Patterns
Number Patterns
A number pattern follows a rule. The rule can be to add (2, 4, 6, 8 is +2), subtract (20, 15, 10 is −5) or multiply (1, 2, 4, 8 is ×2). Find the rule first, then continue the pattern.
Example 1: Find the rule and next number: 5, 10, 15, 20, ___
The rule is +5, so the next number is 25.
Example 2: Find the rule and next number: 1, 2, 4, 8, ___
The rule is ×2, so the next number is 16.
Quick recap
- Patterns follow a rule: add, subtract or multiply.
- Find the rule, then continue.
✓ Quick check
Continue: 100, 90, 80, ___ ?
The rule is −10, so 80 − 10 = 70.
Continue: 2, 6, 18, ___ ?
The rule is ×3, so 18 × 3 = 54.
Growing, Repeating & Shape Patterns
A repeating pattern repeats the same set, like AABB AABB. A growing pattern increases by a changing amount, like the triangular numbers 1, 3, 6, 10 (add 2, then 3, then 4). Shape patterns can grow or repeat too, and may show symmetry.
Example 1: Continue the repeating pattern: AABB AABB ___
AABB — the same block repeats.
Example 2: Continue the growing pattern: 1, 3, 6, 10, ___
Add 5 next: 10 + 5 = 15.
Quick recap
- Repeating pattern: the same block comes again.
- Growing pattern: the step changes each time.
✓ Quick check
Continue: ▲▲■ ▲▲■ ▲▲ ___ ?
After two triangles comes a square (■).
Continue the square numbers: 1, 4, 9, 16, ___ ?
These are 1×1, 2×2, 3×3, 4×4, 5×5, so the next is 25.
Magic Squares
A magic square is a grid where every row, every column and both diagonals add up to the same total, the magic sum. A 3×3 magic square using the numbers 1 to 9 has a magic sum of 15, and the centre number is 5.
Example 1: What is the magic sum of a 3×3 magic square that uses 1 to 9?
Every line adds to 15.
Example 2: A row has 8 and 1. What is the missing number if the line sums to 15?
15 − 8 − 1 = 6.
Quick recap
- Every row, column and diagonal has the same total.
- For 1 to 9, the magic sum is 15 and the centre is 5.
✓ Quick check
In a 3×3 magic square using 1 to 9, every line adds up to ___ ?
The magic sum is 15.
A row has 4 and 9. If the line sums to 15, the missing number is ___ ?
15 − 4 − 9 = 2.
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