Free IB Maths AI HL lesson: Graph theory — adjacency & weighted matrices
A ready-to-teach IB Maths AI HL lesson on Graph theory — adjacency & weighted matrices (Unit 3 · Geometry & Trigonometry): editable slides and teacher notes, free; a printable worksheet in 3 levels with answers for school plans. About 55 minutes.
Free with a teacher account. Sign in with Google, Microsoft or email and download the slides and teacher notes.
What's inside
- Slides (PowerPoint, editable) · freeabout 12 slides: do now, objectives, key ideas, a worked example step by step, “your turn”, practice QR code, exit ticket
- Teacher notes (PDF) · freelesson plan with timings, common mistakes, homework links
- Worksheet (PDF) · school plans6 questions, 26 marks: Fluency, Reasoning, Exam-style. Included with school plans and the teacher trial.
- Answers (PDF) · school plansthe answer to every worksheet question, from its mark scheme. Included with school plans and the teacher trial.
Learning objectives
- Vertices, Edges, Degree, Simple & Complete Graphs
- Directed & Weighted Graphs, Subgraphs & Trees
- Adjacency Matrices & Counting Walks
- Eulerian & Hamiltonian Trails and Circuits
- Minimum Spanning Trees — Kruskal's & Prim's Algorithms
- The Travelling Salesman Problem — Upper Bounds (Nearest Neighbour)
- Lower Bounds — the Deleted-Vertex Algorithm
- Walks of Length k with Adjacency Matrix Powers
- Travelling Salesman — Tables of Least Distances
Key vocabulary
- vertex: A point (node) of a graph.
- edge: A connection between two vertices.
- degree: The number of edges meeting at a vertex (a loop counts twice).
- walk: A sequence of edges, where vertices and edges may repeat.
- order: The size of a matrix: rows × columns.
Common mistakes this lesson tackles
- Graph algorithms: Prim vs nearest neighbour, no method shown, bounds mixed up. Show the algorithm: list edges in the order chosen, with weights, and say when it stops. Upper bound (nearest neighbour): best = smallest found. Lower bound (deleted vertex): MST of the rest + two shortest edges to the deleted vertex; best = largest found.
- Complex numbers and transformation matrices. Expand complex products fully (i² = −1), then collect real and imaginary parts. Work in radians. Learn the rotation and reflection matrices in the formula booklet and what their products represent.
- Counting a loop as degree 1.
Lesson plan
| 0–5 min | Do now: students write down what they remember about Cross product & shortest distances and Vector equation of a line |
| 5–8 min | Share the learning objective and success criteria |
| 8–20 min | Teach: the worked example, step by step; students copy the method |
| 20–25 min | Your turn: 1 mini-whiteboard question; check every board before moving on |
| 25–42 min | Practise: the worksheet (6 questions in 3 levels, with school plans and the teacher trial) or the topic's practice questions online; move up a level after two right in a row |
| 42–47 min | Plenary: 1-question exit ticket; collect it to plan the next lesson |
For students: practise this topic
The worksheet's QR code opens the IB Maths AI HL Unit 3: Graph Theory practice questions.
What schools get
- Set this lesson as homework, marked by AI against the mark scheme, with every result in your markbook (school Pro plan).
- This lesson's worksheet in three levels, with its answers, ready to print.
- Support, Core and Stretch versions and A/B copies of the worksheet from the full question bank, in the worksheet builder.
- Create lesson: this lesson rebuilt for your class's next scheme-of-work lesson, from the full bank.
School licences from €490 a year. Try everything free for 30 days as a teacher: no card.
Questions teachers ask
Is this lesson free?
The slides and the teacher notes are free to download with a free IB Math Revision teacher account (sign in with Google, Microsoft or email); no card. The printable worksheet in three levels and its answers are included with school plans and the free 30-day teacher trial.
Can I edit the slides?
Yes. The slides are an ordinary PowerPoint file: change, add or delete anything. They also open in Google Slides and Keynote. The logo and web address sit on the slide master, so your edits do not move them.
What do students use for homework?
The practice slide's QR code and web address take students to the IB Maths AI HL Unit 3: Graph Theory practice questions on ibmathrevision.com, where the free questions are open and the full bank comes with a plan.