• Understand negative numbers as positions on a number line; order, add and subtract positive and negative integers in context.
  • Use simple tests of divisibility.
  • Recognise the first few triangular numbers, squares of numbers to at least 12 ´ 12 and the corresponding roots.
  • Generate terms of a simple sequence given a rule.
  • Generate sequences from practical contexts and describe the general term in simple cases.


  • Add, subtract, multiply and divide integers.
  • Recognise and use multiples, factors (divisors), common factor, highest common factor, lowest common multiple and primes; find the prime factor decomposition of a number (e.g. 8000 = 26 ´ 53).
  • Use squares, positive and negative square roots, cubes and cube roots, and index notation for small positive integer powers.
  • Generate and describe integer sequences.
  • Generate terms of a linear sequence using term-to-term and position-to-term definitions of the sequence, on paper and using a spreadsheet or graphical calculator.
  • Begin to use linear expressions to describe the nth term of an arithmetic sequence, justifying its form by referring to the activity or practical context from which it was generated.


  • Use the prime factor decomposition of a number.
  • Use ICT to estimate square roots and cube roots.
  • Use index notation for integer powers and simple instances of the index laws.

Key Vocabulary:

  • sequence, term, nth term, consecutive, predict, rule, generate, continue, finite, infinite, ascending, descending, symbol, expression, algebra, integer, index, factors, multiples, square root, cube root, HCF, LCM.

Suggested Lesson Outcomes:



Teaching & Learning Resources:

Negative Numbers Resources
Counting On Resources
Sequences Resources
Linear Sequences Resources
Mapping Resources
nth Term Resources
Powers Resources
Multiples Resources
Factors Resources
PFD Resources
Estimating Roots Resources