Primary Type: Lesson Plan
Status: Published
This is a resource from CPALMS (www.cpalms.org) where all educators go for bright ideas!
Resource ID#: 130065
Construction Junction
Students will learn how to construct an equilateral triangle and a regular hexagon inscribed in a circle using a compass and a straightedge.
Subject(s): Mathematics
Grade Level(s): 9, 10, 11, 12
Intended Audience: Educators
Suggested Technology: Document Camera,
Overhead Projector, GeoGebra Free Software
(Download the Free GeoGebra Software)
Instructional Time: 45 Minute(s)
Keywords: constructions, equilateral triangle, regular hexagon, inscribed, inscribed in a circle
Resource Collection: FCR-STEMLearn Geometry
ATTACHMENTS
Bell Ringer.docx
Bell Ringer Answer Key.docx
Guided Construction.docx
Guided Construction Answer Key.docx
Independent Construction.docx
Independent Construction Answer Key.docx
Exit Pass.docx
Exit Pass Answer Key.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 use a compass and a straightedge:
to construct an equilateral triangle inscribed in a circle.
to construct a regular hexagon inscribed in a circle.
Prior Knowledge: What prior knowledge should students have for this lesson?
Students should
know the properties of a regular hexagon, an equilateral triangle, and a circle.
be familiar with using a compass and a straight edge.
As a warm-up activity, the teacher should pass out the Bell Ringer worksheet (see attachments). The bell ringer reviews equilateral triangle properties and regular
hexagon properties. Students can check with a shoulder buddy to compare their answers. The teacher should call on volunteers to share their answers and then clear
up any misconceptions.
page 1 of 4 Guiding Questions: What are the guiding questions for this lesson?
How can constructions be useful in the real world?
Can you think of a job that would require constructions?
Teaching Phase: How will the teacher present the concept or skill to students?
Pre-Teaching: The teacher will need some method of demonstrating the constructions such as a document camera, a large compass to use on the board, a string and
pen compass, or other technology such as Smart Board Tools. If possible, use different colors during the constructions to help students identify the marks for each
step.
The teacher should introduce the lesson by asking the following questions of the class.
What is true when a polygon is inscribed in a circle? (All vertices of the polygon must touch the circle.)
What is true if an equilateral triangle is inscribe in circle? (Answers will vary but may include: There will be 3 vertices on the circle. The verticies of the triangle are
all equidistance from the center of the circle. The circumference of the circle will be divided into 3 equal arcs.)
Have the students watch while the teacher constructs a equilateral triangle in a circle. The teacher should clearly state what is being done at each step. Steps for the
construction:
1. Using a straight edge, draw a line through the center of the circle (the diameter). Label the new points of intersection B and C. Label the center A.
2. Set the compass to the width from Point A to Point C. Stress to the students the importance of keeping the compass set at this width for the rest of the construction.
3. Place the compass on Point C and make an arc on both sides of the circle. Label the points created by these intersections Point D and Point E, respectively.
4. Draw a segment connecting Point D and Point E.
5. Draw a segment connecting Point D to Point B
6. Draw a segment connecting Point E to Point B
Next, ask:
What is a regular hexagon made up of?
Sample Answer: six equilateral triangles
What do you know about the perimeter of an equilateral triangle and a regular hexagon inscribed in the same size circle?
Sample Answer: They will be the same.
The teacher should lead a discussion with the class on how equilateral triangles and regular hexagons are related. A list of possible questions to ask is provided
below.
Circulate through the room as student proceed to problem 2, offering assistance as needed.
Once students finish, encourage them to check with a shoulder buddy. (This should take approximately 5 minutes.)
Repeat the construction steps one at a time, allowing students time to complete each step before proceeding to the next.
Steps to construct the inscribed hexagon:
Pass out the Guided Constructions worksheet (see attachments), compasses, and straightedges.
The teacher should start a new construction as if he or she were going to inscribe another triangle but then stop after marking point E.
