Download Unit 4

Unit 4
Common Core
Size, Shape, and Symmetry
Mathematical Practices (MP)
Domains
• Number and Operations in Base Ten (NBT)
• Measurement and Data (MD)
• Geometry (G)
INVESTIG ATION 1
Linear Measurement Teach this Investigation as is.
Day
1 1.1­
2 1.2­
Session
Measurement
Benchmarks
Measurement Tools
3 1.3
Assessment: How Long Is
Our Classroom?
4 1.4
Measuring Length
5 1.5
Common Core Adaptation
Common Core Standards
MP5
4.NBT.4, 4.MD.1, 4.MD.3
MP5
4.NBT.4, 4.MD.1
MP5
4.NBT.4, 4.MD.1, 4.MD.2,
4.MD.3
MP5, MP6
4.NBT.4, 4.MD.1, 4.MD.3
MP5
4.NBT.4, 4.MD.1, 4.MD.2,
4.MD.3
Common Core Adaptation
Common Core Standards
MP6
4.G.1, 4.G.2
MP6
4.G.1
MP5, MP6
4.NBT.4, 4.MD.5.a,
4.G.1, 4.G.2
MP5, MP6
4.MD.3, 4.G.1, 4.G.2
Measuring Length,
continued
INVESTIG ATION 2
Polygons of Many Types
Day
6 2.1­
Session
Is It a Polygon?
7
2.2­
8
2.3A­ Identifying Geometric
Figures
9
2.3­
CC12 Making Polygons
Sorting Polygons
See p. CC16.
UNIT 4 Size, Shape, and Symmetry
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INVESTIG ATION 2
Polygons of Many Types, continued
Day
10 2.4
Session
Sorting Quadrilaterals
MATH WORKSHOP
2A Guess My Rule with
Quadrilaterals
Discussion
All Quadrilaterals…
Some Quadrilaterals
11 2.5
Common Core Adaptation
Teaching Note
Parallel and Perpendicular Lines Suggest that students
use parallel lines and perpendicular lines as rules in Guess My
Rule with Quadrilaterals.
Teaching Note
Parallel and Perpendicular Lines as Attributes of
Quadrilaterals Use the terms perpendicular lines and
parallel lines as you create the “All Quadrilaterals…” and
“Some Quadrilaterals…” chart with students.
Assessment: What Is a
Quadrilateral?
MATH WORKSHOP
3A Guess My Rule (with
Power Polygons or
Shape Cards)
Common Core Standards
MP3, MP6
4.G.1, 4.G.2
MP3, MP6
4.G.1, 4.G.2
Teaching Note
Parallel and Perpendicular Lines in Guess My
Rule Suggest that students use parallel lines, perpendicular
lines, and right triangles as rules in Guess My Rule.
INVESTIG ATION 3
Measuring Angles
Day
12 3.1
Session
Making Right Angles
Discussion
How Many Degrees?
Common Core Adaptation
Teaching Note
Equations for Making Right Angles Write equations on
the board that represent what students found out about the
measures of the angles. After students state the measure of
the small angles in shape E, write on the board:
“45° + 45° = 90°.” After students state the measure of
the angles in shape O, write on the board:
“30° + 30° + 30° = 90°. “
Common Core Standards
MP5
4.NBT.4, 4.MD.6, 4.MD.7
Instructional Plan CC13
INV12_TE04_U04.indd 13
6/2/11 4:36 PM
INVESTIG ATION 3
Measuring Angles, continued
Day
13 3.2
Session
More or Less Than
90 Degrees?
MATH WORKSHOP
Teaching Note
Equations for How Many Degrees? Tell students that for
each problem on Student Activity Book pages 39–40, they
should write an equation that shows how they knew how
many degrees were in each unknown angle. Tell students for
each problem on Student Activity Book pages 41–43, they
should also write addition equations that represent the
smaller angles they added together to make the larger angle.
SESSION FOLLOW-UP
Daily Practice: In addition to Student Activity Book page 44,
students complete Student Activity Book page 46 or C12 (Sides
and Angles) for reinforcement of the content of this unit.
2A How Many Degrees?
Daily Practice and
Homework
14 3.3
Common Core Adaptation
MP5
4.NBT.4, 4.MD.6, 4.MD.7
Assessment: Building
Angles
DISCUSSION
Teaching Note
Addition and Subtraction Equations As students share
their ideas about how to find the measurement of the
unknown angle in Problem 1, record equations that represent
their thinking. For example: 30° + 30° = 60° or
90° − 30° = 60°.
