Powers, factors and multiples

Every whole number is built from smaller pieces. In this topic you'll learn the laws that let you rearrange a calculation to make it easier, write repeated multiplication in a short way using powers, and break numbers down into their factors and primes. These ideas help you calculate quickly in your head, and they come back again with fractions and algebra.

What you'll learn

• 2.01 Number operation properties: the commutative, associative and distributive laws, and how they make mental maths easier.
• 2.02 Square numbers: what makes a number square, and how to work out squares like 12 × 12.
• 2.03 Square roots: undoing a square, and estimating square roots that aren't whole numbers.
• 2.04 Powers of whole numbers: writing repeated multiplication with a base and an index, and working out powers.
• 2.05 Powers of ten: writing numbers in expanded notation using powers of ten.
• 2.06 Factors and multiples: factor pairs, multiples, divisibility tests, and prime and composite numbers.
• 2.07 Prime factorisations: factor trees, and writing any number as a product of primes.
• Investigation: Celtic knots. Draw knot patterns on grids and discover what decides how many strands they have.
• 2.08 HCF and LCM: the highest common factor and the lowest common multiple, and the problems they solve.
• Investigation: the sieve of Eratosthenes. Find every prime number up to 100 the way people did over 2000 years ago.

Which level should I pick?

Every worksheet comes in three levels. Each one covers the same skills.

• Level 1 · Warm-up: smaller numbers and more help along the way. A good place to start.
• Level 2 · Core: the main worksheet for the lesson.
• Level 3 · Challenge: bigger numbers and harder problems, for when the Core level feels easy.

Not sure? Start with Level 2. If the first few questions feel tricky, drop to Level 1. If you finish quickly and get them right, try Level 3. Download the worksheet, print it, and write your answers in the boxes.

Practice tests

When you've finished the lessons, try the three practice tests. Each one is like the real topic test: 45 minutes, 40 marks, a section without a calculator and a section with one. Write your working under each question, then copy your final answers onto the answer sheet on the last page, just like you will in the real test.