Soccer Ball Math

The Ball Story

It happened to me yesterday. Like all non-expecting, well-intentioned, hard-working coaches who happened to be in the wrong place at the wrong time. 

I was positioned 10 feet outside of the goal frame instructing my goal keeper on a few points. The rest of the team lined up around the 18' mark, poised and ready for taking shots on our keeper. 

Just as I turned ever so slightly to face the next shooter and motion for her to take the shot. That's when it hit me, literally. That's when the cry of all self respecting men rang out around the world. That's when the wayward shot from the foot of the quietest girl on the team came like a comet screaming for my manhood and hit me square, causing every woman and child in viewing distance to pause, gasp, and then burst out into laughter.  

I dropped. 

I cried.

They laughed. 

The Ball Story Problem

Being a soccer coach I am fascinated with the different designs of a soccer ball. However, the traditional design offers geeky teachers a challenging math problem involving areas of two dimensional regular polygons that are linked together to form a three dimensional solid. 

So, in honor of attending NCTM 13 in Denver this week (and of course the story above) I thought I would share this problem. The students do an entertaining job of explaining the problem in the video below. 

Problem: Find the surface area and radius of the traditional size 5 soccer ball when given the side of the regular pentagonal panels is 4.2 cm. 


Simply handing the students a soccer ball and asking them to find the surface area is also a nice way to address the math practice standards of 'persevering in problem solving.' Hopefully after presenting this problem students will ask good questions such as; What do I need to know in order to find the radius and the surface area? What shapes make up the surface area of the ball? How can I find the area of one of those shapes? etc. 

Obviously you can scaffold the information as you see fit for your students. As you can tell from the video we chose to tell them how many pentagons and hexagons made up the surface of the ball. You could also chose to give them more information such as the formulas for finding the area of a regular polygon. Or you could simply hand them a ball and a ruler and tell them to come up with as an exact of a measure for the surface area and radius as they can. 

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