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

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

Students should be comfortable reading and representing whole numbers, using place value, and explaining simple addition, subtraction or equal-group relationships from earlier years. Begin with a short concrete or visual recall task before moving to Unit Fractions and Multiples.

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

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.

• 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. Which description means one-third?

   • 1 of 3 equal parts
   • 3 of 1 part
   • 1 of 3 unequal pieces
   • 3 whole objects

2. Complete the fraction statement.

   Prompt: □ fifths make one whole.

3. Which fraction completes 3/4 to make one whole?

   • 1/4
   • 3/4
   • 1/3
   • 4/3

4. Draw or describe a model that shows 7/10.

5. Match the fraction to its description.

   Match: 2/3 • 4/5 • 3/4 ↔ 3 of 4 equal parts • 2 of 3 equal parts • 4 of 5 equal parts

6. Complete the whole.

   Prompt: 2/5 + □/5 = 1

1. Create two different fraction combinations with denominator 10 that each make one whole.

2. Design a fraction strip puzzle using halves, quarters and tenths, and explain how a student can check the parts are equal.

Explain the reasoning, not only the final answer.

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.

• I can identify unit fractions.
• I can represent multiples.
• I can use equal parts.
• I can combine same denominators.
• I can complete a whole.

Quick check: Show one-third of a strip. • How many fifths make a whole? • What fraction completes 3/4 to make 1?

Read the topic guide and use the teacher slide for instruction. Students can then use the worksheet for written work, open Practice for supported feedback, or take the Test when they are ready.

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

• Australian Curriculum Version 9.0 — ACARA
• Victorian Curriculum — VCAA
• NSW Curriculum — NESA

Official curriculum sites are the source of record.

• AC9M3N01 — Numbers Beyond 10 000
• AC9M3N03 — Add and Subtract with Place Value
• All Year 3 Mathematics topics

Curriculum equivalents for And represent unit fractions including \frac12, \frac13, \frac14, \frac15 and...

Mapped skill: 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

These references identify matching or closely related learning. Curriculum sequence, terminology and depth vary, so teachers should use the mapped skill and lesson difficulty to confirm suitability.

Australian Curriculum v9.0 is the canonical source for this SkillrHub lesson. Victoria and NSW entries name the closest published state codes or outcomes; international entries are planning references rather than claims of identical curricula.