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					                    Miniature Golf – Teacher Notes – page 1

Problem #1: How can you hit the ball, B, around the obstacle and into the hole, H,
in one shot?
                                      H




                                              B




Solution: You need to bounce the ball off one of the walls to get it around the
obstacle. Picture the image of the hole, H’, reflected across the wall you are
bouncing off of. This is what you should aim for.
                                H'        H




                                                  B




Problem #2: This hole cannot be reached with simply one bounce off the wall.
We will need to try 3 bounces (wall, obstacle, wall).

                                          H




                                          B
                     Miniature Golf – Teacher Notes – page 1

Solution: Begin by visualizing the path the ball will travel and which walls it will
hit off of. Then work backward. Which wall will the ball hit last? Reflect the
hole across that wall first.
                                            H                         H'




                                                              this
                                                              wall


                                            B




Next reflect H’ across the obstacle wall it will hit before that.

                                  H''           H                      H'




                                                this
                                                wall




                                                B




Since the ball will bounce three times, reflect H” across the wall again, producing
H”’.
                            H''         H                        H'         H'''




                                                       this
                                                       wall




                                        B
                    Miniature Golf – Teacher Notes – page 1

H”’ is the place where you should aim. Observe the path the ball will take.
                           H''     H              H'      H'''




                                   B




Problem #3: The direct path from the ball to the hole is blocked by the corner of
the wall. For this hole, you might need to try 2 different bounces.

                                                  H




                                       B




Visualize the path of the ball hitting two walls and into the hole.
                         H''                             H'



                                                         H




                                              B
                    Miniature Golf – Teacher Notes – page 1

Can you think of another way to get the ball to the hole in one shot? Draw it on
the next picture. Be sure to include the correctly-labeled reflections. You may
wish to use Patty Paper to help you with the reflections.




                                                H




                                   B

				
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