Download Classifying Triangles - Math Interventions Matrix

Classifying Triangles
Student Probe
How are triangles A, B, and C alike?
How are triangles A, B, and C different?
A
B
C
Answer: They are alike because they each have 3
sides and 3 angles. They are different because A is
a right triangle, B is an equilateral (or equiangular)
triangle, and C is an obtuse triangle.
Lesson Description
This lesson uses triangles and their properties to
help students develop an understanding of
classifying two-dimensional figures.
Rationale
The study of geometry is dependent upon
deductive reasoning and syllogism. Student success
in geometry, evidenced by van Hiele’s work, is
dependent upon students’ understanding of spatial
ideas. Before students can be successful in a
rigorous geometry course, they must be able to
make use of informal deduction and make sense of
the relationships among geometric objects. This
lesson provides students with opportunities to
make sense of triangles and their properties.
At a Glance
What: Classify triangles by their properties
Common Core Standard: CC.5.G.4. Classify
two-dimensional figures in a hierarchy
based on properties.
Mathematical Practices:
Construct viable arguments and critique
the reasoning of others.
Look for and make use of structure.
Who: Students who cannot classify triangles
according to their properties
Grade Level: 5
Prerequisite Vocabulary: right angle,
congruent, equilateral triangle, isosceles
triangle, scalene triangle, acute angle, right
triangle, obtuse angle, obtuse triangle
Delivery Format: Small Groups of 2 to 3
Lesson Length: 30 minutes
Materials, Resources, Technology: Pre-cut
shapes
Student Worksheets: Guess My Rule Cards
(.pdf)
Preparation
Prepare a set of standard triangle shapes for each student. The shapes are found in the Guess
My Rule Cards handout.
Lesson
The teacher says or does…
1. We are going to work with
triangles today. Sort all of the
triangles out of your set and
put the rest away.
What are triangles?
2. In what ways are triangles
alike?
3. In what ways can triangles be
different?
Let’s take a look at some of
their differences.
4. Make a group of all the right
triangles.
5. Do all these figures look the
same?
How are they alike?
How are they different?
6. Now make a group of Cards 3,
11, and 12.
How are they alike?
We call these triangles
equilateral. That means the
sides are congruent.
7. Look at the angles of the
triangles in this group. What
do you notice?
Are any of the angles right
angles?
Are the angles acute?
Are the angles obtuse?
Expect students to say or
do…
Polygons with exactly 3
sides.
If students do not, then the
teacher says or does…
We will only be using cards
numbered 1-12. Put the
rest of the cards away for
now.
Answers may vary.
They all have:
3 sides
3 angles
3 vertices
Answers may vary, but listen
for:
Different side lengths
Different angles
Prompt students.
Group contains cards 1, 4, 5,
and 8.
No.
They all contain a right
angle.
The lengths of their sides are
different.
What is a right triangle?
Prompt students.
Are their sides the same
length?
Their sides are the same.
The angles are congruent.
No.
Yes.
No.
Are their angles
congruent?
Do they have any angles
equal to 90o ?
Do they have any angles
less than 90o ?
Do they have any angles
greater than 90o ?
The teacher says or does…
Expect students to say or
do…
8. We also call these triangles
equiangular. That means the
angles are all congruent.
9. Make a group using Cards 2, 7,
and 9.
How are they alike?
Look at the angles of the
triangles in this group. What
do you notice?
Are any of the angles right
angles?
Are the angles acute?
Are the angles obtuse?
10. These are obtuse triangles.
That means they have exactly
one obtuse angle.
11. Make a group using Cards 3,
4, 6, 9, 11, and 12. We have
used some of these cards
before. This time I want you
to focus on the lengths of the
sides.
Do they all have 3 congruent
sides?
(Yes, some of them do, but
that does not describe the
whole group.)
That means they cannot be __.
12. Do they have at least 2
congruent sides?
We call triangles that have at
least 2 congruent sides
isosceles triangles.
Answers may vary.
They have one obtuse angle.
No.
Yes.
Yes.
No.
Equilateral
Yes
If students do not, then the
teacher says or does…
Are their angles
congruent?
Do they have any angles
equal to 90o ?
Do they have any angles
less than 90o ?
Do they have any angles
greater than 90o ?
Are their angles
congruent?
Do they have any angles
equal to 90o ?
Do they have any angles
less than 90o ?
Do they have any angles
greater than 90o ?
The teacher says or does…
13. Can someone make a
statement about equilateral
and isosceles triangles?
14. Is it possible to have a right
triangle that is isosceles?
Show me a card with a right
isosceles triangle?
15. Is it possible to have an
obtuse triangle that is
isosceles?
Show me a card with an
obtuse isosceles triangle.
16. Is it possible to have a right
triangle that is obtuse?
Show me a card with a right
obtuse triangle.
(See Teacher Notes.)
17. Repeat with additional
groupings to deepen students’
understanding of the
properties of triangles.
Expect students to say or
do…
Answers may vary, but listen
for, “All equilateral triangles
are isosceles. Some
isosceles triangles are
equilateral.”
If students do not, then the
teacher says or does…
Are all equilateral triangles
isosceles?
Are all isosceles triangles
equilateral?
Prompt students.
Yes, Card 4
Prompt students.
Yes, Card 9
No, it is not possible
Teacher Notes
1. An important property of triangles is the sum of the measures of the interior angles is 180o .
To demonstrate this property, cut a triangular region from a sheet of paper or note card.
Tear the three corners off and lay them side by side with the vertices (“points”) together.
They will form a straight line, which measures 180o .
2. Since the sum of the measures of a triangle is 180o , no triangle can contain more than one
right or obtuse angle.
Variations
None
Formative Assessment
Grant said that he drew a right triangle that was also isosceles. Draw a triangle like Grant’s.
References
Mathematics Preparation for Algebra. (n.d.). Retrieved 1 4, 2011, from Doing What Works.
TERC. (2008). Investigations in Number, Data, and Space. Boston: Pearson.
Van de Walle, J. A., & Lovin, L. H. (2006). Teaching Student-Centered Mathematics Grades 5-8
Volume 3. Boston, MA: Pearson Education, Inc.