Fourth Grade Everyday Mathematics

Objectives To guide students as they classify angles as acute,
right, obtuse, straight, and reflex; and to provide practice using a
half-circle protractor to measure and draw angles.
1
materials
Teaching the Lesson
Key Activities
Students identify types of angles and measure angles with a half-circle protractor.
They identify an angle as obtuse or acute to help them determine which
protractor scale they should use. They draw angles with a half-circle protractor.
Key Concepts and Skills
Math Journal 1, pp. 157 and 158
Study Link 6 6
half-circle protractor (Geometry Template;
optional)
protractor for demonstration purposes
straightedge
slate
• Use reference points to estimate the measures of angles.
[Measurement and Reference Frames Goal 1]
• Use a half-circle protractor to measure and draw angles.
[Measurement and Reference Frames Goal 1]
• Classify angles according to their measure. [Geometry Goal 1]
Key Vocabulary acute angle • obtuse angle • reflex angle • straight angle •
half-circle protractor • base line
Ongoing Assessment: Recognizing Student Achievement
Use Mental Math and Reflexes. [Number and Numeration Goal 1]
Ongoing Assessment: Informing Instruction See page 440.
2
materials
Ongoing Learning & Practice
Math Journal 1,
pp. 159, 171
(optional), 172–173,
180, and 181
Student Reference
Book
Students resume the World Tour in Europe.
Students practice and maintain skills through Math Boxes and
Study Link activities.
3
materials
Differentiation Options
READINESS
Students model
angles with a
rope.
ENRICHMENT
Students
determine that
the sum of the
measures of the
angles of any
triangle is 180°.
Study Link Master
(Math Masters, p. 192)
Teaching Aid Masters
(Math Masters,
pp. 419–421; optional)
ENRICHMENT
ELL SUPPORT
Students read
Sir Cumference
and the Great
Knight of
Angleland.
Students create
a graphic
organizer for
the word angle.
Student Reference Book, p. 93
Teaching Masters (Math Masters, p. 193)
Teaching Aid Master (Math Masters, pp. 388 or 389)
Differentiation Handbook
rope/string; protractor; straightedge; glue/tape
See Advance Preparation
Additional Information
Advance Preparation For the optional Enrichment activity in Part 3, obtain the book
Sir Cumference and the Great Knight of Angleland by Cindy Neuschwander (Charlesbridge
Publishing, 2001).
Technology
Assessment Management System
Mental Math and Reflexes
See the iTLG.
Lesson 6 7
437
Getting Started
Mental Math and Reflexes
Math Message
Write decimals on the board and have volunteers read
them aloud. Suggestions:
3.45
12.358
0.27
60.893
6.89
83.591
Ask questions such as:
• What digit is in the hundredths place?
• What is the value of the digit x?
Complete the Math Message problems on
journal page 157.
10.005
2.6074
26.0801
Study Link 6 6 Follow-Up
Students compare answers. Make sure they
understand that the directional arc shows the
path and direction of the rotation.
Ongoing Assessment:
Recognizing Student Achievement
Mental Math
and Reflexes
Use Mental Math and Reflexes to assess students’ ability to identify places in
decimals and the values of the digits in those places. Students are making
adequate progress if they can correctly identify and express the values of digits
through thousandths. Some students may correctly identify and express the
values of digits through ten thousandths.
[Number and Numeration Goal 1]
1 Teaching the Lesson
Math Message Follow-Up
WHOLE-CLASS
ACTIVITY
(Math Journal 1, p. 157)
In discussing the answers, talk about the angles in terms of
1
1
rotations: A is less than a 4 turn, B is more than a 4 turn but
1
1
less than a 2 turn, and C is between a 2 turn and 1 full turn.
Call attention to the names for the various types of angles. To
support English language learners, write the names on chart
paper next to an example of each. Display the chart paper
throughout the unit.
Links to the Future
Identifying and describing acute, obtuse,
straight, and reflex angles and proficient use
of a half-circle protractor are Grade 5 Goals.
An acute angle is greater than 0° and less than 90°.
An obtuse angle is greater than 90° and less than 180°.
A reflex angle is greater than 180°.
