Protractor Golfing
This activity can grow with the maturity of your
students.
1. Have your students (or you can do this) draw
some golf holes with sand and/or water hazards - decide on a
symbol for sand and another for water.
2. The placement of the tee/ball on the game board should be represented by a
compass marking (0-180 degrees or 0-360 degrees). The
original ball placement is at the crosshairs of the diagram
to the right.
3. Put a flag on the game board to identify where the hole is.
4. Copy the following table many times and give one to each
student to glue on their holes.
Angle Length Strokes
water hazard = +2
sand trap = +1
Total
5. To determine par for each hole, have 5 students play the hole (level 2) and take
the average number of strokes and use it for par or come up with a formula
based on number of hazards and length of golf shot that needs to be made.
Feel free to have your students make up their own rules for finding par. They’ll
have a good time!
* If you want to be able to use these golf holes over and over again, either make
transparencies of each of them, laminate (or put clear contact paper on) each hole, or
put the holes inside the clear plastic protectors (which makes them easy to store in a
three ring binder for later use. Let students use overhead markers or grease pencils
when they play.
Nancy Powell and Andrew Moore –Bloomington High School, Bloomington, IL NCTM, 2006
Golf - Page Page 1 of 12
Sample Game Board/Golf Hole
Angle Length Strokes
water hazard = +2
sand trap = +1
Total
RULES
Level 1: Have students work individually. Measure distance and angle measures to hit
the hole in one shot from the original ball placement. Decide if you want the students
to measure in centimeters or inches. Have students record the number of the hole
and their measurements for each hole on a sheet of paper.
Level 2: Have students work in pairs. One student estimates the angle and the
length of the hit. The second student records the guess and measures according to
the estimation. If the ball goes in the hole or within 5 mm of the hole, that hole is
over and the student records the number of strokes on his/her score card. However,
if the ball did not go in the hole, the number of strokes (including penalty strokes)
should be recorded, the first player guesses again - the second shot begins where the
first estimate left off. . . and continue recording estimations and playing. Make up
Nancy Powell and Andrew Moore –Bloomington High School, Bloomington, IL NCTM, 2006
Golf - Page Page 2 of 12
your own rules about balls that go into a water hazard! (Do you start in the water on
the next hit, or do you move the ball to a place outside the water and how do you
determine this place?) Continue playing until the ball goes in the hole.
Then change game boards (holes) and have the student who was the recorder and
measurer trade and do the estimating and the player that did the estimating then
becomes the recorder/measurer. Have students keep a score card at the end of each
hole for the holes they play. Note: Make sure to change holes or player #2 definitely
has an advantage because of the estimates of player #1 made on the same hole.
Golf SCORE CARD
Name:
Hole # ______ Par _____ ________ Strokes
Hole # ______ Par _____ ________ Strokes
Hole # ______ Par _____ ________ Strokes
Hole # ______ Par _____ ________ Strokes
Hole # ______ Par _____ ________ Strokes
TOTALS ________ Strokes
If you want to identify the class pro. . . have students divide their strokes by the
total of the pars for the holes that they played. The best score is the smallest
decimal. A score of 1 indicates that the golfer made par, a score less than one
indicates that the golfer had a score below par (VERY GOOD!), and a score greater
than one indicates that the golfer’s average was over par for the holes that he/she
played.
Level 3: Either put each of the student’s holes on a transparency and then put a
piece of graph paper under each transparency or have students draw their holes on cm
or ¼” graph paper to begin with! The rules of the game remain the same as Level 2.
However, students can use the grid to help them estimate the distance to hit the ball
using the Pythagorean theorem and estimate the angle to hit the ball using their
knowledge of right triangle trigonometry. Calculators would be helpful here! There
still will be an element of estimation because of the size graph paper used and it is
very important for students to know their trig ratios even if they have a calculator.
Adapted from “Golfing with a Protractor” by Ronald Souza, Arithmetic Teacher, April
1988
Nancy Powell and Andrew Moore –Bloomington High School, Bloomington, IL NCTM, 2006
Golf - Page Page 3 of 12
Here is a sample hole if you want to use trig or Pythagorean theorem with the aid of graph paper!
