Math // Fractions

Comparing fractions (age 10+)

Compare and order fractions including fractions greater than 1, by converting to common denominators or using benchmarks

Ages
10 to 11
Type
Method
Builds on
2 topics
Leads to
0 topics
Standards
1 code

Quick check

If the learner needs to sort 5/3, 7/4, and 2/1 in order from smallest to biggest, can they convert them to a common denominator and order them correctly?

Ask this to see whether the topic is secure.

Topic // Mastery

What mastery looks like

What a learner can do once this topic is secure.
  • Order 3/4, 7/8, 5/6, and 11/12 from smallest to largest
  • Compare 7/5 and 4/3 using common denominators
  • Place improper fractions and mixed numbers on a number line in correct order

Topic // Map

Where this fits

What to learn first and what this topic opens up, with the reason for each link. Required links come first.
  • RequiredMust come first
  • HelpfulHelps, but not essential

Before this

2 topics
  • Comparing fractions (age 9+)Required

    Fractions // Ages 9 to 10

    Comparing fractions >1 extends Y5 fraction comparison

  • Simplifying FractionsRequired

    Fractions // Ages 10 to 11

    Comparing fractions requires ability to find common denominators via simplification

You are here

Comparing fractions (age 10+)

Ages 10 to 11 // Method

Leads to

0 topics

Nothing in the catalogue builds on this topic yet. Browse Fractions

Topic // Research-informed

Teaching notes

From the Marble Skill Taxonomy. These notes have not been validated in classrooms, so treat them as a starting point for your own judgement.

The approach

Help learners (age 10–11) compare and order fractions, including fractions greater than 1, by reasoning about value rather than digit size. Core strategies: common denominators (always reliable), benchmarking to 1/2 and 1, and complement-to-1 for sets clustered just below a whole (e.g. 3/4, 7/8, 5/6, 11/12, where the gaps to 1 are 3/4 → 1/4, 7/8 → 1/8, 5/6 → 1/6, 11/12 → 1/12, so the smallest gap means the largest fraction). For fractions above 1, convert to a common denominator (7/5 = 21/15 vs 4/3 = 20/15) or to mixed numbers and place on a number line. Throughout, the discriminating goal is a justified ordering, since whole-number bias can produce a correct rank for the wrong reason on favourable sets.

Common misconceptions

  • Whole-number bias: bigger numerator and/or denominator means a bigger fraction (may land the right order for the wrong reason)
  • Compares numerators and denominators separately ('7 > 4 and 5 > 3 so 7/5 > 4/3')
  • Same-numerator lock reversed — with equal numerators, picks the bigger denominator as bigger (2/5 > 2/3)
  • Treats a fraction greater than 1 as if it were less than 1, or places it wrongly on the line
  • Compares without finding a common denominator

Useful representations

  • Number line spanning past 1 (place 7/5, 4/3 and mixed numbers)
  • Common-denominator fraction strips
  • Benchmark markers at 1/2 and 1
  • Complement-to-1 gap diagram for near-whole sets

Teaching practices

  • Choose a strategy that fits the numbers: common denominators always work; benchmark to 1/2 or 1; complement-to-1 for sets clustered near a whole
  • Recognise a fraction greater than 1 sits past 1 on the number line, and convert improper↔mixed to place and order it
  • Justify the ordering (why one is bigger), not just rank the symbols
  • Use a common denominator to make numerators directly comparable, rather than comparing tops and bottoms separately
  • Simplify or find common multiples to reach a shared denominator efficiently

Activities to try

  1. 1

    Place and order fractions on a number line, measuring each gap to 1

    Why it works: Fraction size is one quantity located on the number line, not two independent whole numbers. For a near-whole set the fraction closest to 1 is largest; fractions greater than 1 sit past 1; and a common denominator turns any comparison into a single numerator comparison.

    1. Place the set 3/4, 7/8, 5/6, 11/12 onto a number line running from 0 past 2.
    2. For each fraction, mark or measure the distance from the fraction to the '1' mark (its gap to a whole): 3/4 → 1/4, 7/8 → 1/8, 5/6 → 1/6, 11/12 → 1/12.
    3. State the order smallest to largest (3/4 < 5/6 < 7/8 < 11/12) and explain the link: the BIGGEST gap to 1 means the SMALLEST fraction, so 3/4 is smallest and 11/12 (hugging 1) is largest.
    4. Place 7/5 and 4/3 on the same line and notice both land PAST 1; convert each to a mixed number (7/5 = 1 2/5) to confirm position.
    5. Rewrite 7/5 and 4/3 over a common denominator (21/15 vs 20/15) and compare the numerators to decide which is larger.
  2. 2

    Justify the ordering, not just the rank

    Why it works: A correct ranking is not the same as a correct method; the justification is what shows genuine understanding, and the chosen strategy should fit the numbers.

    1. Order a fresh near-whole set (e.g. 2/3, 5/6, 9/10, 7/8) using the complement-to-1 method, writing each gap to 1 and explaining your reasoning.
    2. Then tackle a pair where digit size and value DISAGREE — for example 5/6 vs 7/9, where '7 > 5 and 9 > 6' wrongly suggests 7/9 is larger — and settle it by writing both over a common denominator and comparing the deciding numerators.
    3. Explain in words why comparing numerators and denominators separately is not a valid method, using the pair above as the case where it breaks down.
    4. State for each answer the strategy you chose (common denominator, benchmark, or complement-to-1) and why it fitted those numbers.
  3. 3

    Short comparison and placement checks

    Why it works: Learners can apply comparison strategies quickly and avoid common distractors (choosing 'equal', choosing 4/3 'because 4 and 3 are bigger', or choosing 2/5 because its denominator is larger).

    1. Order 3/4, 7/8, 5/6, 11/12 smallest to largest.
    2. Decide which is larger, 7/5 or 4/3, and show the common-denominator working.
    3. Decide which is larger, 2/3 or 2/5, and explain the role of the denominator.
    4. Place 7/5 on a 0–2 number line.

Topic // Standards

Curriculum standards

Codes for the curriculum statements this topic maps to. Each publisher owns its standard text.
The national curriculum in England: Key stages 1 and 2 framework document
Ma6/2.3b

Math // Fractions

More in Fractions

All 67 topics