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Science of NHL Hockey: Hockey Geometry
Subject Area: Physical Science, Geometry
Grade Level: 5–8 (Physical Science, Geometry)
Lesson Title: Hockey Geometry
National Science Education Standards:
 Science as Inquiry: 5–8
 Motions and Forces: 5–8
Common Core State Standards for Mathematics
 Geometry, 5–8
Suggested Prior Knowledge: concepts of angle, circle, and quadrilateral; lab techniques for
measuring angles and distances
Purpose and Introduction: This video focuses on the geometry of the perfect hockey shot—the
angle that gets the puck into the goal. The activity will give students an understanding of the
basic properties of angles and the basic properties of circles and rectangles that can be applied to
the game of hockey.
Key Vocabulary:
angle—two rays with the same endpoint, the vertex.
angle of incidence—the angle that a straight line, ray of light, etc., meeting a surface, makes
with a perpendicular to the surface.
angle of reflection—the angle that a straight line, ray of light, etc., reflecting off a surface,
makes with a perpendicular to the surface.
circle—a closed curve in which all points are the same distance from the center.
quadrilateral—a closed figure formed by four line segments linked end to end; a four-sided
polygon.
Objectives:
1. Students will investigate some properties of quadrilaterals and circles.
2. Students will investigate the angles occupied (subtended) by objects and how those
change with distance.
3. Students will explore the relationship of the angle of incidence to the angle of reflection.
Materials:
- safety goggles
- assorted paper rectangles, parallelograms, trapezoids, and circles
- compass
- ruler
- rectangular block
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- pencil
- can
- newsprint
- marker
- tennis, golf, or table tennis ball
- tape
- meter stick
- framing square
- mirror (optional)
- carbon paper or cooking spray (optional)
Procedure:
1. After students view the hockey video, have them recall the various geometric shapes that
appear on a hockey rink. Ask volunteers to create operational definitions of rectangles,
circles, and angles using information from the video. Then, elicit instructions from the class
in drawing a diagram that illustrates angle of incidence and angle of reflection. Use questions
such as the following to encourage discussion:
 What are some examples of rectangles (circles, angles) encountered in everyday life?
What makes each example a good one?
 A hockey goalie wants to make an attacker’s angle of access as small as possible.
What are examples of angles you would like to be as small as possible? What angles
would you like to be as large as possible?
 If you drop a ball vertically on the floor, it will bounce back vertically, following the
same line. Suppose you want to bounce a ball to a friend nearby (for instance, you
make a bounce pass to a basketball teammate). Then the path of the ball is no longer
exactly vertical. For the ball you bounced, which is the angle of incidence and which
is the angle of reflection?
2. Lab protocols should be followed, incorporating safety equipment. Goggles must be worn at
all times.
3. Encourage students to speculate on geometric relations and ways of exploring them with the
apparatus supplied. The following questions can help focus their plans and guide them:
 What relation describes the four angles of a quadrilateral?
 What are the relationships of the four sides of a quadrilateral?
 How can you measure the angle occupied (subtended) by an object?
 How does the angle occupied by an object vary with distance?
 How does a reflected light ray resemble the path of a bouncing ball?
 How can you measure the angle of incidence and angle of reflection for a light ray?
4. Students should explore possible relations involving the angles of the quadrilaterals by
measuring the angles of the paper quadrilaterals. Depending on their grade level, students
may not be aware that the sum of the interior angles of a quadrilateral is always 360°.
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5. Again, depending on their grade level, students may not be aware of the differences between
a trapezoid, a parallelogram, and a rectangle. Using the ruler and compass, they can explore
which pairs of sides are parallel and which pairs are equal in length in each figure.
6. Encourage students to explore the central angles formed in a circle, and perhaps
approximations to measuring the circumference. They can manipulate the paper circles—
folding them in half and then into quarters or smaller segments.