DISCUSSION
Teaching Note
More Strategies for
How Many Degrees
Common Core Standards
MP5
4.NBT.4, 4.MD.6, 4.MD.7
How Do You Know It Is
Equations for Angles That Make 120 Degrees As
120 Degrees?
students share how they combined angles to make 120
degrees, write addition equations that represent the angles
they added together to make 120 degrees. For example:
60° + 30° + 30° = 120°.
15 3.4A
CC14 Lines and Angles
See p. CC21.
MP5
4.NBT.4, 4.MD.5.a,
4.MD.5.b, 4.MD.6, 4.G.1
UNIT 4 Size, Shape, and Symmetry
INV12_TE04_U04.indd
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5/4/11
2:39 PM
INVESTIG ATION 4
Finding Area
Day
16 4.1
Session
Symmetry
TEN-MINUTE MATH
Quick Images: 2-D
17 4.2­
Common Core Adaptation
Also ask students:
• Are there parallel lines, perpendicular lines, or right
triangles in this image? If so, where are they?
Symmetry and Area
TEN-MINUTE MATH
Quick Images: 2-D
18 4.3
Also ask students:
• Are there parallel lines, perpendicular lines, or right
triangles in this image? If so, where are they?
Finding Halves of
Crazy Cakes
TEN-MINUTE MATH
Quick Images: 2-D
SESSION FOLLOW-UP
Daily Practice and
Homework
19 4.4­
Quick Images: 2-D
20 4.5
Area of Rectangles
21 4.6
Area of Polygons
22 4.7
End-of-Unit Assessment
MP5
4.MD.3 , 4.G.2, 4.G.3
MP5
4.MD.3, 4.G.2, 4.G.3
Also ask students:
• Are there parallel lines, perpendicular lines, or right
triangles in this image? If so, where are they?
Daily Practice: In addition to Student Activity Book page
60, students complete Student Activity Book page 62 or C16
(More Lines and Angles) for reinforcement of the content of
this unit.
Decomposing Shapes
TEN-MINUTE MATH
Common Core Standards
MP5
4.MD.3, 4.G.2, 4.G.3
Also ask students:
• Are there parallel lines, perpendicular lines, or right
triangles in this image? If so, where are they?
MP5
4.MD.3, 4.G.2, 4.G.3
MP5
4.NBT.4, 4.MD.3
MP5
4.NBT.4, 4.MD.3, 4.G.3
MP1, MP2, MP6
4.NBT.4, 4.MD.3, 4.G.1,
4.G.2
Instructional Plan INV12_TE04_U04.indd
15
CC15
5/4/11
2:40 PM
session 2.3A
Identifying Geometric
Figures
Vocabulary
Identifying right triangles
point
line
ray
line segment
perpendicular
lines
Today’s Plan
Materials
Math Focus Points
Identifying parallel lines and perpendicular lines
Identifying right angles, acute angles, and obtuse angles
activity
Parallel and
Perpendicular Lines
•Student Activity Book, p. 22A or
30 Min Class
Pairs
Activity
Kinds of Angles
C9, Parallel and Perpendicular Lines Make copies. (as needed)
Power Polygons™
•
•Power Polygons
15 Min
Class
Pairs
Activity
Right Triangles
parallel lines
angle
right angle
acute angle
obtuse angle
right triangle
•Student Activity Book, p. 22B or
15 Min
Class
SESSION FOLLOW-UP
Pairs
C10, Angles and Right Triangles Make copies. (as needed)
T47
Power Polygons
•
•
•Student Activity Book, p. 22D or
Daily Practice
C11, Sorting Shapes Make copies.
(as needed)
Ten-Minute Math
Today’s Number: Broken Calculator Students create five expressions that equal 925.
They must use both addition and subtraction in their expressions. The 5 and 9 keys are
broken. Have two or three students share their equations and explain how they know
that the answer is correct. (Examples: 1,000 – 80 + 2 + 3 = 925 or
200 + 700 + 26 – 1 = 925)
CC16 INVESTIGATION 2 Polygons of Many Types
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1 Activity 2 Activity 3 Activity 4 Session Follow-Up
AC TIVIT Y
Parallel and Perpendicular
Lines
30 Min
class
pairs
Begin by discussing points, lines, rays, and line segments. As you
do so, draw and label examples on the board. You may want to
draw and label the geometric figures presented on chart paper and
keep the chart posted in the classroom throughout the unit for
student reference.
A point is an exact location. You’ll see it drawn as a dot. A line
goes on and on forever in a straight path in two directions. The
arrowheads remind you that a line keeps going. Rays and line
segments are parts of lines. A ray has one endpoint and goes on
forever in one direction. A line segment has two endpoints.
Point
Line
Ray
Line Segment
We can use pencils to model lines. You need to imagine that they
go on forever. [Use two pencils to show two lines intersecting to
form square corners.] I am modeling perpendicular lines. Two
perpendicular lines intersect to form square corners.
