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LINE IT UP, ANGLE IT OUT
MASTER TEACHER Lori Morrison
GRADES 4 - 6
OVERVIEW
This lesson provides students with the opportunity to explore
mathematical lines and angles. After defining lines and angles, students
will participate in various hands-on methods to discover lines and angles within
their environment. Students use their person, everyday materials, and a
protractor to assign degrees to angles. Finally, students locate angles
and lines in the real world.
ETV SERIES
Math Vantage: #107 What's Your Angle?
LEARNING OBJECTIVES
Students will be able to:
*define mathematical lines
*define angles
*explore the relationship between lines and angles
*identify angles
*measure angles
*locate and label angles in the real world
MATERIALS
poster board (1 per group of 5 students)
Per student
pipe cleaners (2 per student) or two pieces of tag board cut
1" x 4" and a brad
colorful index cards cut into thirds (each student gets a third)
toothpicks (8-10 per student)
clear transparencies (1 per student)
erasable markers
protractor
magazine or newspaper
glue
construction paper
Measure Me/Draw Me Worksheet
Angle Scavenger Hunt Worksheet
Teacher:
overhead protractor
overhead transparencies of nature/real world
old clock with movable hands or classroom manipulative clock
VOCABULARY
point - Simplest of geometric shapes. Like a dot
only smaller. (Dot made with pencil only marks the location of a point.)
ray - A straight line extending from a point.
line A geometric line is a string of points in a
row.
line segment - A part of a geometric line.
parallel lines - Lines that go in the same direction and
stay the same distance apart.
intersecting lines - Lines that cross.
perpendicular lines - Intersecting lines that form right
angles ("square corners").
angle - An opening between two intersecting lines.
right angle - A square angle, often marked with a square.
(90 degrees)
acute angle - An angle that is less than a right angle.
(less than 90 degrees)
obtuse angle - An angle greater than a right angle but
less than a straight angle. (between degrees and 180 degrees)
straight angle - An angle that forms a straight line.
(180 degrees)
reflex angle - An angle that is greater than a straight
angle. (greater than 180 degrees)
PRE-VIEWING ACTIVITIES
(Prior to lesson, have students arranged in groups of 4 or
5.)Have students find examples of lines and angles in the classroom.
Prompt students to find specific lines or angles, i.e., number line (line of
connecting points that goes on forever), corner of the classroom (square corner,
right angle), lines on the calendar or map (intersecting lines that also have a
"square corner" or right angles). Write down all student
responses on the chalkboard next to the drawing of the line or angle.
After your findings are listed, show students hand/forearm symbols for line,
parallel lines, intersecting lines, and perpendicular lines. (Example: arms
spaced and next to each other going in the same direction are parallel) As
a group, have students make a line poster with different combinations of lines
and angles with toothpicks and glue. Students can label the different
designs or examples of lines (i.e., students may use the two L's in parallel to
show the definition of the word by gluing two toothpicks in place of the L's)
Ask students what type of lines makeup angles. (Lines that open and intersect.)
Tell students that lines converge to make different angles. Ask students
to practice throwing a paper ball into the trash can. Tell students that
the paper ball had to go into the trash can by angling. Tell students that
today we are going to reinforce what we know about lines and apply that
knowledge to the study of angles. Ask students how we measure temperature.
(Degrees) Show students an overhead protractor and tell them that we
measure angles in degrees. Tell students that in this lesson we will find
angles, measure them in degrees, and give them proper mathematical names.
FOCUS FOR VIEWING
To give students a specific responsibility for viewing say,
"You are going to see a video with a lady, Ms. Ellen Withrow, and a clock.
Ms. Withrow is going to show you how the clock hands can move and make different
angles. I want you to listen to Ms. Withrow as she gives the degrees of
each type of angle and I want you to be able to tell me the name of each type of
angle." Have angle degrees listed on the chalkboard so that students
can match the name of the angle with the proper degrees once the video segment
is completed.(less than 90 degrees, 90 degrees, between 90 degrees and 180
degrees, 180 degrees, greater than 180 degrees)
VIEWING ACTIVITIES
Begin tape Math Vantage #107 What's Your Angle?, as
Ellen Withrow is saying, "A clock has angles too, as time flies by the
hands of a clock open to create increasing larger angles." Visual is
a clock. Stop video with visual of a clock with hands spinning.
