• Read and write positive integer powers of 10; multiply and divide integers and decimals by 0.1, 0.01.
  • Consolidate standard column procedures for addition and subtraction of integers and decimals with up to two places.
  • Use standard column procedures for multiplication and division of integers and decimals, including by decimals such as 0.6 or 0.06; understand where to position the decimal point by considering equivalent calculations.
  • Solve more complex problems by breaking them into smaller steps or tasks, choosing and using efficient techniques for calculation.


  • Extend knowledge of integer powers of 10; multiply and divide by any integer power of 10.
  • Use rounding to make estimates; round numbers to the nearest whole number or to one or two decimal places.
  • Know that a recurring decimal is an exact fraction.
  • Use standard column procedures to add and subtract integers and decimals of any size, including a mixture of large and small numbers with differing numbers of decimal places; multiply and divide by decimals, dividing by transforming to division by an integer.
  • Check results using appropriate methods.
  • Use a calculator efficiently and appropriately to perform complex calculations with numbers of any size, knowing not to round during intermediate steps of a calculation; use the constant, p and sign change keys, function keys for powers, roots and fractions, brackets and the memory.
  • Enter numbers into a calculator and interpret the display in context (negative numbers, fractions, decimals, percentages, money, metric measures, time).
  • Solve substantial problems by breaking them into simpler tasks, using a range of efficient techniques, methods and resources, including ICT; use trial and improvement where a more efficient method is not obvious.


  • Write numbers in standard form.
  • Understand upper and lower bounds; round numbers to three decimal places and a given number of significant figures.
  • Use algebraic methods to convert a recurring decimal to a fraction in simple cases.
  • Use the reciprocal key of a calculator.
  • Enter numbers in standard form into a calculator and interpret the display.

Key Vocabulary:

  • integer, positive, negative, tenths, hundredths, thousandths, estimate, less than, greater than, >, <, compare.
  • Multiply, divide, add, subtract, sum, total, difference, product, multiple, factor, prime, prime factor, prime factor decomposition, square, square number, square root, cube, cube number, cube root, powers, to the power of …, index, indices, roots, approximating, rounding off.
  • reciprocal, estimate, approximate, rounding off, product, BIDMAS, significant figures (s.f.), square, square number, square root, cube, cube number, cube root, powers, to the power of …, index, indices, roots.

Suggested Lesson Outcomes:



Teaching & Learning Resources:

4 Operations Resources
Decimals Resources
Powers Resources
Rounding Resources
Calculator Resources
Bounds Resources
Reciprocal Resources