Brainstorming a Penalty Kick 3 Act Task

I came across the following video in my twitter feed, and think it would make a great 3 act task for my Trig/Precalculus class, and maybe could work something out with my geometry class as well, although probably without the algebraic equations. Maybe something we could hash out nicely in Geogebra.

The biggest question is how much information to give. My initial answer is usually none, but especially at the beginning of the year, as students are just getting used to my style of making them work for the information they need, is it necessary to give them a bit more to go on? I think a lot will depend on the students that I have in the classes, their cultural and mathematical backgrounds.

I’m thinking about finding a couple students from the soccer team at the beginning of the year to practice penalty kicks while I record it. Not sure exactly where this really fits, though conic sections seems to be a good bet. I tend to do conics later in the year, and have generally had students in four groups lead the lessons on each of the conics. It’s a nice setup for the unit that I’ve found really successful, but sometimes it’s worth trying something new, just because. Plus, I’ve had a number of my students on the soccer team, so maybe this is just a good way to help them score some more points, win some more games, and answer for themselves, “When am I going to use this?”2015 Mid Pen Coed Soccer 0017.jpg

It would also pair nicely with Henri Picciotto’s Soccer Angles problem that I was already planning to add to my toolbox for next year, so putting together a combination of tasks related to soccer, even across different classes (Trig/Precalculus and Geometry), would be a lot of fun. Plus, hopefully it will help us maybe win the league championship that we’ve been close to the past couple of years. Go Dragons!




2 thoughts on “Brainstorming a Penalty Kick 3 Act Task

  1. Neat! One way this might go:

    1) Students see a stick figure goalie in front of a goal. We ask the students: “Where would you try to kick it?” They click and we show the overlay of their picks. Betting a lot of kids pick outside the goalie’s reach circle.

    2) We then automatically kick ten soccer balls in the direction of that point. The student just clicks “Kick.” They don’t all go exactly to that point. We insert some variance. The goalie gets her hands on one or two. Another one hits the crossbar. Our interest here is in how accurate the students are using their intuition alone. Because the goalie is a stick figure, we can actually show the goalie attempting to swat the ball.

    3) Then we show four goalies in front of four different goals. We ask students what changes and what stays the same about each goalie. We highlight key observations. The width and height of the goal changes. The height and arm length of the goalie change.

    4) We ask students to use a sketch tool to “re-draw this picture of a goalie and a goal to show only the information that seems important to answer our question.” They don’t re-create the grass, the clouds, etc. This is where we’ll want to introduce the goalie’s reach circle if nobody does.

    5) Now we give students the original goal & goalie in a Desmos graph. Can they find the point that’s the same distance from the goalie’s reach circle and the bar and post? They can do this by adjusting sliders if they want.

    6) We re-run the experiment where they kick ten soccer bars. Now they’re more successful.

    7) If we want to motivate a general formula, we ask them to find the target point given 50 randomly generated scenarios involving different goals and different goalies. They can use sliders, but variables would be more exact and effective. Thanks for posting the video. Great food for thought.


    1. I love all these ideas – thanks for adding so much! Now I’m wondering about the how for the kicking simulation (parts 2 and 6). I know Desmos can do practically anything, but I’d need some help and time setting that simulation up graphically, and I’m curious if you (or anyone else) knows of anything already out there. Then again, we could do it with an actual goalie and striker because field trips (500 feet from my classroom to the soccer goal) are always awesome. I’ll play around with this, and post more as I get more fleshed out.
      Thanks again, Dan – and sorry you were originally marked as spam. Thanks also for helping me figure that out!


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