Audio is a cuckoo sound.(If needed, replay the clock segment.) Give each
group a few minutes to discuss the different types of angles that were addressed
in the video. Ask a representative from each group to share one of the
answers while listing it on the chalkboard next to the proper degrees. (Angles:
less than 90 degrees ñ acute [small, "a cute" little angle],
exactly 90 degrees ñ right angle ["square corner"], between 90
degrees and 180 degrees ñ obtuse angle ["obese angle"], exactly 180
degrees ñ straight angle [makes a line], greater than 180 degrees ñ reflex
angle [compare to a strong leg reflex]). While listing the different
angles and their degrees, show students a visual with the hands of an actual
clock. Also, motion your own arms to represent the various angles.
Have students mimic arm positions matching the degrees or the angle name with
the arm motion. Rewind tape to visual of Ellen Withrow's body bent
into different angular positions. The angle degree is displayed on each of
the different body positions. Audio is Ms. Withrow saying, "So,
what's your favorite angle?" Pause tape when all of Ellen's
positions are complete with the degrees labeled; 45 degrees, 90 degrees, 120
degrees, and 180 degrees. Audio is music. Using a dry erase marker,
have students mark the angles Ellen has made with her body on the television
screen. Tell students that as humans we can position our bodies like
angles. Erase the television screen. Tell students that the average
human can move their head from side to side making a 90 degree turn. Also,
let students tilt their head down, chin to chest, to show that the average human
can tilt comfortably to 60 degrees. Mention to the students that humans
use lines and angles in many ways. (Discuss all reasonable answers.) Tell
students that you want them to watch a Karate expert as he moves his body at
different angles. Fast forward tape to visual of a man dressed in
Karate attire (Ray Silverstrend). Audio is Ms. Withrow saying,
"Angles are the basis of all movement in the martial Arts. Resume.
Pause video with visual of circle marked off with the different degrees
and Karate man. Audio is Oriental music. Have students stand up and
move at different degrees. (Front of classroom is 0 degrees) Have students
move their bodies when you mention degrees or the name of the angle. (i.e., move
90 degrees or move your body to the right making a right angle) Tell
students now that they have named, showed, discussed, and displayed angles, we
are going to take an individual test. Construct "angle makers"
with pipe cleaners or brads and tag board rectangles. Ask students to show
the following angles; acute, right, obtuse, straight, and reflex. Ask
students to show various degrees; 45, 90,180, 270, and 360. Have students
call out the name of the angle with the correct degree. (i.e., A 90 degree angle
is a Ö[right angle]) Make a visual assessment of the students to see who
needs re-teaching. Tell students that moving the pipe cleaners to match a
degree was fine for our test but many times angles must be measured accurately.
Say, "There are many different tools that can measure angles. Tell
students that you want them to watch the video to see some of the tools that are
used to measure angles. Ask students to listen to the tape and find out
who used the sextant and what it does. Also, why does the orthodontist use
a protractor? (Sailors used a sextant to measure the correct latitude and
longitude of a place on earth. The orthodontist uses a protractor and a
ruler to show relationships of jaws, teeth, and the face. He measures the
key positions and proportions to plan for orthodontic treatment.) Resume
tape. Pause tape with visual of teeth chattering. Audio is Ms.
Withrow saying, "Öand to evaluate the great results." Remind
students that there are many types of tools that measure angles and many other
professions that use angular measurements. Tell students that in
mathematics class we will use a tool that the orthodontist used in the video,
the protractor. Show students a protractor on the overhead. Display
the correct protractor usage by measuring some angles on the overhead.
Tell students that they are going to practice correct measurement techniques
with the protractor. Using the overhead copy of the "Measure Me/Draw
Me" worksheet, practice measuring angles with your students. Have
students do half of the worksheet on their own as you monitor. Ask
students if there is a way we could tell if an angle is exactly 90 degrees
without using our protractors. Give students the "Official Right
Angle Finder". (Index card pieces) Show students how to
"fit" the angle finder into an angle to see if it is 90 degrees.
Inform students that they can always use the corner of their paper to check an
angle, even on a test, because a piece of notebook paper has four square
corners. Mention to students that we really know our angles! Tell
students that it is time to extend our learning and apply what we have learned.
