Download Help me Find my Relationship!

Primary Type: Lesson Plan
Status: Published
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Resource ID#: 38211
Help me Find my Relationship!
In this lesson, students will investigate the relationship between angles when parallel lines are cut by a transversal. Students will identify angles, find
angle measures, and they will use the free application GeoGebra (see download link under Suggested Technology) to provide students with a visual
representation of angles relationships.
Subject(s): Mathematics
Grade Level(s): 8
Intended Audience: Educators
Suggested Technology: Computer for Presenter,
Internet Connection, LCD Projector, Java Plugin,
GeoGebra Free Software (Download the Free
GeoGebra Software)
Instructional Time: 2 Hour(s)
Freely Available: Yes
Keywords: Transversal, interior angles, exterior angles, corresponding angles, alternate interior angles, alternate
exterior angles
Instructional Design Framework(s): Direct Instruction
Resource Collection: CPALMS Lesson Plan Development Initiative
ATTACHMENTS
Activity2 revisions.doc
Activity1 revisions.doc
LESSON CONTENT
Lesson Plan Template: General Lesson Plan
Learning Objectives: What should students know and be able to do as a result of this lesson?
Using GeoGebra and one other method (graph paper, colored pencils and patty paper), student will describe the relationship between angles on parallel lines cut by a
transversal; identify another pair of angles with the same relationship; and achieve 100% on the independent practice.
Prior Knowledge: What prior knowledge should students have for this lesson?
Students must have prior knowledge and understanding of angles in a polygon, identifying congruent figures, similarity and solving two-step equations. In addition, they
must know how to use a ruler and protractor to measure angles. It would be helpful if the students had some prior experience manipulating constructions using
GeoGebra. (GeoGebra is a free software application that can be accessed at http://www.geogebra.org/cms/)
Guiding Questions: What are the guiding questions for this lesson?
1. What is a transversal? ("a line that intersects two or more lines at different points.")
2. If we have two parallel lines or non-parallel lines cut by a transversal, how many angles are created? ("8")
3. What are exterior angles? ("angles that lie on the outside of the parallel lines cut by the transversal.")
4. What are interior angles? ("angles that lie between the parallel lines cut by the transversal.")
5. What are vertical angles? (" a pair of angles opposite to each other formed by two intersecting lines.")
6. What are alternate interior angles? ("pair of angles between the parallel lines and on opposite sides of the transversal.")
7. What are alternate exterior angles?("pair of angles on the outside of the parallel lines and on opposite sides of the transversal.")
8. What is the difference between alternate interior angles and alternate exterior angles? (Alternate interior angles are between the parallel lines and on opposite
page 1 of 7 sides of the transversal while alternate exterior angles are outside the parallel lines and on opposite sides of the transversal.)
9. What are corresponding angles? ("If two angles occupy corresponding positions, they are called corresponding angles. If the lines intersected by the transversal
are parallel, the corresponding angles are congruent.")
Teaching Phase: How will the teacher present the concept or skill to students?
During the Teaching Phase, teacher uses the GeoGebraTube applet "Parallel Lines Cut by a Transversal" to give visual definitions and demonstrations of angle
relationships.
Transversal
Definition
"A Transversal is a line that intersects two or more different lines at different points."
Demonstration
Clear all boxes in the GeoGebraTube applet
Check the box next to "Show all angles" to show the 8 angles that are formed.(Guiding Question #2)
Move points A or B to change the orientation of the parallel lines.
Move points C or D to change the orientation of the transversal.
Ask: "What happens when the orientations of the transversal or parallel lines change?" (There are always 8 angles.)
Transversal Examples
Teacher then asks students to look around the classroom. Have students identify and call out examples of two lines with an intersecting transversal. Examples might
be:
Tile patterns in the ceiling
Filing cabinet drawers
Windows
Letter "Z"
(See examples in the photographs below)
Related Terminology
After discussing classroom examples of transversals and parallel lines, the teacher proceeds with definitions and demonstrations of important terms. The terms
include:
Vertical Angles
Interior Angles
Exterior Angles
page 2 of 7 Alternate Interior Angles
Alternate Exterior Angles
Corresponding Angles
Vertical Angles
Definition
"Interior Angles are the angles that lie between two parallel lines cut by a transversal." (Guiding Question #4)
Demonstration
Clear all checkboxes in the GeoGebraTube applet.
