AC9M5N03
Official content description
compare and order fractions with the same and related denominators including mixed numerals, applying knowledge of factors and multiples; represent these fractions on a number line
What AC9M5N03 actually looks like when you teach it
By Year 5 the fraction wall should be a tool rather than a lesson, used to reason with rather than to build. Comparing fractions with related denominators means finding a common one — and the factors and multiples work from earlier in the year is exactly what makes that possible, so teach them near each other if you can. Mixed numerals are worth their own attention: converting between 7/4 and 1 3/4 is easy on a number line and unreliable as a remembered procedure. Keep the number line central.
What the class will get wrong — and what to do about it
The error
Comparing fractions by size of denominator alone — deciding 3/8 is larger than 1/2 because eighths sound like more pieces, without converting to a common denominator.
How to confront it
Require an estimate against a half before any calculation: is this fraction more or less than a half? 3/8 is less, 1/2 is exactly a half, so the answer is settled before any common denominator is found. Benchmarking to 0, 1/2 and 1 catches most errors of this kind.
Ready to put on the board
We are learning to compare and order fractions with related denominators, including mixed numerals.
- I can decide whether a fraction is more or less than a half.
- I can find a common denominator to compare two fractions.
- I can place mixed numerals on a number line.
More or less than a half
- Hand out one fraction card each — a mix of proper fractions and mixed numerals.
- Round one: stand to the left or right of the half mark. Just that, no ordering yet.
- Fix any disagreements as a class, using the benchmark rather than calculation.
- Round two: now order yourselves precisely along the line. This is where common denominators become necessary.
- Record the final order on the board and ask which comparison needed the most work — that's the one to revisit tomorrow.
Free to use in your classroom. Written for AC9M5N03, not adapted from another year level.
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The Year 5 Maths planning scaffold
A one-page planning sheet with the official achievement standard, every content description grouped by strand, and space for your assessment and week-by-week sequence. Print it and plan on paper, or use it as the skeleton for a unit.
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What Year 5 Maths students should achieve
Coverage is judged against the achievement standard — not by ticking every content description. These are the official Year 5 Maths standard sentences this code builds towards:
- They choose and use appropriate metric units to measure the attributes of length, mass and capacity, and to solve problems involving perimeter and area.
- They represent common percentages and connect them to their fraction and decimal equivalents.
- They estimate, construct and measure angles in degrees.
- Students perform and describe the results of transformations and identify any symmetries.
- Students convert between 12- and 24-hour time.
- By the end of Year 5, students use place value to write and order decimals including decimals greater than one.
The Number progression either side of AC9M5N03
A class can only meet this descriptor if they were taught the one before it. If yours hasn't, that's where the lesson starts — not here.
Taught before · Year 4
- AC9M4N01recognise and extend the application of place value to tenths and hundredths and use the conventions of decimal notation to name and represent decimals
- AC9M4N02explain and use the properties of odd and even numbers
- AC9M4N03find equivalent representations of fractions using related denominators and make connections between fractions and decimal notation
Builds towards · Year 6
- AC9M6N01recognise situations, including financial contexts, that use integers; locate and represent integers on a number line and as coordinates on the Cartesian plane
- AC9M6N02identify and describe the properties of prime, composite and square numbers and use these properties to solve problems and simplify calculations
- AC9M6N03apply knowledge of equivalence to compare, order and represent common fractions including halves, thirds and quarters on the same number line and justify their order
Other Year 5 Number codes
- AC9M5N01interpret, compare and order numbers with more than 2 decimal places, including numbers greater than one, using place value understanding; represent these on a number line
- AC9M5N010create and use algorithms involving a sequence of steps and decisions and digital tools to experiment with factors, multiples and divisibility; identify, interpret and describe emerging patterns
- AC9M5N02express natural numbers as products of their factors, recognise multiples and determine if one number is divisible by another
- AC9M5N04recognise that 100% represents the complete whole and use percentages to describe, represent and compare relative size; connect familiar percentages to their decimal and fraction equivalents
- AC9M5N05solve problems involving addition and subtraction of fractions with the same or related denominators, using different strategies
- AC9M5N06solve problems involving multiplication of larger numbers by one- or two-digit numbers, choosing efficient calculation strategies and using digital tools where appropriate; check the reasonableness of answers
- AC9M5N07solve problems involving division, choosing efficient strategies and using digital tools where appropriate; interpret any remainder according to the context and express results as a whole number, decimal or fraction
- AC9M5N08check and explain the reasonableness of solutions to problems including financial contexts using estimation strategies appropriate to the context
Content description and achievement standard © Australian Curriculum, Assessment and Reporting Authority (ACARA), Australian Curriculum Version 9, used under CC BY 4.0. TeachKoala is not affiliated with or endorsed by ACARA.