Breadth-layer map
Discover each reachable node once and justify its minimum number of hops.
Adult planning suggestion: about6–9 · Logic & rule checking
- Players
- 2–4 per group
- Time
- 15–20 minutes
- Materials
- Six labelled node cards A–F, edge list, pencil and distance table.
Prepare
Use undirected edges AB,AC,BD,CD,DE. F is isolated. Draw nodes anywhere; line length has no meaning. Put A at distance 0, and prepare a queue initially containing only A. Mark a node seen as soon as it enters the queue, not after it leaves.
Play
Take the front node. Add its unseen neighbours at the back, in alphabetical order, and assign their distance as this node’s distance plus one. Cross off the processed node. Continue until the queue is empty. Already-seen neighbours are not queued again even if another route reaches them.
Worked example
Process A to discover B,C at 1. B discovers D at 2; C sees D already marked and adds nothing. D discovers E at 3. The queue sequence is A,B,C,D,E. F remains unreachable; a blank distance is not a zero.
Finish and check
Write a shortest A-to-E route and explain its three hops. ABDE and ACDE are both valid. The goal is not to visit every drawn node regardless of connectivity. Finish when the queue is empty and all visited entries have a predecessor except A.
Adaptation and limits
Thirty learners can use ten trios: queue manager, recorder and auditor. Begin with the same six-node example before inventing another. Permit paper counters or large node slips. The reference is a computer-science explanation, not proof of an age-specific learning outcome.
Purpose, observation and provenance
Within this activity: Discover each reachable node once and justify its minimum number of hops.
Watch for revisiting a node through a cycle or treating edge length on the drawing as cost.
Our rules, examples and printable diagrams are separately prepared. The earliest inventor of the broader mechanism is not established here.
Open Data Structures — Graph Traversal — Technical BFS definition; the paper graph, six-node example and grouping are our adaptation.
Age bands are planning suggestions. Goals describe observable actions, not measured long-term gains or institutional endorsement.
Free alternative: Copy the supplied grids, labels and cards onto reused paper. No specialist product is needed. Adults may prepare pieces or act as a scribe.
Printable materials
Preview at 100% scale, with browser headers and footers off. Cut with suitable help. Keep host keys separate. This is a manual tabletop kit, not an online opponent, automatic judge or solver.
Player materials · Breadth-layer map
Undirected edges: AB AC BD CD DE; F isolated.
Queue front → back: ______; node / predecessor / hop count: ______.
| Node | Neighbours |
|---|---|
| A | B C |
| B | A D |
| C | A D |
| D | B C E |
| E | D |
| F | — |
Player record · keep the host key separate
| Node | Parent | Distance | Queue |
|---|---|---|---|
| ________ | ________ | ________ | ________ |
| ________ | ________ | ________ | ________ |
| ________ | ________ | ________ | ________ |
| ________ | ________ | ________ | ________ |
| ________ | ________ | ________ | ________ |
| ________ | ________ | ________ | ________ |
| ________ | ________ | ________ | ________ |
| ________ | ________ | ________ | ________ |
Host key · separate from players
A0; B1; C1; D2; E3; F unreachable. Queue visits A,B,C,D,E.
Run the round
Use undirected edges AB,AC,BD,CD,DE. F is isolated. Draw nodes anywhere; line length has no meaning. Put A at distance 0, and prepare a queue initially containing only A. Mark a node seen as soon as it enters the queue, not after it leaves.
Take the front node. Add its unseen neighbours at the back, in alphabetical order, and assign their distance as this node’s distance plus one. Cross off the processed node. Continue until the queue is empty. Already-seen neighbours are not queued again even if another route reaches them.
Process A to discover B,C at 1. B discovers D at 2; C sees D already marked and adds nothing. D discovers E at 3. The queue sequence is A,B,C,D,E. F remains unreachable; a blank distance is not a zero.
Write a shortest A-to-E route and explain its three hops. ABDE and ACDE are both valid. The goal is not to visit every drawn node regardless of connectivity. Finish when the queue is empty and all visited entries have a predecessor except A.
Thirty learners can use ten trios: queue manager, recorder and auditor. Begin with the same six-node example before inventing another. Permit paper counters or large node slips. The reference is a computer-science explanation, not proof of an age-specific learning outcome.
Related activities
Activity library · Weighted bridge network: rules and printable materials