Measuring Angles

Measuring Angles
Objective To guide children as they measure angles.
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Teaching the Lesson
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Assessment
Management
Common
Core State
Standards
Ongoing Learning & Practice
Key Concepts and Skills
Finding Area and Perimeter
• Determine fractional parts of a circle. Math Masters, p. 205A
Children determine the areas of given
shapes and select the shape with the
shortest perimeter measure.
[Number and Numeration Goal 2]
• Identify quarter-turns and 90 degrees
as measures of right angles. [Geometry Goal 1]
• Investigate the degrees of a circle. [Geometry Goal 2]
• Introduce the degree as a unit of measure
for turns. Math Boxes 6 8
Math Journal 1, p. 145
Children practice and maintain skills
through Math Box problems.
Home Link 6 8
[Measurement and Reference Frames Goal 1]
Key Activities
Children model turns by rotating connected
straws. They make an angle measurer by
folding a circle and then measure angles
with it.
Math Masters, p. 182
Children practice and maintain skills
through Home Link activities.
Curriculum
Focal Points
Interactive
Teacher’s
Lesson Guide
Differentiation Options
ENRICHMENT
Solving Degree Problems Using
a Clock Face
Math Masters, pp. 183 and 184
straws and twist-ties
Children solve degree problems on a clock.
EXTRA PRACTICE
Minute Math +
Minute Math ®+, p. 59
Children use degree measures to
describe shapes.
Ongoing Assessment:
Informing Instruction See page 447.
Ongoing Assessment:
Recognizing Student Achievement
Use journal page 144. [Geometry Goal 1]
Key Vocabulary
degree
Materials
Math Journal 1, pp. 143 and 144
Home Link 67
Math Masters, p. 428
transparency of Math Masters, p. 428
(optional) tool-kit clocks 2 straws and
1 twist-tie per child scissors calculator
(optional) wax paper (optional)
Advance Preparation
Make one copy of Math Masters, page 428 per four children. Have a few extras available.
Teacher’s Reference Manual, Grades 1–3 p. 161
444
Unit 6
Geometry
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Getting Started
Mental Math and Reflexes
Math Message
Pose multiplication number stories like the following.
Children share solution strategies. Encourage children to
use division to check their results.
How many minutes does it take the minute
1
hand on a clock to turn _4 of the way around the clock face?
5 people. 4 slices of pizza per person. How many slices of pizza
in all? 20 slices of pizza
3 dogs. 4 legs per dog. How many legs in all? 12 legs
6 jackets. 4 pockets per jacket. How many pockets in all?
24 pockets
6 boxes. 6 crayons per box. How many crayons in all?
36 crayons
3 boxes. 1 dozen doughnuts per box. How many doughnuts in all?
36 doughnuts
6 hours. 60 minutes per hour. How many minutes? 360 minutes
1
_
2
of the way around?
3
_
4
of the way around?
All the way around?
Home Link 6 7 Follow-Up
Draw a circle like the one on Home Link 6-7
on the board. Ask volunteers to mark the
answers on the circle. Note that there is more than one
correct answer for Problems 4, 5, and 6.
1 Teaching the Lesson
NOTE To review acute
and obtuse angles, go to
www.everydaymathonline.com.
Math Message Follow-Up
WHOLE-CLASS
ACTIVITY
Have children turn the minute hand on their tool-kit clocks as you
go over the answers. _14 turn = 15 minutes; _12 turn = 30 minutes;
3
_
4
turn = 45 minutes; all the way around = 60 minutes
Ask: How long does it take the minute hand to turn _13 of the way
around the clock face? 20 minutes _23 of the way? 40 minutes _16 of
the way? 10 minutes How long does it take to make 1_12 turns
around the clock face? 90 minutes
Student Page
Date
LESSON
Introducing the Degree as
a Unit of Measure for Turns
WHOLE-CLASS
ACTIVITY
ELL
(Math Journal 1, p. 143)
68
Time
Marking Angle Measures
Connect 2 straws with a twist-tie. Bend the twist-tie at the connection
to form a vertex.
Place the straws with the vertex on the center of the circle.
Place both straws pointing to 0°.
Keep one straw pointing to 0°. Move the other straw to form angles.
