes meet, and write the angle calculation that shows the tiles fit there. Label one transformation used to repeat the pattern.