Tell students that we are now ready to find lines and angles in nature.
Say, "I am going to play the video showing Ellen in a tropical environment.
See how many angles you can locate in nature. Try to locate the lines and
angles before they are highlighted on the screen." Rewind tape with
visual of Ellen Withrow in a sweatshirt standing in a tropical forest.
Audio is Ellen saying, "No matter where you look, it's plain to see, nature
is full of angles." Pause tape in various places where angles
are highlighted on plants and animals. Students can be asked to highlight
non-highlighted angles with a dry erase marker. Use the "Official
Right Angle Finder" and the protractor directly on the television screen.
Measure and name the angles. Stop the tape with visual of Ellen
waving and standing on a bamboo bridge. Audio is Caribbean music.
Ask students if they are ready to go on an angle scavenger hunt.
POST-VIEWING ACTIVITIES
Students work individually or in pairs. Tell students that
we are going to find angles in nature. Slice an orange crosswise and
display the angles shown on the inside of the orange. Tell students that
they may find angles in a magazine, newspaper, or an old book. Students
cut out the picture they find and mount it on construction paper. Using an
overhead transparency, students can cover the picture and highlight (trace)
angles. Using their protractor, students measure the angles as they find
them. On the angle scavenger hunt worksheet, students write the place
where the angle is found, the type of angle, and the measured degrees.
Once the student has found at least 10 angles he may switch pictures with
another student. The partner student gets the picture and the angle
scavenger hunt worksheet that goes with the picture. With a marker, the
partner student marks the listed angles directly on the picture. Once the
partner student has finished, the transparency can be given to the student to
see if the angles match up.
ACTION PLAN
Arrange a field trip to an art museum, park, or nature trail.
Have students carry their math notebooks and protractors. Have students go
on an angle search. Those angles that can be measured can be recorded
(Where it is found, on what, the angle size - degrees, and the name of the
angle.) It would be beneficial if the teacher visited the field trip site
prior to the actual trip to make a list of specific places to find specific
angles.
EXTENSIONS
Language Arts
Make an inverted triangle poem. An inverted triangle poem
describes an object, tells a brief narrative, or expresses a feeling.
First write a practice poem about an angle or a line.
Format:
Angle
Line 1 - 5 syllables Measured in Degrees
Line 2 - 4 syllables Two Rays or
Lines
Line 3 - 3 syllables
Connecting
Line 4 - 2 syllables
Corner
Line 5 - 1 syllables
Point
Health
Have an orthodontist visit the classroom with sample x-rays and
a skull. Discuss angle importance and how the actual measurement takes
place with the patient.
Art
Angle art works. Students create collages with different
angles made with different textures. (i.e., straws, toothpicks, material, glue,
etc.)
Physical Education
Research and display sports that use angle. Have students
show the angle various athletes must use to win a competition. (i.e., pole
vaulter and his pole, basketball player making a shot at the basket, volleyball
player serving the volleyball.)
Engineering
Explore structures on video. (See Eddie Files #103 Geometry:
Invasion of the Polygons or Bill Nye #106 Structures) Or, take a field
trip to a business area with many different structures. Find angles in the
structures. Have a structural engineer visit your class to discuss the
importance of angles within a structure. Ask the engineer to discuss the
way angles support a structure. Have the students use what they have
learned about structures to build their own structures. Students could
have a "Build the Tallest Structure Contest." Give students time
to brainstorm how they would build the tallest structure with 30 toothpicks, 30
gumdrops, in 30 minutes.
Math
Extend the angle lesson by studying triangles. (See Math Vantage
#108 Trusting Triangles) Discuss the importance of angles in triangles and
the characteristics of triangles. You may want to play "I Have.., Who
Has?"(i.e., Who has an equilateral triangle? I have a triangle with
three angles that measure 60 degrees.) Once students are familiar with the
different types of triangles, have the students create their own triangle books
to share with the class.
Internet Connection/Math
Ask Dr. Math about different types of angles or submit a
problem-solving question that involves angle measurements. Visit Dr. Math
at:
http://forum.swarthmore.edu/dr.math/dr-math.html
Updated: April 01, 2008
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