0°
A standard unit of measure called the degree is used to measure
turns and angles. To support English language learners, discuss
the different contexts and meanings of the word degree. Show a 1°
angle on the overhead projector and point out that it is very small.
Have children generate a list of objects that are about the size of
a 1° angle. A sliver of wood, the tip of a pencil, a pin, and so on
To measure the size of a turn, we think of a circle being divided
into 360 equal parts. Each part is called a degree. Ask children to
imagine a round pizza cut into 360 equal pieces. Think about how
small the pieces would be! Write the symbol for degrees (°) on the
board. For example, 30 degrees can be written using the word or
the symbol (30°).
143
Math Journal 1, p. 143
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Lesson 6 8
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360
0
˚
315
˚
45
˚
Have children form an angle with two straws and a twist-tie. Ask
children to open their journals to page 143. Show them how to
place the straws with the vertex on the center of the circle, with
both straws pointing approximately to the 0-degree mark.
˚
90
270
˚
˚
135
225
˚
˚
180
˚
Have children keep one straw pointing to the 0-degree mark and
move the other straw clockwise all the way around the circle. The
full turn measures 360°.
Next have children move the straw clockwise _14 turn. Ask: What is
the degree measure of a quarter turn? 90°; a full turn measures
360°, and _14 of 360° = 90° Tell children to make a mark on the
rim of the circle at the quarter-turn point and to label it 90°. Ask:
What is another name for a 90° angle? A right angle
Repeat this routine with a half-turn and a three-quarter turn.
Before each turn, children return both straws to the starting
position. They move one straw the specified fraction of a turn
clockwise and make a mark on the rim. They share strategies for
finding the number of degrees of the turn, and record the number
of degrees next to the mark. _14 turn: 90°, so _12 turn: 2 × 90°, or
180°; _34 turn: 3 × 90° or 270°
Finally, repeat the above routine with _18 , _38 , _58 , and _78 turns.
Teaching Aid Master
1
_
8
turn is _12 of _14 turn and _14 turn is 90°, so _18 turn is _12 of 90°, or 45°
3
_
8
turn: 3 × 45°, or 135°
5
_
8
turn: 5 × 45°, or 225°
7
_
8
turn: 7 × 45°, or 315°
Adjusting the Activity
Cut the sheet into four parts along the dashed lines.
Have children use calculators to determine the degree measures. Note
that some calculators have Deg keys on them. This key sets the unit of measure
for advanced functions and has nothing to do with the use of degrees in this
activity.
Share the circles with the members of your group. Each person will cut
out his or her own circle.
A U D I T O R Y
Name
Date
Time
Circles for Angle Measures
K I N E S T H E T I C
T A C T I L E
V I S U A L
Links to the Future
Expect that some children will be able to determine the number of degrees in
turns with the use of a calculator, but do not expect that all children will be able
to multiply fractions or work with multiplication fact extensions at this time. In
Unit 7, children revisit using basic multiplication facts to compute fact extensions.
Solving problems involving the multiplication of fractions is a Grade 5 Goal.
Math Masters, p. 428
446
Unit 6 Geometry
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Making an Angle Measurer
SMALL-GROUP
ACTIVITY
(Math Masters, p. 428)
Divide the class into groups of four. Give each group a copy of
Math Masters, page 428 and proceed as follows:
0°
360°
315°
45°
1. Children cut the master into four parts along the dashed lines.
2. Each child carefully cuts out one circle.
270°
90°
NOTE It is helpful to model Steps 3, 4, and 5 for the children with an extra circle.
3. To divide the circle into eight equal parts, children fold their
circles in half, in half again, and then in half once more.
225°
135°
180°
4. Children unfold their circles, make marks on the rim at the
folds, and label each mark with the appropriate degree
measure, as shown in the margin. Have children add an arrow
at the 0° mark.
An angle measurer
5. Children punch a small hole in the center of the circle with the
point of a pencil or pen.
NOTE An angle measurer can also be made from a piece of wax paper the size
of the circles on Math Masters, page 428. The advantage to the wax paper
measurer is that it is transparent enough to be placed directly over the angles on
journal page 144.
