Moving 20 Liters Uphill
A fifth-grade team must move 20 L of rainwater from a rain barrel to a garden bed 8 m away and 1.2 m higher, without using electricity from a wall outlet. The requirements are: cost under $25, move the 20 L in under 10 minutes, and survive being left outdoors through tropical rain. They build and test three prototypes.
A: a hand pump built from a bicycle pump - 20 L in 14 min, costs $22, but the hose pops off twice under pressure. B: cotton wick cloths draped over a board - 20 L in 55 min, costs $6, never leaks. C: a small solar fountain pump - 20 L in 6 min, costs $38, stops working when shaded.
The team must choose one prototype to revise and justify the choice.
1. Check each prototype against all three requirements. Which requirement does each one fail, and why should "under $25" and "under 10 minutes" not be treated as the same kind of limit?
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Checking each prototype
| Prototype | Cost under $25? | 20 L in under 10 min? | Survives outdoors? |
|---|---|---|---|
| A (hand pump) | Yes ($22) | No (14 min) | Questionable - hose pops off |
| B (wick) | Yes ($6) | No (55 min) | Yes, likely - nothing to break |
| C (solar pump) | No ($38) | Yes (6 min) | Questionable - stops when shaded |
Every prototype fails at least one requirement, so no option can be accepted as-is; the choice is about which failure is easiest to fix.
Why the two limits are different in kind
- The $25 limit is a constraint set by the budget - the team cannot decide to spend $40. C cannot be fixed by trying harder; it needs a cheaper pump or fewer parts.
- The 10-minute limit is a criterion the design is judged against, and it can be improved by redesign (a bigger pump, a wider hose, better sealing).
- So a design that is over budget is out unless the parts are changed, while a design that is too slow is still in the running if its speed can be improved.
2. Which prototype should the team revise? Justify your choice, describe two specific changes, and outline a fair test of the revised design.
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Choice: revise A (the hand pump). It is already within budget ($22, only $3 of room), is closest to the time limit (14 min vs. 10 min), and its failure - a hose popping off - has a clear physical cause that can be fixed. B is 45 minutes over the limit, which is far too much to close by redesign. C is over budget by $13 and depends on sun, which the team cannot control.
Two changes
- Add a hose clamp (or double-wrap and tie the hose) at the pump outlet so pressure cannot pop it off. Cost must stay under $3.
- Widen the outlet hose and shorten its run to reduce the resistance the pump has to push against, so each stroke moves more water and the 20 L is delivered faster.
Fair test plan
- Run three trials of the revised pump under the same conditions: same 20 L starting volume, same 1.2 m lift, same hose length, same two students pumping at a steady pace.
- Record time to move all 20 L for each trial and average them.
- Record whether the hose stays attached in all three trials.
- Compare the average time and leak record to the original 14 min and two pop-offs.
Success means average time under 10 min, no leaks, and total cost still under $25.
3. The team wants to declare a winner after one trial of each prototype. Explain why one trial per design is weak evidence and name two variables they must control so their comparison is fair.
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Why one trial is weak
- A single run cannot show whether a result is typical or a fluke. If A's hose popped off because a student pumped unusually hard that day, the team would reject a design that might usually work.
- Small differences, such as 6 min vs. 10 min or $22 vs. $25, are easily erased by one odd trial. Repeating trials and averaging gives a number the team can actually defend.
- One trial also hides variation: B might take 50 min one day and 60 min another, and only repeats would show that range.
Variables to control
- Volume and lift: exactly 20 L moved, with the barrel and garden bed in the same positions (8 m apart, 1.2 m rise) for every prototype.
- Who operates and how: the same students pumping or setting up each device, at the same steady effort, and the same hose length and diameter where possible.
Also worth holding constant The same timekeeping method and the same weather/shade conditions, since C's performance depends on sunlight. If C is tested in shade and A in sun, the comparison tells the team nothing about the designs.