Have students model perpendicular lines with pencils. On the
board, draw two perpendicular lines.
Now use your two pencils to show two lines that will never
intersect. [Have students show this with their pencils.] We are
modeling parallel lines. Parallel lines do not intersect.
Draw two parallel lines on the board.
Perpendicular Lines
Parallel Lines
Session 2.3A Identifying Geometric Figures INV12_TE04_U04_S2.3A.indd 17
CC17
6/2/11 4:44 PM
1 Activity 2 Activity 3 Activity 4 Session Follow-Up
Teaching Note
Right, acute, and
obtuse angles are studied further in
Investigation 3.
1 Working With Angles Name
Date
Size, Shape, and Symmetry
Parallel and Perpendicular Lines
In Problems 1–4, write point, line, ray, or line segment.
1.
2.
3.
Hold up a sheet of paper and point out parallel sides and
perpendicular sides of the rectangle. Give each pair of students a set
of Power Polygons and have students look for parallel sides and
perpendicular sides in each shape. Then have students complete
Student Activity Book page 22A or C9.
2
3
1
Students might say:
“Perpendicular lines could be two streets
that cross each other and make four
square corners. Parallel lines would be two
streets that never meet.”
4.
For Problems 5 and 6, use the
polygon at the right.
Can you describe examples of some things in the real world that
look like perpendicular lines or parallel lines?
4
5
5. Give the numbers for a pair of parallel sides.
6. Give the numbers for a pair of perpendicular
sides.
For Problems 7 and 8, use the map below.
7. Name a pair of parallel streets.
8. Name a pair of perpendicular streets.
ce
AC TIVIT Y
22A
Law
Unit 4
Session 2.3A
▲ Student Activity Book, Unit 4, p. 22A;
Resource Masters, C9
INV12_SE04_U4.indd
Kinds of Angles
© Pearson Education 4
ren
Lincoln
Ford
Howard
Evans
1
6/1/11
9:04 AM
15 Min
class
pairs
Let’s imagine your two pencils are rays, and the erasers are the
endpoints. Hold them so they touch just at their endpoints.
[Demonstrate with your own pencils.] We are modeling an angle.
Hold your pencils so that the angle looks like a square corner.
That’s a right angle. Now close up the opening. That’s an acute
angle. It’s smaller than a right angle. Now make an opening
bigger than a right angle. That’s an obtuse angle.
Draw examples on the board.
Right Angle
Acute Angle
Obtuse Angle
Give each pair of students a set of Power Polygons. Have them take
turns choosing a polygon and describing each of the angles. For
example, shape J has one obtuse angle and two acute angles. 1
Ongoing Assessment: Observing Students at Work
• Do students recognize right angles, acute angles, and
obtuse angles? Do they use a square corner on a Power
Polygon or the corner of a sheet of paper to check?
CC18 INVESTIGATION 2 Polygons of Many Types
INV12_TE04_U04_S2.3A.indd 18
6/2/11 4:48 PM
1 Activity 2 Activity 3 Activity 4 Session Follow-Up
Name
AC TIVIT Y
Right Triangles
Date
Size, Shape, and Symmetry
15 Min
class
Shape Cards (page 1 of 2)
pairs
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11
11111 1
11111
1
On the overhead, display Shapes 1 and 3 of Shape Cards (T47).
Take a look at Shape 1 and Shape 3. How are these shapes the
same? How are they different?
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99999 9
99999
9
Display the other triangles from T47. Ask students to identify
those triangles that are right triangles and those triangles that are
not right triangles. Students should recognize Shapes 1, 4, 5, and 8
as right triangles. Ask volunteers to point to the right angle in each
of these triangles. Students may show that an angle is a right angle
or is not a right angle by using the corner of a piece of paper, a
strategy they may remember from third grade, or by using a Power
Polygon, such as shape A.
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© Pearson
© Pearson
Education
Education
4
4
[Derek] said Shape 1 has a right angle. A triangle that has a right
angle in it is called a right triangle.
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7
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66666
6
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5
Students should recognize both shapes as triangles, and notice the
differences in the angles.
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Sessions 2.3, 2.4, 2.5
M19
Unit 4
T47
First Pass
24084_001-029_RM_G4-U04 19
▲ Transparencies, T47
6/2/11 5:05 PM
Second
First
PassPass
Confirming
Second PassPass
24084_42-52_OHT_G4_U4.indd 47
6/16/11 12:23 PM
PDF
Proof Pass
Confirming
PDF Proof
Name
Date
Size, Shape, and Symmetry
Angles and Right Triangles
In Problems 1–3, write right angle, acute angle, or obtuse angle.
1.
2.
3.
