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Technologies K–10 · Years 5–6

Sorting with a balance scale: counting comparisons

Design and Production (NSW Science and Technology K–6, 2017) (algorithms); Digital Technologies: Processes and production skills, Generating and designing (ACARA v9)

Practical, model not builtLow risk

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The idea

Different sorting algorithms put the same 8 containers in order but need different numbers of comparisons, so an algorithm can be judged by how many steps it takes.

What you need

  • 8 identical opaque containers (for example film canisters) filled with different amounts of sand, labelled A to H
  • 1 pan balance
  • 1 kitchen scale reading to 1 g, kept covered until the end
  • Tally sheet for comparisons

How to do it

  1. Find the heaviest container: compare A with B, keep the heavier, compare it with C, and so on. Tally each comparison.
  2. Selection sort: find the heaviest, set it aside, then find the heaviest of those left, until all 8 are in order. Tally every comparison.
  3. Shuffle. Merge sort: sort 4 pairs, merge the pairs into 2 groups of 4, then merge into 8. Tally every comparison.
  4. Uncover the kitchen scale and weigh all 8 to check the order.
  5. Compare the tallies and explain which algorithm would be better for 100 containers.

What you should see

Finding the heaviest of 8 takes exactly 7 comparisons. Selection sort takes 28 (7 + 6 + 5 + 4 + 3 + 2 + 1). Merge sort takes at most 17, and fewer when a merge finishes early. The kitchen scale confirms the order. The learner knows it worked when the final order matches the scale and the tallies match these counts.

What changes

This activity lists no variables to change, measure and keep the same.

Common misconceptions

Each of these ideas is wrong, and the activity is a chance to test it.

  • All sorting methods take the same number of steps (they can differ a great deal as the list grows).
  • Computers sort by looking at everything at once (they compare two items at a time).
  • The fastest method for 8 items is always fastest for 1000 (the gap between methods grows with n).

Safety card

Low riskLearners carry it out

Hazards

  • Sand spills

Controls

  • Containers taped shut

Note

No chemicals or heat.

Curriculum references

The NSW syllabus outcomes and Australian Curriculum v9 codes this activity supports. They are references, not a verified or complete curriculum alignment.

  • Science and Technology K–6 Syllabus (2017), NESA. The syllabus taught in 2026; the 2024 syllabus replaces it from 2027. Code read from the official syllabus document (DOCX) on 2026-09-22.ST3-3DP-T
  • Science and Technology K–6 Syllabus (2024), NESA. Implementation from 2027, so this code describes the future syllabus. Code read from the outcomes page on 2026-09-22.ST3-DDT-02
  • Australian Curriculum v9AC9TDI6P02

Sources

The pages the author read to write this activity.

  1. www.nsw.gov.au/education-and-training/nesa/curriculum/science/science-and-technology-k-6-2017
  2. curriculum.nsw.edu.au/learning-areas/science/science-and-technology-k-6-2024/outcomes
  3. classic.csunplugged.org/activities/sorting-algorithms
  4. www.digitaltechnologieshub.edu.au/plan-and-prepare/scope-and-sequence-f-10/years-5-6

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