Back to Planning and Decision Making

Higher Applications of Mathematics

Activity networks

Representing tasks, dependencies and project order.

Planning referencePlanning mixed quiz

Planning reference

Check networks, timing, float, PERT, Gantt charts, risk and expected value.

Mixed revision quiz

Review Planning and Decision Making with adaptive feedback.

Before you start

  • Be confident reading information from tables and diagrams.
  • Check time units, costs and probabilities before calculating.
  • Be ready to explain what the result means for the project or decision.

Method helper

Which planning method do I use?

Do tasks depend on other tasks being completed first?

Draw an activity network.

Are task times uncertain?

Use PERT estimates.

Do you need the minimum project duration?

Find the critical path.

Do you need to know which activities can be delayed?

Calculate float.

Do you need to show a project schedule on a timeline?

Create a Gantt chart.

Are you comparing uncertain financial outcomes?

Calculate expected value.

Are you comparing options with risk, cost and benefit?

Use risk and decision making.

Do you need a written recommendation?

Explain the decision in context with limitations.

Planning lesson

Key idea

  • This topic focuses on representing project tasks, durations and dependencies using activity-on-node networks. Planning and decision making uses mathematics to organise real projects and compare choices under constraints.
  • A good planning answer identifies the activities or options, uses the correct method, and explains the result in the context of the project.
  • For Higher Applications, the conclusion matters. You should mention timing, risk, cost, uncertainty or limitations where they affect the decision.

Key definitions, methods and formulae

  • An activity is a task in the project.
  • A dependency means one activity must happen before another.
  • In an activity-on-node network, arrows show the order of activities.

Worked examples

Planning walkthrough 1

Set up the information

A school is organising a charity ceilidh with booking, publicity, ticketing and setup tasks.

  1. List each activity with a short label.
  2. Record each duration in the same unit.
  3. Write immediate predecessors for each activity.

The network makes the order of the project visible before any timings are calculated.

Planning walkthrough 2

Carry out the method

A school is organising a charity ceilidh with booking, publicity, ticketing and setup tasks.

  1. Place activities with no predecessors at the start.
  2. Draw arrows from each predecessor to the activity that depends on it.
  3. Check every dependency in the table appears on the network.

A correct activity network prevents impossible schedules.

Planning walkthrough 3

Interpret the decision

A school is organising a charity ceilidh with booking, publicity, ticketing and setup tasks.

  1. Read through the network from start to finish.
  2. Check no task starts before its prerequisites are complete.
  3. Explain what the network shows about the project order.

The diagram supports later critical path or Gantt chart work.

Watch out

  • Ignoring dependencies and allowing activities to start too early.
  • Mixing time units, such as hours and days, without converting.
  • Choosing the cheapest option without considering risk or impact.
  • Treating expected value as a guaranteed outcome.
  • Giving a schedule or calculation without explaining what it means for the project.

Connected topics

Related Higher Applications topics

Modelling: Variables, formulae and models

Next step

Move into practice

Use the learning notes to read dependencies and constraints, then try varied schedules, precedence tables and decision contexts.

Planning mixed quiz