Download Geometry and Spatial Reasoning Activity: Triangle Properties TEKS

Mathematics TEKS Refinement 2006 – 6-8
Tarleton State University
Geometry and Spatial Reasoning
Activity:
Triangle Properties
TEKS:
(6.6) Geometry and spatial reasoning. The student uses geometric
vocabulary to describe angles, polygons, and circles.
The student is expected to:
(A) use angle measurements to classify angles as acute, obtuse, or
right;
(B) identify relationships involving angles in triangles and
quadrilaterals;
(6.11) Underlying processes and mathematical tools. The student
applies Grade 6 mathematics to solve problems connected to everyday
experiences, investigations in other disciplines, and activities in and
outside of school.
The student is expected to:
(D) select tools such as real objects, manipulatives, paper/pencil, and
technology or techniques such as mental math, estimation, and
number sense to solve problems.
(6.12) Underlying processes and mathematical tools. The student
communicates about Grade 6 mathematics through informal and
mathematical language, representations, and models.
The student is expected to:
(A) communicate mathematical ideas using language, efficient tools,
appropriate units, and graphical, numerical, physical, or algebraic
mathematical models;
(6.13) Underlying processes and mathematical tools. The student uses
logical reasoning to make conjectures and verify conclusions.
The student is expected to:
(B) validate his/her conclusions using mathematical properties and
relationships.
Measurement Connection:
(6.8) Measurement. The student solves application problems involving
estimation and measurement of length, area, time, temperature, volume,
weight, and angles.
The student is expected to:
(B) select and use appropriate units, tools, or formulas to measure
and to solve problems involving length (including perimeter), area,
time, temperature, volume, and weight;
(C) measure angles;
Geometry and Spatial Reasoning
Triangle Properties
Grade 6
Page 1
Mathematics TEKS Refinement 2006 – 6-8
Tarleton State University
Overview:
Students will identify, compare, and contrast triangles according to
properties of sides and properties of angles.
Materials:
Paper
Rulers
Protractors
Blackline master (various triangles)
Possible or Impossible game cards on transparency
Large index cards, 1 per teams of 2
Grouping:
Pairing of two students
Time:
60 minutes
Lesson:
Procedures
1. (5-10 minutes) Review the fact that
triangles are classified: by properties of
sides and properties of angles. Give
students the meaning of equilateral,
isosceles, scalene, acute, obtuse, and
right triangles.
Notes
Have students repeat definitions of the
triangles using correct mathematical
attributes. Encourage note taking
during this time.
2. (20 minutes) Provide each student with a
ruler, protractor, and backline master that
contains a variety of triangles. With their
partner, each student is to classify each
triangle according to both properties of
angles and sides. They must justify the
naming of each triangle through use of the
ruler and protractors and provide the
measures of the angles and length of
sides.
Question: Consider equilateral,
isosceles, and scalene triangles.
Which of these triangles can have right
angles? Acute angles? Obtuse
angles?
Vocabulary: congruent, equilateral,
isosceles, scalene, acute, obtuse, and
right triangles.
Watch for misreading of the protractor.
Have students measure side lengths in
cm units.
Student responses must be justified by
providing an example of each case
that they state is possible.
3. (10-15 minutes)
Play Possible or Impossible.
Have students write the words Possible
and Impossible on an index card, each
word on a different side using a marker.
Geometry and Spatial Reasoning
Triangle Properties
Students must justify their answer by
either drawing a picture or stating
orally why they chose the answer
being held.
Oral explanations and/or drawings
must be justified with correct math
Grade 6
Page 2
Mathematics TEKS Refinement 2006 – 6-8
Procedures
Make a transparency of the master for the
game.
Cut out each card from the transparency
master, shuffle.
Tarleton State University
Notes
terminology and reasoning.
You may add additional attribute cards
to extend the game.
Place two cards on the overhead at a
time. One card must be the type of
triangle (right, acute, obtuse, scalene,
isosceles, or equilateral).
Ask students if this type of triangle is
possible or impossible. Allow teams to
discuss. Once a decision has been made,
students hold up the card to indicate
whether it is possible or impossible.
4. (5 minutes) Student Reflection: Write a
brief paragraph that compares and
contrasts equilateral, isosceles, scalene,
acute, obtuse, and right triangles. Select
4 types of triangles and explain how they
are alike and how they are different. Give
an example of a triangle that is
impossible.
Homework:
Use a ruler and protractor to draw triangles based on angle measures
and side lengths that fit into each classification of triangles. Note
triangles which may be considered as more than one type. Support
each drawing with mathematical terminology and measurements. You
may extend this to have students find the perimeter and area for each
triangle drawn to make a connection to measurement.
Assessment:
Use student reflections to identify any misconceptions that still exist.
Extensions:
Extend the Possible or Impossible game to include having pictures of
triangles placed on the overhead and students providing the type of
triangle.
Modifications: While playing the game, students may have several triangles drawn on
a worksheet. Students would identify which triangle on the sheet
matches the description placed on the overhead.
Geometry and Spatial Reasoning
Triangle Properties
Grade 6
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Geometry and Spatial Reasoning
Triangle Properties
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Mathematics TEKS Refinement 2006 – 6-8
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Grade 6
Page 4
Tarleton State University
Tarleton State University
Acute
Obtuse
Two
One angle One angle
angles =
greater
measures
90º
than 90º
67º
Sum of
Sum of
All angles
angles
angles
less than
measures measures
90º
less than equals 180º
180º
Scalene
Equilateral
No sides
congruent
Geometry and Spatial Reasoning
Triangle Properties
Right
Sum of
angles
measures
greater
than 180º
Two sides
congruent
One angle
= 90º
Grade 6
Page 5
Isosceles
One angle
measures
85º
All sides
congruent
Possible or Impossible Game Transparency Master
Mathematics TEKS Refinement 2006 – 6-8