path-length-comparison-and-shortest-path
Compare or minimize total length over a finite collection of routes. The routes may be drawn on a figure (visual comparison: straight vs curved vs zigzag) or described as a small weighted graph (numerical shortest path). The structural move is the same: identify the candidate routes, compute or compare their lengths.
풀이 전략
- Replace one curved segment with a zigzag of the same endpoints to keep the visual ordering intact while changing the look
- Add a single edge to the graph that opens a tempting longer route, so students must check more options
- For a numerical variant, choose edge weights so the optimum is unique and not on an obvious 'all small numbers' path
세부 유형 분포 (3)
한 줄을 클릭하면 그 안의 문제를 볼 수 있어요.
- sum-known-path-segments 33% (2)
The path is fully prescribed and made of clearly named geometric pieces (arcs of given radius, straight segments along axes or grid lines). The student decomposes the path into pieces, computes each using a single formula (arc fraction of 2*pi*r, Manhattan block count, side difference), and adds. There is no choice of route — only correct decomposition and arithmetic.
- shortest-route-in-network 50% (3)
A weighted graph (towns with labeled edges, or candidate paths drawn on a figure) is given, and the student must select the minimum-length route. The mechanic is enumerate-and-compare: build shortest distances to intermediate nodes (relaxation) or rank whole paths using straight-vs-curved / straight-vs-zigzag inequalities, then pick the minimum.
- distance-from-fixed-point-along-path 17% (1)
A mover travels a closed path and the student tracks straight-line distance from a fixed reference point (usually the start). The mechanic is qualitative: identify distance at key waypoints (corners, peaks), determine where the distance is max/min, then match the rise-and-fall profile against candidate graphs. Output is a graph shape, not a numeric total.
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도구 fingerprint (1–17)
학년 분포
- Gr 2 2
- Gr 3 1
- Gr 7 1
- Gr 8 1