Number Play

Overview

Number Play explores patterns, puzzles and properties hidden in numbers. We investigate odd and even numbers, sequences, and clever ways numbers behave.

Key concepts

• Patterns in sequences of numbers and figures.
• Odd, even, square and triangular numbers.
• Adding consecutive odd numbers gives square numbers.
• Predicting the next term using a rule.

Important formulae

• Sum of first n odd numbers = n²
• nth triangular number = n × (n + 1) ÷ 2
• Even number = 2n; odd number = 2n + 1

Solved example

1. Find the sum of the first 5 odd numbers.
2. Use sum = n² with n = 5.
3. Sum = 5² = 25 (check: 1+3+5+7+9 = 25).

Important questions

1. What is the next term in 2, 5, 10, 17, ... ?
2. Find the 6th triangular number.
3. Is the sum of two odd numbers odd or even?
4. Write the first four square numbers.

Quick revision

Look for the rule that links the terms. Squares come from adding odd numbers, and triangular numbers come from adding counting numbers. Patterns make prediction easy.