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Subject Matter:
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Mathematics – Geometry
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Grade Levels:
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8-12
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Time Allotment:
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Three 50-minute class sessions
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Overview
In this lesson, students will learn the definitions of ray and
angle and then the classification of angles based on the degrees
they represent. Using digital cameras, students will photograph
objects or scenes representing the angles and produce a poster of
the photographs. The photographs will be labeled with the degrees
and the correct characteristics of each angle.
Learning Objectives
Students will be able to:
- Identify and define a ray and an angle with these classifications:
obtuse, acute, right, straight, congruent, interior and exterior.
- Measure angles, label them and identify their classifications.
- Identify and label angles in everyday life using common objects
and landscapes.
- Produce a poster of digital photos with correct labeling of
the angles found.
Oregon Standards Available at:
http://www.ode.state.or.us/cifs
Mathematics – Geometry
Analyze characteristics and properties of two- and three-dimensional
geometric shapes and develop mathematical arguments about geometric
relationships.
Properties and Relationships:
- Determine defining properties that characterize classes of triangles
including side and angle measurements and their component parts
(e.g., angle bisectors, altitudes, medians).
- Determine the measures of corresponding angles, sides and corresponding
parts, congruent and similar figures.
Media Components
Video
Check the link at http://www.opb.org/edmedia/trs/ to find access to the video(s) from unitedstreaming™ referenced in this lesson plan.
- "History in Focus: 1960-1969 (57:11)
o Clip: "Sports and Games" (01:32)
- "Many-Sided World of Geometry, The, Program 1: Geometry
Basics" (26:00)
o Clip: "Part Two: Angles - Section A - Angles Defined"
(05:50)
- "Many-Sided World of Geometry, The, Program 2:
Angles 101" (26:00)
o Clip: "Review: Geometry Basics" (04:12)
Web
- Types of Angles
This interactive site allows students to check their understanding
of the definitions of obtuse, acute, corresponding, adjacent,
and interior and exterior angles.
http://www.utc.edu/~cpmawata/geom/geom1.htm
- Introduction to Angles: Concentration Game
This interactive Web site allows students to play Concentration
with the characteristics of angles and their definitions.
http://www.quia.com/cc/65822.html
Materials
Per Student:
Per
Class and/or Group:
- Digital camera with floppy or storage card
- Poster board
- Scissors and paste
- Access to a color printer (Black and white will work, though.)
- Computer with network connectivity for downloading images from
the camera
- Camera drivers (if necessary) on computers
- Protractors and pencils
- Markers and drawing materials
- Poster scoring guide found at: http://www.bcpl.net/~sullivan/modules/tips/rubrics_sec/poster.html
Prep for Teachers
When using media, provide students with a Focus for Media
Interaction, a specific task to complete and/or information
to identify during or after viewing of video, Web sites or other
multimedia elements.
Make a copy of the Review of Angles and Their Definitions/Photo
Shoot Storyboard handout for each student.
Session 1: Bookmark all Web sites and download
video clips. Preview them for specific points you will use to teach
students about the types of angles and their vocabulary. Schedule
the computer lab or mobile lab and allow one computer per group.
Check for the availability of printers for those computers. Check
to see if the proper Windows Media Player is installed on the demonstration
computer you will use for instruction. Make sure that this computer
can be connected to a projector or a large-screen monitor for large-group
instruction. Depending on the readiness of the students, you may
need to review/instruct them on how to measure angles with protractors.
A protractor made for overhead projectors or an opaque overhead
projector like an Elmo projector can aid in this instruction.
Session 2: Make sure drivers for the digital cameras
are installed on the corresponding computers. Charge all cameras.
If handhelds are used, make sure docking cables are available at
each computer station for downloading pictures.
If possible, ask another adult to help manage students during the
photo shoot as the student groups will finish at different times.
Some groups will move back into the computer lab/classroom/library
(the scene of instruction for Session 2) to download photos to the
computer for printing while other groups are finishing up outside.
Session 3: Depending on the ease of the use of
the cameras and their software, and the computer savvy of the students
involved, Session 3 may be necessary to finish up the poster project.
In this session, you will also need the computer lab or enough computers
for every two students. Bookmark the interactive Web site: http://www.quia.com/cc/65822.html
Introductory Activity
Step 1: Start out the lesson by sharing this quotation
from Ralph Waldo Emerson: "What is life but the angle of vision?
A man is measured by the angle at which he looks at objects. What
is life but what a man is thinking of all day? This is his fate
and his employer. Knowing is the measure of the man. By how much
we know, so much we are."
