• Recognise multiples up to 10 ´ 10; know simple tests of divisibility.
  • Identify factors of two-digit numbers.
  • Consolidate mental methods:
    • find a difference by counting up;
    • add or subtract a multiple of 10 then adjust.
    • Add and subtract mentally pairs of two-digit numbers.
  • Approximate first and use informal pencil and paper methods to EXTENSION addition and subtraction.
  • Extend written methods to:
    • ThHTU ´ U and U.t ´ U;
    • TU ´ TU;
    • HTU ÷ U.
  • Divide £.p by a two-digit number to give £.p.
  • Round up or down after division, depending on context.


  • Recognise and use multiples, factors (divisors), common factor, highest common factor and lowest common multiple in simple cases, and primes (less than 100); use simple tests of divisibility.
  • Consolidate the rapid recall of number facts, including positive integer complements to 100 and multiplication facts to 10 ´ 10, and quickly derive associated division facts.
  • Consolidate and extend mental methods to include decimals, fractions and percentages, accompanied where appropriate by suitable jottings; solve simple word problems mentally.
  • Make and justify estimates and approximations of calculations.
  • Use standard column procedures to add and subtract whole numbers and decimals with up to two places.
  • Multiply and divide three-digit by two-digit whole numbers; extend to multiplying and dividing decimals with one or two places by single-digit whole numbers.
  • Check a result by considering whether it is of the right order of magnitude and by working the problem backwards.
  • Carry out calculations with more than one step using brackets and the memory; use the square root and sign change keys.
  • Interpret the display of a calculator in different contexts (decimals, percentages).
  • Calculate simple fractions of quantities and measurements (whole-number answers); multiply a fraction by an integer.
  • Recognise the equivalence of percentages, fractions and decimals; calculate simple percentages and use percentages to compare simple proportions.
  • Break a complex calculation into simpler steps, choosing and using appropriate and efficient operations, methods and resources, including ICT.


  • Find the prime factor decomposition of a number.
  • Recall known facts, including fraction to decimal conversions; use known facts to derive unknown facts, including products such as 0.7 and 6, and 0.03 and 8.
  • Extend mental calculations to squares and square roots, cubes and cube roots.
  • Multiply and divide integers and decimals, including by decimals such as 0.6 and. 0.06; understand where to position the decimal point by considering equivalent calculations.
  • Calculate fractions of quantities and measurements (fraction answers); multiply and divide an integer by a fraction.

Key Vocabulary:

  • multiple, common multiple, LCM, factor, common factor, HCF, divisor, divisible, divisibility, prime, prime factor, factorise, multiply, divide, add, subtract, product, sum, fraction, decimal, percentage, simplify, equivalent, root, square, cube, integer.

Suggested Lesson Outcomes:



Teaching & Learning Resources:

Place Value Resources
Decimals Resources
Negative Numbers Resources
Number Facts Resources
Estimating Resources
Using Calculators Resources
Fractions Resources
Decimals Resources
Mental Methods Resources
Equivalent Fractions Resources
Fraction Arithmetic Resources
Percentages Resources
FDP Resources
Recurring Decimal Resources
Fraction of Amount Resources