AC9M5A02: Find unknown values in numerical equations involving multiplication and division using the properties of numbers and operations

Students identify the role of an unknown, use inverse operations, factor relationships and distributive properties, then substitute the solution to verify both sides of an equation.

Solving an equation means finding a value that makes the two expressions equal, not moving numbers by an unexplained rule.

The inverse operation finds the missing factor. Substitution confirms that the equality is true.

Identify whether the unknown is a factor, dividend or divisor. Multiplication can be regrouped; division order cannot be swapped casually.

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

Success looks like

• Represent accurately
• Explain the relationship
• Choose a suitable method or unit
• Apply in context
• Check and justify

equation

statement that two expressions have equal value

unknown

value to be determined

substitution

replacing a symbol with a value to test the equation

Content description: find unknown values in numerical equations involving multiplication and division using the properties of numbers and operations.

• E1: using knowledge of equivalent number sentences to form and find unknown values in numerical equations; for example, given that 3\times5=15 and 30\div2=15 then 3\times5=30\div2 therefore the solution to 3\times5=30\div\square is 2
• E2: using relational thinking, an understanding of equivalence and number properties to determine and reason about numerical equations; for example, explaining whether an equation involving equivalent multiplication number sentences is true, such as 15 ÷ 3 = 30 ÷ 6
• E3: using materials, diagrams and arrays to demonstrate that multiplication is associative and commutative but division is not; for example, using arrays to demonstrate that 2 \times 3 = 3 \times 2 but 6 ÷ 3 does not equal 3 ÷ 6; demonstrating that 2 \times 2 \times 3 = 12 and 2 \times3 \times2 = 12 and 3 \times 2 \times 2 = 12; understanding that 8 ÷ 2 ÷ 2 = (8 ÷ 2) ÷ 2 = 2 but 8 ÷ (2 ÷ 2) = 8 ÷ 1 = 8
• E4: using materials, diagrams or arrays to recognise and explain the distributive property; for example, where 4 \times 13 = 4 \times 10 + 4 \times 3
• E5: constructing equivalent number sentences involving multiplication to form a numerical equation, and applying knowledge of factors, multiples and the associative property to find unknown values in numerical equations; for example, considering 3 \times 4 = 12 and knowing 2 \times 2 = 4 then 3 \times 4 can be written as 3\times (2 \times 2) and using the associative property (3 \times 2) \times 2 so 3 \times 4 = 6 \times 2 and so 6 is the solution to 3 \times 4 = \square\times 2

Core idea: Solving an equation means finding a value that makes the two expressions equal, not moving numbers by an unexplained rule.

Remember

• Represent accurately
• Explain the relationship
• Choose a suitable method or unit
• Apply in context
• Check and justify

Important questions

• Solve 24 × □ = 1 008. Explain using the model or evidence above.
• Solve □ ÷ 18 = 35. Explain using the model or evidence above.
• Solve 1 440 ÷ □ = 24. Explain using the model or evidence above.
• Regroup 6 × □ × 5. Explain using the model or evidence above.
• Substitute and check. 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.

• Same inverse used for every unknown position — Identify factor, dividend or divisor first.
• Equals sign read as an instruction only — It states balance between expressions.
• Division reversed — a ÷ b is not generally b ÷ a.
• Solution not checked — Substitute into the original equation.

Curriculum equivalents for Find unknown values in numerical equations involving multiplication and division...

Mapped skill: find unknown values in numerical equations involving multiplication and division using the properties of numbers and operations

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
• AC9M5N03: Comparing and Ordering Fractions
• AC9M5N04: Percentages, Fractions and Decimals
• AC9M5N05: Adding and Subtracting Fractions
• AC9M5N06: Multiplying Larger Numbers