Ask the students how many points are one the circle (4) and how many points are needed for an inscribed hexagon? (6)
Ask the students if they can think of a way to get the 2 needed points. (Hopefully a student will explain that if you use the compass, still set at the same opening,
and mark off two more arcs, you will get the last two points.)
Steps for construction:
1. Complete the construction by placing the compass at point B and make an arc on both sides of the circle and label the points of intersection as Point F and Point
G, respectively.
2. Then place the compass back on B and make an arc in the other direction that intersects the circle. Label this point G.
3. Connect the adjacent points to create the regular hexagon.
Ask the students to turn to page 2 of Guided Constructions.
Now repeat the construction steps, for the inscribed hexagon one at a time, allowing students time to complete each step before proceeding to the next.
Once students finish, encourage them to check with a shoulder buddy. (This should take approximately 8 minutes.)
Circulate through the room as student proceed to problem 2, offering assistance as needed.
Before starting the independent practice, answer any remaining questions about either process.
Guided Practice: What activities or exercises will the students complete with teacher guidance?
The guided practice is embedded in the Teaching Phase. Students will complete the Guided Constructions practice while the teacher monitors and assists as
necessary.
Independent Practice: What activities or exercises will students complete to reinforce the concepts and skills developed in the
lesson?
Following the student hexagon practice, the teacher should:
Pass out the Independent Constructions worksheet (see attachments).
Have students compare with a shoulder partner as they finish each construction
Walk around and check individual papers.
After students have finished the constructions, show examples of correct student work under the document camera if possible. If a document camera is not
available the teacher may project the answer keys for the class to see.
This should take approximately 15 minutes.
page 2 of 4 Closure: How will the teacher assist students in organizing the knowledge gained in the lesson?
The teacher should:
lead the class in a discussion about why they were able to create the constructions using the given methods.
discuss properties that are similar with hexagons and equilateral triangles.
pass out the Exit Pass worksheet (see attachments).
This should take approximately 8 minutes.
Summative Assessment
A summative assessment is provided that can be given as an exit pass or a warm-up the following day.
Formative Assessment
Formative assessment will take place throughout the lesson.
The bell ringer will allow the teacher to determine the students' knowledge of regular polygons.
During the guided practice the teacher will circulate through the classroom assisting students as needed. The teacher can also use the built in questions to assess
the students' level of understand of why the constructions work.
During the independent practice, the teacher will circulate through the room, observing student work for accuracy and offering assistance as needed.
Feedback to Students
The teacher should:
clear up any misconceptions about the proprieties of regular polygons during the warm-up before moving on to the constructions.
circulate around the room after each step of the construction is done (during guided practice) and provide feedback to the students.
offer individual assistance as needed.
check student work to insure accuracy.
ACCOMMODATIONS & RECOMMENDATIONS
Accommodations:
Students with physical limitations can be paired with another student.
Special needs students could be allowed to use the notes for all the assignments.
Students could have worksheets with only 1 circle printed on a page. (This would help many student with spatial issues.)
Extensions:
Students could practice the constructions using patty paper or GeoGebra.
Students could be challenged to find another method for these constructions.
Suggested Technology: Document Camera, Overhead Projector, GeoGebra Free Software
Special Materials Needed:
Compass
Straightedge
Large teacher compass (optional)
String and pen compass (optional)
Colored pencils (optional)
Patty paper (optional)
Additional Information/Instructions
By Author/Submitter
Applicable Mathematical Practices:
MAFS.K12.MP.5.1 Use appropriate tools strategically.
MAFS.K12.MP.6.1 Attend to precision.
SOURCE AND ACCESS INFORMATION
Contributed by: Christy Wood
Name of Author/Source: Christy Wood
District/Organization of Contributor(s): Gulf
Access Privileges: Public
License: CPALMS License - no distribution - non commercial
page 3 of 4 Related Standards
Name
MAFS.912.G-CO.4.13:
Description
Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle.
page 4 of 4