Primary Type: Lesson Plan
Status: Published
This is a resource from CPALMS (www.cpalms.org) where all educators go for bright ideas!
Resource ID#: 51063
Accurately Acquired Angles
Students will start the lesson by playing a game to review angle pairs formed by two lines cut by a transversal. Once students are comfortable with
the angle pairs the teacher will review the relationships that are created once the pair of lines become parallel. The teacher will give an example of a
proof using the angle pairs formed by two parallel lines cut by a transversal. The students are then challenged to prove their own theorem in groups
of four. The class will then participate in a Stay and Stray to view the other group's proofs. The lesson is wrapped up through white board questions
answered within groups and then as a whole class.
Subject(s): Mathematics
Grade Level(s): 9, 10, 11, 12
Intended Audience: Educators
Suggested Technology: Document Camera
Instructional Time: 59 Minute(s)
Freely Available: Yes
Keywords: Parallel lines, Corresponding angles, Alternate Exterior angles, Alternate Interior angles, Same side
interior angles, proof
Instructional Design Framework(s): Direct Instruction, Cooperative Learning
Resource Collection: CPALMS Lesson Plan Development Initiative
ATTACHMENTS
Bellwork Quiz.docx
Measuring angle pairs.docx
Show Down Questions.docx
Modified Individual Questions.docx
Show Down Answers.docx
Proof of Corresponding angles theorem.docx
Sample White Board Questions with Answers.docx
Sample Game Questions with Answers.docx
Individual Questions.docx
Individual Questions Answers.docx
Bellwork Quiz Answers.docx
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?
Students will be able to:
prove theorems about angle pairs formed by two parallel lines cut by a transversal.
use the theorems about angle pairs formed by two parallel lines cut by a transversal to solve for unknown values.
Prior Knowledge: What prior knowledge should students have for this lesson?
Students need to be familiar with the angle pairs formed by two lines cut by a transversal (alternate interior angles, same side interior)
Students need to know what a vertical angle is and that vertical angles are congruent.
Students need to know what a linear pair is and that the angles are supplementary.
page 1 of 4 Guiding Questions: What are the guiding questions for this lesson?
While the students are writing proofs:
What do you know? (the given information; the two lines are parallel)
What do you need to prove? (the proof statement)
Is there any information that will help you link the two? (Answers will vary based on the proof, but pointing out linked angle pairs such as vertical or corresponding
angles could be helpful.)
Teaching Phase: How will the teacher present the concept or skill to students?
Opening Activity:
On the wall near each group of four students the teacher will use painters tape to create two lines (not necessarily parallel) and a transversal with all angles labeled
1-8.
Each student in the group should be provided a different color sticky note pad.
Students will stand near their lines on the wall.
The teacher will call out an angle pair and an angle such as "An angle corresponding to angle 5" and each student should place a sticky note on an angle
corresponding to angle 5 (angle 1 in this case). Some examples of questions with answers.
The teacher will then ask for the correct angle.
The teacher could create a more competitive game by saying that the first sticky note in the angle gets a point, and assign someone in each group to keep score.
The teacher should observe the groups to see how well the students are able to identify the correct angle pairs. This game could last between 5 to 10 minutes as
needed.
Review Prior Knowledge:
The teacher will then have students go back to their seats and the teacher will remind students about the relationships between angle pairs formed by two parallel
lines cut by a transversal.
If students need remediation on these relationships the teacher could have the students discover the relationships using a set of parallel lines, a ruler and a
protractor.
Here is a sample sheet.
Example Proof:
Once the teacher feels that the class is comfortable with the relationships they will transition into proofs.
The teacher will explain to the class that in geometry we prove everything. This allows us to use the theorems in more complex proofs as well as use the
information to solve for unknown values.
The teacher will explain that as a class they will go over the proof for corresponding angles and then each group will take one of the other theorems and prove it.
In the proof of corresponding angles, the vertical angles theorem is used as well as an assumption that alternate interior angles formed by two parallel lines and a
transversal are congruent. Here is the proof.
Once the class understands this proof they may use it in future proofs.
Guided Practice: What activities or exercises will the students complete with teacher guidance?
Using the Theorem Examples:
The teacher will demonstrate how to use the theorem to solve for unknown values. Here is an example question.
Independent Practice: What activities or exercises will students complete to reinforce the concepts and skills developed in the
lesson?
Proof Activity:
Once the teacher finishes the proof of corresponding angles, the teacher will give each group one of the remaining theorems. Sample Proofs
Same-Side Interior Angles
Alternate Interior Angles
Alternate Exterior Angles
Each group will be challenged with the task of proving their theorem.
page 2 of 4 Once they complete the proof they will transfer it to chart paper or large white boards and hang them around the room.
