Soccer is a low-scoring game despite the large size of the goal and the fact that there are few people spread about a very large field acting to defend the goal. It would seem that the defenders maximize their effectiveness by arranging themselves in the most efficient positions.
Today you will explore how stationary "defenders" might most efficiently shield a goal from an approaching ball or object. The defenders will be toothpicks and the ball will be a marble.
Research Assignment
Your job is to determine the most effective way to arrange a given number of toothpicks to block a ball that your partner attempts to roll from one side of a styrofoam rectangle to the other. Here are some guidelines:
- Divide the "field" into thirds. Make your division lines lightly in pencil, and perpendicular to the long side of your styrofoam rectangle.
- One end of the field will be the end that the ball is rolled from, and the other end will be the goal (the entire end will be the goal•not "There will be a goal on the other end.")
- You and your partner should agree to the number of defenders (toothpicks) you will use, and then one of you should arrange that number in the middle third of the field. Both of you should draw in your journals the arrangement that is used
- Note that the number of defenders that will trivally allow perfect defense is (w/d)-1, where w is the width of the field and d is the diameter of the ball. (It would be a valuable exercise to derive this in your journal.) You and your partner should agree to use some fraction of this number•say, 1/2 or 3/4.
- Each of you should try to roll a ball through the other's arrangement in ten different ways. (Doing the same thing ten times is pointless.) On your diagram in your journal, make a line each time the ball is rolled to show the path it took. Mark which toothpick the ball hit, or if the ball made it all the way through.
- If you'd like, you could make a competition out of it. You get a point each time your toothpicks block a ball from rolling through to the other side. Note that you should not roll the balls hard enough to knock the toothpicks over. If a toothpick is knocked over, the shot is considered blocked, and the defender gets a point.
- Play the game as many times as you can in your lab time, recording all of your shots (and your opponent's shots) in your journal (sort of like keeping score at a baseball game).
Journaling: What Did You Learn?
Write at least three sentences that summarize your work today. Be prepared to share your reflections with the class.