Adding Fractions (Unlike Denominators)

MathematicsFractionsAges 10–11

Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions to produce a common denominator

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Teaching Table

Set out your lesson

Add and subtract unlike-denominator fractions, including mixed numbers, by making equal-sized parts.

Activity

Ask the learner to rename 2/3 in twelfths and subtract like-denominator fractions. If either is uncertain, return to mt_b7T-CjOYUR and mt_-V7EnqU7gG. Mixed-number conversion may need a short replay of mt_o_p-3tCxiM. Canonical ages are 10–11, not a readiness guarantee. These activity checks are inferred; source availability is not mastery.

Policy

Check learner readiness directly; prerequisite availability is not attainment.

Instructions

Use the supplied screen sheets or print only the active sheet. A pencil and scrap paper are enough; no printer, purchase, cutting, cooking, food handling or personal disclosure is required. Read Show first, then use Together with support. Put Show and adult keys aside before Try. Stories are fictional; no activity is evidence until the learner actually attempts it. Allow drawing, pointing, oral explanation or adult scribing; record the support actually used. Scribed mathematics is not independent handwriting. Pause or return to a prerequisite when needed, without treating uncertainty as failure.

Teach The Idea

Before combining fractional amounts, name the same whole and the same-sized part. A common multiple of the denominators gives a shared partition. Rename both fractions without changing their values; combine the numerators, not the denominators. Mixed numbers can be converted to improper fractions first.

Teaching Procedure

Read the Show model aloud while tracing the relevant unit. In Together, invite an attempt before giving the private hint. Ask the learner to explain why the operation fits. For Try, remove worked material and let the learner choose a representation. Discuss mistakes after recording the attempt, then retry another day if useful.

Models And Materials

Supplied fixed-unit models make partition size, equal sharing or square-area units visible. Learner diagrams are blank scaffolds or stated givens, not worked answers. Screen or paper drawing serves the purpose; no digital interactive is needed.

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.

A small set of tasks cannot establish mastery or general fluency. Try uses changed quantities and contexts but the taught operations, not an untested claim of broad transfer. Oral or scribed work does not demonstrate independent handwriting. Check actual learner readiness and observe the explanation.

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

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Add and subtract unlike-denominator fractions, including mixed numbers, by making equal-sized parts.

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Check understanding

Compute 2/3 + 5/4 by converting to twelfths: 8/12 + 15/12 = 23/12
Subtract 1 3/5 from 3 1/4 using a common denominator
Explain the strategy of finding a common denominator and verify using a visual model

“If a recipe uses 2/3 of a cup of one ingredient and 3/4 of another, can your child add those fractions together — even though the denominators are different?”

Curriculum record

Type: Procedural
Subject: Mathematics
Domain: Fractions
Age range: Ages 10–11