Testing a Paper Airplane Claim
A student claims that adding paper clips to the nose of a paper airplane makes it fly farther. She folds 10 identical airplanes. She adds 0, 1, 2, or 3 clips to different planes and throws each from the same spot, measuring distance. Results are messy: the 0-clip plane flew 6 m once; the 3-clip plane flew 9 m once but nosedived twice; the 1-clip plane flew between 7 and 8 m on all three throws. She concludes, "More clips always means farther flights, because the 3-clip plane went the farthest." A classmate says one throw per plane is enough because 'the numbers speak for themselves.'
1. Identify the problems with the student's conclusion and with the classmate's 'one throw is enough' reasoning, and describe how to redesign the test.
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Problems with the conclusion: (1) The 3-clip plane's 9 m was a single throw and it also nosedived twice-so 'more clips always means farther' ignores contradicting trials. (2) 'Always' is too strong for one lucky throw. (3) Different planes got different numbers of throws, so they aren't fairly compared. Problems with the classmate's reasoning: repeated trials are needed because throws vary (wind, release angle, hand position). One throw can't separate the effect of clips from random variation. Redesign: use the same number of throws (e.g., 5) for each clip count; keep the thrower, location, and release method constant; measure each flight; compare averages (and note the spread). Change only the number of clips-the independent variable-while distance is the dependent variable and everything else is controlled. Then a fair comparison can support or refute the claim.
2. The 1-clip plane gave consistent 7–8 m flights across three throws. Explain why this consistency matters for judging the claim, and what it suggests compared with the erratic 3-clip results.
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Consistency matters because it shows the measurement is repeatable-when results cluster tightly (7–8 m), we can trust that the number reflects the plane's real behavior rather than luck. The 3-clip plane's results were erratic (one 9 m, two nosedives), which signals high variability: the single long flight may be an outlier, not a reliable effect of 3 clips. So the reliable evidence (1 clip, consistent) does not support 'more clips always farther,' and the erratic evidence (3 clips) is the weakest basis for a sweeping claim. A careful conclusion: 1 clip may give a modest, repeatable improvement, while 3 clips is unpredictable and sometimes fails. To confirm, run more trials of each and compare averages and ranges; if 3-clip flights stay erratic, the claim fails.