Year 6 Mathematics · AC9M6A03

Algorithms, Decisions and Emerging Patterns

Create, trace, debug and generalise number-generating processes

Ready to project and teach

Learning goalsSay it simply

Learning goal

Students write complete algorithms with inputs, ordered operations, decisions, loops and stopping conditions, then analyse output sets and test generalisations.

Success criteria

  • I can represent or identify the concept.
  • I can explain the underlying relationship.
  • I can select an appropriate strategy or feature.
  • I can apply it in a new context.
  • I can justify and verify the response.

Teaching routine

  1. Represent
  2. Reason
  3. Calculate
  4. Interpret
  5. Verify
Curriculum focus: create and use algorithms involving a sequence of steps and decisions that use rules to generate sets of numbers; identify, interpret and explain emerging patterns
Key conceptTeach from the board

Trace an even–odd decision algorithm

Use the visual model first. Ask students to identify the quantities, structure or conditions before calculating or explaining.

1Inputn from 1 to 12
2DecisionIs n even?
3Even branchoutput 3n
4Odd branchoutput 3n + 1
5Recordplace output in table
6Analysecompare parity and differences

Every possible input needs a defined path. Output patterns depend on both the arithmetic rule and which inputs follow each branch.

Debug and use loops

Connect the central relationship to a new context, then verify the conclusion with a second representation, estimate, inverse operation or reasonableness check.

problemrepairno ‘no’ branchdefine action for false conditionloop never stopsadd stopping conditionstep order ambiguousnumber instructions and define operationspattern from 3 outputstest more inputs and seek reasoningdigital result onlytrace sample inputs manually

A program or spreadsheet can generate many outputs, but explanation requires identifying why the pattern emerges.

Clean visual examplesOne-page board

Clean one-page examples

AC9M6A03 - Algorithms, Decisions and Emerging Patterns
Example 1

problem repair no ‘no’ branch define action for false condition loop never stops add stopping condition step order ambiguous number instructions and define operations pattern from 3 outputs test more inputs and seek reasoning digital result only trace sample inputs manually

Example 2

: using an algorithm to create extended number sequences involving rational numbers, using a rule and digital tools, explaining any emerging patterns

Example 3

: designing an algorithm to model operations, using the concept of input and output, describing and explaining relationships and any emerging patterns; for example, using function machines to model operations and recognising and comparing additive and multiplicative relationships

Example 4

: designing an algorithm or writing a simple program to generate a sequence of numbers based on the user’s input and a chosen operation, discussing any emerging patterns; for example, generating a sequence of numbers and comparing how quickly the sequences are growing in comparison to each other using the rule adding 2 to the input number compared to multiplying the input number by 2

Curriculum examplesCopied content

AC9M6A03: create and use algorithms involving a sequence of steps and decisions that use rules to generate sets of numbers; identify, interpret and explain emerging patterns

  • E1: using an algorithm to create extended number sequences involving rational numbers, using a rule and digital tools, explaining any emerging patterns
  • E2: designing an algorithm to model operations, using the concept of input and output, describing and explaining relationships and any emerging patterns; for example, using function machines to model operations and recognising and comparing additive and multiplicative relationships
  • E3: designing an algorithm or writing a simple program to generate a sequence of numbers based on the user’s input and a chosen operation, discussing any emerging patterns; for example, generating a sequence of numbers and comparing how quickly the sequences are growing in comparison to each other using the rule adding 2 to the input number compared to multiplying the input number by 2

Use the central and application models above to connect each elaboration to the same underlying concept.

Questions and answersWith answers

Check understanding

  • Trace inputs 1–6.
  • Add a missing branch.
  • Write a stopping condition.
  • Describe output parity.
  • Test a conjecture.

Evidence of mastery

  • Represent or identify the concept
  • Explain the underlying relationship
  • Select an appropriate strategy or feature
  • Apply it in a new context
  • Justify and verify the response

Decision: continue when students can explain the model, apply it to a new example and justify their check. Otherwise return to the central model and reduce the numerical or representational load.

Practice and reviewReady for practice
Only the yes branch definedInclude every outcome.
Order of operations unspecifiedUse exact language and brackets.
Loop has no stopping conditionEnsure termination.
Output pattern described without input ruleConnect pattern to algorithm structure.
Curriculum alignmentStart here

Learning goal

Students write complete algorithms with inputs, ordered operations, decisions, loops and stopping conditions, then analyse output sets and test generalisations.

Success criteria

  • I can represent or identify the concept.
  • I can explain the underlying relationship.
  • I can select an appropriate strategy or feature.
  • I can apply it in a new context.
  • I can justify and verify the response.

Teaching routine

  1. Represent
  2. Reason
  3. Calculate
  4. Interpret
  5. Verify
Curriculum focus: create and use algorithms involving a sequence of steps and decisions that use rules to generate sets of numbers; identify, interpret and explain emerging patterns
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