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MathematicsFractionsAges 10–13

Simplifying Fractions

Use common factors to simplify fractions to their simplest form; use common multiples to express fractions with a common denominator

Lesson

Set out your lesson

Use common factors to simplify and common multiples to express a pair with a common denominator.

Before teaching

Use this short check, then start teaching.

Activity

Ask for common factors of 8 and 12, and common multiples of 3 and 4. If unavailable, revisit mt_FHIAv6dfhU and the vocabulary in mt_vKcxX6iNOA. Check same-factor equivalence first. 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.

Printer, credit, and teaching notes

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.

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

Next: Show

Adult extras
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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Teaching approaches

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Use common factors to simplify and common multiples to express a pair with a common denominator.

Use common factors to simplify and common multiples to express a pair with a common denominator.

Family records and proof options

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View learner plans ($12/mo per learner) See sample family archive

Learning resources

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

Illustrative Mathematics · Practice link — not the full lesson

Listing fractions in increasing size

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

Listing fractions in increasing size supports simplifying and comparing equivalent-size thinking. Not every mixed-number drill alone.

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 order the fractions and name one that can be written more simply.

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. “Listing fractions in increasing size.” 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

  • Simplify 18/24 to 3/4 by identifying the HCF of 18 and 24
  • Express 2/3 and 5/8 with a common denominator of 24
  • Explain why dividing numerator and denominator by a common factor produces an equivalent fraction
“If your child has the fraction 12/16, can they simplify it to its lowest terms — and explain what they divided the top and bottom by?”

Curriculum record

Type
Procedural
Subject
Mathematics
Domain
Fractions
Age range
Ages 10–13

Standards

the-ontario-curriculum-mathematics-2020:ON-MATH-2020-G7-B1.4uk-nc-2013:Ma6/2.3a