Ask students, "What
is Emerson talking about?" (Answers may vary, but look for
a way to progress to angles in a physical visual sense – not
the metaphysical sense.) "What other kind of way can we look
at angles?" Ask the students if any of them have played pool
or putt-putted. When they respond, ask them if they can name a skill
that may help them improve in those two activities. (Answers will
vary. Look for a response that can lead to determining the path
of the ball, such as using angles of the pool table or the lay of
the rough.) Then say, "Let's look at the part angles play in
professional sports." View the clip, "Sports and Games"
(01:32), from the video, "History in Focus, 1960-1969"
(57:11). As a Focus for Media Interaction, have
the students sketch the different angles related to baseball, football,
hockey, basketball and golf that they observe in the video clip.
Step 2:
After viewing the video clip, have students share answers. (Possible
answers are: In baseball, angles are to be taken into account for
pitching (ball and strikes), foul balls and throwing to bases. In
golf, putting depends on angles. To score a goal in hockey, angles
put the puck into the goal. Successfully rebounding a basketball
depends on the angle the basketball leaves the hoop. In football,
the angle of a throw determines the trajectory.)
Step 3: Continue the discussion by applying angles
to occupations and activities. What jobs use angles? (Planing timber,
sewing, lighting technicians for theaters, etc.) (15 minutes total)
Learning Activities
Session 1
Step 1: To
familiarize the students with the vocabulary and provide a Focus
for Media Interaction, distribute the What's Your Angle?
Definitions handout and direct the students to fill in the definitions
as they hear them on the video clip with sketches or words that
will help them remember the angles' characteristics.
Step 2:
Play the video clip, "Part Two: Angles - Section
A - Angles Defined" (05:50), from the video, "The Many-Sided
World of Geometry, Program 1: Geometry Basics" (26:00). Play
it through once in its entirety. Then play it again
and pause after each definition so students can
take notes and make sketches on their handouts.
Step 3: (if
necessary) Instruct students in how to measure angles using a protractor.
Use the Activity Sheet #3: Angles, Angles Everywhere handout found
at http://www.scetv.org/ntti/lessons/1998lessons/activities/anglesanglesA3.html
Step 4: If instruction is not necessary in measuring angles, have students practice naming angles as obtuse, acute and right angles using the Geometry handout found at http://members.aol.com/tts009/downloads/Geometry2.html.
Step 5:
As a Focus for Media Interaction, have the students
practice identifying angles by going to the Web site, "Types
of Angles," found at http://www.utc.edu/~cpmawata/geom/geom1.htm.
It is best if there is at least a two-to-one ratio of students to
computers for this activity. Review with the students the first
half of the page. This site demonstrates the point at which an acute
angle becomes an obtuse angle. Stop the applet on the Web page at
89 degrees and ask the students, "What happens when the measurement
becomes 90 degrees? What about 91 degrees? What about 180 degrees?"
Have the students then explore the following applet and identify
10 other angles as obtuse, right, straight or acute. Have them note
the angle measurements and their answers on the Gathering Sheet
handout located at the end of this lesson plan. Return as a whole
group to the Web site for an applet demonstration of complementary
and supplementary angles. Have the students return to their Gathering
Sheet handouts and draw complementary and supplementary angles.
Step 6:
For the last five minutes of class, have students go to the interactive
Web site, "Folding Tape," found at http://www.studyworksonline.com/cda/content/applet/0,,NAV2-21_SAP561,00.shtml.
Using the java applet, have students demonstrate right, obtuse and
acute angles in that order. The "open" button will open
the tape to a flat plane. Hints 1 and 2 label the angles and the
"init" button allows you to manipulate the vertex of the
folding tape.
Session 2
Step 1:
It is now time for students to review the terms and definitions
before applying this information to real-life situations. As a Focus
for Media Interaction, have the students use the Review
of Angles and Their Definitions/Photo Shoot Storyboard handout and
match the terms to the definitions as they view the video clip,
"Review: Geometry Basics" (04:12), from the video, "Many-Sided
World of Geometry, The, Program 2: Angles 101" (26:00). Cue
the clip starting halfway through to the part about angles (a blonde
girl is speaking). Play the video clip. Share answers,
especially the terms not covered in the clip: obtuse, acute, straight
and right angles.
Step 2: Ask the students to see if they can detect angles around the classroom. (Answers will vary. Ask for the correct terms. Example: "Yes. There is a right angle where the desk meets the legs under the desk." "The flag comes from the wall in two supplementary angles — one above the flag pole and one below.") Tell the students that they will be divided into groups of four and that their job is to go out in the Commons or outside area (one that can be monitored) to snap five pictures of angles. The shots can be landscapes and close-ups. Each group should find a variety of angles with no two angles alike. Share the scoring guide you will use for the group poster that will result from the photo shoot. It is found at: http://www.bcpl.net/%7Esullivan/modules/tips/rubrics_sec/poster.html.