Once all of the groups have completed their proof and placed them around the room, each group will stand near their proof. The class will then participate in a Stay
N Stray activity.
Explain to the students that one person will be chosen at random to stay with their proof and the rest of the group will rotate clockwise around the room.
Make sure that the proofs are displayed so that each group will travel to the two other proofs in their travels.
Have each student pick a number 1-4 and randomly chose a number.
Every student with that number will stay with their proof and explain it to the next group.
Explain to the students that as they travel from proof to proof they need to pay attention to the explanation, because they may be randomly chosen to stay at their
new proof and have to explain it to the next group.
Depending on how much time is available you may want the groups to travel to the two new groups or continue to see how others groups proved the same
theorem.
Depending on the amount of time available, suggestions for independent practice include:
Show Down:
In groups the students will answer questions about unknown values or proofs individually on a white board.
One student will be the leader for the first question.
They will flip over the top card and read it aloud for the group.
Each student will answer the question on their board, including the leader.
Once everyone in the group has finished the question the leader will call "Show Down" and everyone will flip over their board. (one tip would be for the groups to
have a signal when they are done with the problem, such as markers down, or flipping over the white board).
The group will then check their answer with the rest of the group, correct and coach as needed.
The next student clockwise from the original leader will become the leader for the next question.
This continues with the leader rotating each question for the allotted amount of time.
Show Down Questions
Homework/Independent work:
Students are provided the attached worksheet to complete on their own.
Individual Questions
Individual Questions Answers
Closure: How will the teacher assist students in organizing the knowledge gained in the lesson?
Discussion:
The teacher will bring the class back together and highlight the important parts of the lesson.
Mention briefly that we usually take what we know to begin a proof, see what we want to prove, and determine what linking angles will lead us from the given to the
proof statement.
If time allows, the teacher could then have the students apply the theorems by asking questions and having the students answer questions on white boards. Here are
sample questions with answers.
Summative Assessment
The day following the lesson the students will be asked to prove a theorem about angle pairs formed by two parallel lines and a transversal. The bellwork will also
include solving for unknown values using the angle pairs formed by two parallel lines and a transversal.
Bellwork Quiz
Bellwork Quiz Answers
Formative Assessment
Prior to the Lesson:
Students will participate in a game where they find angle pairs, see teaching phase. The teacher will observe groups to assess understanding of angle pairs.
During the Lesson:
Teacher will circulate the room as groups prove each theorem, and then again as the groups rotate and explain their proofs.
Closure:
Students will answer questions related to the angle pairs formed by two parallel lines and a transversal. They will answer the questions on white boards and show them
to their groups for coaching, the teacher will circulate to ensure groups are correctly answering the questions.
Feedback to Students
The students will see how well they know the different angle pairs through the game.
Students will work together to prove a theorem about angles formed by two parallel lines and a transversal. Through working together they will see how well they
are able to prove theorems and understand the relationships.
At the end of the lesson students will answer questions pertaining to the angle pairs as an exit ticket. The groups will correct each other, as the teacher circulates
and helps when needed, so the students are sure they are correct.
ACCOMMODATIONS & RECOMMENDATIONS
Accommodations: Individual Practice could be modified to include some information allowing the student to just fill in the blanks. Modified Individual Questions
Additional prompting and hints could be provided if needed.
Sitting students in homogeneous groups will help scaffold the struggling students.
page 3 of 4 Extensions: Opening Activity:
For more advanced students extra lines could be added to allow for multiple correct answers to any question.
After Lesson:
Students could be challenged to create and prove the converse of each of the proofs. Prove that lines are parallel based on two angles stated as congruent.
Suggested Technology: Document Camera
Special Materials Needed:
Painters tape
Sticky notes in four colors, enough for each student to have 5 - 10
White boards for each student
Chart paper, enough for one per group
Dry Erase marker for each student
Straightedge
Protractor
Additional Information/Instructions
By Author/Submitter
This resource supports the following Standards for Mathematical Practice:
MAFS.K12.MP.1.1 - Make sense of problems and persevere in solving them.
MAFS.K12.MP.3.1 - Construct viable arguments and critique the reasoning of others.
SOURCE AND ACCESS INFORMATION
Contributed by: Megan Hannon
Name of Author/Source: Megan Hannon
District/Organization of Contributor(s): Orange
Is this Resource freely Available? Yes
Access Privileges: Public
License: CPALMS License - no distribution - non commercial
Related Standards
Name
MAFS.912.G-CO.3.9:
Description
Prove theorems about lines and angles; use theorems about lines and angles to solve problems. Theorems include:
vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and
corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant
from the segment’s endpoints.
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