Equivalent fractions (age 9+)

MathematicsFractionsAges 9–10

Explain why a fraction a/b is equivalent to (n×a)/(n×b) using visual models; use this principle to recognise and generate equivalent fractions, including tenths and hundredths

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Teaching Table

Set out your lesson

Explain same-factor equivalence, including tenths and hundredths, rather than only memorising a rule.

Activity

Ask for 1/3 in sixths with a same-whole sketch. If this is uncertain, use mt_FP-mjXaq3B first. Ask what the numerator and denominator count. 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.

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

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Explain same-factor equivalence, including tenths and hundredths, rather than only memorising a rule.

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Check understanding

Use a fraction strip to show 2/3 = 4/6 = 6/9
Explain that multiplying numerator and denominator by the same number gives an equivalent fraction because the size of the whole is unchanged
Generate three fractions equivalent to 3/5 and verify with diagrams

“If your child needs to make 2/3 look different without changing its value, can they multiply the top and bottom by the same number and explain why the fraction stays the same?”

Curriculum record

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