• Order decimals.
  • Add and subtract fractions by writing them with a common denominator; calculate fractions of quantities (fraction answers); multiply and divide an integer by a fraction.
  • Interpret percentage as the operator ‘so many hundredths of’; express one given number as a percentage of another.
  • Reduce a ratio to its simplest form, including a ratio expressed in different units; divide a quantity into two or more parts in a given ratio; use the unitary method to solve simple word problems involving ratio and direct proportion.
  • Recall known facts, including fraction to decimal conversions.
  • Round positive numbers to any given power of 10 and decimals to the nearest whole number, 1 or 2 decimal places.


  • Use efficient methods to add, subtract, multiply and divide fractions, interpreting division as a multiplicative inverse; cancel common factors before multiplying or dividing.
  • Recognise when fractions or percentages are needed to compare proportions; solve problems involving percentage changes.
  • Use proportional reasoning to solve a problem, choosing the correct numbers to take as 100%, or as a whole; compare two ratios; interpret and use ratio in a range of contexts, including solving word problems.
  • Understand the effects of multiplying and dividing by numbers between 0 and 1; use the laws of arithmetic and inverse operations.
  • Understand the order of precedence and effect of powers.
  • Use known facts to derive unknown facts; extend mental methods of calculation, working with decimals, fractions, percentages, factors, powers and roots; solve word problems mentally.
  • Make and justify estimates and approximations of calculations.
  • Check results using appropriate methods.


  • Understand and use proportionality and calculate the result of any proportional change using only multiplicative methods; understand the implications of enlargement for area and volume.
  • Recognise and use reciprocals.
  • Estimate calculations by rounding numbers to one significant figure and multiplying or dividing mentally.

Key Vocabulary:

  • Arithmetic: add, subtract, divide, multiply;
  • Fractions: FDPRP, equivalence, numerator, denominator , simplify, cancel, ratio, proportion; LCM
  • Percentage calculations: cost price, selling price, interest, compound interest); ratio: (unitary, (3:4), proportional to (  ), proportionality

Suggested Lesson Outcomes:



Teaching & Learning Resources:

Fractions Resources
Percentages Resources
Number Facts Resources
Written Methods Resources
Mental Methods Resources
Estimating Resources
Ratio Resources
Proportion Resources