AC9M4N09 • Homework

Algorithms that Generate Number Sets worksheet

Use this printable homework sheet for written working, application and reflection alongside the online learning activities.

Open practice

Write, model and explain

Complete the eight tasks below on paper or download the matching PDF homework. Use the stated digital tool for digital tasks and show your work to a parent or teacher.

  1. Write an algorithm that records the positive multiples of 3 from 3 to 21 inclusive, then stops. Include a decision and follow your own steps.

  2. Draw a two-branch flowchart: if an input is even, multiply by 5; otherwise add 7. Run inputs 1, 2, 3, 4 in order, recording one output each, then stop. Use a separate sheet for the flowchart.

  3. Compare two algorithms on input 6: add 2 then multiply by 3; multiply by 3 then add 2. Show each intermediate value and explain the difference.

  4. Create a flowchart that records the starting value 2 before its first multiplication, then repeatedly multiplies the current value by 4 and records each value at most 150. Use a calculator to follow it, explain a pattern and check one product another way. Use a separate sheet for the flowchart.

  5. A rule starts at 4, records, adds 5 and stops only when exactly 20 is reached. Show why this stop fails, then rewrite a rule that records only values at most 20.

  6. Use a spreadsheet: put 1 in A1 and =A1+1 in A2, then fill the A2 formula through A100. Put =A1*6 in B1 and fill through B100. Record B1, B2, B10, B100, inspect the formula in B10 and explain the output pattern.

  7. Cells A1 through A100 contain 1 through 100 in order. Each B formula should multiply the A input in its own row by 6. B1 contains =A1*6 and shows 6. Someone puts =B1*6 in B2. Explain the mistake and write the repair.

  8. Choose a multiplier from 1 to 10. Create a rule generating its first six positive multiples. Record them, explain a pattern from your rule and say whether the mathematical sequence must end there.

Answer and work checks

  1. One model: start at 3; if at most 21, record, add 3 and return to the test; otherwise stop. Outputs: 3, 6, 9, 12, 15, 18, 21. Inspect actual runnable instructions, recording point and both decision destinations. Also accept inputs 1 through 7 multiplied by 3, with a clear final-input stop.

  2. Outputs: 8, 10, 10, 20. Inspect separate yes/no branches, exactly one record per input, an instruction to move to the next input and a stop after input 4. Accept one shared record step or a record step in each separate branch. Both outputs of 10 are valid.

  3. First: 6 + 2 = 8, then 8 × 3 = 24. Second: 6 × 3 = 18, then 18 + 2 = 20. Require both ordered traces and an explanation that changing step order changes what is multiplied.

  4. Recorded values: 2, 8, 32, 128; the next value, 512, is excluded. Each output is four times the previous output. Inspect an actual flowchart with both decision paths, a loop and a calculator-generated record. Accept testing before every record or safely recording the initial 2 first and checking all later values. One check: double 32 twice to get 64 then 128.

  5. The values 4, 9, 14, 19, 24 skip 20. One repair: test at most 20 before recording; yes, record, add 5 and return; no, stop. Repaired list: 4, 9, 14, 19. Inspect the rewritten decision and output timing. Accept a safe initial record followed by a correct test for all later values.

  6. B1 = 6, B2 = 12, B10 = 60, B100 = 600; B10 contains =A10*6. Inspect actual increasing inputs and filled formulas with matching-row references. Require an explanation that outputs have gaps of 6 because each next input is 1 larger, adding one more group of 6. Paper predictions alone do not show digital fill-down.

  7. =B1*6 uses the previous output, 6, giving 36. The intended second input is A2 = 2, so =A2*6 gives 12. Require both explanations and the corrected formula.

  8. Inspect a chosen multiplier, six correct successive positive multiples and a runnable rule with a finite recording stop. Accept repeated addition or successive inputs 1 through 6 multiplied by the chosen number. Require a correct pattern justified by the rule. The recorded list stops after six values, but another multiple can always be generated mathematically.

Inspect the actual models, working and algorithms. A correct final number or completion tick alone does not show the required reasoning.