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Tessellations and Fractions
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Tessellations and Fractions
A community art festival needs a repeating tile design. Solve the fraction clues, then plan a tessellation with no gaps or overlaps. Show your working where needed.
Read the festival brief
The tile wall has 24 equal-sized tiles. Xavier colours 1/3 of them teal, 1/4 of them gold, and leaves the rest white. The tiles repeat edge-to-edge across the wall.
1.Which statement best describes a tessellation?
- A pattern of shapes with gaps between them
- A pattern of shapes that covers a surface without gaps or overlaps
- A pile of shapes of different sizes
- A pattern made only from circles
2.Which of these regular shapes can tessellate on their own? Select every correct answer: equilateral triangles, squares, regular hexagons, and regular pentagons.
3.Xavier has 24 tiles. Find 1/3 of 24 tiles. Show how you work it out.
4.Find 1/4 of the 24 tiles. How many are gold?
5.How many tiles are left white after the teal and gold tiles are coloured?
6.What fraction of all 24 tiles are white? Write the fraction and simplify it.
7.The artist changes the plan: 1/6 of the 24 tiles will be purple. How many tiles is that?
8.Compare 1/3 and 1/4 of the same 24 tiles. Which amount is greater, and by how many tiles?
9.A rectangular sample panel has 16 square tiles. If 3/8 of them are orange, how many orange tiles are there?
10.Explain why regular pentagons cannot cover a flat surface by themselves without gaps or overlaps. (A regular pentagon has interior angles of 108°.)
11.Design a repeating tessellation using squares, equilateral triangles or regular hexagons. Draw at least 12 tiles, then shade exactly 1/2 of them blue and 1/4 of them yellow. How many tiles should remain unshaded?
Draw at least 12 tiles. Use repeating shapes that fit without gaps or overlaps. Shade 1/2 blue and 1/4 yellow.
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