Pattern & symmetry
Pattern and symmetry
Patterns can be made by adding or taking away the same amount each time. Some patterns also have lines of symmetry.
Extending a pattern
To extend a pattern, you keep adding the same amount each time. For example, adding 2 triangles each time gives 2, 4, 6 triangles — these are multiples of 2.
The constant
The amount you add (or take away) each time is called the constant. In the pattern 3, 6, 9, 12 the constant is 3, because you add 3 every step.
Shortening a pattern
A pattern can also get smaller. If you take away the same amount each time, the pattern gets shorter. Starting from 16 and taking away 4 each time gives 16, 12, 8, 4.
Patterns and symmetry
Patterns can be made using symmetry. A symmetrical pattern has a line of symmetry — sometimes a vertical line, a horizontal line, or both.
Worked examples
Extend by adding 2 each time
- Start with 2 triangles.
- Add 2 more each time: 2, then 4, then 6.
Answer: The pattern is 2, 4, 6 — the constant is 2.
Extend by adding 3 each time
- Start with 3 circles and add 3 each time.
- 3 + 3 = 6, 6 + 3 = 9, 9 + 3 = 12.
Answer: The next number after 9 is 12; the constant is 3.
Shorten by taking away 4
- Start with 16 squares.
- Take away 4 each time: 16, 12, 8, 4.
Answer: The pattern is 16, 12, 8, 4 — the constant is 4.
A symmetrical pattern
- Make a pattern of shapes.
- Check if one side is a mirror image of the other.
Answer: If both sides match along a line, the pattern is symmetrical.
Where you see this in real life
- Tiles on a floor that repeat the same shapes.
- Beads on a necklace in a repeating order of colours.
- Wallpaper with a pattern that repeats.
- Counting steps as you climb, going up in the same amount each time.
Key words
- Pattern
- Shapes or numbers that follow a rule and repeat or grow.
- Constant
- The same amount added or taken away each time in a pattern.
- Extend
- To make a pattern longer by continuing it.
- Shorten
- To make a pattern smaller by taking away each time.
- Multiple
- A number you reach by counting up in equal steps, like 2, 4, 6.
- Symmetry
- When one side of a pattern is a mirror image of the other.