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Math in Action: Hockey, Slap Shots and Math

Posted by The LearnBop Team

Mar 1, 2017 1:32:21 PM


Ever have a kid ask you when they'll use advanced math concepts in real life? The next time it comes up, strap on some skates, dig out your hockey sticks and let that youngster unleash a few hard slap shots at the nearest goaltender.


Some of the trickiest concepts in mathematics — geometry, physics, calculus, statistics — all come to life on a clean sheet of ice. Hockey is essentially math in action.


“If Sidney Crosby is coming down the ice, the angle at which the defenders must move to stop him is essentially a mathematical equation that must be done in the defenseman’s head, in a split second,” says Dave Smith, head coach of the Canisius College men’s ice hockey team. “He’s thinking of when they are going to collide, how long is his stick, and how soon will he run out of space.  It is absolutely math.”


It's challenging to get your student excited to learn about something that they don't think is relevant. However, math is in action all around us, and an understanding of its principles can help your child recognize math at work in the things that they love — like hockey.

Math Is Everywhere

Unless you are an biochemist, mathematician or a physicist, you probably don't spend much time thinking about the ways in which life can be broken down into chemical reactions, algebraic formulas and principles of physics. Math, however, makes our world work, and is the driving force behind the sports we love.


While recognizing and adapting to elements like speed, space and velocity may be second nature to experienced athletes, you can start to point out these elements to youngsters as you watch a hockey game together.


How do the players move the puck? How do they successfully work around obstacles in their paths? How do they angle their shots to get through a crowd of players in front of the net? What kind of parabola must they skate to maintain speed while turning back towards a play?


That’s math in action — hard-hitting action, at times. Professional hockey players can skate over 20 miles per hour, and hard slap shots come regularly flying through traffic at 90 miles per hour.


“If you’re a fan of the game, a beginning step would be to focus on the puck and the angles that the puck moves,” Coach Smith says.  “If I bank it off the boards, that’s a new angle, another point would be the angles that the players are moving...I think some players instinctively understand angles and understand the flex of a stick and how it feels and how it reacts to their instinctive body movement as a player, how they have learned it.”


Math makes the best hockey players even better

Clearly, it takes more than just an understanding of mathematics to be a star hockey player (knowing how to skate helps, too). According to Coach Smith, however, math isn’t a bad place to start.


"The best players understand speed and space and time better than others," explains Smith. "As a coach, recruiter or scout, we call it processing speed. We're processing the angle, we're processing the speed, the side of the impact is those two things collide. There are some extremely intelligent hockey players who can track who is going to collide and they can avoid the collision, protect the puck, and have the time and space. On the other hand, There are players that can skate fast, but they can’t calculate the speed relative to space, and they crash."

In other words, you don't have to be the fastest or the strongest player to be outstanding — the greatest player in the history of the National Hockey League, Wayne Gretzky, was never the biggest, fastest or strongest player on the ice.


Gretzky, however, had an innate understanding of how geometry and physics affect the game. He knew how place his body, and the puck, where other players weren’t going to be — often before they knew it themselves.


Ask your child to think about their own skating experiences. Do they need better balance and strength? Ask her to find center of gravity and draw strength from there. Is she a little too clumsy on the ice? Remind her to pay attention to her speed in relation to space and time; she'll find herself thinking ahead, visualizing her movements and angles, and crashing a lot less!


If accuracy on her passing or shooting is an issue, ask her to think about the angle a puck must travel to snap past a goaltender or to move through a forest of sticks to a teammate. These exercises help math come to life (and, if you’re really lucky, may put her on the road to a scholarship).


Math in action: The slap shot

The slap shot is a perfect example of math in action. When it comes to successfully executing this shot, which is used when a hard, accurate shot from the very edge of the attacking zone is the goal, it's all about technique.

In The Physics of Hockey, author Alain Hache explains that the slap shot is laid out in three stages:

  1. The player winds up his hockey stick.
  2. This is the interesting part that many non-hockey fans (or even some longtime fans) may not have known: the player swings out of his windup, "slaps" the ice with his stick and uses his body weight to bend it, causing energy to be stored in the stick. This is called “loading” the stick (and is often where you’ll see a stick break on a slap shot attempt).
  3. After slapping the ice, the player follows through/ The face of the stick strikes the puck, and the player shifts his weight so that the stored energy is released through the puck

“We start by assuming that the upper body and the stick rotate together with the same angular velocity about a certain point — the pivot, or fulcrum — located somewhere near the players center of gravity,” Hache writes.  “The idea in a slap shot is to convert the large about of angular momentum carried by the player and the stick (and some linear momentum if the player is skating forward) into linear momentum for the puck.”


The key, Hache continues, is body weight transfer — the player is shooting while moving in the direction of the shot, from back leg (windup) to front (release). In this way, taking a slap shot is almost like a pitcher in baseball’s throwing motion — moving all of that energy from back to front to create speed and accuracy.


Perfecting that motion takes work.


“Even though physics helps up understand how things work, firing a good slap shot takes practice above all else. I have seen countless lightweight players shoot much faster than stronger ones, simply because they had the proper technique,” Hache writes.  “There’s a lot of fine-tuning to do before a player can claim to master the slap shot. For example, the puck must be hit with the center of the curved blade, otherwise the stick flips and cannot generate the same amount of force. Some points like that are obvious, but it’s nice to see that physics often agrees with intuition.”


In sports and math — as in life — there’s no substitute for practice.


Make math fun.


Looking for a solution to help a student you know excel at math? LearnBop offers a fun, intuitive online experience that allows students to learn at their own pace while mastering the concepts that make math work. Learn more about LearnBop’s math tutoring software today.



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