Three Catapults, One Revision Period
A seventh-grade engineering class is building catapults that must launch a ping-pong ball into a target zone 3 meters away. Constraints: only the materials in the kit (10 craft sticks, 5 rubber bands, 1 plastic spoon, 30 cm of string, 2 paper clips), 40 minutes of build time, and no tape. Three prototypes are being tested. Team A launches 2.1 m on every trial but never reaches the zone. Team B reaches 4.0 m but scatters left and right, landing outside a 1 m wide corridor on four of five tries. Team C reaches 3.0 m once out of five tries and averages 2.4 m. The teacher has one class period for revision and wants students to use data rather than preference to decide what to change.
1. Diagnose each prototype's failure mode and recommend the highest-value change for each, staying inside the material constraints.
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The three failures are different in kind, and treating them as 'not far enough' would be a mistake.
Team A is consistent but underpowered. The launch distance is identical every trial, which means the mechanism is repeatable and the problem is stored energy or launch angle. Highest-value changes: add rubber bands at the same anchor points to increase elastic energy, and lengthen the throwing arm (spoon position) relative to the pivot to increase the arc. Both use existing materials. A 2.1 m to 3.0 m gain is roughly a 40 percent increase, which is plausible with one or two more bands, whereas changing the base design risks losing the consistency that is Team A's main asset.
Team B has excess energy and poor control. Four of five launches outside the corridor suggests the ball is being released at inconsistent points or the frame is twisting. Highest-value changes: remove energy rather than add it, fix the launch angle with a paper-clip stop, and attach a string guide to constrain lateral motion. Reducing power to gain accuracy is the counterintuitive move students resist.
Team C is inconsistent. One success in five with a low mean points to variable draw length, release point, or anchoring rather than insufficient power. Adding bands before standardizing the launch protocol would raise the mean but probably not the hit rate.
2. What should Team C do first, and why is raising the average the wrong goal for them?
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Team C should standardize the launch before changing the machine. The evidence is the spread: a maximum of 3.0 m and a mean of 2.4 m over five trials means the same device is producing very different outputs. That variation comes from how the device is used - how far the arm is pulled, where the ball is seated, whether the base is held or free, and where the release happens. None of those is fixed by adding rubber bands.
The reason raising the average is the wrong goal is that a mean without reduced variance can look like progress while making the hit rate worse. If Team C adds a band and the mean rises to 3.2 m with a range from 2.0 to 4.0 m, the target zone is still being hit by luck. Reliability, not distance, is the engineering problem: the design will be judged on whether it can repeat, and a repeatable 2.6 m is a better platform for a controlled change than a volatile 2.4 m.
Practical first steps: mark the draw length with a pencil line on the craft stick, mark the ball position in the spoon, have one person launch while another holds the base, and record every trial including misses. Once the spread narrows, one additional change can be made and its effect read cleanly.
3. How should the teacher structure the revision period so that students decide from data, and what should count as evidence of improvement?
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The period should begin with a two-minute data display, not with materials. Each team posts its five trial distances and the number of corridor hits on the board, and the class reads across: Team A has one value repeated, Team B has five values with a wide spread and few hits, Team C has a wide spread with one hit. Naming the shape of each data set before touching craft sticks forces the diagnosis to precede the fix.
Then a rule for the revision: each team changes exactly one thing, writes a prediction before testing ('we predict the mean will rise by at least 0.5 m because...'), and runs five trials with the same launch protocol. Changing two variables at once is the same fair-test error students meet in science, and the engineering version has the same consequence - no way to attribute the change.
Evidence of improvement should be defined as hit rate plus reduced spread, with distance as a secondary measure. A team that moves from one hit in five to three in five has improved even if the mean is unchanged. A team that moves from 2.1 m repeated to 3.1 m repeated has improved. A team that raises the mean while its range widens has not demonstrated anything yet.
Close with a one-sentence engineering claim per team naming the change, the effect, and the remaining limitation.