Number Bridges: Build One Connected Web of Islands
Generate fresh island positions, neighboring links, and single/double bridge counts.
Correct Counts, Broken Graph: The Trap of the Isolated Island
Generate fresh island positions, neighboring links, and single/double bridge counts. Networks must be connected, noncrossing, and match every island count, with one clue-determined solution.
Weighing Competing Conditions: A Grade 4–8 Reasoning Stretch
Number Bridges sits after students add small sums fluently (3.OA, 4.NBT) and are ready to juggle competing conditions instead of one rule at a time. It grows the deductive habits the MP standards prize — interpreting a tangled setup (MP.1), building an argument from forced moves (MP.3), and reading structure to shortcut work (MP.7). Those same moves later power systems of constraints and the graph thinking students meet across middle-school math.
Learning Points
- logical elimination
- candidate tracking
- island bridge counts and network connectivity
- pattern validation
Steps and completion rules
- Inspect corner islands or islands with few possible neighbors and count their required bridges.
- Select two neighboring islands aligned horizontally or vertically to cycle their bridge count from 0 to 1 to 2 and back to 0. Watch both endpoint totals.
- Remove crossings and isolated groups so every island count is satisfied in one connected network.
Teacher / Parent Note
Discuss the risk of locally correct counts forming disconnected groups, and explain the purpose of the final connecting bridge.