Remind students that a 90° angle is called a right angle.
Complete the list of angle names by mentioning that a 180° angle
is called a straight angle. Ask: Why is this a good name for this
angle? In a 180° angle, the two sides meet to form a straight line.
438
Unit 6 Division; Map Reference Frames; Measures of Angles
Student Page
Introducing the Half-Circle
WHOLE-CLASS
ACTIVITY
Protractor
Date
Time
LESSON
Drawing and Measuring Angles
6 7
Math Message
92 93
141
Use a straightedge to draw the following angles. Do not use a protractor.
Have students examine their half-circle protractors. Students can
use either the protractor on the Geometry Template or any other
protractor. If some students’ protractors do not have labels for
the 0° and 180° marks, have them write the labels. The marks
may smear and disappear later, but they are helpful for this
introduction to the half-circle protractor.
Ask partnerships to decide how the half-circle protractor is
different from the full-circle protractor they used in the previous
lesson. Review observations. Have students indicate “thumbs-up”
if they had a similar answer.
A: any angle
less than 90°
B: any angle more than
90° and less than 180°
Sample answers:
B
C
A
A is called an acute angle.
B is called an obtuse angle.
There are two scales on the half-circle protractor: one scale
goes from 0° to 180° in a clockwise direction and the other from
0° to 180° in a counterclockwise direction. To support English
language learners, discuss the meaning of scale in this context.
C is called a reflex angle.
Measuring Angles with a Protractor
Write whether the angle is acute or obtuse. Then measure it as accurately as you can.
T
V
R
S
E
C
O
The curved edge of the protractor is a half circle. The edge of
the full-circle protractor is a full circle.
C: any angle
more than 180°
R
D
SDE is
acute
COR is
.
55
SDE is about
°
.
acute
COR is about
RTV is
.
40
°
.
obtuse .
°
.
140
RTV is about
Answers may vary by 3 degrees either way.
157
Math Journal 1, p. 157
The 0° mark on one side of the half-circle protractor is
connected with the 180° mark on the other side by a line
segment. This segment is the base line of the protractor.
The midpoint of the base line is the center of the half-circle
protractor. There is often a hole at the center.
Measuring Angles with a
WHOLE-CLASS
ACTIVITY
Half-Circle Protractor
(Math Journal 1, p. 157)
Draw an angle on the board or overhead projector, but omit the
arc that indicates the direction of the rotation. Mention that
without the directional arc, this angle could represent a rotation
less than 180° or a rotation greater than 180°. Draw directional
arcs with arrowheads to show the two possible angles. Explain
that if no arc is shown, the smaller of the two angles is intended.
(See margin.)
The arc indicates which angle to consider.
Draw another angle on the board or overhead. Use your
demonstration protractor to show how to measure the angle.
80
100
90
100
80
110
70
110
70
12
60 0
13
50 0
3
15 0
0
4
14 0
0
20
160
10
170
3
15 0
0
20
160
100
80
170
10
10
170
90
160
20
180
0
180
0
0
180
80
100
0
15 0
3
170
10
baseline
70
0
60 0 11
12
0
14 0
4
160
20
3. Move the protractor so that one side of the angle is on the
base line, as shown in the margin. Make sure the center of the
protractor remains over the vertex.
50 0
13
0
15 0
3
2. Put the center of the protractor over the vertex of the angle.
12
60 0
13
50 0
4
14 0
0
70
0
60 0 11
12
0
14 0
4
50 0
13
0
180
1. Students should first estimate whether the angle measures
more or less than 90°. Ask: Is the angle acute or obtuse?
They can also use 45° and 180° as reference angles to refine
their estimate. If students develop this good habit, they will
seldom read the wrong scale.
center
a 40° angle
a 115° angle
Lesson 6 7
439
EM07TLG1_G4_U06_L07.qxd 7/26/07 2:19 PM Page 440
Student Page
Date
LESSON
6 7
䉬
1.
Time
4. Find the place where the other side of the angle crosses a
mark on the edge of the protractor.
Drawing Angles
Draw a 35° angle, using
line segment GH as one
of its sides.
143
G
2.
