The Jacuzzi of Math
or
HOW TO APPROACH A MATH PROBLEM


Often the hardest part of solving a problem is getting started.  This is particularly true of puzzles and word problems.  You probably wouldn't jump into a pool before checking whether it is full of water.  I'd want to make sure there's nothing on or under the surface that I wouldn't mind bumping into.  I might even check the water temperature.  But even if the water is clear, blue, deep, fresh and warm, I wouldn't dive in unless I knew how to swim.

If you're not confident in your ability to swim through math, why not step over to the wading pool-- or better yet, the jacuzzi! It is only three or four feet deep.  It's filled with luxurious, swirling, bubbly, hot water.  You'd have to work pretty hard to drown in a jacuzzi.  No need to dive.  There are some handy-dandy steps and even a supporting rail to hold onto until you're comfortably seated.

So let's consider the following puzzle not a raging sea but a delightfully warm jacuzzi.

Here's the challenge:

Split this figure into five, identical shapes, each containing one of the five dots?

How will you go about solving this problem?  What kind of cuts or separating lines will you make?  Will you make curved cuts? Angled cuts?  Rectangular cuts?  (*You could even imagine that you're looking down into a yellow jacuzzi occupied by five blue bathers.  Each bather is seated on a built-in, immovable seat.  Your task then is to divide the jacuzzi into five identically shaped areas, each of which contains a seat).

Don't worry about the answer yet!  Enjoy the jacuzzi. Let your imagination play!  Since the exterior lines are all straight, does it follow that each resulting shape will have at least one straight edge?  What about the corners?  If one has a corner, they all must have a corner.  There are seemingly endless ways the shape can be divided.  What other information might help you before you start dividing?

 Hints to solve the problem             See the final solution