Patterns and sequences
📖 In short
Red, blue, red, blue… What color comes next? 2, 4, 6, 8… What number comes next? These are patterns: things that repeat or change by a rule. When we discover the rule we can tell what comes next, and that's one of the best games in math.
🤩 Did you know?
- A chessboard has 64 squares, and if we doubled the grains of wheat on each square we'd need more than 18 billion billion grains.
- The square numbers 1, 4, 9, 16, 25 are made by arranging dots in squares.
- The triangular numbers 1, 3, 6, 10, 15 are made by arranging dots in triangles, like pool balls.
- Music is patterns too: a rhythm that repeats and a tune that comes back.
🔎 Find out more
🌟 Repeating patterns
On a necklace: one red bead then two blue beads, then repeat. In the week: Saturday, then Sunday… then Saturday comes round again. Rugs and zellige tiles are full of repeating patterns.
🔍 Growing patterns
2, 4, 6, 8: we add 2 each time. 5, 10, 15, 20: we add 5. These are “arithmetic sequences”. They can also go down: 50, 40, 30… we subtract 10.
💡 Doubling patterns
1, 2, 4, 8, 16: we multiply by 2 each time. This pattern grows really fast! The story goes that the inventor of chess asked for one grain of wheat on the first square, two on the second, four on the third… and all the wheat in the world wasn't enough!
🎯 How do we find the rule?
We compare each number with the one before: how much did it go up? Down? Did it double? Then we check the rule works for all the numbers, and then we carry on.
🧮 Worked examples
- 3, 6, 9, 12, □We add 3 each time, so the hidden number is 15.
- 40, 35, 30, □We subtract 5 each time, so the hidden number is 25.
- 2, 4, 8, 16, □We multiply by 2 each time, so the hidden number is 32.
📚 Key words
- Pattern
- Something that repeats or changes by a fixed rule
- Sequence
- Numbers in order that follow a rule
- Rule
- What we do to get from one number to the next
🧪 Try it at home
Make a necklace of colored pasta with a pattern you invent (for example: red, yellow, yellow). Then ask someone to work out your rule and finish the necklace.
🧩 Test yourself
1 What comes next: 10, 20, 30, 40, ?
2 What is the rule for the sequence 1, 2, 4, 8?
3 What comes next: 25, 20, 15, ?