MathematicsFractionsAges 9–11

Adding and subtracting mixed numbers

Add and subtract mixed numbers with like denominators, including by converting to improper fractions or using properties of operations

Lesson

Set out your lesson

Add and subtract mixed numbers with like denominators, including exchanging a whole for fractional parts.

Before teaching

Use this short check, then start teaching.

Activity

Ask for 1 2/5 as an improper fraction and 4/5 + 3/5 as a mixed number. If uncertain, use mt_o_p-3tCxiM or mt_VgOePicFYK 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. In the two-batch example, 2/5 + 3/5 reaches exactly one whole, not more. The total is four cups. A different Try example uses 3/8 + 7/8 to practise exceeding one whole; the original wording is not treated as true.

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

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Teaching approaches

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Selected Default Gakuva

Add and subtract mixed numbers with like denominators, including exchanging a whole for fractional parts.

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

Finding Common Denominators to Add

Open practice(new tab)

Before you open · source notes

Common denominators support adding and subtracting mixed numbers. 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 rename two fractions with a common denominator and add them.

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. “Finding Common Denominators to Add.” 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

Calculate 2 3/5 + 1 4/5 and express as a mixed number
Subtract 3 1/4 from 5 3/4
Solve 4 2/6 − 1 5/6 by regrouping the whole number

“If a recipe calls for 1 and 2/5 cups of oats and another batch needs 2 and 3/5 cups, can your child add them together to get the total — including converting when the fifths add up past a whole?”

Curriculum record

Type: Procedural
Subject: Mathematics
Domain: Fractions
Age range: Ages 9–11

Standards

acara-v9:AC9M5N05ccss-math:4.NF.3.c