Lesson Title: Bisect a segment and Perpendicular Bisector Construction Course: Common Core Geometry, Unit 2
Date: _____________ Teacher(s): ____________________
Start/end times: _________________________
Lesson Standards/Objective(s): What mathematical skill(s) and understanding(s) will be developed? Which
Mathematical Practices do you expect students to engage in during the lesson?
G.CO.C.12 Make formal geometric constructions with a variety of tools and methods (compass and straightedge,
string, reflective devices, paper folding, dynamic geometric software, etc), including bisecting a segment and a
perpendicular bisector of a line segment.
G.CO.A.1 Know precise definitions.
MP4: Model with mathematics.
MP5: Use appropriate tools strategically.
Lesson Launch Notes: Exactly how will you use the
first five minutes of the lesson?
Have students write, draw or discuss the definitions of
bisect and perpendicular.
As a class, come to a consensus. Allow students to
share their drawings and definitions.
Lesson Closure Notes: Exactly what summary activity,
questions, and discussion will close the lesson and
connect big ideas? List the questions. Provide a
foreshadowing of tomorrow.
Which tools do you think will be most helpful in future
lessons?
Why do you think the bisector of a line segment may be
important? What about a perpendicular line segment?
Lesson Tasks, Problems, and Activities (attach resource sheets): What specific activities, investigations,
problems, questions, or tasks will students be working on during the lesson? Be sure to indicate strategic
connections to appropriate mathematical practices.
1. Organize the stations around the room and separate the students into groups.
2. Have students rotate through four stations. Each station will have students create a bisector of a segment and a
perpendicular bisector of a segment. (At each station look for evidence MP4 and MP5.)
 Station 1- The students will use a compass and a straightedge to construct the bisector and the
perpendicular bisector. Here is a link for a demonstration on how to construct a perpendicular bisector
http://www.mathopenref.com/constbisectline.html. There are also printable steps on the site.
 Station 2 – The students will use patty paper to bisect a line segment and also make a perpendicular
bisector.
 Station 3 - The students will use a marker, string and chart paper to bisect a line segment and also make
a perpendicular bisector.
 Station 4 – The students will use dynamic geometric software to bisect a line segment and also make a
perpendicular bisector.
3. Regroup as a class and discuss the student’s work. Which stations did they find the most successful or difficult?
Review the vocabulary if needed.
4. Allow students to choose a station to return to and complete the following activity. Students will each draw a
triangle at the station. Then, students will bisect each side of their triangle. Note: The bisected lines will meet at
a point of concurrency called the circumcenter. Note: depending on the type of triangle some circumcenters may
not be inside the triangle. (Look for evidence of MP4 and MP5)
5. Regroup as a class and discuss the findings of their triangle bisections. What happens to the circumcenter when
you have an acute, obtuse or right triangle?
HCPSS Secondary Mathematics Office (v2.1); adapted from: Leinwand, S. (2009). Accessible mathematics: 10 instructional shifts that raise student
achievement. Portsmouth, NH: Heinemann.
Lesson Title: Bisect a segment and Perpendicular Bisector Construction Course: Common Core Geometry, Unit 2
Date: _____________ Teacher(s): ____________________
Start/end times: _________________________
Evidence of Success: What exactly do I expect students to be able to do by the end of the lesson, and how will I
measure student success? That is, deliberate consideration of what performances will convince you (and any outside
observer) that your students have developed a deepened and conceptual understanding.
After this lesson, students will be able to construct a bisector and a perpendicular bisector of a segment with multiple
tools.
The teacher will examine the accuracy of the students various constructions.
Students will be able to see that a triangle that has the sides bisected will have a point of concurrency called the
circumcenter.
Notes and Nuances: Vocabulary, connections, anticipated misconceptions (and how they will be addressed), etc.
Vocabulary bisector, perpendicular
After the stations, students should make the connection that a bisector creates two equal sections of a line segment.
They should also recognize that a perpendicular bisector of a line segment creates 90 degree angles as it divides the
line segment into two equal sections. Students may confuse the two, so note that not all bisectors are perpendicular.
Resources: What materials or resources are essential
for students to successfully complete the lesson tasks or
activities?
Compasses
Chart paper
String
Markers
Computers with dynamic geometric software
Patty paper
Homework: Exactly what follow-up homework tasks,
problems, and/or exercises will be assigned upon the
completion of the lesson?
Have students teach their parents how to use two different
tools to bisect and perpendicular bisect a line segment.
Have them bring in their constructions to share.
Note: Allow students to take home patty paper if needed.
Lesson Reflections: How do you know that you were effective? What questions, connected to the lesson
standards/objectives and evidence of success, will you use to reflect on the effectiveness of this lesson?
Are students able to successfully bisect and perpendicular bisect a line segment?
Can the students use the various tools successfully?
Howard County Public Schools Office of Secondary Mathematics Curricular Projects has licensed this
product under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License.
HCPSS Secondary Mathematics Office (v2.1); adapted from: Leinwand, S. (2009). Accessible mathematics: 10 instructional shifts that raise student
achievement. Portsmouth, NH: Heinemann.