Give it a try:
How to Make a Third
Out of Fourths
Bob told his friend Mark that he could make the fraction
1/3 just by using fourths. Mark did not
believe him, so Bob showed him how:
(1/4) + (1/4)2 + (1/4)3
+ (1/4)4 + … = (1/3)
Mark did not think this could be true, so Bob explained by
saying, “Look at the picture below.”
“Ahhhh…..” Mark said.
“Now I get it.”
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You and your team need to do two things in your
submission:
1.
Explain the meaning of the equation using
words. Come up with words that make the meaning
of all those symbols clear.
2.
Figure out how the picture relates to the
equation. Come up with pictures,
drawings or other explanations that would help a skeptic understand why the
picture proved Bob’s point.
For students who had quick success with this problem, an additional challenge was
given:
How to Make a Third
Out of Fourths --
A New Challenge!
By now, you have become convinced that this equation is
true:
(1/4) + (1/4)2 + (1/4)3
+ (1/4)4 + … = (1/3)
You have seen how the triangle picture can be used to explain
it.
Your challenge now is to come up with a different picture
to demonstrate the truth of the equation.
Instead of a triangle, perhaps you could start with a square. Can you think of ways to capture the ideas in
the equation by starting with a square?
