Estimation Exercise (Leaky Water)

Black ink is what I am planning on asking the students -blue is what I hope some of the responses might be, red is notes for us:

Someone reports that almost 6,000 gallons of water is lost every year on campus due to leaky sinks.

You are asked to evaluate the truth of the statement.

1) What questions do you have about the statement?
where did the number come from?
what counts as a sink?
what constitutes a leak?
how were the leaks measured?
where is or what was the data used? or how was it collected?
what campus?
(ie how did the researcher arrive at this number? -what assumptions or baselines did she start out with?)

2) What are ways to determine the truth of the statement?
Ask the researcher the answer to the above questions so you can retrace her steps (practical, not always possible)
Measure the leak of every sink on campus for a year (exhaustive, will give an answer, but not practical we have an hour not a year)
Make your own estimate and compare to the researcher’s.

3) Find you own estimate (in the next 15 minutes purposeful time limit) -in groups

4) Report it as a statement and ask your classmates to evaluate the truth of your statement. (Keep in mind what they will need to know about your process in order to make that evaluation.) (Possibly do this as a gallery walk? -asking each group to write two questions or comments on each poster? Do we still have giant post-its?)

After report out discussion: (Possibly the first journal assignment)

5) What are the limitations of your group’s estimate?

6) What would you change about the way you completed your estimate and why (Given a little more time and the ability to leave the classroom is there anything that might help ensure a more accurate estimate?)

7) Which estimate from class do you think is the most accurate and why?

Points for us to make:
Scientific research is reported as statements with supporting assumptions and evidence.
A scientist gives an interpretation of the evidence (sometimes using a particular method) based on her assumptions, previous knowledge, and experiences.
Other scientists review the work before it is published -generally checking the assumptions, the method and the stated results.
Are the assumptions reasonable? If there is data, what is its source and/or how was it collected? Is the method applied correctly? Do the stated results follow logically?
Research can be affected by outside limitations -time, funding, manpower, etc.

How I came up with the estimate (quick and dirty and tons of room for improvement):

There are approximately 15 non dorm buildings on campus each with approximately four bathrooms, each bathroom with approximately 2 sinks. There are about 8 dorms on campus each with approximately 6 bathrooms and 8 sinks in each bathroom. This gives an approximate total of about 504 sinks on campus. Of the sinks on campus, probably 20% of them have leaks. Or about 100.8 rounded to 101 leaky sinks on campus. On average, each leaky sink probably loses 2.5 cups of water a day -so a total of 252.5 cups of water, rounded to 253 cups, a day is lost. There are 16 cups in a gallon so 15.8125 gallons rounded to 16 gallons per day is lost due to leaky sinks. There are 365 days in a year so 5,840 gallons lost in a year.

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