7. Suggest students use the block, can, and ball to explore how the angle an object occupies
depends on its distance from an observer and on the way it is oriented. For instance, students
might measure angles occupied by the objects at distances of 10, 30, and 50 cm and with two
or three different angles of orientation. Then, remind students that a hockey player likes to be
directly in front of the goal and as close as possible when he or she takes a shot. Elicit from
students that in that position, the angle of attack is as large as possible and the goalie’s task is
to block as much of that angle as possible. After students come to this conclusion, review just
this portion of the video to confirm their thinking.
8. Give small groups of students a tennis, golf, or table tennis ball and challenge them to track
the path of the moving ball as it is reflected off a vertical surface. If needed, suggest they
appoint spotters that will identify the point of each action in the process—start, reflection
point, and end. Students might roll the ball over sheets of newsprint and have spotters use
markers to document each of these points. Then students should recreate the path of the puck
with a straightedge and establish the perpendicular. Students might also roll a ball over
carbon paper or coat a ball with a substance that will leave a trail, such as cooking spray.
Direct students to measure the resulting angles and draw a diagram with the angles labeled.
Some students may need to be reminded that the perpendicular forms two right angles (which
have a sum of 180°).
9. Remind students that, just as a ball that is dropped vertically bounces back vertically, a
hockey puck that strikes the boards perpendicularly bounces straight back along the same
path. Explain that in that case the angle of incidence and the angle of reflection are both zero.
Refer students back to the video to observe that if the path of the puck before it strikes the
boards is not perpendicular to the boards, then the puck has an angle of incidence of a certain
number of degrees. The path of the puck’s rebound also makes an angle to the perpendicular,
and the angle of reflection is equal to the angle of incidence. Have students compare this with
their drawings.
10. After the students have finished their investigations, present this challenge problem to them:
A hockey player stands on the center line in a rink, a few meters to one side of the center, and
shoots the puck into the opponents’ goal. The path of the puck is not exactly perpendicular to
the center line. It makes an angle α with the perpendicular. Now suppose the player instead
takes a shot on his own goal. What angle does the puck’s path make with the perpendicular to
the center line? Ask students to draw what they think is going to happen first and then
discuss their ideas in small groups. The groups can then try out the activity and report back to
the class where comparisons can be made and a mathematical rule based on their
observations established.
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Connect to Optics: You might use this video in conjunction with students’ study of optics as
well. Tell students that tracking the path of a ball or a hockey puck can be difficult, and ask them
if they can think of anything else that might obey the same law. Asking what else they know that
reflects should bring light rays to mind. If not, then ask what reflects from a mirror. If they think
that they cannot track the path of a light ray directly, suggest that a line of sight is the same as the
path of a ray of light. Encourage them to experiment with the mirror to make observations about
the reflection of light. If they are making slow progress, give hints about a procedure similar to
the following:
Measuring angles of incidence and reflection with a mirror is straightforward. One
student looks at his feet in the mirror, and another marks the spot on the mirror where the feet
appear to be. Using the framing square, the second student constructs a perpendicular to the
mirror surface at that spot. The students then measure the angles made by the sight lines to the
first student’s eyes and to his feet.
Additional Resources:
 http://www.nscdiscovery.org/TeacherTools/Adobe/MirrorMirrorontheWall.pdf
 www.goalrobber.com/links_39_2505472894.pptx
 http://biology.wsc.ma.edu/Math251/node/15
 http://icehockey.isport.com/icehockey-videos/play/geometry-of-a-slap-shot-10961
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Student Worksheet for Hockey Geometry
Experiment Title: _____________________________Date: __________Name: _____________
Student Hypothesis or Question:
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Materials:
- safety goggles
- assorted paper rectangles, parallelograms, trapezoids, and circles
- compass
- ruler
- rectangular block
- pencil
- can
- newsprint
- marker
- tennis, golf, or table tennis ball
- tape
- meter stick
- framing square
- mirror (optional)
- carbon paper or cooking spray (optional)
Procedure: (Include all safety procedures)
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Analysis of Data:
Conclusion: ___________________________________________________________________
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