Using GeoGebra, check the box "Interior Angles." This gives students a visual representation of interior angles.
Exterior Angles
Defintion
"Exterior Angles are the angles that lie on the outside of two parallel lines cut by a transversal." (See Guiding Question #3)
Demonstration
Clear all checkboxes in the GeoGebraTube applet.
Check the box "Exterior Angles." This gives students a visual representation of interior angles.
Alternate Interior Angles
Teacher Note - During demonstration of alternate interior angles, the teacher can optionally introduce complementary and supplementary angles.
Definition
"Alternate Interior Angles are the pair of angles between the parallel lines and on opposite sides of a transversal." (Guiding Question #6)
Demonstration
Clear all checkboxes in the GeoGebraTube applet.
Check the box "Alternate Interior" angles to give students a visual representation of alternate interior angles.
page 3 of 7 Move points A & B as well as C & D to change the orientations of the two parallel lines and the transversal. Ask students what they notice. ("Alternate interior
angles are always equal.")
Check the box "Interior Angles." Ask students to identify the other pair of alternate interior angles.
Alternate Exterior Angles
Teacher Note - During demonstration of alternate exterior angles, the teacher can optionally introduce complementary and supplementary angles.
Definition
"Alternate Exterior Angles are the pair of angles on the outside of the parallel lines and on opposite sides of a transversal." (Guiding Question #7)
Demonstration
Clear all checkboxes in the GeoGebraTube applet.
Check the box "Alternate Exterior" angles. This gives students a visual representation of alternate exterior angles.
Move points A & B as well as C & D to change the orientations of the two parallel lines and the transversal.
Ask students what they notice. ("Alternate exterior angles are always equal.")
Check the box "Exterior Angles." Ask students to identify the other pair of alternate exterior angles.
Corresponding Angles
Definition
"Two angles that occupy corresponding positions are called Corresponding Angles." (Guiding Question #9)
Demonstration
Clear all checkboxes in the GeoGebraTube applet.
Check the box "Corresponding Angles." This gives students a visual representation of corresponding angles.
Use GeoGebra to highlight other pairs of corresponding angles. Teacher may check boxes 2, 3 and 4 (one at a time) to show them.
Using GeoGebra to demonstrate, ask students to conjecture the relationship between corresponding angles, for any orientation of the two parallel lines and
transversal. ("The measures of corresponding angles are always equal; in other words, they are congruent.")
Guided Practice: What activities or exercises will the students complete with teacher guidance?
Activity 1
Students will use patty paper and pencil to discover vertical angles when a transversal cuts two parallel lines.
Students Practice
Give each student a sheet of patty paper and the Activity-1.doc worksheet.
While students work, teacher circulates to help students and clarify misconceptions.
When students are finished, refocus them as a whole for the discussion.
Have students share which pairs of vertical angles they found. (“Angles 1 & 4; Angles 2 & 3; Angles 5 & 8; Angles 6 & 7”)
Students share what these vertical angles have in common. ("They are opposite from each other; they have the same measure; their angles are congruent".)
page 4 of 7 Activity 1 Answers
1. Congruent pair of angles: 1 & 4, 1 & 5 and 1 & 8.
2. Angle 4.
3. Vertical Angles.
4. Congruent pair of angles: 2 & 3, 2 & 6 and 2 & 7.
5. Angle 6 and Angle 7.
6. Angles 6 and 7 are congruent vertical angles.
7. Vertical angles are the pair of angles opposite to each other formed by two intersecting lines.
8. Vertical Angles: 1 & 4, 2 & 3, 5 & 8, 6 & 7.
Common Mistakes
Not realizing vertical angles are always equal.
Not finding vertical angles correctly.
Activity 2
Students will use patty paper and colored pencil to discover alternate interior and alternate exterior angles when a transversal cuts two parallel lines.
Students Practice
Students do the Activity-2 worksheet.
While students work, teacher circulates to help students and clarify misconceptions.
When students are finished, refocus them as a whole for the discussion.
Students share their answers for the activity.
Activity 2 Answers
1. Angle 6
2. Angle 5
3. Alternate interior angles
4. Angle 8
5. Angle 7
6. Alternate exterior angle
Common Mistakes
Mixing up interior and exterior angles.
