Download 3 Classifying Triangles by Angles - Mr.Kerley`s class Mr.Kerley`s class

CHAPTER 7
3
Classifying Triangles by Angles
STUDENT BOOK PAGES 194–196
Guided Activity
Goal Investigate angle measures in triangles.
Prerequisite Skills/Concepts
Expectations
• Understand the definition
of a polygon.
• Use a protractor to measure
the angles within shapes.
5m76 classify two-dimensional shapes according to angle and side properties
5m78 measure and construct angles using a protractor
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
• estimate and measure different types of angles:
obtuse, acute, and right
• Students will be able to look at angles and
estimate obtuse or acute angles. They may need
to measure right angles because they are exact.
• Students may not be able to estimate the different
angles. Provide students with opportunities to
measure to get an “angle sense.” Students can use
the square corner (90°) from a piece of cardboard
as a referent. For example, if the angle they are
measuring is wider that the square corner, it is
an obtuse angle. If the angle is smaller than the
square corner, it is an acute angle. Students can
then measure and confirm their estimate. If students
have difficulty using a protractor, review the activities
from Lesson 2.
• classify triangles according to their angles as
obtuse-angled and right-angled
• Students will be able to classify obtuse-angled
triangles or right-angled triangles once they measure
one angle in a triangle. They will first identify the
angle to be measured through estimation.
• Students might think that they need to measure all
the angles in a triangle to classify it. Guide them to
look for either a right angle (square corner) or an
obtuse angle (wider than a square corner), and then
measure that angle.
• classify an acute-angled triangle
• Students will understand that all angles have to
be acute for a triangle to be classified as acuteangled. They may also realize that if the largest
angle is acute, then the triangle is acute-angled
because the other angles will be smaller.
• Students might think that they need to measure all
angles in a triangle to classify it. Guide them to look
for the largest angle in the triangle. If the largest
angle is narrower than a right angle (square corner),
then the triangle is an acute-angled triangle.
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)
Masters
• Optional: Chapter 7 Mental Math
p. 61
Workbook
p. 64
Vocabulary/
Symbols
acute, obtuse, right, acute-angled
triangle, obtuse-angled triangle,
right-angled triangle
Key
Assessment
of Learning
Question
Question 5, Understanding
of Concepts
Copyright © 2005 by Thomson Nelson
Meeting Individual Needs
Extra Challenge
• Encourage students to find as many applications and uses for different
types of angles and triangles in the environment as they can.
• Ask students to explain why there can only be one right angle in a rightangled triangle or one obtuse angle in an obtuse-angled triangle.
Extra Support
• Have students play a game to visually match the angles to the names of
the angles. Students are dealt name cards of angles: acute, obtuse, or right.
Then they take turns picking one card from a deck of angle cards. If they
correctly identify the angle, they keep the card. The player with the most
angle cards at the end of the game wins.
• Post a triangle of the day on the board or wall, out of reach of the students
so that they will not be able to measure the angles using a protractor. Label
the vertices A, B, and C. Ask students to classify the triangle by estimating
the angle or angles.
Lesson 3: Classifying Triangles by Angles
21
1.
Introduction (Whole Class)
➧ 5–10 min
Ask students to look around the classroom and identify
some triangular shapes, such as a coat hangar or a triangle
shape in a geometry set. Find at least one example each of
an acute-angled triangle, right-angled triangle, and obtuseangled triangle, and sketch these triangles on the board.
Point out that some angles in the room have square corners
(right), some angles are wider than a square corner, and
some angles are narrower than a square corner.
Sample Discourse
“How are these triangles the same and how are they different?
• They have three sides, three vertices, and three angles. But
the sides are different lengths.
• The angles are different sizes.
Tell students that they will be classifying triangles by
their angle measures.
2.
Teaching and Learning (Pairs/Whole Class) ➧ 20–30 min
Ask students to turn to Student Book page 194. As a class,
read about the roof angles and the central question. Discuss
Teresa’s Solution. Draw the roof triangles on an overhead
or on the board, and demonstrate how to measure and classify
the angles. Explain that the classification of the angles enables
us to classify triangles. Talk about how we can estimate
obtuse angles and acute angles because of their sizes, but
that we need to measure right angles.
Have students complete prompts A to E. To complete
prompt B, guide students to draw a right angle for the
peak of the roof for one of the triangles. Talk about how
the peak measure relates to steepness.
Reflecting
Students will reflect on their experiences with classifying
triangles and draw conclusions about how many angles
measures are needed.
22
Chapter 7: 2-D Geometry
Sample Discourse
1. a) • I would measure angle A because it is the biggest.
If the angle is a right angle, then I know the triangle
is a right-angled triangle.
• I would measure angle A because it looks like a
right angle.
b) • I would measure angle D because it is the biggest and
it looks like an obtuse angle. If it is, then the triangle
is an obtuse-angled triangle.
• I would measure angle D because it looks like an
obtuse angle.
c) • I would measure angle I because it looks close to 90°.
If it is less than 90°, then I know that the other angles
are acute and it is an acute-angled triangle.
