HCPSS Worthwhile Math Task
Angles in Field Hockey
Common Core Standard
7.G.B.5. Use facts about supplementary, complementary, vertical, and adjacent angles in a multistep problem to write and solve simple equations for an unknown angle in a figure.
MP1:
MP2:
MP4:
MP5:
MP6:
Make sense of problems and persevere in solving them.
Reason abstractly and quantitatively.
Model with mathematics.
Use appropriate tools strategically.
Attend to precision.
The Task
Different sports use angles in many different ways. A basketball hoop backboard has a
“sweet spot” allowing players to make the shot if the basketball bounces off at a particular angle.
Baseball players look for a particular angle to hit the ball so they can run more bases. Soccer
players have to position themselves at certain angles on the field to kick the ball in the goal.
Field hockey is a sport that also uses angle measures. As a player, you have to choose the
best angle at which to pass the ball to another player or to aim for the goal. As a goalie you have
to be aware of your positioning and angle measures so you can stop a shot heading towards the
goal cage.
The Stevenson University Field Hockey team is working on a play to use during a game.
Their coach has designed two different plays she wants to try in the upcoming game. She also
used a triangle to symbolize where opponents usually are on the field. This is for players to be
aware of as they are passing. The smaller the angle measure from the player to their opponent,
the easier it is for the opponent to intercept and steal the ball. The team wants to choose the play
that has the least number of passes with angle measures that are less than 40 degrees so they will
have a greater chance of finishing the play and scoring. Compute the missing angle measures in
order to determine which play will increase their chances of scoring.
Howard County Public Schools Office of Secondary Mathematics Curricular Projects has
licensed this product under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0
Unported License.
HCPSS Worthwhile Math Task
Facilitator Notes
1. Introduce the task to the students. Display What is Field Hockey? Student Resource or
distribute for students to read independently.
2. Distribute Angles in Field Hockey Field Map Play #1 and Play #2 to each student. (You
may choose to distribute both Play #1 and Play #2 to each student or you may choose to
distribute Play #1 to half of the class and Play #2 to the other half and have them compare
results.)
3. Students may work individually or in groups.
4. Allow students a few minutes to read the task and to begin developing a strategy for
solving. (Look for evidence of MP1 and MP2.)
5. Have a discussion about the types of angles on the Angles in Field Hockey Field Map.
(Look for evidence of MP3.)
6. Provide students with a calculator, scrap paper, patty paper, and any other materials
except a protractor. (Look for evidence of MP5 and MP6.)
7. As students work, circulate to monitor what strategies are being used to solve the
problem. Once groups have had an opportunity to solve the task, have groups compare
solutions and strategies (either through a gallery walk, a jigsaw, or through group
presentations). (Look for evidence of MP3.)
8. Make sure to highlight key ideas, such as vertical angles, supplementary angles,
complementary angles, adjacent angles, variables, setting up and solving simple
equations to find the unknown, etc. (Look for evidence of MP6.)
Follow-Up Questions
1. What strategy did you use to determine the opponent to player angle measures?
2. Explain how you used knowledge of types of angles in order to solve this task.
3. What are some other factors that need to be considered when a player is making a pass
besides angle measures?
Solutions
Sample Answer
Play #1 should be used because there are only 2 angles less than 40 degrees, which gives the
players a higher chance of completing the play and scoring. Play #2 has 4 angles less than 40
degrees meaning there is a higher chance of an opponent intercepting the pass and causing a
turnover in the field hockey game.
Howard County Public Schools Office of Secondary Mathematics Curricular Projects has
licensed this product under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0
Unported License.
HCPSS Worthwhile Math Task
Howard County Public Schools Office of Secondary Mathematics Curricular Projects has
licensed this product under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0
Unported License.
HCPSS Worthwhile Math Task
Howard County Public Schools Office of Secondary Mathematics Curricular Projects has
licensed this product under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0
Unported License.
HCPSS Worthwhile Math Task
Follow Up Questions:
1. What strategy did you use to determine the angle measures?
Setting up equations to find the unknown angle measure.
2. Explain how you used knowledge of types of angles in order to solve this task.
Supplementary angles =180 degrees, Complementary angles=90 degrees, Vertical angles are
equal to each other. Students should talk about how they used this knowledge to set up their
equation properly to find the unknown angle measure.
3. What are some other factors that need to be considered when a player is making a pass besides
angle measures?
Other factors include distance from player to opponent, speed of ball and player, if the direction
of the ball changes, if the opponent changes position, etc.
Howard County Public Schools Office of Secondary Mathematics Curricular Projects has
licensed this product under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0
Unported License.