S6 ICT | IT Project Management (Critical Path and Earned Value): Tutor Prep Guide (45-minute flow, script, common errors)

2026-11-15

Tutor lesson-prep guides · Secondary ICT

Students can draw a Gantt chart, then ask how short the project can be and they start guessing at paths. This lesson turns a dependency table into two operations: the longest path sets the finish date, and the gap is float.

Objectives — By the end of the lesson students can: (1) draw the network from a dependency table and find the three paths of 7, 9 and 11 days, naming the longest as the critical path; (2) compute a float of 2 days for B and 4 days for C, and explain that a task with zero float delays the finish date; (3) compute a CPI of 0.84 and an SPI of 0.875 from BAC 120,000, PV 48,000, EV 42,000 and AC 50,000; (4) compute an EAC of about 142,857 from a CPI of 0.84 and state the overspend of 22,857.

01 Prerequisites (3-minute check)

If any of these fails, fix it before the lesson starts.

Skill	Quick check	Pass mark
Addition and comparison	Three paths of 7, 9 and 11 days: which one sets the finish date	The 11-day path
Percentages	What is 35 per cent of a BAC of 120,000	42,000
Ratios	EV of 42,000 divided by AC of 50,000	0.84
Reading a dependency table	A takes 3 days and D waits for A, so when can D start	Day 4

02 Lesson flow (45 minutes)

Time	Stage	Tutor does	Student does
0-6 min	Entry check	Ask the three path lengths, 35 per cent, 42,000 over 50,000 and the start day; keep answers on the board	Spoken answers, working on paper
6-14 min	Act one: draw the network first	Build arrows from the dependency table, write each duration on its arrow, add a start and an end node	Students draw the same network
14-24 min	Act two: the critical path is the longest one	Paths A-C-E at 7 days, A-B-E at 9 and A-D-F at 11, so 11 days is the critical path	Students name the tasks on the critical path
24-34 min	Act three: float and earned value	Float is critical length minus that path; BAC 120,000, PV 48,000, EV 42,000, AC 50,000 give CPI 0.84, SPI 0.875 and EAC 142,857	Students compute the floats and the CPI
34-42 min	Question types with new numbers	Six tasks and a new BAC, four phrasings of the same chain	Students do one and write the unit
42-45 min	Exit check	Three spoken questions; note which act each error comes from	All three correct

03 Teaching script (read it out)

Scene 1: Act one: table to network, and the network decides everything

A project question hands you a table: task code, duration, predecessors. Step one is always the network diagram, not a Gantt chart. Start from the start node: A has no predecessor, so one arrow leaves the start to A with 3 days on it. B, C and D all list A, so three arrows leave A. E waits for both B and C, so two arrows point into E. F waits only for D. Both E and F point into the end node. Once the diagram is right, every later question is just adding numbers along arrows.

E has two predecessors, so how many arrows point into E, and why?

Scene 2: Act two: the critical path is the longest path, not the shortest

Walk from start to end and add each path: A 3 plus C 2 plus E 2 is 7 days; A 3 plus B 4 plus E 2 is 9 days; A 3 plus D 5 plus F 3 is 11 days. The longest is 11, so the shortest possible project duration is 11 days, and that path is critical. Why the longest? Parallel work overlaps, but E waits for both B and C, so the people on the 9-day path finish and then wait for the 11-day path before the project closes. Tasks on the critical path have zero float: delay D by a day and the finish slips a day.

If D took 7 days instead of 5, would the critical path change, and what would the finish date become?

Scene 3: Act three: float is subtraction, earned value is two ratios

Float is the critical length minus the length of that path. The A-B-E crew needs 9 days against an 11-day critical path, so they have 2 days of slack, called float of 2 days; A-C-E at 7 days has a float of 4 days. Zero float means not one day of delay is allowed. Earned value asks for four numbers. PV is the value the plan says you should have delivered today, 40 per cent of 120,000, so 48,000. EV is the value actually delivered, 35 per cent, so 42,000. AC is the money actually spent, 50,000. CPI is EV over AC, 42,000 over 50,000, giving 0.84, below one meaning overspend. SPI is EV over PV, 42,000 over 48,000, giving 0.875, below one meaning behind schedule. EAC is BAC over CPI, 120,000 over 0.84, about 142,857, so at this rate the project overspends by 22,857.

