Download 4 Classifying Triangles by Side Lengths

CHAPTER 7
4
STUDENT BOOK PAGES 198–200
Classifying Triangles
by Side Lengths
Guided Activity
Goal Investigate side lengths of triangles.
Prerequisite Skills/Concepts
Expectations
• Use a protractor to measure
the angles of shapes.
• Know that triangles have
three angles.
5m76 classify two-dimensional shapes according to angle and side properties
5m83 recognize and explain the occurrence and application of geometric properties
and principles in the everyday world
5m85 discuss ideas, make conjectures, and articulate hypotheses about geometric
properties and relationships
Assessment for Feedback
What You Will See Students Doing…
Students will
When Students Understand
If Students Misunderstand
• classify triangles according to their side lengths
as isosceles, scalene, or equilateral triangles
• Students will measure the sides of a triangle and
classify it according to their measurement results.
• Students may not be able to classify triangles.
Provide students with the following guidelines:
Measure the sides of the triangle and look at the
side lengths. If all the sides are equal, it is an
equilateral triangle. Identify the part of the word
that means equal. If two sides are equal, it is an
isosceles triangle. If all sides are unequal, it is a
scalene triangle. Scalene means uneven.
• classify triangles according to their side lengths
and angle measure
• Students will relate their knowledge of classifying
according to side lengths to the classification of
triangles according to angle measures.
• Students may be confused when classifying triangles
according to both side lengths and angle measures.
Prepare and post a chart showing how to classify
triangles. Encourage students to consult it regularly.
The chart could have the following headings:
Triangle; Side length measurements; Type
(equilateral, isosceles, or scalene); Angle
measurement(s); Type (right-angled, obtuse-angled,
or acute-angled). As an example, the first row
would read: ABC; 3 cm, 4 cm, 5 cm; scalene;
90 degrees; right-angled.
Preparation and Planning
Pacing
5–10 min Introduction
20–30 min Teaching and Learning
15–20 min Consolidation
Materials
•ruler (1/student)
•protractor (1/student)
•set of coloured pipe cleaners or
straws: red (5 cm), yellow (7 cm),
and blue (9 cm) (10 of each
colour/small group)
•set of pencil crayons (1/small group)
• Optional: Cuisenaire rods
• Optional: transparent mirror
Masters
• Optional: Chapter 7 Mental Math
p. 62
Workbook
p. 65
Vocabulary/
Symbols
equilateral, isosceles, scalene
Key
Assessment
of Learning
Question
Question 5, Understanding
of Concepts
Copyright © 2005 by Thomson Nelson
Meeting Individual Needs
Extra Challenge
• Students can classify triangles jointly according to their side lengths and
angle measures. They can list all the combinations in the following
categories: Set A is obtuse-angled, acute-angled, and right-angled triangles,
and set B is isosceles, scalene, and equilateral triangles. Encourage students
to make all the combinations by choosing one from each set. Ask students
to explain why it may not be possible to construct a triangle for every pair.
Extra Support
• Have students play a similar game to that described in Lesson 3. This time
students visually match the triangles to the names of the triangles. Students
are dealt name cards: equilateral, isosceles, and scalene. Then they take turns
picking one card from a deck of triangle cards. The triangles on these cards
are drawn with the same colour and proportional length as the pipe cleaners
used in the lesson.
• Assign a triangle, such as an isosceles triangle, of the day. Ask students to
look for isosceles triangles in their environment.
Lesson 4: Classifying Triangles by Side Lengths
25
1.
Introduction (Whole Class)
➧ 5–10 min
Draw an isosceles triangle on the board and ask students if
they can find the line of symmetry. Have one student draw
the line of symmetry using a different colour. Point to the
hypotenuse of both congruent halves and ask students
what they know about the lengths of the sides. Students
should understand that the sides are equal because the
triangles are congruent. Draw examples of an equilateral
triangle and a scalene triangle. Ask students how they are
the same and how they are different. Encourage them to
talk about the side lengths.
Tell students that they will be classifying triangles
according to their side lengths.
2.
Teaching and Learning (Whole Class/Small Groups) ➧ 20–30 min
Ask students to turn to Student Book page 198. As a class,
read the goal, the central question, and Camille’s Pipe
Cleaner Models.
Have students work in small groups to complete prompts
A to F. It is very important that the students be given enough
time to explore and construct different triangles with the
pipe cleaners (or straws or Cuisenaire rods). For prompt A,
make sure students understand that their task is to construct
as many different triangles as they can using only one pipe
cleaner for each side. They will be able make ten different
triangles altogether. For prompt B, they need to record their
findings on chart paper using the same colour pencils as the
pipe cleaners are (you may want to substitute orange for
yellow because yellow is hard to see). For prompt F, students
will look at their findings and classify the triangles. Guide
their thinking into looking at the similarities between the
sides. For example, equilateral triangles are triangles made
of the same colour pipe cleaners; isosceles triangles are made
of two different colour pipe cleaners; and scalene triangles
are made of different colours. Since each colour of pipe
cleaner has a specific length, it’s easy for the students to
transfer their thinking from classifying by colours to
classifying by lengths.
