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Maths

Fractions on a Number Line

Overview

Using the number line as a visual model, students develop an intuitive sense of the relative sizes of fractions — countering the common misconception that larger denominators mean larger fractions.

Learning Objective
Students place unit fractions on a number line from 0 to 1, understand that the larger the denominator the smaller the fraction, and order fractions using a number line as a reference.

Resources needed

  • Number lines (drawn or printed, from 0 to 1)
  • Fraction cards (1/2, 1/3, 1/4, 1/5, 1/6, 1/8, 1/10)

Lesson stages

0 / 7 done
  1. 1 Draw a line from 0 to 1. 'Halfway between 0 and 1 is...?' (1/2). Mark it. 'What fraction is exactly halfway between 0 and 1/2?' (1/4). 'And halfway between 1/2 and 1?' (3/4). Build up the quarters.
  2. 2 Divide the 0-to-1 line into three equal sections. Mark 1/3 and 2/3. 'Which is bigger — 1/3 or 1/4?' Students predict, then mark both on the same number line to compare visually. (1/3 is to the right of 1/4 — it is bigger.)
  3. 3 Mark 1/2, 1/3, 1/4, 1/5, 1/6, 1/8, 1/10 on a single number line. 'What do you notice as the denominator gets bigger?' (The fraction gets smaller — it is closer to 0.) Discuss why: 'If you split a pizza into more slices, each slice is smaller.'
  4. 4 Students are given six fraction cards and must order them from smallest to largest by placing them on their number line. Check: does the order match the denominator size for unit fractions?
  5. 5 'Name a fraction between 1/4 and 1/2.' Students suggest (e.g. 1/3). Verify by marking it. 'Is 1/3 really between 1/4 and 1/2?' (Yes — check positions.) Challenge: find a fraction between 1/3 and 1/2.
  6. 6 Show that 2/4 and 1/2 land on the same point. '2/4 = 1/2 — they are equivalent fractions.' Also 2/6 = 1/3. Students find one more pair of equivalent fractions using their number line.
  7. 7 On a blank 0-to-1 number line, students mark 1/2, 1/4, 3/4, and one fraction of their choice. They write: '___ is between ___ and ___.'

Tap a step to mark it as done.

Variations

  • Extend to number lines from 0 to 2 including improper fractions and mixed numbers
  • Compare non-unit fractions (3/4 vs 2/3)
  • Use a human number line — students stand in order holding fraction cards
More information

Display: numerator, denominator, unit fraction (numerator = 1), equivalent. Use: 'The denominator tells us how many equal parts. The bigger the denominator, the smaller each part.'

Provide pre-drawn number lines with some fractions already marked. Focus on halves and quarters only for those needing support. Use physical fraction strips alongside the number line.

Do students correctly place fractions to the right (larger) or left (smaller) of benchmarks? Do they understand that 1/8 < 1/4? Can they identify equivalent fractions from the number line?

Draw number lines on plain paper. Fraction cards replaced by writing fractions on scraps of paper or using the number line and marking directly.

Students commonly say 1/8 > 1/4 because 8 > 4. The number line directly challenges this — use it explicitly to show the smaller fraction is closer to zero.

Activity details
Primary Medium 25 minutes 5 minutes prep Pairs, Whole Class Indoor
Topics
Fractions Number Line Ordering Equivalence