Year 5 Mathematics · AC9M5N10

Create and use algorithms involving a sequence of steps and decisions and digital tools to experiment with factors, multiples and divisibility

create and use algorithms involving a sequence of steps and decisions and digital tools to experiment with factors, multiples and divisibility; identify, interpret and…

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Learning goalsSay it simply

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
Key conceptTeach from the board

Create a factor-testing algorithm

1Inputnatural number n
2Set divisord = 1
3DecisionDoes n ÷ d give a whole number?
4RecordIf yes, record d
5Repeatincrease d until d × d > n
6Outputall paired factors

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

  1. Read every label and identify the quantities, parts or evidence.
  2. Explain the relationship shown—not just the final answer.
  3. Check the conclusion against the original question and units.

Use digital tools to investigate patterns

Inputdivisible by 3?divisible by 6?factor count18yesyes621yesno424yesyes830yesyes8

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

Now transfer the same relationship to a new situation and justify the result with precise vocabulary.

Clean visual examplesOne-page board

Clean one-page examples

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
Example 1

Input divisible by 3? divisible by 6? factor count 18 yes yes 6 21 yes no 4 24 yes yes 8 30 yes yes 8

Example 2

Input divisible by 3? divisible by 6? factor count 18 yes yes 6 21 yes no 4 24 yes yes 8 30 yes yes 8

Example 3

Trace a factor algorithm for 24. Write a stopping condition. Debug a missing no branch. Describe one divisibility pattern.

Example 4

Create a factor-testing algorithm 1 Input natural number n 2 Set divisor d = 1 3 Decision Does n ÷ d give a whole number? 4 Record If yes, record d 5 Repeat increase d until d × d > n 6 Output all paired factors Stopping at the square root avoids retesting reversed factor pairs, but every recorded factor below the root must be paired with n ÷ d. Read every label and identify the quantities, parts or evidence. Explain the relationship shown—not just the final answer. Check the conclusion against the original question and units.

Curriculum examplesCopied content

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
Questions and answersWith answers

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.
Practice and reviewReady for practice
  • 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.

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

Curriculum alignmentStart here

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
Related resourcesKeep teaching

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Classroom sequence

Teach: algorithms are ordered instructions. Model: start at 4, double, then add 3. Ask: what changes if the steps swap? Guided try: classify a number using factor and multiple evidence. Misconception check: a remainder means a divisor did not divide evenly. Independent try: design and test a short decision algorithm.