AC9M5N03: 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

Students compare fractions by using common denominators, benchmark fractions and number-line position, including values greater than one expressed as improper fractions or mixed numerals.

Fractions can be compared when they refer to the same whole and are rewritten with common-sized parts.

Because 3/4 = 6/8, it is greater than 5/8. Scaling numerator and denominator by the same factor preserves value.

Compare whole-number parts first, then fractional parts. Use common denominators or convert mixed and improper forms when necessary.

Learning routine: Represent → Reason → Calculate → Interpret → Verify

Success looks like

• Represent the concept accurately
• Explain the place-value or number relationship
• Select an efficient strategy
• Apply it to a new context
• Verify and justify the result

related denominators

denominators connected by multiplication or common factors

benchmark fraction

familiar value such as 0, 1/2 or 1 used for comparison

mixed numeral

whole number combined with a proper fraction

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.

• E1: using pattern blocks to represent equivalent fractions; selecting one block or a combination of blocks to represent one whole, and making a design with shapes; recording the fractions to justify the total
• E2: creating a fraction wall from paper tape to model and compare a range of different fractions with related denominators; using the model to play fraction wall games
• E3: connecting a fraction wall model and a number line model of fractions to say how they are the same and how they are different; for example, explaining \frac14 on a fraction wall represents the area of one-quarter of the whole while on the number line \frac14 is identified as a point that is one-quarter of the distance between zero and one
• E4: using an understanding of factors and multiples as well as equivalence to recognise efficient methods for the location of fractions with related denominators on parallel number lines; for example, explaining on parallel number lines that \frac2{10} is located at the same position on a parallel number line as \frac15 because \frac15 is equivalent to \frac2{10}
• E5: converting between mixed numerals and improper fractions to assist with locating them on a number line

Core idea: Fractions can be compared when they refer to the same whole and are rewritten with common-sized parts.

Remember

• Represent the concept accurately
• Explain the place-value or number relationship
• Select an efficient strategy
• Apply it to a new context
• Verify and justify the result

Important questions

• Compare 3/4 and 5/8. Explain using the model or evidence above.
• Order 2/3, 3/4 and 5/6. Explain using the model or evidence above.
• Locate 1 5/8. Explain using the model or evidence above.
• Rename 9/4. Explain using the model or evidence above.
• Use 1/2 as a benchmark. Explain using the model or evidence above.

Learn from the Topic Guide and fixed Teacher Slides, complete the Practice Sheet, use Practice for supported feedback, then take the Test when ready.

Project the fixed branded slide deck one slide at a time.

• Larger denominator means larger fraction — With the same numerator, more equal parts means smaller parts.
• Numerators compared when denominators differ — First establish common-sized parts or use a benchmark.
• Mixed numeral whole part ignored — Compare whole numbers before fractional remainders.
• Different-sized wholes used — Fraction comparison assumes the same whole.

Curriculum equivalents for And order fractions with the same and related denominators including...

Mapped skill: 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

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.

Australian Curriculum Version 9.0

• AC9M5N01: Decimals Beyond Hundredths
• AC9M5N02: Factors, Multiples and Divisibility
• AC9M5N04: Percentages, Fractions and Decimals
• AC9M5N05: Adding and Subtracting Fractions
• AC9M5N06: Multiplying Larger Numbers
• AC9M5N07: Division and Interpreting Remainders