Follow and create algorithms involving a sequence of steps and decisions that use addition or multiplication to generate sets of numbers; identify and describe any emerging patterns
follow and create algorithms involving a sequence of steps and decisions that use addition or multiplication to generate sets of numbers; identify and describe any…
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Learning goalsSay it simply
An algorithm is a precise sequence of instructions. Repeating addition or multiplication rules can generate number sets, while decisions route inputs through different steps and produce patterns worth explaining.
Learning intention: I can follow, test and create number algorithms with clear steps and decisions, then describe and explain the outputs.
Learning routine: Choose the start or inputs → Follow the ordered steps → Check each decision → Record at the stated point → Test the outputs → Explain the pattern
Success looks like
Follow both decision outcomes correctly.
State when to record, repeat and stop.
Create an algorithm that another person can follow.
Use a calculator or spreadsheet to generate and check numbers.
Describe how the outputs change and connect that pattern to the rule.
Clean visual examplesOne-page board
Clean visual examples
AC9M4N09 · Models and worked thinking
Example 1
Generate a set with a decision rule
Process inputs 1 to 10 in order. Use the chart once for each input, record its output, then move to the next input. Stop after processing input 10.
The odd inputs 1,3,5,7,9 give outputs 6,8,10,12,14. The even inputs 2,4,6,8,10 give 6,12,18,24,30. Only one operation branch runs for each input. The two branches share some output values even though their inputs differ.
Teacher asks: Which path does input 4 take? Answer: It is even, so 4 × 3 = 12. Input 5 instead takes the other path, giving 5 + 5 = 10. If a learner adds after multiplying, physically cover the unused branch and trace the arrows again.
Example 2
Use an input–output table to test a rule
Each new input is one larger, so its product contains one more group of 4. Adding the same 2 to each product leaves gaps of 4 between the outputs. For input 7, the output is 7 × 4 + 2 = 30.
Check the distinction: “Multiply each input by 4” uses a new input each time. “Multiply the previous output by 4” instead keeps changing one current value and gives a different sequence.
Example 3
1. Flowchart walk
Place number cards 1 to 6 at the input. If a card is even, multiply its value by 4; otherwise add 3. Learners physically follow one branch, announce the result and return for the next card. Stop after the sixth input.
Output record: 4,8,6,16,8,24 for inputs 1,2,3,4,5,6. The different outputs are 4,6,8,16,24. Repeated outputs in the full record are valid because different inputs can reach the same value.
Example 4
2. Rule machine
Use inputs 1,2,3,4. Multiply each by 5, then add 2. The outputs are 7,12,17,22. Explain why the gap is 5, then apply the same rule to input 6 to obtain 32.
Checkpoint: Does each output equal the previous output multiplied by 5? No. The rule operates on each new input. A partner should point to the input that produced each result.
Example 5
3. Debug and improve
Compare “add 3, then double” with “double, then add 3” using input 4. The first gives (4 + 3) × 2 = 14; the second gives 4 × 2 + 3 = 11. Ordered steps matter.
Now inspect: “Start at 1; record; add 4; stop only when exactly 10 is reached.” The values 1,5,9,13 skip 10, so that stopping test is never met. Repair it by testing whether the value is at most 10 before recording. The repaired output list is 1,5,9.
Peer check: Can another learner follow every step without guessing? Check both branches, the first record and the stopping boundary. A few matching outputs alone do not uniquely establish an unstated rule.
Curriculum examplesCopied content
The official description and elaborations define this lesson. The worked expansions below show how each requirement is taught.
Content description: follow and create algorithms involving a sequence of steps and decisions that use addition or multiplication to generate sets of numbers; identify and describe any emerging patterns
E1: creating an algorithm that will generate number sequences involving multiples of one to 10 using digital tools to assist, identifying and explaining emerging patterns, recognising that number sequences can be extended indefinitely
E2: creating a basic flow chart that represents an algorithm that will generate a sequence of numbers using multiplication by a constant term; using a calculator to model and follow the algorithm, and record the sequence of numbers generated; checking results and describing any emerging patterns
E3: using a multiplication formula in a spreadsheet and the “fill down” function to generate a sequence of numbers; for example, entering the number one in the cell A1, using “fill down” to cell A100, entering the formula “ = A1*4 “ in the cell B1 and using the “fill down” function to generate a sequence of 100 numbers; describing emerging patterns
E1 expansion: generate multiples and explain continuation
Choose a multiplier from 1 to 10. To generate its positive multiples, start at that multiplier and repeatedly add the same amount. With 6, the first five outputs are 6,12,18,24,30. With 1, they are 1,2,3,4,5; with 10, they are 10,20,30,40,50.
Create and test: Partners choose different multipliers from 1 to 10, write a precise rule and use a calculator to check six outputs. Explain the constant gap using an extra equal group at each step. A chosen stop after six values limits the recorded list, not the mathematical pattern: another multiple can always be generated.
This bounded example records 6,12,18,24,30 and stops before 36. Compare a test of “less than 30”: it would omit 30. Learners test the last included value and the first excluded value.
E2 expansion: create a constant-multiplication flowchart
The recorded sequence is 1,2,4,8,16,32. The next value, 64, fails the test and is not recorded. The multiplier stays at 2; the current value changes. Each output doubles. The gaps between consecutive outputs are 1, 2, 4, 8 and 16, so the gaps also double.
