Summary: Activities require students to make their own protractor and use it to identify and measure various angles.
Main Curriculum Tie: Mathematics Grade 4 Strand: MEASUREMENT AND DATA (4.MD) Standard 4.MD.5 Recognize angles as geometric figures that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement. Materials: Invitation to Learn
Using a Protractor
 Label a Protractor
 Overhead protractor
 Overhead projector
 Math Journal
 Glue
Classroom Protractors
Additional Resources
Books
Sir Cumference and the Great Kingdom of Angleland: A Math Adventure, by Cindy
Neuschander; ISBN10: 157091169X
Angles (Let’s Investigate), by Ted Evans; ISBN10: 1854354663
Angles are Easy as Pie, by Robert Froman & Byron Barton; ISBN10: 069000916X
Attachments
Web Sites
Background For Teachers:
The protractor is an instrument of measurement. A protractor is
used to construct and measure angles. The simple protractor is an
ancient device used for plotting the position of boats on navigational
charts. There are different kinds of protractors, but the one used in
elementary school is called a simple protractor. We have units for
measuring angles and they are called degrees. These are not the same
as temperature degrees, even though the same word is used. The
simple protractor looks like a semicircular disk marked with degrees,
from 0o to 180o.
Angles are formed when two rays intersect. Angles are measured in
degrees. A complete circle measures 360 degrees. If you take a circle
and cut it into 360 slices, each of those slices is one degree. Why 360
degrees? Historians believe this is because old calendars, such as the
Persian Calendar, used 360 days for a year. When they watched the
stars they saw them revolve around the North Star one degree per day.
This ancient measurement is still recognized today as the measurement
of a circle.
To adequately use and understand using a protractor, students need
to have background knowledge of the following vocabulary: angle,
acute, obtuse, right, straight, reflex, vertex, and arms.
Students in 4th grade need to recognize benchmark angles:
90 degree angle= 1⁄4 of a circle
180 degree angle = 1⁄2 of a circle
270 degree angle = 3⁄4 of a circle
360 degrees = full circle
Intended Learning Outcomes:
2. Become mathematical problem solvers.
4. Communicate mathematically. Instructional Procedures:
Invitation to Learn
Place the strip of preprinted letters on each student’s desk. The
students will cut the letters apart and manipulate the letters until
they figure out what the mystery word is. Instruct students when
they discover the mystery word to write it down on a piece of paper
and wait for teacher to verify the word.
R C R P T R T O A O (Protractor)
After all students have discovered the mystery word, protractor,
introduce the protractor lesson.
Instructional Procedures
Using a Protractor
 The teacher will demonstrate how to read and label a protractor.
(overhead protractor).
 Cut out preprinted protractor. Glue in math journal.
 The students will record how to read and label a protractor in
their journal.
 Points to label: outer scale, inner scale, center mark and zero
edge.
Cut out the protractor and place in Math Journals. Divide the page
into 4 equal sections. Label the sections with the following headings.
Review and discuss how to label. Record directions in journal.
ZeroEdge
The zeroedge is always at the same
level as the 0 mark. 
Center Mark
The center mark is always at the
middle of the zeroedge. 
Inner Scale
The numbers on the inner edge of
the protractor. 
Outer Scale
The numbers on the outer edge of
the protractor. 
Classroom Protractors
Fourth grade students generally find it difficult to read and
calculate the degree marks accurately. A “homemade” protractor
(with a dark thread) helps eliminate this problem. Manipulating
the thread to lay on the exact degree, helps the students identify the
exact degree on the protractor.
Constructing a Student Protractor
 Cut out laminated protractor.
 Thread needle and tie knot at end.
 Bring needle up through the center mark on the protractor. Tape
thread securely in place.
 Students will manipulate the thread to line up with the angle to
be measured.
 Use the angle worksheet to practice measuring angles.
To Measure an Angle
 Find the center mark on the straight edge of the protractor.
 Place the hole over the vertex, or point, of the angle you wish to
measure.
 Line up the zero on the straight edge of the protractor with one
of the sides of angle.
 Find the point where the second side of angle intersects the
curved edge of the protractor.
 Place the thread on the second angle line.
 Read the number that is written on the protractor at the point of
intersection. This is the measurement of the angle in degrees.
 There are two sets of scales on the protractor, an outer scale and
inner scale. The degrees start at 0 on the straight edge, each going
in opposite directions. The lines are the same so when naming
angles make sure you identify which angle is being measured.
Constructing an Angle
 Use the straight edge of the protractor to draw a straight line.
This line will form one side of your angle.
 Find the center hole on the straight edge of the protractor.
 Place the hole over one end point of the line you have drawn.
 Line up the zero on the straight edge of the protractor with the
line.
 Make a mark at the number on the curved edge of the protractor
that corresponds to the desired measure of our angle. For
example, mark at 90 for a 90 degree angle
 Use the straight edge of the protractor to connect the mark to the
end point of the first line, forming an angle.
Independent Practice
 The protractor worksheet What’s My Angle is given to each
student.
 Students will classify angles as acute, straight, obtuse or right.
 Guide students in measuring various angles.
 Record the measurements and type of angle on the worksheet.
 Group students in pairs to check each other’s work.
 Next, on reverse side of worksheet, students will draw 3 angles to
be measured by the other student.
 Teacher will assess for accuracy.
What’s My Name Worth?
 How much is a first name worth? Calculate the value of your
name by identifying angles. Start this activity by showing the
class the “angle price list.”
acute angles = 10 cents each
obtuse angles = 8 cents each
right angles = 5 cents each
vertical lines = 3 cents each
horizontal lines = 2 cents each
diagonal lines = 1 cent each
 Each student will use the preprinted alphabet to print his/her first
name in capital letters.
 The student then examines the name for obtuse angles, acute
angles, right angles, vertical lines and horizontal lines.
 Next the student adds the various amounts and comes up with a
total.
Example:
J A N E 
5 acute angles @ 10 cents each =