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Chapter 7: 2-D Geometry
Reflecting
Here students reflect upon how to classify triangles according
to their side lengths.
Sample Discourse
1. • My strategy for deciding whether a triangle is equilateral,
isosceles, or scalene is to measure the side lengths. If there
are different side lengths, then it is a scalene triangle.
If two sides are the same length, then it is an isosceles
triangle. If all the sides are the same length, then it is
an equilateral triangle.
2. a) • I noticed that in equilateral triangles, all the angles
were equal.
b) • I noticed that in isosceles triangles, the angles next to
the two equal sides were also equal. The angle that is
between the two equal sides was different from the others.
c) • I noticed that in scalene triangles, none of the angles
were the same.
Copyright © 2005 by Thomson Nelson
3.
Consolidation ➧ 15–20 min
Checking (Whole Class)
For intervention strategies, refer to Meeting Individual
Needs or the Assessment for Feedback chart.
Practising (Individual)
6. Students might need review in looking for lines of
symmetry with a transparent mirror.
Related Questions to Ask
Ask
Possible Response
About Question 5:
• Can a right-angled triangle also
be an equilateral triangle?
• Can an obtuse-angled triangle
also be an equilateral triangle?
• What angles must an equilateral
triangle have?
• No, a right-angled triangle cannot
also be an equilateral triangle. It
has to have at least two
unequal sides.
• No, an obtuse-angled triangle
cannot also be an equilateral
triangle. It has to have at least
two unequal sides.
• An equilateral triangle can only
have acute angles so it is also
an acute-angled triangle.
Key Assessment of Learning Question (See chart on next page.)
Closing (Whole Class)
Answers
A. & B. For example,
C. For example, the red and yellow triangles are similar to
the blue triangle because all the sides are the same length.
Also, the triangles are the same shape, but different in size.
D. For example, a triangle that has one red side and two
blue sides, and a triangle with two blue sides and one
yellow side are like the triangle with two yellow sides and
one blue side. The triangles are alike because two of the
sides are the same colour, which means that they are the
same length.
E. For example, the three-coloured triangle is the only
triangle that is made of different-coloured pipe cleaners,
which means that the lengths are different on all sides.
Copyright © 2005 by Thomson Nelson
Have students summarize their learning by explaining how
they classify triangles according to the lengths of sides. As
an extension, ask, “How is classifying triangles according
to the lengths of their sides related to classifying by lines
of symmetry?”
• An equilateral triangle has three lines of symmetry, an isosceles
triangle has one line of symmetry, and a scalene triangle has
no line of symmetry. So we can classify the triangles by the
number of lines of symmetry and get the same results as
when we classify by side lengths.
F. For example, the equilateral triangles are the ones with all
sides the same colour and length, the isosceles triangles
are the ones with two sides the same colour and length,
and the scalene triangle is the one that has all different
side colours and lengths.
1. For example, my strategy for deciding whether a triangle
is equilateral, isosceles, or scalene is to measure the side
lengths. If the sides are different lengths, then it is a
scalene triangle. If two sides are the same length and one
is different, then it is an isosceles triangle. If all the sides
are the same length, then it is an equilateral triangle.
(Lesson 4 Answers continued on p. 80)
Lesson 4: Classifying Triangles by Side Lengths
27
Assessment of Learning—What to Look for in Student Work…
Assessment Strategy: short answer
Understanding of Concepts
Key Assessment Question 5
Classify the triangles by the lengths of their sides.
(Score correct responses out of 6.)
Extra Practice and Extension
At Home
• You might assign any of the questions related to this lesson,
which are cross-referenced in the chart below.
• Students might enjoy looking for specific triangles in their
home environment. Ask students to make a list of the
equilateral, isosceles, and scalene triangles that they find in
their home and indicate where they are found.
Mid-Chapter Review
Student Book p. 201, Question 4
Mental Imagery
Student Book p. 203
Skills Bank
Student Book p. 211, Question 5
Problem Bank
Student Book p. 212, Questions 2 & 3
Chapter Review
Student Book p. 214, Question 4
Workbook
p. 65, all questions
Nelson Web Site
Visit www.mathK8.nelson.com and follow the
links to Nelson Mathematics 5, Chapter 7.
Optional: Chapter 7
Mental Math p. 62
Math Background
Both scalene and isosceles triangles can contain all three types
of angles: acute, obtuse, and right. It’s entirely possible to
have acute-angled, obtuse-angled, and right-angled scalene
and isosceles triangles. However, the equilateral triangle has
all three sides are equal, which means that all three angles
are equal. Since the angle sum of triangles is equal to 180°,
it follows that each angle in an equilateral triangle has to
be 60°. Therefore, an equilateral triangle can only be an
acute-angled triangle.
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Chapter 7: 2-D Geometry
Copyright © 2005 by Thomson Nelson