Angle Length Strokes
water hazard = +2
sand trap = +1
Total
Nancy Powell and Andrew Moore, Bloomington High School, Bloomington IL – NCTM, 2006
Golf - Page Page 4 of 12
How to get a Hole-in-One
Miniature Golf
Objective: Find a path for the ball to follow to make a hole-in one using
reflections to find angles of incidence equal to angles of reflection.
Materials: You’ll need paper, tape, a compass and straightedge or a mira
(sometimes called a geo reflector, geo reflecta, or something similar)
Banking the ball off of one wall – make sure to have a large enough piece of paper to
construct/find the points of reflection --- be ready to tape another piece of paper to the original one if
you need it!
1. Locate the hole (H) & beginning position of the ball (B).
2. Pick a wall to bank the ball off of and label it W1.
3. With a compass or mira, reflect the hole (H) over wall 1 and mark it H’.
4. With a straight edge, connect the ball (B) with H’ using a dotted line to locate where on
the wall the ball needs to reflect off of.
5. Connect the hole (H) to the point of intersection of the wall and the line from the ball to
H’ to complete the path of the ball. The solid lines show the path the ball will take to
make the hole in one. Realize that speed of the ball, the type of surface used on the
hole, the accuracy of the golfer, and other factors may influence the actual success of
the hole-in one! (See the diagrams below showing two examples of the same golf hole but
banking the ball off of different walls.)
Example 1: H' Example 2:
Hole-in-One
banked off of Hole-in-One
one wall! banked off of
one wall!
H H'
H Wall 1
B
Wall 1
Ball
Ball
Nancy Powell and Andrew Moore, Bloomington High School, Bloomington IL – NCTM, 2006
Golf - Page Page 5 of 12
Banking the ball off of 2 walls
(*Note: not all choices of walls will result in possible holes-in-one because of the design of the
hole. If you begin connecting points and the points of contact do not end up on the correct wall,
that path is not possible and other walls should be chosen or the placement of the ball or the
hole must be changed.)
H'' 1. Locate the hole (H) & beginning position of the ball
(B).
Hole-in-One 2. Pick and label the walls starting at the hole and
banked off of working backwards from the hole. Mark the walls
two walls! W1 for the last wall the ball will hit before landing
in the hole, and W2 for the 2nd to last wall (in this
case the first wall hit by the ball).
W2 3. With a compass or mira, reflect the hole (H) over
H the wall 1 (W1 on this example) and mark it H’. You
may have to extend a wall to be able to complete a
reflection.
4. With a compass or mira, reflect H’ over wall 2 (W2)
W1 and mark it H’’.
H'
H' H''
W1
Ball B
H
5. With a straight edge, connect the
ball (B) with H’’ to locate where on
the wall the ball needs to hit. Then
connect that point of
contact/intersection with H’ to W2
locate where on wall 1 the ball needs B Hole-in-One
to hit.
banked off of
6. Finally, connect the point of
two walls!
contact/intersection on the wall 1
with the hole (H) to complete the
path of the ball. (See the diagrams.)
Nancy Powell and Andrew Moore, Bloomington High School, Bloomington IL – NCTM, 2006
Golf - Page Page 6 of 12
Banking the ball off of 3 or more walls
(*Note: not all choices of walls will result in possible holes-in-one because of the design of the
hole. If you begin connecting points and the points of contact do not end up on a wall, that path
is not possible and other walls should be chosen or the placement of the ball or the hole must be
changed.)
1. Locate the hole (H) & beginning position of the ball (B).
2. Pick and label the walls starting at the hole and working backwards from the hole. Mark
the walls W1 for the last wall the ball will hit before landing in the hole, W2 for the
second to last wall, W3 for the third to last, etc.).
3. With a compass or mira, reflect the hole (H) over wall 1 (W1 on this example) and mark it
H’. You may have to extend a wall to be able to complete a reflection.
4. With a compass or mira, reflect
H’ over wall 2 (W2) and mark it
H’’. Then reflect H’’ over wall 3 H H'
(W3) and label it H’’’.
5. With a straight edge, connect
the ball (B) with H’’’ to locate H''
where on the wall the ball needs Wall 2
to hit. Then connect that point W2 Wall 1
W1
of contact/intersection with H’’
to locate where on wall 2 the
ball needs to hit. Then continue Ball
until all of the walls chosen have B
points of contact/intesection.