What does a CPI of 0.84 say about the value delivered per dollar spent, and what does below one mean?

04 Question types and worked steps

Type	Example	Steps	Answer
Find the critical path	A 3, B 4 after A, C 2 after A, D 5 after A, E 2 after B and C, F 3 after D	Draw the network, list every path, take the longest	A-D-F at 11 days
Compute float	Its path is 9 days and the critical path is 11	Critical length minus that path length	2 days for B and 4 days for C
Compute CPI and SPI	BAC 120,000, PV 48,000, EV 42,000, AC 50,000	CPI is EV over AC, SPI is EV over PV	CPI 0.84, SPI 0.875, both below one
Compute EAC	CPI 0.84 with BAC 120,000	EAC is BAC over CPI, then subtract BAC	About 142,857, an overspend of 22,857

Sanity check (teach this): Four checks: (1) the critical path total must equal the project duration, and any mismatch means a path was missed; (2) every task on the critical path must have zero float, and a non-zero float means the wrong path was chosen; (3) both CPI and SPI use EV as the numerator, so AC over EV is always wrong; (4) with a CPI below one the EAC must be at least BAC, and an EAC below BAC means the division is inverted.

05 Independent practice (3 questions)

Question	Answer	What to watch
A 3, B 4 after A, C 2 after A, D 5 after A, E 2 after B and C, F 3 after D: what is the shortest duration	11 days, on the path A-D-F	Watch for students missing the 9-day A-B-E path
What is the float of task B	2 days, that is 11 minus 9	Check that the critical length is subtracted, not the task duration
BAC 120,000, PV 48,000, EV 42,000, AC 50,000: what is the CPI	0.84	42,000 over 50,000, and the numerator is EV

06 Common mistakes and what to say

Mistake	Student writes	Say this
Calling the shortest path critical	Answering 7 days with A-C-E	The critical path is the longest. The shortest path finishes early and waits, and the project still runs to the longest path.
Reversing the arrows	Pointing the arrow from D to A	An arrow means finishes before it starts. A precedes D, so the arrow runs A to D; reversing it makes every date wrong.
Inverting the CPI	Dividing AC by EV to get 1.19 and calling it healthy	EV is the value delivered and AC is the money spent, so 0.84 is right and below one means overspend.
Reading zero float as cannot start	Delaying critical work to avoid a clash	Zero float means no delay is allowed, not that work cannot begin. Critical tasks start at their earliest date and never slip.

07 Homework (paper, section and question numbers)

S6 ICT Practice Paper 1, project management section — Section C, questions 9 to 11

08 Exit check (last 5 minutes)

Question	Answer	Decision
A-D-F takes 11 days and A-B-E takes 9, so what is the shortest duration	11 days	Wrong: reteach act two, the longest path sets the finish
BAC 120,000, EV 42,000, AC 50,000: the CPI	0.84, an overspend	Wrong: reteach act three, EV is the numerator
CPI 0.84 with BAC 120,000: the EAC	About 142,857	Wrong: reteach act three, EAC is BAC over CPI

09 Tutor FAQ

Which year level is this for?

Hong Kong S6 ICT asks students to find the critical path from a dependency table, explain float and judge project health from earned value figures. The S4 work on percentages and ratios is the prerequisite, so revise what one number divided by another means first.

Is 45 minutes enough?

Yes, provided act two gets ten minutes. The commonest error is calling the shortest path critical, so make students say out loud that the short path finishes early and waits.

Are these a real project figures?

No. 120,000, 50,000 and 35 per cent are teaching numbers for mental arithmetic. Real projects carry decimals, and the point is the relationship between the four figures and the direction of the judgement.

Find a tutor — free Tutor Registration →

A TutorZone lesson-prep guide. Written by the TutorZone team; questions and lesson flow are original and are not taken from any school or publisher material.