Working with Decimal Numbers

Students learn how to use place value to add, subtract, multiply and divide with decimal numbers using the column method.  As learning progresses they learn how to round to a given accuracy and use multiplication to solve a range of real life problems.

This unit takes place in , and follows on from place value.

Working with Decimal Numbers Lessons

Prerequisite Knowledge
  • Multiply multi-digit numbers up to 4 digits by a two-digit whole number using the formal written method of long multiplication
  • Divide numbers up to 4 digits by a two-digit whole number using the formal written method of long division, and interpret remainders as whole number remainders, fractions, or by rounding, as appropriate for the context
  • Solve problems involving addition, subtraction, multiplication and division
  • Multiply one-digit numbers with up to two decimal places by whole numbers
  • Use written division methods in cases where the answer has up to two decimal places

Key Concepts
  • Students should have a good understanding of the place value table to add and subtract with decimal numbers.
  • When multiplying with decimal numbers students should be able to use a range of range of written methods.
  • Estimations should be made when dividing and multiplying with decimals.
  • When rounding to a decimal place the number is rounded up if it is exactly midway between two numbers.

Working mathematically

Develop fluency

  • Consolidate their numerical and mathematical capability from key stage 2 and extend their understanding of the number system and place value to include decimals

Reason mathematically

  • Extend their understanding of the number system; make connections between number relationships

Solve problems

  • Develop their mathematical knowledge, in part through solving problems and evaluating the outcomes, including multi-step problems
  • Develop their use of formal mathematical knowledge to interpret and solve problems, including in financial mathematics

Subject Content


  • Understand and use place value for decimals, measures and integers of any size
  • Order positive and negative integers, decimals and fractions; use the number line as a model for ordering of the real numbers; use the symbols =, ≠, <, >, ≤, ≥

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