The Paper Bridge That Sags: Revising Under a Time Limit
A fifth-grade team has 5 sheets of paper, 40 cm of tape, and 20 minutes to build a bridge spanning a 25 cm gap between two desks that holds a 200 g mass at the center for 10 seconds. Design 1 - a single flat sheet taped across the gap - sags immediately and dumps the mass in under a second. Design 2 - one sheet folded into a 2 cm-deep accordion - supports the mass but sags 8 cm at the center, and the mass slides off before 10 seconds can be counted. The team has 8 minutes and the same materials left. Their notebook lists three ideas: (a) add more tape at the ends, (b) fold the accordion deeper, (c) cut the paper into strips and bundle them into a beam.
1. Evaluate the three ideas against the evidence from the two failures. Which should the team try, and what reasoning supports that choice?
Read the worked answer
Read the failure modes first
- Design 1 failed by bending: a flat sheet has almost no depth, so it offers little resistance to bending and sags under load.
- Design 2 failed by excessive sag plus sliding. The accordion did carry the load, which tells the team that folding works - the shape, not the paper, was the key change. The remaining problem is stiffness and a sloped top surface.
Evaluating the options
- (a) More tape at the ends addresses anchorage. Nothing in the evidence suggests the ends pulled loose, so this treats a failure that did not occur.
- (b) Deeper folds increase the distance between the top and bottom surfaces of the bridge, which is exactly what resists bending. This directly targets the observed sag and is the cheapest change to test.
- (c) Bundling strips into a beam also adds depth and material, but it consumes most of the remaining paper and time and creates a new construction problem under an 8-minute deadline.
Best choice: try (b) first, ideally with the accordion's ridges running across the span rather than along it, and flatten the top by taping a single flat sheet over the ridges. That fixes sliding without adding much mass.
Reasoning habit: connect the proposed fix to a specific observed failure.
2. How should the team use the remaining 8 minutes so the revision counts as engineering design rather than guessing? Include success criteria and what to record.
Read the worked answer
State criteria and constraints before building
- Criteria: spans 25 cm; holds 200 g at the center for 10 seconds; mass stays on the bridge.
- Constraints: 5 sheets, 40 cm of tape, 8 minutes, desk gap fixed.
Testable plan
- Change one thing - fold depth - from 2 cm to about 4 cm, keeping everything else the same so the comparison is meaningful.
- Predict before building: deeper folds should reduce center sag, so the mass should be less likely to slide.
- Build, then test with a quick trial using a book of similar mass before committing the 200 g load. Measure center sag with a ruler and time how long the load stays on.
- Record the numbers, not adjectives: sag in centimeters, hold time in seconds, whether the mass slid.
- If sag improves but sliding continues, add the flat deck sheet - one change, then retest.
What to capture in the notebook
A simple table of design version, change made, sag, hold time, and result. A failure with recorded numbers is usable evidence; a failure described only as 'it didn't work' is not.
Discussion prompt afterward: which change produced the biggest improvement per sheet of paper used? This is the trade-off thinking the standard is asking for.