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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 twostep 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?
 What is a transversal? ("a line that intersects two or more lines at different points.")
 If we have two parallel lines or nonparallel lines cut by a transversal, how many angles are created? ("8")
 What are exterior angles? ("angles that lie on the outside of the parallel lines cut by the transversal.")
 What are interior angles? ("angles that lie between the parallel lines cut by the transversal.")
 What are vertical angles? (" a pair of angles opposite to each other formed by two intersecting lines.")
 What are alternate interior angles? ("pair of angles between the parallel lines and on opposite sides of the transversal.")
 What are alternate exterior angles?("pair of angles on the outside of the parallel lines and on opposite sides of the transversal.")
 What is the difference between alternate interior angles and alternate exterior angles? (Alternate interior angles are between the parallel lines and on opposite sides of the transversal while alternate exterior angles are outside the parallel lines and on opposite sides of the transversal.)
 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
 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.
 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 Activity1.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".)
Activity 1 Answers
 Congruent pair of angles: 1 & 4, 1 & 5 and 1 & 8.
 Angle 4.
 Vertical Angles.
 Congruent pair of angles: 2 & 3, 2 & 6 and 2 & 7.
 Angle 6 and Angle 7.
 Angles 6 and 7 are congruent vertical angles.
 Vertical angles are the pair of angles opposite to each other formed by two intersecting lines.
 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 Activity2 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
 Angle 6
 Angle 5
 Alternate interior angles
 Angle 8
 Angle 7
 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 Activity3 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
 Angle 5
 Angle 7
 Angle 6
 Angle 8
 Corresponding Angles
 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 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.
ASSESSMENT
 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.
 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.
ACCOMMODATIONS & RECOMMENDATIONS
Accommodations:
During this lesson students are working on realworld 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 thinksharepair 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 ShareAlike license:
http://creativecommons.org/licenses/bysa/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
* Please note that examples of resources are not intended as complete curriculum.
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