C
Draw a 60° angle, using
ray EF as one of its sides.
Ongoing Assessment: Informing Instruction
Watch that students are measuring carefully. A difference of 3 degrees either
way should be enough leeway.
E
F
4.
Ask students to measure angles SDE, COR, and RTV at the
bottom of journal page 157 and compare their measurements.
Draw a 150° angle, using
ray CD as one of its sides.
D
3.
5. Decide which of the two 0°-to-180° scales to use to determine
the degree measure of the angle. If it is acute, use the smaller
number; if it is obtuse, use the larger number.
H
Draw a 15° angle, using
ray AB as one of its sides.
A
B
Try This
5.
Drawing Angles with a
Draw a 330° angle, using
ray IJ as one of its sides.
I
J
INDEPENDENT
ACTIVITY
Half-Circle Protractor
(Math Journal 1, p. 158)
Math Journal 1, p. 158
Have students complete Problem 1 on journal page 158 with a
partner or on their own. Ask students to describe a procedure for
using a half-circle protractor to draw angles while you or a student
demonstrates at the board or overhead.
Step 1
One method:
1. Draw a ray.
2. Place the center of the protractor at the endpoint of the ray
so that the base line is along the ray.
Steps 2 and 3
80
100
90
100
80
110
70
12
60 0
13
50 0
4
14 0
0
70
0
60 0 11
12
0
14 0
4
50 0
13
3
15 0
0
0
15 0
3
20
160
160
20
3. Use the scale that shows 0° where the ray crosses the edge of
the protractor. Make a dot where the other ray should cross
the edge of the protractor.
180
0
0
180
10
170
170
10
Step 4
4. Draw a ray from the vertex through the dot.
Have students complete journal page 158 on their own. Remind
students that they can check whether they have chosen the appropriate scale for drawing an angle by noting if the angle is acute or
obtuse.
Share strategies for solving Problem 5, which requires students to
draw a reflex angle. One possible strategy: Subtract 330° from
360° ( 30°). Draw a 30° angle; then draw an arc on the “outside”
of the 30° angle.
440
Unit 6 Division; Map Reference Frames; Measures of Angles
Student Page
Date
2 Ongoing Learning & Practice
Time
LESSON
Math Boxes
6 7
1. Insert parentheses to make each number
2. Draw a line segment that is 2 inches
sentence true.
World Tour Option:
(
long. Mark and label the following inch
measurements on the line segment:
)
a. 12 15 2 1
(
SMALL-GROUP
ACTIVITY
1 3
, ,
4 4
)
b. 66 16 4 200
(
)(
)
c. 49 4 3 42 / 6
Visiting Europe
1, 114 and 112
1 1 12
1
4
3
4
1 14
150
(Math Journal 1, pp. 171–173, 180, and 181; Student Reference Book;
Math Masters, pp. 419–421)
128
3. Six classrooms collected newspapers
4. Multiply with a paper-and-pencil algorithm.
for one week. If they collected a total of
582 newspapers by the end of the week,
on average about how many newspapers
did each class collect?
67 34 2,278
582 / 6 97
97 newspapers
Number model:
Social Studies Link If you have chosen to extend the scope
of the World Tour for your class, divide students into groups
of 4 or 5. Each group visits one of the remaining countries in
Europe and records their country data on journal pages 180 and
181, or on Math Masters, pages 419 and 420.
Answer:
22 23
18 19
1
6. Circle the square that has 3 shaded.
5. How many centimeters are in 9.7 meters?
Circle the best answer.
A.
B.
A. 907
Math Boxes 6 7
B. 900.7
INDEPENDENT
ACTIVITY
C. 970
D. 9,700
(Math Journal 1, p. 159)
129 315
44
159
Mixed Practice Math Boxes in this lesson are paired
with Math Boxes in Lesson 6-5. The skill in Problem 6
previews Unit 7 content.
Math Journal 1, p. 159
Writing/Reasoning Have students write a response to the
1
following: Wei said that both squares in Problem 6 have 3
shaded. Do you agree or disagree? Explain your answer.
