Graduate Fellows in K-12 Education
Lesson Title: Table Talk with Triangles
Discipline Focus: Math - Geometry
Grade level: 11/12
Length of lesson: 45 min.
Stage 1 – Desired Results
Content Standard(s):
From: http://www.nctm.org/resources/content.aspx?id=12638
Geometry Standard for Grades 9-12: analyze properties and determine attributes of twoand three-dimensional objects, establish the validity of geometric conjectures using
deduction, prove theorems, and critique arguments made by others.
Understanding (s)/goals
Students will understand:
 Properties of right, acute, and
obtuse triangles:
o Scalene, isosceles, and
equilateral
o Edge lengths relationships
o Angle measure relationships
Essential Question(s):
 What properties can right, acute,
and obtuse triangles have?
 What properties must right, acute
and obtuse triangles have?
 How are triangles similar/different?
Student objectives (outcomes):
Students will be able to:
 Analyze properties and determine attributes of triangles
 Establish the validity of properties of triangles, give and critique defending
arguments
Stage 2 – Assessment Evidence
Performance Task(s):
Other Evidence:
 Complete a table of properties of
 The trends students describe in
three types of triangles
their exit reflections
 Exit reflection
Stage 3 – Learning Plan
Learning Activities:
Introduction:
Before class begins, draw enough tables (see attached) for the class to divide itself into
groups of 5 or 6. Do not include the Acute Triangle and Obtuse Triangle columns, so
that students are not intimidated by the task. (Note: Save these for later in the activity.
I recommend doing this activity after learning the properties of right triangles, so
students will start with confidence. )
Explain the motivation for the activity is to transition into the challenging subject of
trigonometry by starting with something the students have already learned. Give the
instructions: summarize properties of triangles by determining what properties a triangle
Graduate Fellows in K-12 Education
has. Give some history: At one point these were new discoveries and they were initially
based on a hunch then defended and validated. Instruct students to form groups of
their choosing at each of the tables. (5 minutes)
Learning Activities:
Students should be encouraged to convince each other of their answers. Tell them to
ask each other “Why?”, because if they can’t defend their answer, then it might not be
correct. Students should be most familiar with right triangles and so will probably finish
quickly. They should also be aware of the definitions of acute and obtuse triangles but
not necessarily their properties. (Note: As algebra juniors and seniors, they will have
learned this vocabulary at some point, so at least one student in each group will
probably remember it. If not, we can fill in the blanks as we circulate between the
groups.) When they’re finished with right triangle properties, have them create a column
for acute triangles. Then when their finished with that, add an obtuse triangle column
and complete it. (35 minutes)
While the students work, circulate through the groups. Some of the properties are more
difficult to determine than others. Make sure they are giving and critiquing arguments
each other’s arguments. Encourage them to draw many triangles (they may need
protractors/rulers).
Conclusion:
Let students work almost the entire time. Go over each group’s results with them while
the others continue working. They will probably finish around the same time but with
enough time in between to visit each group a last time. For the last five minutes, have
the students take their seats and ask them to describe on a sheet of paper one trend
they observe in the properties tables (This is the exit reflection.). (5 minutes)
Graduate Fellows in K-12 Education