Year 3 Mathematics · AC9M3N02

Recognise and represent unit fractions including \frac12, \frac13, \frac14, \frac15 and \frac1{10} and their multiples in different ways

recognise and represent unit fractions including \frac12, \frac13, \frac14, \frac15 and \frac1{10} and their multiples in different ways; combine fractions with the same…

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Learning goalsSay it simply

The denominator tells how many equal parts make the whole. Fractions with the same denominator can be combined by counting equal parts.

Learning routine: Identify the whole → Check equal parts → Name one part → Count parts → Complete the whole

Success looks like

  • Identify unit fractions
  • Represent multiples
  • Use equal parts
  • Combine same denominators
  • Complete a whole

Success criteria:

  • Identify unit fractions
  • Represent multiples
  • Use equal parts
  • Combine same denominators
  • Complete a whole
Key conceptTeach from the board

Key idea: The denominator tells how many equal parts make the whole. Fractions with the same denominator can be combined by counting equal parts.

Learning routine: Identify the whole → Check equal parts → Name one part → Count parts → Complete the whole

unit fraction
a fraction with 1 as its numerator
denominator
the number showing how many equal parts make one whole
equivalent whole
all equal parts combined to make one
Clean visual examplesOne-page board

Clean one-page examples

AC9M3N02 - Recognise and represent unit fractions including \frac12, \frac13, \frac14, \frac15 and \frac1{10} and their multiples in different ways; combine fractions with the same denominator to complete the whole
Example 1

Represent three-quarters 3/4 The whole is split into 4 equal parts and 3 parts are selected. Read every label and identify what each quantity or feature represents. Describe the relationship shown by the model. Check that the conclusion answers the original question.

Example 2

Complete a whole using the same denominator + 2/5 + 3/5 = 1 Five fifths make one whole. Apply the same relationship to the new context, then justify the answer using the labels and evidence shown.

Example 3

1. Fraction strip Fold or draw strips into halves, thirds, quarters, fifths and tenths. 1/2 1/3 1/4 1/5 1/10

Example 4

2. Same-whole check Compare fraction models only after checking that the wholes are the same size. 2/3

Curriculum examplesCopied content

The content description and elaborations below show the curriculum ideas taught in this unit. Items marked as teaching context support lesson planning.

  • Content description: recognise and represent unit fractions including \frac12, \frac13, \frac14, \frac15 and \frac1{10} and their multiples in different ways; combine fractions with the same denominator to complete the whole
  • E1: recognising that unit fractions represent equal parts of a whole; for example, one-third is one of 3 equal parts of a whole
  • E2: representing unit fractions and their multiples in different ways; for example, using a Think Board to represent three-quarters using a diagram, concrete materials, a situation and fraction notation
  • E3: cutting objects such as oranges, sandwiches or playdough into halves, quarters or fifths and reassembling them to demonstrate; for example, two-halves make a whole, four-quarters make a whole, counting the fractions as they go
  • E4: sharing collections of objects, such as pop sticks or counters, between 3, 4 and 5 people and connecting division with fractions; for example, sharing between 3 people gives \frac13 of the collection to each and sharing between 5 people gives \frac15 of the collection to each

Australian, Victorian and NSW alignment retained from the previous page

RegionCurriculumClosest mapping
AustraliaAustralian Curriculum v9.0AC9M3N02 — recognise and represent unit fractions including \frac12, \frac13, \frac14, \frac15 and \frac1{10} and their multiples in different ways; combine fractions with the same denominator to complete the whole
VictoriaVictorian Curriculum F-10Year 3 Maths: closest match in Number. Use this page as a VIC-aligned practice and worksheet reference.
NSWNSW CurriculumStage 2 Maths: closest content focus for Recognise and represent unit fractions including \frac12, \frac13, \frac14, \frac15 and \frac1{10} and their multiples in different ways; combine fractions with the same denominator to complete the whole and related outcomes.
Questions and answersWith answers
What is the big idea in this topic?
The denominator tells how many equal parts make the whole. Fractions with the same denominator can be combined by counting equal parts.
What routine should I use?
Identify the whole → Check equal parts → Name one part → Count parts → Complete the whole
How do I know I am ready to move on?
You can identify unit fractions, represent multiples, use equal parts, combine same denominators, complete a whole and explain how your model or calculation supports the answer.
Practice and reviewReady for practice
  • Unequal parts called fractions — The parts must be equal.
  • Adding denominators — When parts are the same size, count numerators and keep the denominator.
  • Ignoring the whole — Fractions must refer to a clearly identified whole.

  1. Explain why 2/4 and 2/5 do not show the same amount when the wholes are equal.

  2. A student adds 2/5 + 1/5 and writes 3/10. Explain the correct reasoning.

Review hint: Follow the routine “Identify the whole → Check equal parts → Name one part → Count parts → Complete the whole” and use the worked model to check whether your answer is reasonable.

Curriculum alignmentStart here

The denominator tells how many equal parts make the whole. Fractions with the same denominator can be combined by counting equal parts.

Learning routine: Identify the whole → Check equal parts → Name one part → Count parts → Complete the whole

Success looks like

  • Identify unit fractions
  • Represent multiples
  • Use equal parts
  • Combine same denominators
  • Complete a whole

Success criteria:

  • Identify unit fractions
  • Represent multiples
  • Use equal parts
  • Combine same denominators
  • Complete a whole
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