Measuring Angles with
the Angle Measurer
WHOLE-CLASS
ACTIVITY
PROBLEM
PRO
P
RO
R
OB
BLE
BL
L
LE
LEM
EM
SOLVING
SO
S
OL
O
L
LV
VIN
V
IIN
NG
(Math Journal 1, p. 144; Math Masters, p. 428)
Show children how to use the angle measurer using the
transparency of Math Masters, page 428.
1. Place the hole in the center of the measurer over the vertex of
the angle.
2. Align the 0° mark on the measurer with the side of the angle
where the curved arrow begins.
3. Look in the direction of the curved arrow. Read the degree
measure where the other side of the angle crosses the rim of
the measurer.
Children measure each angle and record the result in the table.
For angle C, suggest that they express the result as between x
degrees and y degrees. Circulate and help as needed. Bring the
class together to compare measurements.
Student Page
Date
Time
LESSON
Measuring Angles
68
Use your angle measurer to measure the angles on this page.
Record your measurements in the table. Then circle the right angle below.
Angle
45 °
90 °
between 90
°
about 180
°
135
about
°
about 225
A
about
B
about
C
D
E
F
B
Ongoing Assessment: Informing Instruction
Measurement
°
and
135 °
C
D
A
Watch for children who have difficulty lining up the 0° mark on the measurer
with the side of the angle where the arrow begins. Have them trace their fingers
along the arrow that denotes the turning prior to using the angle measurer.
E
F
Math Journal 1, p. 144
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Teaching Master
Name
Date
Time
Area and Perimeter
LESSON
68
Ongoing Assessment:
Recognizing Student Achievement
In the spring, the Garden Club will plant a garden. Each child will have
one square meter of dirt to plant. There are 16 children in the club, so
the area of the garden has to equal 16 square meters. The children
drew the shapes below for the garden.
the shapes that do not have areas of 16 square meters. Show how
you found the areas.
4m
b.
1m
4m
7m
7
Area =
square meters
Area =
16
d.
2m
c.
[Geometry Goal 1]
square meters
1m
5m
3m
16 m
3m
2m
2 Ongoing Learning & Practice
5m
Area =
16
Area =
square meters
Use journal page 144 to assess children’s ability to recognize a right angle.
Children are making adequate progress if they circle the right angle on the
journal page. Some children may recognize which angles are larger or smaller
than 90° without measuring.
1. Circle the shapes that have areas of 16 square meters. Cross out
a.
Journal
page 144
16
square meters
2. The club wants to build a fence around their garden, but they don’t
want to spend a lot of money. They need to find a shape that has an
area of 16 square meters and the shortest perimeter.
Finding Area and Perimeter
Which of the above shapes has an area of 16 square meters and
the shortest perimeter? Shape b
How did you find the perimeter for this shape?
Sample answer: Since
(Math Masters, p. 205A)
each side is 4 meters, I multiplied 4 × 4 to find the
perimeter. The perimeter is 16 meters.
Math Masters, p. 205A
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The activities in this lesson are an early
exposure to measuring angles. Determining
angle measures is a Grade 5 Goal.
Mixed Practice Math Boxes in this lesson are paired with
Math Boxes in Lesson 6-6. The skill in Problem 6 previews
Unit 7 content.
Time
68
Math Boxes
2. If each grid is ONE, what part of each
1. Continue the pattern.
grid is shaded? Write the decimal.
Writing/Reasoning Have children write an answer to the
following: Explain how the shaded grids in Problem 2 help
you decide which decimal is smaller. Sample answer:
Because both grids are ONE, the grid with fewer squares shaded
shows a smaller decimal.
Home Link 6 8
0.73
197
3. Write these numbers in order from
34 36
vans
0.2
smallest
(Math Masters, p. 182)
Home Connection Children estimate the sizes of angles
and match given angles with estimated measures.
How many vans?
0.19
INDEPENDENT
ACTIVITY
4. 49 people in all. 7 people per van.
smallest to largest:
0.2; 0.02; 0.19
0.02
0.8
Circle the smaller number.
INDEPENDENT
ACTIVITY
(Math Journal 1, p. 145)
Student Page
LESSON
Children determine which of the shapes on Math Masters, page
205A have areas of 16 square meters. They also select the shape
with an area of 16 square meters that has the shortest perimeter
measure and explain how they calculated the perimeter. Have
partners work together to complete page 205A.
