Primary Type: Lesson Plan
Status: Published
This is a resource from CPALMS (www.cpalms.org) where all educators go for bright ideas!
Resource ID#: 130062
Triangle Medians
This lesson will have students exploring different types of triangles and their medians. Students will construct mid-points and medians to determine
that the medians meet at a point.
Subject(s): Mathematics
Grade Level(s): 9, 10, 11, 12
Intended Audience: Educators
Suggested Technology: Document Camera,
Interactive Whiteboard, Microsoft Office
Instructional Time: 45 Minute(s)
Keywords: Triangles, Medians, Centroid, construct
Resource Collection: FCR-STEMLearn Geometry
ATTACHMENTS
Warmup.pdf
Warmupanswerkey.pdf
Triangles.pdf
PracticeProblems.pdf
PracticeProblemskey.pdf
Independent Practice.docx
Independent Practice key.docx
Summative assessment.pdf
Summative key.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 midpoints of the sides of a triangle using both paper folding and compass and straightedge.
Students will construct the medians to find the centroid of the triangle.
Prior Knowledge: What prior knowledge should students have for this lesson?
Students should know that the median of a triangle is a segment whose endpoints are a vertex and the midpoint of the opposite side.
Students should know that a vertex is where two line segments meet at a point.
Students should be able to use a compass.
Guiding Questions: What are the guiding questions for this lesson?
Explain why the medians meet at a point for all types of triangles.
What do you know about concurrency?
How can finding the centriod make your life easier?
page 1 of 4 Teaching Phase: How will the teacher present the concept or skill to students?
Prior to instruction you will need to have these items ready for students: straight edge, compass, and construction paper.
1. Students should complete the attached warm-up activity. The teacher should review vocabulary and the warm-up once students have finished. This should not take
more than five minutes.
What are the different types of triangles? (Right, equilateral, isosceles, obtuse, acute, scalene, equiangular)
What is a median? (a median of a triangle is a line segment joining a vertex to the midpoint of the opposing side)
What is a vertex? (point at which the sides of the triangle intersect)
The centroid of a triangle is the point of concurrency of the medians. This point is also called the center of gravity of a triangle because it is the point where a
triangular shape will balance.
2. Next, ask the students, "How can you find the midpoint of a line segment?" Allow the students time to think about it. Have students share their thoughts.
Hand out compass, straight edge, and construction paper, if this hasn't been done.
Guided Practice: What activities or exercises will the students complete with teacher guidance?
1. Activity: Finding the medians of a triangle.
Give the students colored paper.
Have the students carefully draw a triangle with a straightedge and cut it out.
Label the vertices A, B, and C.
Find the midpoint of segment AB by folding along the side so that A collides with B.
Unfold and mark the midpoint of segment AB as D.
The crease DC is a median.
Fold the triangle so that B collides with C.
Unfold and mark the midpoint of segment BC as E.
The crease EA is a median.
Fold the triangle so that A collides with C.
Unfold and mark the midpoint of segment AC as F.
The crease FB is a median.
Students should notice that the medians all intersect at a point. Have them label the Point as G. This point is the centroid. Make sure the students label this point.
2. Next, have students draw another triangle. (See the attached Triangles worksheet, which has pre-drawn triangles that can be printed and cut out prior to class to
save time.) Have them use a compass and straight edge to find the medians of the triangle by first constructing the midpoints of each side. If the students cannot work
the compass you might have to take time to walk them through it. The following link gives printable instructions on how to use a compass:
http://www.mathopenref.com/printmedian.html
3. Once students have finished the guided practice activity, do a demonstration using the centroid to balance a triangle on a pencil. Have the students use the triangles
from the last activity and balance it on the point of a pencil using the centroid. Explain to the students that the centroid is the center of gravity for a triangle.
Independent Practice: What activities or exercises will students complete to reinforce the concepts and skills developed in the
lesson?
Have students repeat the activity with two different size and types of triangles. You can recommend they use either paper folding or a compass to find the midpoints.
Have students write an explanation of how they found the centroid. (Should include: the midpoints are the center for the line segments, the medians are constructed
by connecting each vertex with the midpoint of the opposite side and that all the medians meet at a point called the centroid).
There is a worksheet attached labeled Independent practice to help control the activity.
Finally, give students a chance to practice using the attached Practice Problems worksheet. Ask students, "What tools can be used to find midpoints?"
Closure: How will the teacher assist students in organizing the knowledge gained in the lesson?
Have students explain to a partner how they found the medians and if the medians meet at a point for their triangle. Then have the students write one thing they
learned from the lesson and their partner.
Students will need to clean their area and put all materials back up. Have them turn all work in.
Finally, pass out the summative assessment worksheet.
Summative Assessment
The summative assessment can be done as an exit ticket. The teacher will provide the students the summative worksheet and have them complete it at the end of
class.
As an alternative, the teacher may have students construct their own triangle and then determine the medians and the centroid.
Formative Assessment
The teacher will gather information throughout the lesson by being attentive to students' responses and work.
During the warm-up activity, have students find the midpoints to assess prior knowledge. The teachers should use this information to determine if the students
understand the midpoint formula.
Give the students example problems that require them to find medians. See the attached practice problems worksheet. This can be used for extra questions or as
page 2 of 4 an independent practice worksheet.
During the guided practice, there is a great opportunity for formative assessment. The 3rd activity has the students finding the centroid. Once they find the centroid,
they can balance their triangles on a pencil to demonstrate the center of gravity, which is the centroid.
Feedback to Students
Students will receive verbal feedback from the teacher during the guided practice as the teacher observes students' progress during circulation.
The teacher will check the accuracy of the students work. When the students complete the summative assessment this will be turned in and graded.
Check for accuracy in labeling of triangles and mid-points and provide constructive feedback, pointing out errors.
ACCOMMODATIONS & RECOMMENDATIONS
Accommodations:
Students may need to work with a partner or group.
For students who struggle, the teacher may cut out triangles ahead of time.
Use the pre-drawn triangle sheet rather than having students draw their own.
Extensions:
Students could be asked to find perpendicular bisectors and angle bisectors. Students could also be asked to determine special characteristics of a centroid or asked to
find the altitude of a triangle.
Suggested Technology: Document Camera, Interactive Whiteboard, Microsoft Office
Special Materials Needed:
colored paper
scissors
grid paper
markers
straightedge or ruler
compass
Further Recommendations:
Have prepared examples for students.
Have at least a class set of all worksheets just in case technology fails.
If you decide to have students use a compass, prepare to have time to practice using the tool.
Additional Information/Instructions
By Author/Submitter
Mathematical Practices:
MP1.1 Make sense of problems and persevere in solving them.
MP3.1 Construct viable arguments and critique the reasoning of others.
MP5.1 Use appropriate tools strategically.
SOURCE AND ACCESS INFORMATION
Contributed by: Mckenzie Russell
Name of Author/Source: Mckenzie Russell
District/Organization of Contributor(s): Madison
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
page 3 of 4 phenomenon and can lead to conjectures and proofs.
page 4 of 4