AC9M5N10: Create 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

Students write precise algorithms that test divisibility or generate number sets, trace inputs through decisions, use digital tools for repeated cases and distinguish observed patterns from proven rules.

An algorithm needs ordered steps, complete decision branches and a defined output for every valid input.

Stopping at the square root avoids retesting reversed factor pairs, but every recorded factor below the root must be paired with n ÷ d.

A table or program can reveal patterns quickly. Test counterexamples and use number properties before stating a generalisation.

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

Success looks like

• Represent the problem
• Choose an efficient strategy
• Calculate accurately
• Interpret the context
• Estimate or use an inverse to verify

algorithm

finite ordered instructions for a task

decision branch

different next steps determined by a condition

debugging

finding and correcting an error or ambiguity

Content description: create 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.

• E1: creating algorithms that use multiplication and division facts to determine if a number is a multiple or factor of another number; for example, using a flow chart that determines whether numbers are factors or multiples of other numbers using branching, such as yes/no decisions
• E2: identifying lowest common multiples and highest common factors of pairs or triples of natural numbers; for example, the lowest common multiple of {6, 9} is 18, and the highest common factor is 3; the lowest common multiple of {3, 4, 5} is 60 and the highest common factor is one
• E3: using the “fill down” function of a spreadsheet and a multiplication formula to generate a sequence of numbers that represent the multiples of any number you enter into the cell; describing and explaining the emerging patterns

Core idea: An algorithm needs ordered steps, complete decision branches and a defined output for every valid input.

Remember

• Represent the problem
• Choose an efficient strategy
• Calculate accurately
• Interpret the context
• Estimate or use an inverse to verify

Important questions

• Trace a factor algorithm for 24. Explain using the model or evidence above.
• Write a stopping condition. Explain using the model or evidence above.
• Debug a missing no branch. Explain using the model or evidence above.
• Describe one divisibility pattern. Explain using the model or evidence above.
• Test a counterexample. 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.

• One decision branch missing — Define what happens for both yes and no outcomes.
• Loop never stops — Include a clear stopping condition.
• Pattern from small sample claimed as proof — Test more cases and use reasoning.
• Digital result hides procedure — Trace at least one input manually.

Curriculum equivalents for And use algorithms involving a sequence of steps and decisions...

Mapped skill: create 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

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