Student does: Draw a new flowchart using multiplier 3, a chosen starting value and a stated stop limit. Include a start, a before-record decision, a record step, the multiplication and a return arrow. Label both decision paths. Use a calculator for each stated multiplication, keep the outputs and check one product with repeated addition or known facts.
Teacher looks for: a runnable chart, a correct output record and an explanation of the same multiplicative change. If the stop arrow returns to record, trace a value beyond the limit and repair that destination.
E3 expansion: use a spreadsheet formula and fill down
Make the input column explicitly. Put 1 in A1 and =A1+1 in A2. Fill the A2 formula down through A100. Check that A2 is 2, A3 is 3 and A100 is 100. Copying a constant 1 into every cell would not create these increasing inputs.
Put =A1*4 in B1 and fill that formula down through B100. The relative row reference changes: B2 uses =A2*4; B100 uses =A100*4. The asterisk means multiplication in the spreadsheet.
Expected pattern: Outputs are 4,8,12,…,400, with gaps of 4. Each next row adds one more group of 4. This differs from =B1*4 in B2, which would use the previous output and produce 16 instead of 8.
Digital evidence: Learners show the actual input values, at least one later formula and its result. They check B10 = 40 mentally. Use a classroom or family spreadsheet; a paper table is useful preparation but does not demonstrate filling formulas in a digital tool.
Questions and answersWith answers
Core idea: State the start or inputs, ordered operations, decisions and recording point. Follow the same instructions exactly, then explain the resulting pattern.
Important questions and answers
Apply multiply by 4 then add 2 to input 7. 7 × 4 + 2 = 30. The product is found before adding.
Why must both decision paths be clear? The algorithm must state what to do when its test is true and when it is false. Only the selected branch is followed for that decision.
Why do outputs 6,10,14,18 occur for inputs 1,2,3,4 under this rule? Each next input adds one group of 4. The same extra 2 is added to each product, so consecutive outputs remain 4 apart.
How do you create positive multiples of 6? Start at 6 and repeatedly add 6, recording at a stated point. If a finite list is wanted, state a stop count or bound. The mathematical sequence can continue indefinitely.
What changes when =A1*4 is filled to B10? The relative input reference becomes A10, so the formula is =A10*4. With A10=10, its value is 40. The multiplier stays 4.
Practice and reviewReady for practice
Both branches run — A yes/no decision chooses one alternative. Trace the arrows and cover the unused path.
Recording happens automatically — The record step may come before or after an operation. Follow the stated timing.
Less than includes the endpoint — A strict less-than test excludes equality; at most includes it. Test the boundary.
A stop value will always be reached — A repeated step may skip an exact target. Trace nearby values and use a suitable stated condition.
Every fill copies the intended series — Inspect input values and relative formulas. Explicitly build increasing inputs rather than assuming a lone copied constant will change.
A few terms prove the only possible rule — State and justify the generating steps; a finite list may fit different rules.
Materials: Number cards, paper, pencils, a calculator and a classroom or family spreadsheet.
Support: Trace one input with a finger or counters, colour its chosen path and write each intermediate value. Use small whole numbers and one decision.
Core: Follow and create algorithms with addition/multiplication, record lists, test boundaries, create a constant-multiplication flowchart and use relative spreadsheet formulas.
Extend within this code: Explain a pattern using the generating operation, diagnose a skipped stopping value, or compare new-input multiplication with previous-output multiplication. Formal programming syntax, negative-number rules, exponent notation and general algebraic proofs are not required.
Input 5 follows “add 1; if the new number is even, double it, otherwise add 3”. Find the output.
Review hint: Test the changed value. Answer: 5 + 1 = 6 is even, so 6 × 2 = 12.
Start at 2; while the number is less than 18, record it and add 4. What is recorded?
Review hint: Decide before recording. Answer: 2,6,10,14; 18 is excluded.
Create a multiplication-by-3 flowchart that records 1,3,9,27 and stops before 81.
Review hint: Include a start, record step, multiplication, return and two decision destinations. Answer model: Start at 1; test whether the value is at most 27; yes, record, multiply by 3 and return; no, stop. Inspect the actual chart and follow every arrow.
Read the Topic Guide, then project one Classroom View teaching section at a time. Complete the written worksheet tasks, use Practice for feedback and take the Test when ready. Written model or algorithm tasks require an adult to inspect the actual work against the task-specific checks.
Curriculum alignmentStart here
AC9M4N09
follow and create algorithms involving a sequence of steps and decisions that use addition or multiplication to generate sets of numbers; identify and describe any emerging patterns
For input 4, apply “if greater than 4, double; otherwise add 5”. The test is false, so 4 + 5 = 9.
Start at 2; record, add 3 and repeat while the value is at most 11. List the outputs. 2,5,8,11; the next value 14 is not recorded.
Write an algorithm for positive multiples of 5 up to 20. One model: start at 5; if at most 20, record, add 5 and return to the test; otherwise stop. Require an actual written rule producing 5,10,15,20, with the continuation and stop both clear.
Mastery evidence: The learner can follow and create runnable steps and decisions, justify output patterns and show the required digital model. A next-term answer alone does not demonstrate algorithm creation.
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