Math // Fractions

Comparing fractions (age 7+)

Solve problems involving counting in tenths, fractions of quantities, equivalence, fraction addition/subtraction, and fraction comparison

Ages
7 to 8
Type
Thinking skill
Builds on
3 topics
Leads to
0 topics
Standards
1 code

Quick check

If a bag of 20 sweets is shared equally among 5 friends, can the learner work out what fraction each person gets — and how many sweets that is?

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.
  • Solve a word problem requiring finding a fraction of a quantity
  • Solve a problem that requires comparing or ordering fractions
  • Choose and apply appropriate fraction knowledge to a multi-step problem

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

3 topics
  • Simple Fraction SumsRequired

    Fractions // Ages 7 to 8

    Fraction problems require addition/subtraction of fractions

  • Unit fractionsRequired

    Fractions // Ages 7 to 8

    Fraction problems require finding fractions of quantities

  • Comparing fractionsHelpful

    Fractions // Ages 7 to 8

    Some problems require comparing fractions

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Comparing fractions (age 7+)

Ages 7 to 8 // Thinking skill

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

Capstone for early fractions (ages 7-8): given a word problem, the child must recognise WHICH fraction idea it calls for (finding a fraction of a quantity, comparing/ordering, equivalence, or adding/subtracting), choose a method, carry it out, and judge whether the answer is reasonable. The object of learning is the disposition of a strategic problem-solver — sense-making before calculating, monitoring progress, and checking plausibility — developed through rich, varied, non-routine problems, worked examples that model strategy SELECTION (not just execution), and talk that makes reasoning audible. Recognition-before-calculation is the core skill; key-word matching ('altogether' → add) is the central trap to dismantle.

Common misconceptions

  • Key-word matching: latches onto a surface word ('altogether', 'left') and applies the associated operation regardless of the problem's meaning
  • Applies the most recently taught procedure to every problem regardless of what it asks
  • Calculates without a plan and never checks whether the answer is plausible
  • Cannot start a problem unless the operation is explicitly stated ('but it doesn't tell me to divide')

Useful representations

  • Bar / strip models to represent the quantities and relationships in a word problem before choosing an operation
  • A visible problem-solving frame (understand → plan → do → check) the child fills in
  • Double number line for fraction-of and comparison problems
  • Recording that separates the CHOICE of strategy from its execution (e.g. 'this is a fraction-of problem because...')

Teaching practices

  • Teach strategy selection explicitly: present mixed problem sets where children must first decide 'is this a fraction-of, a compare, an equivalence, or an add/subtract problem?' before doing any arithmetic — the recognition step is the skill.
  • Use worked and partially-worked examples that model the PLANNING and monitoring, not just the answer (Polya / Schoenfeld): understand the problem, choose a strategy, carry it out, look back and check.
  • Insist on a plausibility / looking-back check every time ('a fraction of 20 can't be more than 20'; 'the larger share should have the answer we expect') to build self-monitoring.
  • Keep contexts and surface features varied so children generalise the underlying structure rather than pattern-matching key words ('altogether' → add is a trap).
  • Make reasoning audible: use talk moves (revoicing, 'why did you choose that?', 'does that answer make sense?') so strategic thinking is surfaced, discussed, and named rather than assumed.
  • Include problems with no single stated operation and multi-step problems, so children practise imposing structure themselves.

Activities to try

  1. 1

    Solve it WITH a mentor who never gives the method

    Why it works: Recognising what a problem is really asking — and checking whether an answer is plausible — is the skill, not the arithmetic. The habit becomes owned when the child hears themselves catch a key-word trap and reason from the situation's structure instead.

    1. Work through a mixed bag of fraction word problems with a partner or in-role mentor (a teacher, another child, or a Socratic tutor character) who reads each problem aloud.
    2. Before doing any arithmetic, say out loud what KIND of problem this is — find-a-fraction-of, compare/order, equivalence, or add/subtract — and HOW you can tell from the situation.
    3. Talk through a plan (what will you do first, and why) before calculating.
    4. When the mentor deliberately offers a tempting key word ('it says altogether, so we add?'), decide whether that word really fits the situation or whether the problem is actually about something else (e.g. finding 1/4 of a set).
    5. After getting an answer, check it makes sense ('could 3/4 of 12 be more than 12?') every single time.
  2. 2

    Sort-then-model workspace: tag the problem, build a model, then answer

    Why it works: Externalising the plan-then-do structure — tag, model, then calculate — forces the recognition step and makes the situation's structure (not a key word) the basis for choosing an operation.

    1. For each word problem, first TAG it by type: fraction-of, compare, equivalence, or add/subtract.
    2. Build a bar/strip model — or a double number line for fraction-of and comparison problems — of the situation to show the quantities and relationships BEFORE choosing an operation.
    3. Use the model structure to decide what to do, then calculate.
    4. Pass a 'does this make sense?' check before submitting your answer.
  3. 3

    Mixed problem set that discourages key-word matching

    Why it works: Across varied surface features, the underlying structure determines the method; options that reward key-word matching or last-procedure-applied reveal when a child is pattern-matching instead of reasoning.

    1. Work a mixed set of varied fraction word problems, first categorising each by type.
    2. For problems presented as multiple choice, pick the answer, then check whether your choice came from the situation's structure or from a surface word.
    3. Where possible, write or say why the chosen type fits the situation, not just which answer you picked.

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
Ma/KS2/Y3/F/7

Math // Fractions

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