Download TrainerNotes Block 26 - Math GR. 6-8

Trainer Notes
Title of Event: Demonstrate that the sum of the angles in a triangle is 180-degrees and apply this fact to find
unknown measures of angles
Block: 26
Description: This course will incorporate strategies for effective identification, utilization, and implementation of the NGSSS for
Broward teachers. The primary focus will be on the providing content for teachers to teach how to demonstrate that the sum of the
angles in a triangle equal to 180-degrees if we are referring to Euclidean geometry. Teachers will also solve problems where they must
find missing angles with the idea to identify areas of confusion for students.
Delivery Method: Face-to-face
Target Audience: Middle School Math Teachers
Session Duration: Session __2_ of _3_ (
2 hour training)
Prerequisites: Block 25
Specific Objectives:
Participants will be able to understand and recognize different proofs for the sum of the measures of angles in a triangle
Participants will be able understand and apply hands-on activities that show the sum of the angles in a triangle
Participants will be able to explore GeoGebra files designed to demonstrate the sum of the measures of angles in a triangle and
determine the effectiveness of those files in their own classrooms
Participants will be able to familiarize themselves with the concept of non-Euclidean geometries and understand the main differences
with Euclidean geometries
Participants will be able to practice solving problems that students will have to solve and participants will discuss ways to help their
students complete those exercises with understanding of the concepts behind them.
Participants will be able to identify effective strategies for teaching how to demonstrate tea the sum of the angles in a triangle is 180degrees and apply this fact to find unknown measures of angles.
Participants will be able to identify teacher-specific instructional tools and methods for teaching how to demonstrate tea the sum of the
angles in a triangle is 180-degrees and apply this fact to find unknown measures of angles.
Benchmark:
MA.8.G.2.3 – Demonstrate that the sum of the angles in a triangle is 180-degrees and apply this fact to find
unknown measures of angles in polygons.
Trainer Notes
Time
Frame
Duration
Of
Activity)
Content
30 minutes
Historical
proofs
1. Participants, divided in small groups, will
use the GeoGebra files and determine why
they work
2. Participants will share, as a big group, their
interpretation of those proofs
Powerpoint Slides 1-4
GeoGebra files Pythagoras proof
and Euclid proof
30 minutes
Hands-on
activities
1.
Powerpoint slides 5 – 7
GeoGebra file paper folding
Course
Outline
Process/
Product
Script for each Content Area
Other
GeoGebra
files
Materials/
Resources
Assessment of Training Materials for
Specific
Activities
Objectives
2.
20 minutes
Participant
Evaluation
1.
2.
Participants will
understand that
this proposition
has been proven
by the Greeks
and the
arguments still
stand and our
students can
understand
them
Instructor will guide participants through
Participants will
the 2 hands-on activities
be aware of
Participants will discuss why the paper
some hands-on
folding activity work justifying the steps
forms of
with geometric properties
showing
students the
triangle sum
theorem
Instructor will divide participants into small Participants
groups, each group can preview a GeoGebra should be able
file
to see the
Instructor will facilitate whole class
relationship of
discussion about the pedagogical value of
those files with
Powerpoint slides 8-11
GeoGebra files:
sum_angle_triangle 1, 2, and 3
Trainer Notes
the different files
20 minutes
NonEuclidean
Geometries
1. Instructor will ask if all triangle have an
angle sum equal to 180°
2. Instructor will give a short lecture on some
of the non-Euclidean geometries and how
they compare to Euclidean geometry
20 minutes
Practice
exercises
1. Instructor will give out the worksheet
measures of angles
2. Participants will work through these
problems
3. Participants will discuss the level of
difficulty of the problems and how to help
their students comprehend and use this
theorem
the historical
proofs.
Participants will
have a wide
selection of
ways to let
students explore
the triangle sum
theorem
Participants will Powerpoint slides 12 -16
be aware of the
existence of
other types of
geometry and
that this
particular
theorem has
been
controversial
through out
history
Participants will Powerpoint slides 17-18
try to anticipate Measures of angles worksheet
the difficulties
their students
will encounter
while working
similar
problems to
these ones.