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Marisol Ortiz-Gely
Education Field Experience EDUC 230-01
Professor Purvin
Spring 2012
High School Lesson Plan #2
Audience: 25 heterogeneously grouped students in a Ninth Grade math class in a suburban
High School
Subject:
High School Math-Grade 9
Topic: Geometry/ Triangle Classification
Objective: The students will be able to (SWBAT) identify points in the plane that, when
connected to the endpoints of a given segment, form a specific type of triangle.
 Classify triangles according to sides (scalene, isosceles, equilateral)
 Classify triangles according to angles (right, acute, obtuse)
 End of class students will write their reflection about why the learning about
triangle classification is important in mathematic.
Standards: CCSS for Mathematics G.CO.9 (CCSS, 2010)
Standard: Math G-CO.9. Prove theorems about lines and angles. 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.
Materials: Smart board, laptop, projector, triangles activity sheet, pencils
Prerequisite Skills and Knowledge: The students have recently mastered to proving
theorems about triangles. Theorems include: a line parallel to one side of a triangle divides the
other two proportionally, and conversely; the Pythagorean Theorem proved using triangle and
have learned about different types of angles (acute, right, and obtuse). They also know the
definition of congruent.
Anticipatory Set: Walk into class wearing a triangle shape hat caring a pile of angle activity
sheet on my hands. To begin the class, I will ask the students the following questions:
 How can you classify triangles according to their angles? [right, acute, obtuse]
 How can you classify triangles according to their sides? [equilateral, isosceles, scalene]
Input and Modeling: After the introduction, I will place an overhead copy of the activity
sheet on the projector. I will read the directions aloud to students, and then ask students to
suggest a point C that would create a right triangle. I will call on a volunteer to come to the
overhead projector and, without any explanation, place a dot on the transparency. Then, I will
allow the class to discuss. Would the point form a right triangle? How do you know? During
this discussion, I will ask questions to prompt and further student thinking, but been careful not
to insert comments of my own.
Guided Practice and Checking for Understanding: After a brief discussion, the teacher
distributes the triangle activity sheet to all students. Then I will answer any questions that
students have regarding the activity. Once all questions have been answered and students are
ready, allow them to work for 1-2 minutes individually to identify the various types of
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triangles. During the discussion about right triangles, most students will have begun to think
about the points that form the other types of triangles.
For the next 3-5 minutes, I allow students to share their thoughts with a partner. During these
discussions, students will often realize any errors that they made. In addition, two students
working together will find most, if not all, of the points that form each type of triangle.
Then I will spend the remaining time in class discussing the student discoveries. I will allow a
different student to indicate which points from each of the six different types of triangles.
During this discussion, be sure to review theorems that are needed to solve this problem. For
instance, the circle with the midpoint of AB as its center represents all right triangles with AB
as the hypotenuse; this is true because of the following theorem: "An angle inscribed in a
semicircle is a right angle."
To accompany this discussion, I will draw with different colors of market the triangles on the
overhead projector for demonstration purposes. The red lines in the triangles will indicate the
paths that create right and isosceles triangles. (Then will erase the triangles but leave the
paths.) After all four paths are drawn, I will draw the random triangle in tap of the four paths to
demonstrate the regions where acute and obtuse triangles. The paths representing the points
that form isosceles triangles are three different circles. I will ask students, “How are these
circles similar or different”?
The circle with diameter AB represents those isosceles triangles for which AB is the
hypotenuse. The other two circles represent isosceles triangles for which AB is one of the
congruent legs.
Two lines perpendicular to AB pass through A and B. These lines represent points that form
right triangles. Two circles with centers at A and B represent points that form isosceles
triangles. Then I will ask the students, “What do the intersections of these paths represent”?
Independent Practice and Evaluation: The class will work independently on an angle
activity sheet that will have the following question: The points at which 45- 45- 90 triangles
are formed. What is special about the point(s) where the line perpendicular to AB and passing
through its midpoint intersects the two circles with A or B as the center and AB as the radius? I
will walk around the room to monitor the students. Lastly, I will collect the student work on
this problem and use it to determine each student’s level of understanding.
Closure: Ladies and gentlemen, on the index card, I want you to write down why the
learning about triangle classification is important in mathematic. Please drop your “exit ticket”
index card in the basket on your way out.
Modifications / Accommodations: Students with special needs will receive the triangle
definition sheet, and a triangle classification activity to work on in separate sheets rather than
all in one sheet. The teacher will spend more time with the group in the back of the class to
give them further assistance while completing the worksheet.
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Triangle Classification
NAME _____________________
AB is drawn in a plane.
Find all points C such that ΔABC is:
• right
• acute
• obtuse
• isosceles
• scalene
• equilateral
You may want to use a different color to represent the points for each of the six
classifications. For instance, use green to indicate all points that create right triangles, but
use red for all points that create isosceles triangles.
A
B
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References
Association, National Governors (NGA) and Officers, Council of Chief State School
(CCSSO). (2010) Common Core State Standards Initiative. Retrieved from
http://www.corestandards.org/the-standards/mathematics.
Triangles Worksheets
http://www.mathworksheets4kids.com/triangles.html.