AC9M4N03 • Year 4 Maths
Find equivalent representations of fractions using related denominators and make connections between fractions and decimal notation.
Equivalent fractions name the same point or amount even though they use different-sized parts. Multiplying or dividing the numerator and denominator by the same factor preserves value.
Learning routine: Identify equal whole → Scale numerator and denominator → Verify model → Connect to tenths/hundredths → Compare
Each model covers the same proportion of an equal-sized whole. The number of parts changes, but the shaded amount does not.
Fractions with denominators 10 or 100 connect directly to decimal place value. For the common fractions in this table, the denominators can be multiplied to make 10 or 100. Do not assume every fraction can be written exactly using only tenths or hundredths.
Worked example: 3/5 = 6/10 = 60/100 = 0.6 = 0.60. Splitting fifths into tenths doubles both counts; splitting tenths into hundredths multiplies both counts by 10. The value stays the same.
Quick check: Is 0.04 the same as 4/10? No: 0.04 is four hundredths. Four tenths are 0.4 or 0.40.
Example: 2/3 = ?/12. Each third is divided into four smaller parts. Multiply both numbers by 4: 2/3 = 8/12. In reverse, grouping 8 selected twelfths and all 12 twelfths in fours gives 2/3.
Teacher asks: Why must both numbers change by the same factor? Student explains: The number of selected parts and the total number of parts change together; the same amount of the same whole is represented.
The blue point is 2/4 on the upper line and 3/6 on the lower line. Both points are halfway from 0 to 1, so 2/4 = 3/6 = 1/2.
Content description: find equivalent representations of fractions using related denominators and make connections between fractions and decimal notation.
The following teaching examples cover the curriculum elaborations.
Arrange 20 counters in four equal rows of five. Colour three rows. Fifteen of twenty counters are coloured, and three of four equal rows are coloured: 15/20 = 3/4. Regroup the same collection into ten pairs and identify 2/5 = 4/10 in a separate selection of eight counters.
Look for: The whole collection stays fixed while students change the equal groups. Ask students to show the selected counters, rather than only recite a rule.
Use the same cup as one whole. Half a cup can be measured as two quarter-cups or four eighth-cups: 1/2 = 2/4 = 4/8. Use water or dry counters to model the amounts without needing to read a curved water surface.
Check: How many eighth-cup measures match three quarter-cups? Six, because each quarter contains two eighths.
Fold equal paper rectangles into halves, quarters and eighths. Unfold and shade the same half: 1/2 = 2/4 = 4/8. For a second model, mark a strip into five equal parts, colour two parts, then halve every fifth. Record 2/5 = 4/10 = 0.4.
Check: The outside size and coloured region must remain unchanged; every part within one partition must be equal.
One metre is 100 centimetres. Divide a metre strip into four equal lengths: 100 ÷ 4 = 25, so 1/4 m = 25/100 m = 0.25 m = 25 cm. One tenth of a metre is 10 cm, so 1/10 m = 0.10 m = 10 cm.
Check: Three fifths of a metre are 60 cm or 0.60 m because one fifth is 20 cm.
The array shows 3 × 4 = 12. One of three equal rows contains 4 counters: 12 ÷ 3 = 4 and 1/3 of 12 is 4. One of the four columns contains 3 counters: 12 ÷ 4 = 3 and 1/4 of 12 is 3.
Teacher asks: Why can one third and one quarter of the same collection be different counts? Expected answer: Three equal groups are larger than four equal groups when the total collection is unchanged.
Build a fraction wall and identify aligned endpoints for halves, quarters, fifths, tenths and hundredths.
Start from 2/5 each time and multiply both numerator and denominator by the same number.
These are separate equivalent representations of 2/5; each calculation starts from the original fraction.
Match common fractions to decimal representations and justify using hundredths.
Core idea: Equivalent fractions name the same point or amount even though they use different-sized parts. Multiplying or dividing the numerator and denominator by the same factor preserves value.
Before this lesson: Students recognise equal parts, unit fractions and multiplication/division facts. Support: Use two identical strips and match halves with quarters before using number sentences. Core: Connect a model, related-denominator fraction and decimal for halves, quarters, fifths, tenths and hundredths. Extend within this code: Explain a missing numerator or denominator and justify a fraction such as 9/20 = 45/100 = 0.45.
Boundary: Use models and related denominators. General fraction algorithms, recurring decimals and formal fraction arithmetic are not the target here.
Use the Topic Guide, then project the Classroom View. Complete the written worksheet tasks before Practice and Test. Drawing tasks need an adult to inspect the actual work; a completion tick alone does not establish mastery.
Mastery evidence: Students keep the whole constant and can prove equivalence with a model, a related denominator or decimal place value.
Project the Classroom View and open one teaching section at a time.
Open Classroom View| Australia | Australian Curriculum v9.0 | AC9M4N03 |
| Victoria | Victorian Curriculum F–10 | Year 4 Number: fractions and decimals. |
| NSW | NSW Curriculum | Stage 2 Mathematics: fractions and decimals. |
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:
Khan Academy — See why different fraction names can represent the same amount.
As you watch: What stays the same when the same whole is divided into more equal parts?
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Try it: Draw equal-sized strips for one half and two quarters. Explain why the amounts match.
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Mapped skill: find equivalent representations of fractions using related denominators and make connections between fractions and decimal notation
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 | AC9M4N03 · Year 4 |
| Victoria | Victorian Curriculum F–10 Version 2.0 — Mathematics | VC2M4N03 · Level 4 |
| New South Wales | NSW Mathematics K–10 Syllabus (2022) | MA2-PF-01 · Stage 2 |
| United States (USA) | Common Core State Standards for Mathematics | Grade 4 |
| Canada (Ontario) | Ontario Curriculum — Mathematics | Grade 4 |
| United Kingdom (England) | National Curriculum in England — Mathematics | Year 5, Key Stage 2 |
| India | NCERT / CBSE — Mathematics | Class 4 |
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: AC9M4N03 — AC9M4N03: Equivalent fractions and decimals
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