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

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.

• 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.

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

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

Australian Curriculum Version 9.0

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