MathematicsFractionsAges 9–12

Comparing fractions (age 9+)

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

Lesson

Set out your lesson

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

Before teaching

Use this short check, then start teaching.

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.

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. 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.

Share teaching feedback

Continue learning

Share and support

Family records and proof options

Keep a record of your learning

Save photos, notes, and attendance. Export a proof packet for compliance or portfolio reviews.

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

Using Benchmarks to Compare Fractions

Open practice(new tab)

Before you open · source notes

Fractions are compared using benchmarks such as 0, 1/2, and 1. Use it for benchmark comparisons, not every common-denominator rewrite.

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

Before you open

Ask whether a fraction is closer to 0, 1/2, or 1, then compare two fractions with that reasoning.

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 2026-11-11 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. “Using Benchmarks to Compare Fractions.” 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

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 9–12

Standards

acara-v9:AC9M5N03acara-v9:AC9M6N03ccss-math:4.NF.2the-ontario-curriculum-mathematics-2020:ON-MATH-2020-G4-B1.5uk-nc-2013:Ma5/2.4a

Curriculum