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MathematicsFractionsAges 10–13

Adding Fractions (Unlike Denominators)

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

Lesson

Set out your lesson

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

Before teaching

Use this short check, then start teaching.

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.

Printer, credit, and teaching notes

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.

Use the complete materials on screen or print only the current sheet. Keep adult guidance out of learner view.

Next: Show

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

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

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Learning resources

Extra practice links — they do not replace Gakuva’s teaching approach.

Illustrative Mathematics · Practice link — not the full lesson

Mixed Numbers with Unlike Denominators

Open practice (new tab)
Before you open · source notes

Mixed numbers with unlike denominators support adding fractions. Not every multiplication of fractions.

Free, no sign-in. A teacher solution is on the same page, so use the student view with your child.

Before you open

Ask the learner to add two mixed numbers with different denominators and show the common-denominator step.

Opening this link does not save learning or assess mastery.

Source, access and review notes

Public Illustrative Mathematics task page. The .html address responds HTTP 308 to this URL. An anonymous GET of this URL on 2026-11-12 returned HTTP 200 with no login or payment prompt. Where a teacher solution is present, it is on the same page as the student task; this check did not find a separate locked student view. An adult can use the student view section and should not read a solution aloud. Advertising was not observed in the fetched HTML text; that is not a browser, device, or ad-free guarantee. This is a paper or discussion task, not an automatically marked interactive game. Opening the link does not save practice or assess mastery. Diagrams on the page use missing or filename-only alt text, so they are not an accessible image equivalent. Accessibility still depends on an adult describing the picture.

Illustrative Mathematics. “Mixed Numbers with Unlike Denominators.” Licensed CC BY-NC-SA 4.0. External task; Gakuva does not copy, host, embed, or redistribute it.

CC BY-NC-SA 4.0 — link only

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 10–13

Standards

acara-v9:AC9M6N05ccss-math:5.NF.1the-ontario-curriculum-mathematics-2020:ON-MATH-2020-G6-B2.5the-ontario-curriculum-mathematics-2020:ON-MATH-2020-G7-B2.5uk-nc-2013:Ma6/2.3c