Primary Type: Lesson Plan
Status: Published
This is a resource from CPALMS (www.cpalms.org) where all educators go for bright ideas!
Resource ID#: 130041
Geometric Construction Site
This lesson takes students from simple construction of line segments and angles to an optional extension worksheet for creating triangles.
Subject(s): Mathematics
Grade Level(s): 9, 10, 11, 12
Intended Audience: Educators
Suggested Technology: Document Camera,
Computers for Students, Overhead Projector,
GeoGebra Free Software (Download the Free
GeoGebra Software)
Instructional Time: 45 Minute(s)
Keywords: line segments, angles, construct
Resource Collection: FCR-STEMLearn Geometry
ATTACHMENTS
WeDoWorksheetBecominganExpertonLinesandAngles.docx
AnswerKeyWeDoworksheet.pdf
YouDoWorksheetBecominganExpertonLinesandAngles.docx
AnswerKeyYouDoworksheet.pdf
ExtensionWorksheetBecominganExpertonLinesandAngles.docx
AnswerKeyExtensionworksheet.pdf
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 construct a line segment congruent to a given segment by copying the given line segment using a straightedge and compass.
Students will construct an angle congruent to a given angle by copying a given angle using a straightedge and compass.
Prior Knowledge: What prior knowledge should students have for this lesson?
Students should know the definitions of line segments and angles.
Students should know how to use a compass, ruler, and straightedge.
Guiding Questions: What are the guiding questions for this lesson?
How do tools and certain methods make it easier to reproduce certain objects?
Teaching Phase: How will the teacher present the concept or skill to students?
With students:
Review definitions of line segments and angles.
Introduce the different types of tools.
Gather information to help you: Ask the students if they have used any of the tools you are about to demonstrate.
Use the "I do, We do, They do" teaching method.
page 1 of 3 I Do: Model using a blackboard, whiteboard, document camera, or smart board.
Have students watch as you demonstrate how to use a string, straightedge, and ruler to measure and draw line segments. (This is done just to show students how
to use each tool.)
Have students watch as you demonstrate how to use a straightedge and compass to construct given angles. (This is done just to show students how to use each
tool.)
Next, working only with a straightedge and a compass, demonstrate the following:
Construct segment CD congruent to segment AB:
1. Draw line segment AB.
2. Mark a point C for one endpoint of the new line segment.
3. Set the compass point on point A of the given line segment.
4. Adjust the compass width to the point B. The compass width is now equal to the length of the line segment AB.
5. Without changing the compass width, place the compass point on point C and draw an arc.
6. Put a point D on the arc. That will be the other endpoint of the new line segment.
7. Draw a segment from C to D.
The line segment CD is congruent (equal in length) to the line segment AB. Repeat as necessary until all the students understand.
Construct angle DEF congruent to angle ABC:
1. Draw an angle with vertex B.
2. Mark a point E that will be the vertex of the new angle.
3. From E, draw a ray. This will become one side of the new angle. (This ray can go off in any direction.)
4. Place the compass on point B, set to a width that will intersect the sides of the angle.
5. Draw an arc across both sides of the given angle, creating the points A and C where the arc intersects the two sides of the angle.
6. Without changing the compass width, place the compass point on E and draw a similar arc there, creating point D where the arc intersects the ray.
7. Set the compasses on A and adjust its width to point C.
8. Without changing the compass width, place the compass point on D and draw an arc across the first one, creating point F where they intersect.
9. Draw a ray EF.
The angle ∠DEF is congruent (equal in measure) to angle ∠ABC. Repeat as necessary until all the students understand.
Guided Practice: What activities or exercises will the students complete with teacher guidance?
We Do: Part One
Give each student a copy of the "We Do" worksheet.
Project the worksheet on the board.
Repeat the steps in the "I Do" section while the students work along with you.
Have the students work along with you while you work each part of the handout. Check to make sure all students are able to construct the objects by having
students hold up their work after each step, giving feedback as you work together.
Once students are able to complete this exercise, allow them to move on to the independent practice.
Independent Practice: What activities or exercises will students complete to reinforce the concepts and skills developed in the
lesson?
You Do:
Once each student completes the "We Do" worksheet and has it checked by the teacher, they will pair with an elbow partner.
Each student will make three line segments and three angles on their paper and then trade papers with their elbow partner to construct segments and angles
congruent to the originals.
The teacher will then give feedback to each elbow pair group.
Closure: How will the teacher assist students in organizing the knowledge gained in the lesson?
Ask volunteers to come up and explain how they did their work. Give feedback if:
1. A step is done wrong,
2. They come up with a better way,
3. They have another way to complete task.
After closure, hand out the "You Do: Becoming an expert on Lines and Angles" worksheet as the summative assessment. Students should do this independently and
turn it in before they leave.
Summative Assessment
The students' "you do" worksheet will be their summative assessment. It will be graded for accuracy to measure students' understanding of the learning
objectives.
Formative Assessment
The teacher will circulate around the room during the "we do" and "you do" parts of the lesson comparing the student's work to what is being taught. This will
assess if students are able to follow the directions given.
The teacher will ask students to hold up their construction after each step to check that all students are actively participating and to check for understanding.
Feedback to Students
During the "we do" part of the lesson, the teacher will stop between each construction direction involved in the concept to determine if students understand by the
correct completion of each task. The teacher will ask students to hold up their construction after each step, if problem is found with an individual student feedback
page 2 of 3 will be given to student while other students continue to practice.
The teacher will ask students to hold up their construction after each step. If a problem is found with an individual student's work, feedback will be given to student
while other students continue to practice.
During the "you do" section, the teacher will continue to circulate and give individual feedback when needed.
ACCOMMODATIONS & RECOMMENDATIONS
Accommodations:
Allow lower-level students to pair up with higher level students during the "We Do" worksheet.
Extensions:
Allow students to use GeoGebra to construct lines and angles.
If students finish early, you can assign them the attached Extension worksheet, which explores constructing congruent triangles.
Suggested Technology: Document Camera, Computers for Students, Overhead Projector, GeoGebra Free Software
Special Materials Needed:
Way to project your work for student viewing
Compasses
Straightedges
Handouts
Optional: Geogebra (geogebra.com)
Further Recommendations:
If the teacher needs additional support, watch videos at Math Open Reference to review how to teach construction of line segments and angles
Additional Information/Instructions
By Author/Submitter
Applicable Mathematical Practices:
MAFS.K12.MP.5.1
MAFS.K12.MP.6.1
SOURCE AND ACCESS INFORMATION
Contributed by: Lizabeth Wilson
Name of Author/Source: Lizabeth Wilson
District/Organization of Contributor(s): Jackson
Access Privileges: Public
License: CPALMS License - no distribution - non commercial
Related Standards
Name
MAFS.912.G-CO.4.12:
Description
Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective
devices, paper folding, dynamic geometric software, etc.). Copying a segment; copying an angle; bisecting a segment;
bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and
constructing a line parallel to a given line through a point not on the line.
Remarks/Examples:
Geometry - Fluency Recommendations
Fluency with the use of construction tools, physical and computational, helps students draft a model of a geometric
phenomenon and can lead to conjectures and proofs.
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