Working with Negative Numbers

Students learn how to compare and order negative numbers uisng a number line and the place value table.  As learning progresses they move from using the number line to add and subtract with negatives to using written methods to perform multiplication and division.

This unit takes place in Year 7 Term 3 and follows on from multiples, factors, primes and squares.

Working with Negative Numbers Lessons
Problem Solving Lessons

Prerequisite Knowledge
  • Use negative numbers in context, and calculate intervals across zero
  • Using the number line, pupils use, add and subtract positive and negative integers for measures such as temperature.
  • Interpret negative numbers in context, count forwards and backwards with positive and negative whole numbers, including through zero
Key Concepts
  • A negative sign represents a change in direction on a number line.
  • Using number lines can help students with negative number calculations, especially addition and subtraction.
  • A thermometer is helpful when comparing negative and positive numbers.
  • Students should understand multiplication and division with negatives as an extension of addition and subtraction.
Working mathematically

Develop fluency

  • Consolidate their numerical and mathematical capability from key stage 2 and extend their understanding of the number system.
  • Substitute values in expressions, rearrange and simplify expressions, and solve equations

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
Subject Content


  • order positive and negative integers, decimals and fractions; use the number line as a model for ordering of the real numbers; use the symbols =, ≠, <, >, ≤, ≥
  • use the four operations, including formal written methods, applied to integers, decimals, proper and improper fractions, and mixed numbers, all both positive and negative

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