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Tessellation Pattern Exploration

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Tessellation Pattern Exploration

A community art team is designing repeating tile patterns. Explore how tessellations fit together, then use ratios to plan and scale a design. Show working where useful.

Part A: How tessellations work

Use your geometry knowledge.

1.Which statement best describes a tessellation? Choose one.

Shapes overlap to create a layered picture.
Shapes cover a surface with no gaps or overlaps.
Every shape in a pattern must be a different size.
A pattern must use only one colour.

2.At a point where tiles meet, their angles must total 360°. An equilateral triangle has an interior angle of 60°. How many such triangles meet at one point?

3.True or false? A regular pentagon, whose interior angle is 108°, can tessellate on its own. Explain using the 360° angle rule.

4.Name two transformations that could help repeat tiles in a tessellation. For each, describe the movement.

Part B: Ratios in a tile design

A small prototype uses blue and gold tiles in the ratio 3:2.

5.The prototype has 15 blue tiles. If blue:gold = 3:2, how many gold tiles are needed?

6.The art team wants 35 tiles in total while keeping the blue:gold ratio at 3:2. How many of each colour will they use?

7.Count the blue and gold tiles in the layout above. Write the ratio blue:gold in simplest form. Does it match the target ratio 3:2?

8.The prototype tiles are 4 cm wide. The full-size design uses tiles 10 cm wide. What is the scale factor from prototype to full size? If the prototype pattern is 12 cm long, how long is the full-size pattern?

9.The team mixes blue and gold glaze in the ratio 3:2. They need 2.5 L of mixture. How many litres of each colour should they prepare?

10.In the space below, sketch a repeating tile arrangement that uses two shapes and has no gaps or overlaps. Label the shapes, mark one translation or rotation, and write a possible ratio of the two tile types.