Sample answer: I disagree. Both of the squares are divided into
three parts and both of the squares have one part shaded. However,
1
only A shows 3 because A is divided into equal parts. The three
parts in B are not equal.
Study Link 6 7
Three students, acting as points,
use rope to represent line segments
and form an acute angle.
INDEPENDENT
ACTIVITY
(Math Masters, p. 192)
Study Link Master
Name
Date
STUDY LINK
Home Connection Students measure angles using a
half-circle protractor. Some students may prefer to use a
full-circle protractor from Lesson 6-6.
Time
Measuring Angles with a Protractor
67
First estimate whether the angles measure more or less than 90°. Then use a
half-circle protractor to measure them.
1.
A:
60
°
2.
B:
150
°
3.
C:
143
84
°
B
A
3 Differentiation Options
C
Try This
4.
QRS:
105 °
5.
NOP:
32 °
6.
KLM:
300 °
K
READINESS
Modeling Angles
SMALL-GROUP
ACTIVITY
N
Q
L
5–15 Min
O
(Student Reference Book, p. 93)
M
P
R
S
To explore estimating angle measures using a concrete model,
have students use rope to model angles. (See margin.) Ask the
“vertex” to tell the two “points” the type of angle or the measure
of the angle that they should form. Have students use Student
Reference Book, page 93 as a guide.
Practice
7.
9.
93 6 1,872
558
48 39
3,829
8.
10.
51 64 547 7
3,264
Math Masters, p. 192
Lesson 6 7
441
Teaching Master
Name
Date
LESSON
Time
67
You need 2 sheets of paper, a straightedge, and a protractor.
143
1.
Draw a large triangle on each sheet of paper. The 2 triangles should
not look the same.
Label the vertices of one triangle A, B, and C. Label the vertices of the
other triangle D, E, and F. Be sure to write the labels inside the triangles.
3.
Using your protractor, measure each angle as accurately as you can.
Record the degree measures in the tables below.
4.
Find the sum of the degree measures in triangle ABC and in triangle DEF.
Sample answers:
A
5.
Degree Measure
About
45
°
°
B
About
45
C
About
90
°
Sum
About
180
°
Angle
Degree Measure
About
60
°
E
About
60
°
F
About
60
°
Sum
About
180
°
D
Measuring Angles in Triangles
15–30 Min
(Math Masters, p. 193)
2.
Angle
PARTNER
ACTIVITY
ENRICHMENT
Exploring Triangle Measures
Write a true statement about the sum of the measures of the 3 angles of a triangle.
The sum of the angle measures of a triangle
is 180
.
To apply students’ understanding of measuring angles,
have them draw two triangles, measure the angles, and
find the sum of the angle measures for each triangle. The
sum of the students’ measures of the angles of a triangle should
range from 170° to 190°, with most sums close to 180°.
Guide students as they “prove” that the sum of the measures of
the angles of any triangle is 180°. Have them cut off the three
corners of one of their triangles and arrange them so that the
three angles touch each other but do not overlap. From this, it
should be clear that the angles form a straight angle, and so the
sum of their measures is 180°.
Cut
B
Math Masters, p. 193
Cut
C
A
A
B
C
Cut
Encourage students to extend this exploration to “prove” that the
sum of the measures of the angles of any quadrilateral is 360°.
Students may reason that since any quadrilateral can be divided
into two triangles, the sum of the angles is twice 180°, or 360°.
ENRICHMENT
Exploring Angles in Literature
SMALL-GROUP
ACTIVITY
15–30 Min
(Math Masters, p. 388 or 389)
Literature Link To further explore the half-circle
protractor and angles, have students read and discuss
Sir Cumference and the Great Knight of Angleland by
Cindy Neuschwander (Charlesbridge Publishing, 2001). In a
Math Log or on an Exit Slip, ask students to summarize what
Radius learned on his quest.
ELL SUPPORT
Building Background for
PARTNER
ACTIVITY
5–15 Min
Mathematics Words
(Differentiation Handbook)
To provide language support for angles, have students create a
graphic organizer for the word angle. They may list words and
draw pictures that are connected to the word angle. See the
Differentiation Handbook for more information.
442
Unit 6 Division; Map Reference Frames; Measures of Angles