Comparing fractions (age 9+)

MathematicsFractionsAges 9–10

Compare and order fractions with different numerators and denominators by creating common denominators/numerators or comparing to a benchmark such as 1/2; justify conclusions with visual models

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Teaching Table

Set out your lesson

Compare and order fractions using shared units or a half benchmark, with same-whole visual justification.

Activity

Compare 2/7 with 5/7 and explain the role of the shared denominator. If uncertain, revisit mt_HnKbuCliNS; if common denominators are uncertain, use mt_ebPelt-qAl. This activity check is inferred, not a change to canonical edges. Source availability is not learner mastery.

Policy

Check learner readiness directly; prerequisite availability is not attainment.

Instructions

Screen or supplied sheets, pencil and scrap paper are sufficient; no printer, cutting or purchase is required. Read Setup and Show first; use Together with help, then put worked pages, matching cards and adult keys aside for Try. All story quantities are fictional: no cooking, eating, cutting, buying or collection of personal data. Draw any needed counters; no small objects are required. Read text aloud or let the learner point, draw or explain orally. Adult scribing is supported mathematical work, not independent handwriting. Record any hints actually used; never invent a response.

Teaching Procedure

Read the worked model aloud. Ask the learner to identify the whole and equal-part unit. In Together, let them attempt before offering the listed hint. Ask why a method preserves value. If the readiness skill is uncertain, pause and return to the named prerequisite; do not drill unsupported errors. Use fresh Try contexts without the key; after the attempt compare the method as well as the answer.

Record actual responses, access mode and assistance; never invent observations or infer mastery.

Use the complete materials on screen or print only the current sheet. Keep adult guidance out of learner view. Retain an earlier model only when the current step supplies it as context.

Teaching limits and safe use

These are finite task opportunities, not proof of mastery. Record what was attempted and what support was used.

These finite examples do not establish mastery, age suitability or teaching efficacy. Oral and scribed work can show mathematical reasoning but not independent handwriting. Canonical ages and clauses are preserved; actual readiness must be checked. Comparing fractions of two lunches gives proportions; comparing actual amounts eaten additionally needs equal-sized lunches. That assumption is stated in Together.

Record actual responses, access mode and assistance; never invent observations or infer mastery.

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Compare and order fractions using shared units or a half benchmark, with same-whole visual justification.

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Check understanding

Compare 3/8 and 5/12 by finding a common denominator of 24
Order 2/3, 3/5, and 7/10 from smallest to largest
Use the benchmark 1/2 to decide that 5/8 > 3/7

“If your child has eaten 2/3 of their lunch and a friend has eaten 3/4 of theirs, can they work out who's eaten more — by finding a common way to compare the fractions?”

Curriculum record

Type: Procedural
Subject: Mathematics
Domain: Fractions
Age range: Ages 9–10