Numbers hide beautiful patterns. Read a little, then play. Clear all six games!
What it is
A sequence is a list of numbers that follows a rule. Counting numbers go 1, 2, 3, 4. Even numbers go 2, 4, 6, 8. Odd numbers go 1, 3, 5, 7.
Why it works
Once you spot the rule, like add 2 each time, you can carry a sequence on forever, because the same step repeats again and again.
Why it matters
Patterns are the very heart of mathematics. Spotting them lets you predict what comes next, in numbers, in music and in nature.
A few examples
5, 10, 15, 20 adds 5 each time. 1, 3, 5, 7 are the odd numbers. 3, 6, 9, 12 are multiples of 3.
What it is
Triangular numbers are 1, 3, 6, 10, 15, ... You get them by stacking dots into a triangle, adding one more dot to each new row.
Why it works
Each triangular number is the one before plus the next counting number, because you add a whole new row of dots. So 1, then 1 + 2 = 3, then 3 + 3 = 6, then 6 + 4 = 10.
Why it matters
They show how adding up the counting numbers builds a neat triangle, your first taste of how numbers and shapes connect.
A few examples
1, 3, 6, 10, 15, 21. The 4th triangular number is 10, since 1 + 2 + 3 + 4 = 10.
What it is
Square numbers are 1, 4, 9, 16, 25, ... You get them by arranging dots into a perfect square, the same number of rows as columns.
Why it works
A square number is a number times itself: 3 rows of 3 dots is 3 × 3 = 9. That is why we write it as 3².
Why it matters
Squares turn up everywhere, in area, in tiles and in many patterns, so recognising them at a glance is very useful.
A few examples
1 = 1 × 1. 4 = 2 × 2. 9 = 3 × 3. 16 = 4 × 4. 25 = 5 × 5.
What it is
If you add up the odd numbers in order, you always get a square number. 1 = 1, 1 + 3 = 4, 1 + 3 + 5 = 9, 1 + 3 + 5 + 7 = 16.
Why it works
Each odd number adds an L shaped layer of dots around a square, turning it into the next bigger square. So the first n odd numbers make n × n dots.
Why it matters
It is a lovely surprise: two very different patterns, the odd numbers and the square numbers, turn out to be secretly linked.
A few examples
1 + 3 + 5 = 9 = 3². 1 + 3 + 5 + 7 + 9 = 25 = 5².
What it is
Virahanka numbers, also called Fibonacci numbers, are 1, 2, 3, 5, 8, 13, 21, ... Each number is the sum of the two before it.
Why it works
The rule is simple: add the last two numbers to get the next. 2 + 3 = 5, 3 + 5 = 8, 5 + 8 = 13, and so on for ever.
Why it matters
First written about by the Indian scholar Virahanka, these numbers appear in the petals of flowers and the spirals of shells.
A few examples
1, 2, 3, 5, 8, 13. After 8 and 13 comes 21, because 8 + 13 = 21.
What it is
Doubling means multiplying by 2. Starting from 1 and doubling gives 1, 2, 4, 8, 16, 32, ... These are the powers of 2.
Why it works
Each number is twice the one before, so the sequence grows very fast, which is why doubling soon reaches huge numbers.
Why it matters
Doubling patterns appear in folding paper, in computers, which count in twos, and in many puzzles and games.
A few examples
1, 2, 4, 8, 16, 32, 64. Fold a paper 10 times and it would be 2¹⁰ = 1024 layers.
Have a go on paper first, then tap to see the clear steps.
Q1. What comes next in the pattern: 2, 4, 6, 8, ?
Q2. Find the 5th triangular number.
Q3. Is 49 a square number?
Q4. What is 1 + 3 + 5 + 7?
Q5. Continue the Virahanka pattern: 1, 2, 3, 5, 8, ?
Q6. Continue by doubling: 1, 2, 4, 8, ?