2. • No, I don’t think you need to measure all three angles. If
you measure one angle and it is 90°, then you can classify
the triangle as a right-angled triangle. If you can see that
all the angles are less than 90°, then you can say it is an
acute-angled triangle. If the largest angle is more than
90°, then you can classify the triangle as an obtuseangled triangle.
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.
4. Encourage students to estimate the size of the angles
and to measure if necessary.
Practising (Individual)
5. & 6. Encourage students to construct and classify
triangles according to the angles. This will allow students
to familiarize themselves with the definitions and to
gain experience in estimating angles as acute or obtuse.
Related Question to Ask
Ask
Possible Response
About Question 5:
• How does the length of the
name on the name tag affect
whether the name tag is an
obtuse-angled, right-angled,
or acute-angled triangle?
Key Assessment of Learning Question (See chart on next page.)
Answers
A. Triangle A is a right-angled triangle, triangle B is an
obtuse-angled triangle, and triangle C is an acuteangled triangle.
B.–C. For example,
45°
1
70° 65°
45°
90°
2
45°
115°
32.5° 3 32.5°
D. For example, triangle 1 is an acute-angled triangle,
triangle 2 is a right-angled triangle, and triangle 3 is
an obtuse-angled triangle.
E. For example, as the roofs get steeper, the measures
of the peak angles decrease (the angles get smaller).
1. a) For example, I would measure angle A because it looks
like a right angle. If it is a right angle, then I know
the triangle is a right-angled triangle.
b) For example, I would measure angle D because it is
the greatest angle and it looks like an obtuse angle.
If it is, then the triangle is an obtuse-angled triangle.
Copyright © 2005 by Thomson Nelson
• I think that the longer the name,
the more likely the triangle will
be an obtuse-angled triangle
because the peak angle would
have to be bigger than 90° so
that the triangle is flattened out
to fit the name. For a short name,
the peak angle will be smaller
than 90° so that all angles would
be acute, and the name tag
would be an acute-angled triangle.
Closing (Whole Class)
Have students summarize their learning by thinking about
how they can classify triangles according to their angle sizes.
Ask, “When do you need to measure angles in a triangle to
classify it according to angle size?”
• You need to measure angles only if you are not sure what
type of angle it is.
• You need to measure angles only if you are not sure if the angle
is 90º. If it is 90º, then the triangle is a right-angled triangle.
• You do not need to measure angles if it is obvious that one
of the angles is obtuse because then the triangle is an obtuseangled triangle.
• You do not need to measure angles if it is obvious that all
three angles are acute because then the triangle is an acuteangled triangle.
c) For example, I would measure angle I because it is the
largest angle and it looks close to 90°. If it is less than
90°, then I know that the other angles are acute and it
is an acute-angled triangle.
(Lesson 3 Answers continued on p. 80)
Lesson 3: Classifying Triangles by Angles
23
Assessment of Learning—What to Look for in Student Work…
Assessment Strategy: short answer
Understanding of Concepts
Key Assessment Question 5
Kumiko’s class used triangle name tags for open house. Classify the triangles.
(Score correct responses out of 4.)
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 and classifying angles and
triangles in their homes. Students could list all the obtuse,
right, and acute angles that they find, and then see if they
can find them in triangles as well.
Curious Math
Student Book p. 197
Mid-Chapter Review
Student Book p. 201, Question 3
Mental Imagery
Student Book p. 203
Skills Bank
Student Book p. 210, Question 4
Problem Bank
Student Book p. 212, Question 1
Chapter Review
Student Book p. 214, Question 3
Workbook
p. 64, all questions
Nelson Web Site
Visit www.mathK8.nelson.com and follow the
links to Nelson Mathematics 5, Chapter 7.
Math Background
In an obtuse-angled or right-angled triangle, there needs to
be one obtuse angle or right angle, respectively. However,
there cannot be more than one of these defining angles
since the angle sum of any triangle is 180º. It follows that
acute angles are the most common angles found in triangles.
Not only are they found in acute-angled triangles in which
all three angles are acute, but they are also found in rightangled triangles and obtuse-angled triangles.
STUDENT BOOK PAGE 197
Curious Math: Diagonal Angles
Using Curious Math
Materials: protractor (1/student), ruler (1/student)
When diagonals cross in rectangles, they bisect each
other. The angles formed by the diagonals at the point
of intersection are all equal in a square. In a rectangle, the
diagonals form angles that are close in measurement if the
rectangle approximates the dimensions of a square. There
are two pairs of angles of the same size at the intersection
of two diagonals in a rectangle. The less the rectangle looks
like a square, the greater the difference in size for the angle
pairs in the intersection.
Answers to Curious Math
1. Angle measures
Square
Rectangle
A 90°
B 90°
E 115°
F 65°
C 90°
D 90°
G 115°
H 65°
2. a) For example, I notice that all of the angles where the
diagonals of the square cross are the same.
b) For example, I notice that where the diagonals cross
in the rectangle, the pairs of angles that are opposite
are the same.
3. For example, where the diagonals cross, the opposite
angles are equal.
4. For example, for the square, the distances from the
vertices to the point where the diagonals cross are
all the same. The same is true for the rectangle.
24
Chapter 7: 2-D Geometry
Copyright © 2005 by Thomson Nelson