Mathematics 11–12 · Year 12

Setting up the hall: critical path analysis from timed activities

Critical path analysis (Mathematics Standard 2, Year 12)

Practical, model not builtLow risk

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The idea

When activities depend on one another, the longest chain of dependent activities fixes the shortest possible completion time, and activities off that chain have float.

What you need

A stopwatch and a clipboard for each team
A plan of the school hall set-up for an assembly
A spreadsheet

How to do it

In a rehearsal, time each activity of the set-up (for example: clear the hall, set out chairs, place risers, run sound cables, sound check, put programmes on chairs, final walk-through) and record which activities must finish before each can start.
Write the precedence table and draw the activity network (no more than 10 activities).
Carry out a forward scan for earliest start times and a backward scan for latest start times.
Compute the float of each activity and identify the critical path and the minimum completion time.
Predict the effect of an activity running 5 and 10 minutes late, then test it with the network.

What you should see

Worked check on the model's test table (minutes: A clear hall 10; B chairs 25 after A; C risers 15 after A; D sound cables 10 after C; E sound check 10 after D; F programmes 5 after B; G walk-through 5 after E and F): earliest starts are A 0, B 10, C 10, D 25, E 35, F 35, G 45; the minimum completion time is 50 minutes along the critical path A-C-D-E-G; B and F each have 5 minutes of float. B running 5 minutes late does not move the finish from 50 minutes; running 10 minutes late moves it to 55. The learner knows it worked when every critical activity has zero float and the forward and backward scans agree on the finish time.

What changes

What you change: the duration of each set-up activity, and which activity is delayed
What you measure: the minimum completion time and the float of each activity
What you keep the same: the same precedence table for every scan
the same team sizes and equipment
each activity timed from the same start signal

Common misconceptions

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

Adding extra people to any activity finishes the project sooner; only shortening a critical activity can.
The critical path is the one with the most activities; it is the one with the longest total duration.

Safety card

Low riskLearners carry it out

Hazards

lifting and stacking chairs and risers
trip hazard from sound cables

Controls

lift within the school's manual handling guidance, two people for risers
tape cables flat or run them along walls

Note

No chemicals and no heat are used, so the NSW Department of Education Chemical Safety in Schools package does not apply; ordinary classroom supervision.

Curriculum references

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

Mathematics Standard 11–12 Syllabus (2024), Year 12 Standard 2 focus area Critical path analysis; Year 11 taught from Term 1 2026, Year 12 from Term 4 2026, first HSC examination 2027 (the 2017 syllabus is still taught to Year 12 until then); page read 2026-09-22MST-12-S2-07
Australian Curriculum v9No Australian Curriculum v9 code is listed.

Sources

The pages the author read to write this activity.

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