Download Sandia High School Geometry Team

Sandia High School
Geometry Team
Lesson: Triangle Tessellation
Team Planning
•Our team: Heidi Draper, Andy
Diewald, Jessica Esquibel, Ann
Goswick, Brenda Lyons, and
Noralyn Parsons.
•Our team met at lunch and before
school to work on this lesson. We built
off of the strengths and weaknesses
from previous experiences.
Our Students
• Student Population:
– 68% Anglos, 23% Hispanics, 3.9%
Asians, 2.6% Native Americans, and
2% African-Americans .
– Class observed was an inclusion
class with about 1/3 of the class
being part of the special ed.
program. (Class has two teachers.)
•Students are fairly motivated
and are accustomed to working in
groups and individually.
Overarching Goals
•Students will be able to concisely explain
what they have learned in geometry.
•Students will be self-confident and
willing to take risks.
Lesson Objectives
• Students will understand that when given two
parallel lines and a transversal there are two
groups of congruent angles, big angles and
small angles.
•Students will understand that any big angle is
supplementary to any small angle.
B
S
Previously Learned Concepts
• Students have covered the
following topics prior to this
lesson:
– Angles
– Triangle types (isosceles, equilateral,
scalene)
– Triangle Angle Sum
– Parallel Lines
– Congruency
– Linear Pair
– Straight Angles
– Vertical Angles
– Angle Addition
Concepts to be Learned
•Students will use a tessellation
to:
become familiar with the
terms of the lesson.
understand the properties
associated with the following
types of angles: (alternate
interior, alternate exterior,
corresponding, and same-side
interior).
Concepts to be Used in
Future Lessons
•Students will be able to apply the
knowledge gained from this lesson to:
Solve geometric proofs
Solve problems associated
with polygon angle sum.
Solve problems associated
with exterior angle theorem.
Misconceptions
•Two lines are parallel just because we don’t
see them intersect.
•Students may think that special angles
will always be congruent. They forget
that the lines cut by the transversal must
be parallel.
•Students may confuse the special
angle types. Students seem to
struggle the most with corresponding
angles.
Materials
• Tag board triangles (for the
students)
• White sheets of paper
• 3 colored pencils for each student
• 3 colors of overhead pens
• Overhead triangle
• Overhead transparency of
completed tessellation
Lesson Time Schedule
• 10 minutes to introduce topic
• 30 minutes for students to begin
tessellation
• 10 minutes for discussion
• Following Day: Lesson expands to
specific angle types.
*Note: We did this lesson on a flex day
so we had 75 minutes for the lesson.
Visual Tool
•The key instructional tool in this lesson
is the tessellation and the making of the
tessellation.
Possible Student
Problems/Concerns
• Students will want to know if they have to fill
the whole page with triangles.
•Students may struggle with tracing and rotating
the triangle and with coloring the angles.
•Students’ lines may not come out parallel if
their tracing is off.
Engaged Student Learning
• Students will be tracing triangles and coloring
angles.
• Students will be looking at their tessellation
and exploring angle relationships.
• Students will be writing down their
observations as they work on the tessellation.
• Students will take notes throughout the class
discussion.
 The teacher will be walking
around the room answering questions
and observing throughout the lesson.
Mathematical understanding
• The effectiveness of the lesson will be based
on how well the students grasp the topics
that follow this lesson.
– If students are using the tessellation as a visual
tool and get in the habit of coloring congruent
angles, then the lesson will be a success.
Changes
• Students should write down their
observations as they work on their
tessellation.
•Make sure triangles are not too small.
•When discussing big angles and small
angles, color the two angles that make up
the big angle one color on the overhead
transparency.
•Should students be allowed to use a ruler
to expedite the process?
Summary
• Based on observation, the lesson was a
success.
–Students used the tessellation as a visual tool.
–Students used colored pencils to mark
congruent triangles.
–Students were able to “fall back on” the
ideas of big angles and small angles when they
were struggling with the specific angle types.
–The class was able to use the tessellation in
lessons that followed to discuss different
topics.
Assessment
*Immediate assessment based on observation.
*Unit test results were better than in previous
years without using the lesson.
Students acquired a deeper understanding
of the concepts because of the techniques
used in this lesson.
What The Teachers Learned
•Teaching with a visual tool helps all levels
of students.
• Need to use the visual tool as often as
possible and add more visuals whenever
possible.
• Using smaller terms (big and small angles)
that the students can fall back on helps
ease some students’ stress. This allows the
students to simplify what often seems
overwhelming.
Thank you!