Scale 'n Pop
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A carnival is in town! It offers games of chance and games of skill.
You decide to try your skill at a game called "Scale 'n
Pop." Here's how it works.
A helium-filled balloon is tied to a rod. Just above it, between two
boards, is a gap that leads to a pair of sharp nails. The distance
between the nails is a little less than the width of the gap.
To win the game, you must figure out how to make the balloon small
enough to fit through the gap, yet still large enough to touch (and
be popped by) the nails. You can inflate or deflate it so that its
diameter is a fraction of its original size. (That fraction may be
greater than or less than 1.)
To Do and Notice
To scale your balloon, type a fraction into the box and then click on
the Scale button; your balloon's new size will be displayed.
When you think your balloon is the right size to reach the nails,
click on the Release button. If your balloon doesn't pop, click on
the Reset button, try a different fraction, and
then scale and release it again. Repeat those steps until you win
- What fractions popped the balloon in:
- Review the sequence of fractions you used in booth 3. Explain
your strategy for picking fractions in this sequence.
- Last year a student playing this game in a different booth found
that 3/2 made the diameter too small and 5/3 made the diameter too
large. Recommend a strategy the student might use to find a fraction
that will pop the balloon.
- What is the difference between increasing the numerator and
increasing the denominator of a fraction?