$.50 
2 obtuse angles @ 8 cents each =

.16 
4 right angles @ 5 cents each =

.20 
4 vertical lines @ 3 cents each =

.12 
4 horizontal lines @ 2 cents each =

.08 
1 diagonal lines @ 1 cent each = 
.01 

____
$1.07 
Attachments
Extensions: Curriculum Extensions/Adaptations/
Integration
Students make angles using the Semaphore flag system.
Students make angles any way they can without using pencil
and paper, such as a “people” Clock or drawing/manipulating
the hands of a clock.
Use the price list and find the value of each letter in the
alphabet.
Use a geoboard to construct a figure.
Use a die to determine the number of sides of a figure. Students
who roll a 1 or 2 must roll again. Ten points are awarded for
each angle or line the student can list about their figure.
Instruction is differentiated according to learner needs. The goal
is to help all learners meet the intent of the specified learning
goal.
 For students struggling to identify angles, provide additional
pictures of reallife objects with the angles highlighted or
bolded in the picture. Have these students identify the type
of angle and then show the students a similar object in the
classroom. Have each student run a hand along the angle in
the picture and then along the angle of the real object.
 Other accommodations would be grouping so the student has
a “buddy” within the larger group.
 Describe/rehearse rules of conduct so the child can be
successful.
 Allow each student his/her physical “space” within the group.
 Preteaching vocabulary is especially important for ELL
students.
Family Connections
 Have a family scavenger hunt for angles. A prepared list of
angles could be given each family member to check off as they
find them.
 Look for angles in nature.
 Explore online angle activities together.
Assessment Plan:
 Students draw and measure angles.
 Formal assessment requiring identifying angle type, degrees,
and vocabulary.
Bibliography: Research Basis
Van Hiele, P. M. (1999, February). Developing geometric thinking through activities that
begin with play. Teaching Children Mathematics, 5 (6), 310316.
“For children, geometry begins with play,” writes Pierre van Hiele
(1999). He goes on to say that for students to reach the higher levels
of geometric thinking, their instruction should still begin with an
exploratory phase, gradually building concepts and related language,
and culminating in summary activities that help students integrate
what they have learned into what they already know.”
Ernest, P.S. (1994). Evaluation of the effectiveness and implementation of a math
manipulatives project. (Report No. SE057 682). Nashville, TN: Annual Meeting of the
MidSouth Educational Research Association. (ERIC Document Reproduction Service
No. ED 391 675).
The purpose of manipulatives would be to allow students to learn
a geometric principle in more than one way. In other words, instead
of just hearing about a math principle, they also get to see and feel it.
The study confirms that students are more willing to participate, and
experiment in math projects. Their attitudes towards math improved,
thus raising their selfconfidence in their math ability.
Author: Utah LessonPlans
Created Date : Jul 10 2008 12:13 PM