6. Finally, connect the point of
W3
contact on the wall 1 with the Wall 3
hole (H) to complete the path of
the ball. (See the diagram.)
7. If you want to place obstacles Hole-in-One
on the hole, do it AFTER you banked off of
three walls!
find the path of the ball to
make sure that the obstacle H'''
doesn’t get in the way of the
ball and the path it needs to follow.
Nancy Powell and Andrew Moore, Bloomington High School, Bloomington IL – NCTM, 2006
Golf - Page Page 7 of 12
This diagram shows how to make a hole-in-one by banking the ball off
of 5 walls. Notice that at each point of contact with the wall the angle of
incidence = angle of reflection! (BUT, don’t make the mistake that ALL of
the angles at those points are NOT the same measures!)
H'''''
H''' H' H''
W1
H
W2
W3
W5
B
Ball
W4
Hole-in-One
banked off of
five walls!
H''''
Nancy Powell and Andrew Moore, Bloomington High School, Bloomington IL – NCTM, 2006
Golf - Page Page 8 of 12
Here’s one that doesn’t work….
H''' Look here!
Note: If you're
H''''' connecting a path
to H'', you should
H'
W1 H'' intersect W2!
Does it?
H
W2
W3
W5
B
Ball
W4
This Hole-in-One doesn't work
banked off of five walls
because when you connect
the path between H''' and H''
doesn't hit W2! It hits W1 too
H'''' early!
Nancy Powell and Andrew Moore, Bloomington High School, Bloomington IL – NCTM, 2006
Golf - Page Page 9 of 12
Try this one…
G J
H
F I
E J
B
D K
Nancy Powell and Andrew Moore, Bloomington High School, Bloomington IL – NCTM, 2006
Golf - Page Page 10 of 12
Name ________________________
Nine-Hole Miniature Golf Scale Model Project
Use your imagination and design a three-dimensional 9-hole
miniature golf course around a theme. The base of the complete
model that you construct can be no larger than 22" x 28" (the
size of a piece of poster board/foam core board). There is no
limitation on materials for either the course or design features.
Some suggestions for the surface include foam core board
(lightweight and easy to work with), wood, corrugated cardboard, heavy poster board, etc.
Draw each hole (the same size as the final hole on the model) on a
separate piece of paper that will allow you to
construct the paths for the holes-in-one. Use a red writing utensil
to indicate a path when the ball bounces off of 1 wall, a blue writing
utensil to indicate the path using 2 walls, a green line to indicate
the path of the ball bouncing off of 3 walls, and other colors (make
a key) for additional paths. This collection of drawings (all nine holes) should be checked when
you’ve finished your holes, at least one week before your nine-hole golf course is due. After
your holes have been checked, create your model and get your drawings ready to turn in with
your final model.
The scale model must contain nine holes and a
path between them. Each hole should include
the ball placement, a flag at the hole with the
hole number on it, and a minimum of 3 paths,
color coded and include a color key on your
course and you can be creative as to what you
use to mark the paths on your model. Some
suggestions for marking the paths include
string, embroidery thread, yarn, markers, fabric
paint (but practice with this first!) etc.
On the face of the model, include the following
information:
* your name and date
* color key for your paths
* a name for your golf course
Nancy Powell and Andrew Moore, Bloomington High School, Bloomington IL – NCTM, 2006
Golf - Page Page 11 of 12
Name ____________________________
Date _________________________
Nine-Hole Miniature Golf Evaluation
Points Points Comments
Possible Awarded
Category
Scale Drawings (50 points)
Checked by the deadline 5
Accuracy of Constructions 36
(4 points per hole)
Neatly done and follows 9
required color codes
Scale Model (50 points)
Your name and date 4
Color key for your paths – 5
neat & complete
A name for your golf course - 5
creative and neatly displayed
Paths between holes 9
Accuracy of path placement 27
(3 points per hole)
2 points per hole bonus for a path that 10
banks off of 4 or more walls Extra
Credit
Total -----> 100
Nancy Powell and Andrew Moore, Bloomington High School, Bloomington IL – NCTM, 2006
Golf - Page Page 12 of 12