Grandmother's Quilt — Tiling, Patterns, and Shapes
Grandmothers often sew quilts by joining many small pieces of cloth of different shapes. This chapter explores how shapes can fit together without gaps or overlaps — a concept called tiling or tessellation.
What is Tiling (Tessellation)?
When shapes are arranged to cover a flat surface completely, with no gaps and no overlaps, we say they tile the surface. Squares, rectangles, equilateral triangles, and regular hexagons can tile a flat surface.
Patterns in a Quilt
A quilt is made of a repeating pattern of shapes. The smallest section of the pattern that repeats is called the unit block or tile.
Working with Fractions of a Shape
- A quilt square may be cut diagonally to make triangles, or cut into 4 equal parts.
- Cutting a square diagonally gives 2 equal right-angled triangles, each = 1/2 the square.
- Cutting into 4 equal small squares gives pieces each = 1/4 of the original square.
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A quilt block is made of 2 triangles and 1 small square. If the small square has area 4 sq cm and each triangle = 4 sq cm, what is the total area of one block?
Total = 4 + 4 + 4 = 12 sq cm
A quilt row has 6 identical blocks each 10 cm wide. How long is the row?
Length = 6 x 10 = 60 cm
A square quilt block of side 8 cm is cut diagonally. What is the area of each triangle?
Area of square = 64 sq cm. Each triangle = 64 / 2 = 32 sq cm
A quilt uses 3 colours in the ratio 2:1:1. If there are 40 blocks in total, how many are of each colour?
Colour 1: 40 x 2/4 = 20 blocks. Colours 2 and 3: 10 each.
Can regular pentagons tile a flat surface? No — regular pentagons leave gaps, so they cannot tessellate by themselves.
Common mistakes
- Assuming any shape can tile — regular pentagons and circles cannot.
- Forgetting that the area of a triangle cut from a square is half the square's area.
Summary
Tiling means covering a surface with shapes and no gaps. Quilts show beautiful repeating patterns using squares, triangles, and rectangles. Understanding fractions helps calculate how much cloth is needed.