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Soccer 2v2 - Positioning, Angles, and Dilations


Adding More Players

While considering penalty kicks gives us a good starting point, soccer positions get more complicated as we consider more of the players on the field. To start, let's consider the 2v2 situation pictured below.

1. Predict

OffenseA has the ball, and needs to make a split-second decision. She is deciding between shooting or passing to her teammate, OffenseB. Which do you think is the better decision and why? Explain your reasoning in 2-3 sentences.


2. Investigate

Now play with the applet below. Look at what happens to the angles and dilations when we change the focal point ("Center of Dilation") from OffenseA to OffenseB.

Soccer - 2v2 Example

2a - She takes the shot

Suppose OffenseA has the ball and decides to shoot. How much of the goal is covered by the goalkeeper's dilation? Where does the dilation of DefenderA end up if we use this point as the center of our dilation?

2b - She passes

Change the checkboxes so that OffenseB has the ball now. How did this change the images on the dilation? Are they in the same spot as in 2a? Describe how the images are positioned compared to the center of dilation.

2c - Other Observations

What other geometric properties (angles, area, midpoints, parallel lines) did you find in the scenario? Record your observations.

3. Revise

Now revisit your initial answer. Would you change your advice from part 1, or make the same suggestion? Justify your response with some of your observations from part 2.


4. Create

Design a different "Pass or shoot" scenario in the applet below. In the text box, explain who has the ball, which choice you'd recommend (pass or shoot), and why.

Soccer - 2v2 Example