Build and annotate the model
Represent equivalent fractions on a common number line and label the important parts, quantities or choices.
Learning goals
Learning goal
Students rename fractions with common denominators, use benchmarks and place proper, improper and mixed forms accurately on one continuous number line.
Success criteria
- I can represent or identify the concept.
- I can explain the underlying relationship.
- I can select an appropriate strategy or feature.
- I can apply it in a new context.
- I can justify and verify the response.
Teaching routine
- Represent
- Reason
- Calculate
- Interpret
- Verify
Curriculum focus: apply knowledge of equivalence to compare, order and represent common fractions including halves, thirds and quarters on the same number line and justify their order
Key concept
Compare 2/3, 3/4 and 5/6
Use the visual model first. Ask students to identify the quantities, structure or conditions before calculating or explaining.
2/3 = 8/12
3/4 = 9/12
5/6 = 10/12
A common denominator creates equal-sized parts, so numerators can be compared meaningfully. Equivalent forms occupy the same point.
Worked examples
Locate fractions greater than one
Connect the central relationship to a new context, then verify the conclusion with a second representation, estimate, inverse operation or reasonableness check.
1/23/415/43/21 3/4
02
Partition each whole into equal intervals and preserve the denominator across whole-number boundaries.
Curriculum elaborations explicitly taught
AC9M6N03: apply knowledge of equivalence to compare, order and represent common fractions including halves, thirds and quarters on the same number line and justify their order
- E1: applying factors and multiples to fraction denominators, such as halves with quarters, eighths and twelfths, and thirds with sixths, ninths and twelfths to determine equivalent representations of fractions in order to make comparisons
- E2: representing fractions on the same number line, paying attention to relative position, and using this to explain relationships between denominators
- E3: explaining equivalence and order between fractions using number lines, drawings and models
- E4: comparing and ordering fractions by placing cards on a string line across the room and referring to benchmark fractions to justify their position; for example, \frac58 is greater than \frac12 can be written as \frac58>\frac12, because half of 8 is 4; \frac16 is less than \frac14, because 6 > 4 and can be written \frac16 < \frac14
Use the central and application models above to connect each elaboration to the same underlying concept.
Common misconceptions
Larger denominator means larger valueFor the same numerator, more parts means smaller parts.
Different wholes comparedFractions must refer to equal-sized wholes.
Improper fraction placed below oneCompare numerator with denominator first.
Number-line intervals drawn unequallyEqual numerical steps require equal spacing.
Classroom activities
Compare and reason
Use the application model to compare two cases, explain the relationship and identify a likely error.
Transfer and verify
Apply the idea in an unfamiliar context and use a second method, evidence source or text feature to check it.
Revision Notes and quick mastery check
Check understanding
- Order 2/3, 3/4 and 5/6.
- Show 3/4 = 9/12.
- Locate 5/4.
- Compare 7/8 and 5/6.
- Use 1/2 as a benchmark.
Evidence of mastery
- Represent or identify the concept
- Explain the underlying relationship
- Select an appropriate strategy or feature
- Apply it in a new context
- Justify and verify the response
Decision: continue when students can explain the model, apply it to a new example and justify their check. Otherwise return to the central model and reduce the numerical or representational load.
Curriculum wording and references
Australian Curriculum v9.0
AC9M6N03: apply knowledge of equivalence to compare, order and represent common fractions including halves, thirds and quarters on the same number line and justify their order
The Australian Curriculum code and wording are exact. International teachers can use the underlying mathematical concept while matching the lesson to their local grade or year outcomes.
Resources and next steps
Teacher Slides
Project the fixed, branded four-page teaching sequence.
Open Classroom ViewHomework
Use the printable activity for written practice.
Open HomeworkPractice and Test
Use supported Practice first, then the separate Test when ready.
Open PracticeOpen Test
🎥 Optional Video Lesson
The SkillrHub lesson remains the primary learning resource. This optional video reinforces the explanation; you can complete the lesson and practice without watching.
Before you watch:
- Pause after each worked example.
- Try the examples yourself.
- Return to the SkillrHub lesson before continuing.
Recommended: Comparing Fractions
Math Antics — Compare fractions using equivalent amounts before placing them on a shared number line.
As you watch: Why must the fractions describe the same whole before you compare them?
Load video player Loads YouTube in this lesson. See the video notice below.
Try it: Place 1/2, 2/3 and 3/4 on one number line. Explain their order using twelfths.
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Curriculum equivalents: Victoria, NSW and international
Curriculum equivalents for Apply knowledge of equivalence to compare, order and represent common...
Mapped skill: apply knowledge of equivalence to compare, order and represent common fractions including halves, thirds and quarters on the same number line and justify their order
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.
| Region | Curriculum framework | Closest level or code |
|---|---|---|
| Australia | Australian Curriculum v9.0 | AC9M6N03 · Year 6 |
| Victoria | Victorian Curriculum F–10 Version 2.0 — Mathematics | VC2M6N03 · Level 6 |
| New South Wales | NSW Mathematics K–10 Syllabus (2022) | MA3-RQF-01 + MA3-RQF-02 · Stage 3 |
| United States (USA) | Common Core State Standards for Mathematics | Grade 6 |
| Canada (Ontario) | Ontario Curriculum — Mathematics | Grade 6 |
| United Kingdom (England) | National Curriculum in England — Mathematics | Year 7, Key Stage 3 |
| India | NCERT / CBSE — Mathematics | Class 6 |
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.
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Topic reference: AC9M6N03 — Equivalent Fractions on a Common Number Line
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