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Problem Description Sheet: A
Fool’s Gold Does Not Measure Up
Introduction: One bag of real gold is placed with other bags
of fool’s gold. The bag of real gold has a mass of 404 g.
Each bag of fool’s gold has a mass of 400 g. You have
a balance scale to compare the masses.
Problem:
-
If there are two bags of fool’s gold and one bag of real gold,
explain how you could know for sure which bag is real gold using the
balance only one time.
- If there are six bags of fool’s gold and one bag of real
gold, explain how you could know for sure which bag is real gold
using the balance only two times.
- Now there are twelve bags of fool’s gold and one bag of real
gold. You could be lucky and find out which bag is the real gold
using the balance just once. If you are not this lucky, what is the
least number of times you could use the balance and know for sure
which is the bag of real gold? Explain your answer.
- Now there are 48 bags of fool’s gold and one bag of
real gold. Without depending on luck, what is the least number of
times you could use the balance and know for sure which is the bag of
real gold? Explain your answer.
- Can you find a pattern or rule to figure out the least number of
times you need to use the balance (without depending on luck)? Test
your rule with one bag of real gold among 204 bags of fool’s
gold.
Materials: pencil, paper, calculator, counters (fool’s
gold), counter marked with tape (real gold) |
Topic(s):
Numbers and operations
(N-39, P-4c),
critical and creative thinking, communication
Activity Type:
Group Individual
Assessment:
Scale:
Self Peer Teacher
Include in your portfolio?
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Toward your marks?
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