Not realizing that alternate interior and alternate exterior angles must be on the opposite side of the transversal.
Activity 3
Students will use patty paper and colored pencil to discover corresponding angles when a transversal cuts two parallel lines.
Students Practice
Students do the Activity-3 worksheet.
While students work, teacher circulates to help students and clarify misconceptions.
When students are finished, refocus them as a whole for the discussion.
Students share their answers for the activity.
Activity 3 Answers
1. Angle 5
2. Angle 7
3. Angle 6
4. Angle 8
5. Corresponding Angles
6. Corresponding Angles: 1 & 5, 3 & 7, 2 & 6, 4 & 8
Common Mistakes
Not finding corresponding angles correctly
Not seeing that corresponding angles are located on the same position on parallel lines.
Independent Practice: What activities or exercises will students complete to reinforce the concepts and skills developed in the
lesson?
Students will be given Homework that will be handed in the following day for assessment. The homework is designed to reinforce the day's class work. If students
struggle on the homework, the teacher will be made aware of misunderstandings, and shortcomings of the lesson taught. When "weak" areas are identified on the
page 5 of 7 homework, the teacher can address the areas during the next available class period.
Closure: How will the teacher assist students in organizing the knowledge gained in the lesson?
Summarize lesson by asking students to debrief on what they learned on this lesson. Have students to share what they discovered about the angles by knowing certain
information about the angles formed by a transversal. The teacher will be sure to focus on reinforcing the vocabulary with the class and will ask students to explain
what they learned as a result of the lesson.
Summative Assessment
The teacher will use the homework assignment to determine if the students have reached the learning targets for this lesson. Students must show 100% mastery in the
homework assignment in order for the skill to be considered mastered.
Formative Assessment
Teacher will give students a quiz to gather information about student understanding.
Feedback to Students
Teacher will gives feedback to students during Activities 1, 2, and 3 of the guided practice. The student feedback includes discussion of possible misconceptions.
ACCOMMODATIONS & RECOMMENDATIONS
Accommodations: During this lesson students are working on real-world problem to contextualize the concepts, this will help visual learners to comprehend better
the concept. Students will be working on hands on activities, which will reinforce the skill. Students will be also working in pairs to brainstorm and complete different
tasks during the each activity, this think-share-pair strategy will allow students to learn from each other. Teacher will circulate continuously, monitor and check in with
each group on their progress and understanding of the tasks.
Extensions: The lesson itself can stand alone or can be extended to master other related skills. Teacher might like to extend angles relationships and introduce
complementary and supplementary angles. Students can apply one or two step equations to find missing angle based on the definition of complementary and
supplementary angles. Teacher might also have students to create a map of the streets where they live and have students to identify corresponding, vertical, alternate
exterior or alternate interior angles.
Suggested Technology: Computer for Presenter, Internet Connection, LCD Projector, Java Plugin, GeoGebra Free Software
Special Materials Needed:
For this lesson the following materials are needed
Pencil
Colored Pencil
Patty Paper
Highlighter
Activities #1, #2 and #3 worksheet
Further Recommendations: Before giving the activities to the students is important that the teacher get familiar with the content.
Additional Information/Instructions
By Author/Submitter
Resource may align with the following standards of math practice MAFS.K12.MP.1.1 - Make sense of problems and persevere in solving them.
MAFS.K12.MP.4.1 - Model with mathematics.
MAFS.K12.MP.5.1 - Use appropriate tools strategically.
MAFS.K12.MP.6.1 - Attend to precision.
MAFS.K12.MP.7.1 - Look for and make use of structure.
Use of the following GeoGebraTube resource is acknowledged: "Parallel Lines cut by Transversal" by asewell, accessed from http://www.geogebratube.org/student/m24184,
used under Creative Common Attribution Share-Alike license: http://creativecommons.org/licenses/by-sa/3.0/
SOURCE AND ACCESS INFORMATION
Contributed by: celia segarra
Name of Author/Source: celia segarra
District/Organization of Contributor(s): Broward
Is this Resource freely Available? Yes
Access Privileges: Public
License: CPALMS License - no distribution - non commercial
Related Standards
Name
MAFS.8.G.1.5:
Description
Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles
created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example,
arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an
argument in terms of transversals why this is so.
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