Operations with Integers and Rational Numbers — AC9M8N04

• Use all four operations with integers and rational numbers.
• Explain multiplication/division sign patterns.
• Choose efficient fraction/decimal strategies.
• Apply order of operations and verify sign/magnitude.

Recall integer number lines, equivalent fractions, decimal place value, fraction operations and order of operations.

Signed operations should make sense in context and patterns. Subtracting a negative reverses a downward change: −6−(−9)=−6+9. For multiplication/division, extending patterns shows same signs produce a positive result and unlike signs a negative result.

For rational numbers, choose an efficient representation. Fractions are often best kept exact with common denominators; decimals may be convenient for measurement/money. Use commutative, associative and distributive properties where they reduce work.

Parentheses determine the base of a power: −3²=−9 because exponentiation occurs before the leading negative, while (−3)²=9.

• Two negatives always make a positive. That applies to multiplication/division; addition/subtraction require interpretation.
• Adding denominators. Fraction addition/subtraction requires equivalent denominators.
• Ignoring operation order. Multiplication/division precede addition/subtraction unless grouping changes it.
• −3²=(−3)². Brackets change the base.

1. Calculate −8+13 and −8−13.
2. Explain why (−4)(−6)=24 using a sign pattern.
3. Calculate 5/6−3/4.
4. Evaluate −2² and (−2)².

1. Calculate −17−(−5).
2. Calculate (−8)(7).
3. Calculate (−42)÷(−6).
4. Compute 2/3+5/8 exactly.
5. Compute 1.75−2.4.
6. Evaluate 6−2(−3)+4.
7. Compare −4² and (−4)² and explain.

A student claims “−1/2 is smaller in magnitude than −0.4, so it must be greater.” Diagnose the reasoning using a number line and exact decimal/fraction equivalence.

1. Why does negative×negative give positive? Extending multiplication patterns consistently requires it.
2. Why use common denominators? They express fractions in equal-sized parts before adding/subtracting.
3. When are decimals useful? In measurement/money or when a decimal result is natural.
4. How do brackets affect powers? They determine whether the negative sign is part of the base.

1. Evaluate −3+4(−2)−(−5).
   Apply multiplication before addition/subtraction.
2. Calculate 7/10−5/12 exactly.
   Use a common denominator and simplify.
3. Explain the difference between −5² and (−5)².
   Identify the base before exponentiation.

• I interpret signed operations.
• I calculate exact rational results.
• I use operation order.
• I check sign and magnitude.

Exit ticket: Why is “two negatives make a positive” an incomplete rule for −3−(−5)?

Australian Curriculum v9.0 — AC9M8N04: use the 4 operations with integers and rational numbers, choosing efficient strategies and digital tools where appropriate.

Victorian Curriculum F–10 Version 2.0 — Level 8, VC2M8N04: Exact.

NSW Mathematics K–10 Syllabus (2022) — Stage 4, MA4-INT-C-01; MA4-FRC-C-01; MAO-WM-01: Exact.

• AC9M8N03 — decimal forms
• AC9M8A01 — linear expressions

• Australian Curriculum v9.0
• Victorian Curriculum F–10 Version 2.0
• NSW Mathematics K–10 Syllabus (2022)

Curriculum equivalents for The 4 operations with integers and with rational numbers, choosing...

Mapped skill: use the 4 operations with integers and with rational numbers, choosing and using efficient strategies and digital tools where appropriate

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.