Step 3: Have each student in the group select a job. Each group should have a spotter who defines the shot used from suggestions by the group, a cameraperson, a recorder of the shots and a person who docks and downloads the shots from the camera to the computer.
Step 4: When the group returns to the instruction area, the spotter can retrieve the photos from the printer, the recorder can do the cutting and pasting of the printed photos to the poster board and all group members can measure and label the angles on their poster. Note: It is helpful to have another adult remain behind in the photo shoot area to manage students while the teacher returns to the classroom when a majority of students are ready to download their photos.
Step 5: Each group should turn in a completed poster with the scoring guide attached. The members of the team will sign their poster for assessment.
Session 3
Step 1: If necessary, groups should finish the posters they began the day before. When students finish their posters, direct them to visit http://www.quia.com/cc/65822.html to play a Concentration Game based on angles and their definitions. Instruct the students in how to click on the images to reveal the terms and definitions. As a Focus for Media Interaction, while playing the game students will record their scores and times of their matching activity. Instruct students to play at least twice to see if they can "best" their score.
Step 2: Move on to the Culminating Activity when all groups have completed their posters.
Culminating Activity
Have each group present their poster to the class and ask the class to try to identify other angles in each photo. Refer back to Emerson's quotation: "What is life but the angle of vision? A man is measured by the angle at which he looks at objects." The posters may be rotated to see a different angle. Ask the students if rotating a view produces a complementary or supplementary angle. Students will display their group posters in the Commons area or in a hallway to provide an informative piece to share with others in the learning community.
Cross-Curricular Extensions
Health and Physical Education
- When studying angles, students can determine the role of range of motion in athletics and physical health. Students could measure angles of these motions by using the exercises found at this Web site: http://www.orthop.washington.edu/arthritis/living/exercise/03
- A dance instructor can demonstrate the angles by teaching an Irish dance.
History and Social Studies
- The students can investigate the angles used in strategic battle plans and how angles were used in building famous structures.
English and Language Arts
- Using Emerson's quotation for inspiration, students can write a narrative piece on an incident from two observers' vantage points.
Community Connections
- Guest speakers can be invited to speak to the students about the use of angles in their work. Physical therapists may talk about range of motion, builders about angles in construction, lighting technicians in placing illuminations for plays, clothing designers about angles in clothing construction and manufacturing, bicycle technicians on the strength of angles in various designs of bicycles or landscapers in laying out gardening designs.
Your Name________________________________ Today's Date ______________
What's Your Angle? Definitions
Angle
Ray
Vertex
Interior point
Exterior point
Naming angles
Congruent angles
Acute
Right
Obtuse
Straight
___________________________
 Adjacent angles
Complementary angles
Supplementary angles
_____________________________
Vertical Angles
Your Name________________________________ Today's Date ______________
Gathering Sheet for "Types of Angles" Interactive Web Site
found at http://www.utc.edu/~cpmawata/geom/geom1.htm
Click on the "Go" and then "Stop" buttons in the first applet on this Web page to see examples of acute angles and obtuse angles. After reviewing those angles, go to the next gray box below that on the Web page and record the degrees you see in the white box by the number 1 below. Decide if it is an obtuse or acute angle and record your answer on this sheet. Check your answer against the answer on the Web page. Do this four more times for this section of the paper. Circle the type of angles that you correctly identified the first time. No erasers allowed!
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Measurement |
Type of Angle |
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5. |
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Draw a complementary angle diagram. Remember to label the measures of the angles.
Draw a supplementary angle diagram. Remember to label the measures of the angles.
Matching Exercise – Review of Angles and Their Definitions
Adjacent |
two angles whose sum is 90° |
Complementary |
two angles that have the same measure |
Supplementary |
an angle whose measure is EXACTLY 180 DEGREES |
Vertical |
an angle whose measure is GREATER THAN 90 AND LESS THAN 180 DEGREES |
Congruent |
two angles who sum equals 180 degrees |
Acute |
formed by two rays which begin at the same point |
Right |
an angle whose measure is LESS THAN 90 DEGREES |
Straight |
an angle whose measure is EXACTLY 90 DEGREES |
Obtuse |
are side by side and have a common vertex and ray |
Photo Shoot "Storyboard"
Shot Number |
Location / Object |
1. |
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2. |
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3. |
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4. |
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5. |
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Your Name/Group:
Camera used:
Computer Station used:
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