Patterns in Mathematics

Number sequences and the shapes behind them: odd, triangular, square and cube numbers, and counting matchsticks in growing patterns.

Key ideas

• Odd numbers: 1, 3, 5, 7, … Even numbers: 2, 4, 6, 8, …
• Triangular numbers: 1, 3, 6, 10, 15, … Each adds one more than the last addition.
• Square numbers: 1, 4, 9, 16, 25, … They can be drawn as dots in a square.
• Adding the odd numbers in order gives the square numbers: 1 + 3 + 5 + 7 = 16.
• Two triangular numbers in a row add up to a square number: 6 + 10 = 16.
• In a growing pattern, count what the first shape needs and what each new shape adds.

Remember

Watch out

• Counting the shared stick twice in matchstick patterns.
• Mixing up triangular numbers (1, 3, 6, 10) and square numbers (1, 4, 9, 16).
• Multiplying by n instead of n − 1 for the shapes after the first.

Worked example