AC9M3N07: Follow and create algorithms involving a sequence of steps and decisions to investigate numbers; describe any emerging patterns

An algorithm is an ordered set of instructions. Decisions such as even or odd can change the next step, and recording outputs helps reveal patterns.

Learning routine: Start value → Follow step → Make decision → Repeat → Record pattern

Success looks like

• Follow steps
• Use decisions
• Repeat accurately
• Create algorithms
• Describe patterns

Success criteria:

• Follow steps
• Use decisions
• Repeat accurately
• Create algorithms
• Describe patterns

Students should be comfortable reading and representing whole numbers, using place value, and explaining simple addition, subtraction or equal-group relationships from earlier years. Begin with a short concrete or visual recall task before moving to Number Algorithms and Patterns.

Key idea: An algorithm is an ordered set of instructions. Decisions such as even or odd can change the next step, and recording outputs helps reveal patterns.

Learning routine: Start value → Follow step → Make decision → Repeat → Record pattern

algorithm

an ordered set of steps and decisions

decision

a choice that changes the next step

pattern

a regularity that can be noticed and described

What is the big idea in this topic?

An algorithm is an ordered set of instructions. Decisions such as even or odd can change the next step, and recording outputs helps reveal patterns.

What routine should I use?

Start value → Follow step → Make decision → Repeat → Record pattern

How do I know I am ready to move on?

You can follow steps, use decisions, repeat accurately, create algorithms, describe patterns and explain how your model or calculation supports the answer.

• Changing the order — Algorithms must be followed in the stated sequence.
• Decision checked once — Recheck the decision whenever the algorithm repeats.
• Pattern claimed from one input — Test several inputs.

1. Start at 5, add 3, then double. What is the output?

   • 16
   • 13
   • 10
   • 11

2. Complete the algorithm.

   Prompt: Start 12 → divide by 3 → add 5 → output □.

3. Why can +2 then ×4 differ from ×4 then +2?

   • The order of steps changes the result
   • Addition never works
   • Multiplication has no effect
   • Both always give the same result

4. Follow this algorithm for input 7: if odd, add 1; then divide by 2.

5. Match each input to the output for the rule ×3 + 1.

   Match: 2 • 4 • 6 ↔ 19 • 7 • 13

6. Complete the decision.

   Prompt: If the number is even, divide by 2; if it is odd, add □ to make it even.

1. Create an algorithm with a decision that eventually reaches 1 for several starting numbers. Record and discuss the pattern.

2. Design two algorithms that give the same output for input 5 but different outputs for another input.

Explain the reasoning, not only the final answer.

1. Create a three-step number algorithm and test it with inputs 2 and 5.

2. A student follows ×2 then +3 as +3 then ×2. Use input 4 to explain the error.

Review hint: Follow the routine “Start value → Follow step → Make decision → Repeat → Record pattern” and use the worked model to check whether your answer is reasonable.

• I can follow steps.
• I can use decisions.
• I can repeat accurately.
• I can create algorithms.
• I can describe patterns.

Quick check: Follow: start 5, add 3, double. • Why does order matter? • Create an even/odd decision.

Read the topic guide and use the teacher slide for instruction. Students can then use the worksheet for written work, open Practice for supported feedback, or take the Test when they are ready.

The content description and elaborations below show the curriculum ideas taught in this unit. Items marked as teaching context support lesson planning.

• Content description: follow and create algorithms involving a sequence of steps and decisions to investigate numbers; describe any emerging patterns
• E1: following or creating an algorithm to generate number patterns formed by doubling and halving using technology to assist where appropriate; identifying and describing emerging patterns
• E2: following or creating an algorithm that determines whether a given number is a multiple of 2, 5 or 10, identifying and discussing emerging patterns
• E3: creating an algorithm as a set of instructions that a classmate can follow to generate multiples of 3 using the rule “To multiply by 3 you double the number and add on one more of the number”; for example, for 3 threes you double 3 and add on 3 to get 9, for 3 fours you double 4 and add one more 4 to get 12 ...
• E4: creating a sorting algorithm that will sort a collection of 5 cent and 10 cent coins and providing the total value of the collection by applying knowledge of multiples of 5 and 10

Australian, Victorian and NSW alignment retained from the previous page

• Australian Curriculum Version 9.0 — ACARA
• Victorian Curriculum — VCAA
• NSW Curriculum — NESA

Official curriculum sites are the source of record.

• AC9M3N06 — Mathematical Modelling in Practical Problems
• AC9M3P01 — Chance in Everyday Events
• All Year 3 Mathematics topics

Curriculum equivalents for Follow and create algorithms involving a sequence of steps and...

Mapped skill: follow and create algorithms involving a sequence of steps and decisions to investigate numbers; describe any 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.