Math Boxes 6 8
Links to the Future
Date
PARTNER
ACTIVITY
?
largest
people
per van
people
in all
7
49
49 ÷ 7 = ?
or ? × 7 = 49
7 vans
Number model:
36
Answer:
5. Write the letter that names the right
259
6. Complete the Fact Triangle.
angle.
Write the fact family.
B
B
A
D
C
7 × 8 = 56
8 × 7 = 56
56 ÷ 7 = 8
56 ÷ 8 = 7
98
56
×, ÷
7
8
55
Math Journal 1, p. 145
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Unit 6 Geometry
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Home Link Master
Name
3 Differentiation Options
HOME LINK
68
Family
Note
PARTNER
ACTIVITY
ENRICHMENT
Solving Degree Problems
Date
Time
Degree Measures
Our class has been learning about turns, angles, and angle measures. A full turn can be
1
1
represented by an angle of 360°, a _
turn by an angle of 180°, a _
turn by an angle of 90°,
4
2
and so on. Help your child match the measures below with the angles pictured. (It is not
necessary to measure the angles with a protractor.)
Please return this Home Link to school tomorrow.
Tell which angle has the given measure.
15–30 Min
Using a Clock Face
(Math Masters, pp. 183 and 184)
1. about 180°
angle
2. about 90°
angle
3. about 270°
angle
4. between 0° and 90°
angle
5. between 90° and 180°
To explore the relationship between angle measures and a clock
face, have children use straws and twist-ties to model the
movement of the minute hand on Math Masters, page 184.
Children calculate how many degrees the hands of a clock move
in given amounts of time on Math Masters, page 183.
angle
A
D
E
C or D
A or B
Rotation
1
_
4
1
_
2
3
_
4
Degrees
turn
90°
turn
180°
turn
270°
full turn
360°
B
A
py g
g
p
SMALL-GROUP
ACTIVITY
EXTRA PRACTICE
Minute Math +
E
D
C
5–15 Min
Math Masters, p. 182
To offer children more experience with degree measures, see the
following page in Minute Math+:
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Geometry: p. 59, Level 3.
Teaching Master
Name
LESSON
68
Teaching Master
Date
Time
Name
Modeling Angles on a Clock Face
LESSON
68
Connect 2 straws with a twist-tie.
Date
Time
Clock Angles
1. How many minutes does the minute hand
take to move ...
Model the movement of the minute hand as suggested in each
problem on Math Masters, page 183.
from 10:00 to 11:00?
Refer to your angle measurer to help you figure out the
from 4:00 to 4:30?
measurements in Problems 2 and 3.
from 6:00 to 6:15?
from 9:00 to 9:05?
60 minutes
30 minutes
15 minutes
5 minutes
11
10
12
1
2
9
3
8
4
7
6
5
2. Through how many degrees does the minute hand move ...
11
10
12
360 degrees
180 degrees
90 degrees
30 degrees
from 10:00 to 11:00?
1
from 4:00 to 4:30?
from 6:00 to 6:15?
2
from 9:00 to 9:05?
3. Through how many degrees does the hour hand move ...
9
3
8
in 3 hours?
in 2 hours?
in 1 hour?
4
7
6
Make up your own clock-angle problems.
5
4. Through how many degrees does the
move ...
Math Masters, p. 184
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90 degrees
60 degrees
30 degrees
Answers vary.
in
?
in
?
hand
Math Masters, p. 183
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Name
LESSON
68
Date
Time
Area and Perimeter
In the spring, the Garden Club will plant a garden. Each child will have
one square meter of dirt to plant. There are 16 children in the club, so
the area of the garden has to equal 16 square meters. The children
drew the shapes below for the garden.
1. Circle the shapes that have areas of 16 square meters. Cross out
the shapes that do not have areas of 16 square meters. Show how
you found the areas.
a.
4m
b.
1m
4m
7m
Area =
Area =
square meters
2m
d.
3m
16 m
1m
5m
c.
square meters
3m
2m
5m
square meters
Area =
square meters
2. The club wants to build a fence around their garden, but they don’t
want to spend a lot of money. They need to find a shape that has an
area of 16 square meters and the shortest perimeter.
Which of the above shapes has an area of 16 square meters and
the shortest perimeter?
Copyright © Wright Group/McGraw-Hill
Area =
How did you find the perimeter for this shape?
205A
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