Students will learn about angles by using protractors.
Main Curriculum Tie:
Mathematics Grade 4
Geometric measurement: understand concepts of angle and measure angles. 5.
Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement:
- Chalkboard protractor
- 10-15 different art
For each group:
- Transparency sheets
- Wax pencil
For each student:
Background For Teachers:
Prior to this activity, students should have an understanding of right
angle, acute angle, obtuse angle, and vertex.
The size of an angle depends on the opening between the two sides of
the angle. Angles are measured in units referred to as degrees and labeled
with the ˚ symbol.
The size of an angle can be described in relation to a complete circle
(360˚), 1/2 of a circle (180˚), or 1/4 of a circle (90˚).
It is important to teach students how to extend rays of an angle when
using a protractor. This not only helps them measure but, helps in the
construction of angles. It is also important to make sure students
understand how to use the interior and exterior numbers on a protractor.
When selecting art prints, try to select a wide variety. See Art
Print Suggestions for ideas.
Twizzler Pull Aparts or Wikki Stix can be used in place of paper and
pencil when constructing angles.
This lesson usually takes about three days to teach and assess.
Intended Learning Outcomes:
1. Demonstrate a positive learning attitude toward mathematics.
2. Become mathematical problem solvers.
Invitation to Learn
Have each student spread out his/her fingers and look at his/her hand.
Use the following questions to promote discussion and thinking about
angles, “Do you think people with larger hands have larger angles
between their fingers?” Take student predictions and explain that at the
end of the lesson we will use our class as a sampling to answer the
question, “Can you use your fingers to make a 90˚ angle?” (thumb and
Developing “angle sense”
Use foam or fraction circles to help students visualize angle size in
relation to a 360˚ circle. Start with a whole circle, 1/2s, 1/4s, and 1/8s.
Add along the way (e.g., 1/4 = 90˚ so it will take four 1/4 pieces to equal
the 360˚ whole).
- Give each student an angle
wheel to help further develop “angle
sense.” Before moving on, make sure they understand that angles
are measured in degrees.
- Allow students to experiment with their wheels,
asking them to
look for patterns. For example, the larger the angle the greater the
measurement in degrees.
- Place students in pairs. Partners take turns displaying
while the other partner estimates the measurement of the angle.
- Display sets of angles on the
chalkboard and ask, “Would the
angle wheel be an effective measurement tool to measure these
- Introduce the protractor using the chalkboard protractor. Be
sure to model several examples of measuring angles with a
protractor before handing out individual protractors to each
student. Explain interior and exterior numbers on the protractor. Show students
how to extend rays when necessary for easier
measuring. Does extending the rays of the angle change the
measurement of the angle? Practice measuring angles in
isolation before moving on to measuring angles in the prints.
(Math books include such angles and work well for practicing.)
- Place students
in pairs or groups of three. Using 10-15
different art prints, each pair/group measures an angle from
each piece of art. Record the measurement of an angle from
each print, including a description of the object it belongs to, in
math journals. Allow each group three to five minutes with each
print before passing the print to another group.
- Numbering each print with
a Post-it® note helps make sure
each group has a chance to work with all of the prints. It also
helps the students organize and record information about the
prints in their journals.
- Use transparency sheets to protect the prints.
extension will be necessary for easier measuring of angles.
The students may only write on the transparencies with wax
- Instruct students to select their choice of prints to answer
following questions in their math journals. They must choose a
different print to answer each question.
- How does the artist use angles
to create the overall feel in the
piece of art?
- How does the artist use angles to create depth and/or perspective?
- Which styles/types of art use sharper, more definite angles?
your favorite print. Did the artist use a variety of
- How did the use of angles affect the feel the piece?
- Using the information on
how to measure an existing angle, ask
students how they could use a protractor to create their own
angles. Model angle construction using the chalkboard protractor.
For guided practice, have a few students suggest angles for the
class to construct. The Angle Assessment worksheet may also be
used for guided practice.
- Students use what they have learned by spreading
apart and measuring the angles between them. This works best
when done in pairs. Instruct students to use their protractors,
pencil, and paper to neatly measure and construct the angles
between two of their fingers. Record and compare data to answer the question
posed at the beginning of the lesson.
- The following extension possibilities
work well for students who
need extra support:
- Use a clock manipulative as an example of angles to
recognizing different angles in their surroundings.
- Start with a straight
line (180˚) and progressively create a new
angle every 10˚. This helps students see the correlation
between angle size and the protractor.
- The following extension possibilities
work well for students who
need extra challenges:
- Design a perfect circle using a protractor.
- Use a protractor to design
runs for a ski resort. How will the
angles of the more difficult runs compare to the beginner
- Use a protractor to design ramps for a skate park. How does
the degree of difficulty relate to the measurement of the
- Research the relationship between landslides, glaciers,
erosion, and slope angles.
- Give students a protractor
transparency to take home and
demonstrate their new skills to their families.
- Send family members on an
angle scavenger hunt. For example,
find something in the house that has an angle measurement
between 120˚ and 140˚.
- Have each student choose three to five of the angle
they measured and recorded from the art prints. Using the
measurements, students construct the angles and include them in
their own piece of hand drawn abstract art. Students could also
create a piece that uses angles to create the illusion of depth or perspective
(refer to M.C. Escher print Ascending and
Descending). The use of protractors must be incorporated in their
- Use protractors to complete the Angle Assessment worksheet.
Hartshorn, R. & Boren, S. (1990). Experiential learning of mathematics;
Eric Digest #ED321967
This lesson includes the angle wheel because it serves as a concrete
representation of angles. Research suggests that incorporating the use of
manipulatives in mathematic instruction is “useful in the transition from
concrete to abstract taught in steps, semi-concrete to semi-abstract.” In
this lesson, the angle wheel serves as the concrete and is introduced
before moving on to the abstract—measuring of angles on paper.
Gresham, G., Sloan T., and Vinson B. (1997). Reducing mathematics anxiety
in fourth grade
at risk students. Retrieved January 2, 2005, from Athens Stage College, School
Education Web site: http://www.Athens.edu/vinsobm/research_4.html.
Research also suggests that the use of mathematical manipulatives
reduces the level of math anxiety in high risk students.
Lou, Y., Abrami, P.C., Spence, J.C., Paulsen C., Chambers B., & d’Apollonio,S.
Within-class grouping: a meta analysis. Review of Educational
Research, 66(4), 423-458.
The activities in this lesson plan were designed to be completed in
pairs or groups of three. Research on cooperative learning and group
work indicates that “small teams of three to four members” are more
effective than larger groups. This lesson was created with the intention of
maximizing the benefits of cooperative learning.
Created Date :
Jan 27 2006 08:55 AM