Working with Fractions

In working with fractions students learn how to compare fractions and mixed numbers with different denominators using equivalences.  They progress on from this by adding and subtracting fractions using visual and written methods.

This unit takes place in  Year 7 Term 4, and is followed by multiplying and dividing with fractions in Year 8.

Working with Fractions Lessons
Prerequisite Knowledge
  • Compare and order fractions whose denominators are all multiples of the same number
  • Identify, name and write equivalent fractions of a given fraction, represented visually, including tenths and hundredths
  • Recognise mixed numbers and improper fractions and convert from one form to the other and write mathematical statements > 1 as a mixed number
  • Add and subtract fractions with the same denominator and denominators that are multiples of the same number
  • Use common factors to simplify fractions; use common multiples to express fractions in the same denomination
  • Compare and order fractions, including fractions > 1
Key Concepts
  • Equivalent fractions are found by multiplying the numerator and denominator by the same number or term. Students often benefit having a visual representation back up the written method.
  • To convert between mixed numbers and top heavy fractions students often benefit from drawing diagrams to back up their written methods.
  • To simplify a fraction the numerator and denominator are divided by their highest common factor.
  • When comparing fractions less able students benefit from using the fraction wall. More able students should use equivalent fractions as the written method.
  • Similar to comparing fractions when performing addition and subtraction students can use a fraction wall to visualise the increased or decreased amount.
  • The lowest common multiple is used to make the denominators equal when adding and subtracting fractions.
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 and fractions.

Reason mathematically

  • Extend their understanding of the number system; make connections between number relationships, and their algebraic and graphical representations

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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