'Plausible Estimation' Estimating for
Amazing Facts Tasks - Set #3 (solutions)
Malcolm Swan
Mathematics Education
University of Nottingham
Malcolm.Swan@nottingham.ac.uk
Jim Ridgway
School of Education
University of Durham
Jim.Ridgway@durham.ac.uk
The aim of this assessment is to provide the opportunity for you to:
· develop a chain of reasoning that will enable you to estimate quantities to an appropriate
degree of accuracy
· choose suitable units for your estimate
· communicate the assumptions upon which your estimate is based.
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1. High stack
Suppose you have a very large sheet of paper. You tear it in half and put one half on top of the
other. You now have a stack of two sheets.
You now tear the whole stack in half and place one half on top of the other to make a new stack.
You repeat this process, tearing 50 times. (Yes I know its impossible - just imagine you could).
How high would the stack be? 50 feet? 100 feet? A mile? or more...? Make a sensible estimate,
based on careful reasoning.
Assumptions
· A ream of paper (500 sheets) is about 2 inches thick
Reasoning
Each sheet is therefore approx 1/250th of an inch thick.
After 50 tears, the stack will contain 250 sheets of paper.
This is equal to approximately
1.1259 x 1015 sheets or 4.5 x 1012 inches = 71million miles.
Answer: 71 million miles!
2. The swimming pool and the glass.
How long would it take you to empty an olympic size swimming pool with a glass?
Assumptions
· Dimensions of swimming pool = 50 meters x 20 meters
· Depth of water = 6 feet (2 meters)
· The glass holds half a pint.
· You empty the pool at one glass per second.
Reasoning
This gives volume of pool as 2000 cubic meters or 2 x 106 liters.
One half pint glass has a volume of about 25 x 10-5 cubic meters.
Thus approximately 8 million glasses will empty the pool.
This would take 2,215 hours or about 90 days.
Answer: 92 days or about 3 months, working day and night!
3. The briefcase of cents
Suppose you filled a briefcase with one cent coins.
How much would the money be worth?
Assumptions
· A cent coin has a diameter of 20 mm (0.75 inches) and a thickness of 1.5 mm
· The briefcase is approx 100mm x 350mm x 500mm
Reasoning
The volume of the coin is therefore given by
pr2h = 3.14 x (20/2)2 x 1.5 Å 470 mm3
The volume of the case is approx 500 x 100 x 350 = 17,500,000 mm3
Thus the number of coins that will fit in (assuming no gaps) will be about
17,500,000 Ö 470 = 37,000 (approx).
There would be some gaps between coins, so
Answer: The money will be worth around $350.
(Note that the total weight of the case would be almost 100 kilograms - far too heavy!)