Build and annotate the model
Represent algorithms, decisions and emerging patterns and label the important parts, quantities or choices.
Learning goals
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
- Represent
- Reason
- Calculate
- Interpret
- 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 concept
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.
Worked examples
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.
Curriculum elaborations explicitly taught
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.
Common misconceptions
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.
Classroom activities
Compare and reason
Use the application model to compare two cases, explain the relationship and identify a likely error.
Transfer and verify
Apply the idea in an unfamiliar context and use a second method, evidence source or text feature to check it.
Revision Notes and quick mastery check
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.
Curriculum wording and references
Australian Curriculum v9.0
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
The Australian Curriculum code and wording are exact. International teachers can use the underlying mathematical concept while matching the lesson to their local grade or year outcomes.
Resources and next steps
Teacher Slides
Project the fixed, branded four-page teaching sequence.
Open Classroom ViewHomework
Use the printable activity for written practice.
Open HomeworkPractice and Test
Use supported Practice first, then the separate Test when ready.
Open PracticeOpen Test
🎥 Optional Video Lesson
The SkillrHub lesson remains the primary learning resource. This optional video reinforces the explanation; you can complete the lesson and practice without watching.
Before you watch:
- Pause after each worked example.
- Try the examples yourself.
- Return to the SkillrHub lesson before continuing.
Recommended: Number Patterns
Math Antics — Recognise repeated rules before describing them as a sequence of algorithm steps.
As you watch: Which repeated action generates the next term?
Load video player Loads YouTube in this lesson. See the video notice below.
Try it: Write steps that start at 0.5, add 0.5 each time and stop when the result exceeds 4. Identify the decision and explain the resulting pattern.
Video unavailable, inaccurate or unsuitable for this year? Report a video problem to SkillrHub by email. You can continue with the written lesson and practice resources.
About these videos
Videos are curated from trusted independent educational creators and played through YouTube. Rights remain with their respective owners. Inclusion does not imply that a creator or YouTube endorses SkillrHub.
YouTube’s terms and privacy policy apply to its player. Advertising, recommendations and external links may appear, and videos may change or become unavailable. SkillrHub’s written lessons and practice resources remain available separately.
To report a content, suitability or rights concern, email skillrhublearning@gmail.com with the lesson code and video link. Please do not include personal student information.
Curriculum equivalents: Victoria, NSW and international
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 that use rules to generate sets of numbers; identify, interpret and explain 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.
| Region | Curriculum framework | Closest level or code |
|---|---|---|
| Australia | Australian Curriculum v9.0 | AC9M6A03 · Year 6 |
| Victoria | Victorian Curriculum F–10 Version 2.0 — Mathematics | VC2M6A03 · Level 6 |
| New South Wales | NSW Mathematics K–10 Syllabus (2022) | MA3-MR-02 · Stage 3 |
| United States (USA) | Common Core State Standards for Mathematics | Grade 6 |
| Canada (Ontario) | Ontario Curriculum — Mathematics | Grade 6 |
| United Kingdom (England) | National Curriculum in England — Mathematics | Year 7, Key Stage 3 |
| India | NCERT / CBSE — Mathematics | Class 6 |
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.
Help improve SkillrHub
Questions or feedback?
Ask about this lesson, suggest an improvement or report an error. Facebook opens only when you choose an option below.
Topic reference: AC9M6A03 — Algorithms, Decisions and Emerging Patterns
Privacy: Please don’t share personal student or school information. Younger students should ask a parent, guardian or teacher to post on their behalf.