Adding and subtracting mixed numbers

MathematicsFractionsAges 9–10

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

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Teaching Table

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

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.

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.

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.

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

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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 9–10