Have students complete Student Activity Book page 22B or C10.
4. Complete the chart.
Number of
Right Angles
Differentiation: Supporting the Range of Learners
Some students may have difficulty recognizing
right triangles especially when one side of the right angle is not
horizontal. Encourage them to use the corner of a sheet of paper
to check for right angles.
Number of
Obtuse Angles
5. Circle each right triangle.
© Pearson Education 4
Students may confuse right angle and right triangle.
You might want to work with students in small groups. Provide
drawings to help them distinguish between angle and triangle.
Number of
Acute Angles
Session 2.3A
22B
▲ Student Activity Book, Unit 4, p. 22B;
Resource Masters, C10
INV12_SE04_U4.indd 2
Session 2.3A Identifying Geometric Figures INV12_TE04_U04_S2.3A.indd 19
Unit 4
6/2/11 4:07 PM
CC19
6/16/11 12:25 PM
1 Activity 2 Activity 3 Activity 4 Session Follow-Up
Name
Date
Size, Shape, and Symmetry
Daily Practice
Sorting Shapes
1
Daily Practice
4
3
2
SESSION FOLLOW-UP
note Students identify parallel sides, perpendicular sides, and obtuse angles in polygons.
Write the numbers of all the shapes that belong in
each category.
Daily Practice: For reinforcement of this unit’s content,
have students complete Student Activity Book page 22D
or C11.
9
5
10
8
6
7
14
11
12
13
1. Which shapes have at least one pair of parallel sides?
2. Which shapes have at least one pair of perpendicular
sides?
© Pearson Education 4
3. Which shapes have at least one obtuse angle?
Session 2.3A
Unit 4
22D
▲ Student Activity Book, Unit 4, p. 22D;
Resource Masters, C11
INV12_SE04_U4.indd
CC20 4
5/4/11
1:30 PM
INVESTIGATION 2 Polygons of Many Types
INV12_TE04_U04_S2.3A.indd 20
6/2/11 5:24 PM
session 3.4A
Lines and Angles
Math Focus Points
Drawing lines, parts of lines, and angles
Understanding the relationship between the degree measure of an
angle and circular arcs
Vocabulary
Measuring angles using a protractor
protractor
Today’s Plan
Materials
activity
Drawing Lines and Angles
•Student Activity Book, p. 51A or
20 Min
activity
Using a Protractor
C13, Drawing Lines and Angles Make
copies. (as needed)
Class Individuals
•Student Activity Book, p. 51B or
40 Min
Class
Pairs
Session Follow-Up
Daily Practice
C14, Using a Protractor Make copies. (as
needed)
6-inch paper circles (1 per student)
Protractors (1 per student)
•
•
•Student Activity Book, p. 51C or
C15, Lines and Angles Make copies.
(as needed)
Student Math Handbook, pp. 111–112
•
Ten-Minute Math
Today’s Number: Broken Calculator Students create five expressions that equal 722.
They must use only subtraction in their expressions. The 2 and 7 keys on their
calculators are broken. Have two or three students share their equations and explain
how they know that the answer is correct. (Examples: 838 ∙ 116 ∙ 722 or 1,361 ∙
639 ∙ 722)
INV12_TE04_U04_S3.4A.indd 21
Session 3.4A Lines and Angles CC21
6/3/11 1:17 PM
1 Activity 2 Activity 3 Session Follow-Up
Name
Date
Size, Shape, and Symmetry
AC TIVIT Y
Drawing Lines and Angles
Draw an example of the figure.
1.
2.
Line Segment
4.
Line
5.
Perpendicular Lines
© Pearson Education 4
7.
When you draw a line, you can’t show all of it. So you draw part of
it and add two arrowheads. To draw a ray, be sure to show a dot
for its one endpoint and draw just one arrowhead. For a line
segment, you need to show its two endpoints.
Angle
9.
Acute Angle
Obtuse Angle
Unit 4
51A
▲ Student Activity Book, Unit 4, p. 51A;
Resource Masters, C13
INV12_SE04_U4.indd
1
class Individuals
Begin by reviewing lines, line segments, and rays, and discuss how
to draw them. As you do so, draw and label examples on the board.
Ray
Parallel Lines
Session 3.4A
20 Min
6.
8.
Right Angle
Drawing Lines and Angles
3.
5/4/11
1:31 PM
Line
Ray
Line Segment
Next, discuss parallel lines and perpendicular lines and show how
to draw them. Ask volunteers to explain why each of your examples
shows either perpendicular or parallel lines.
Perpendicular Lines
Parallel Lines
Now, turn your attention to angles. Be sure students remember
that angles are formed by two rays that share a common endpoint.
Show how to draw angles and provide a variety of examples on the
board. Review right angles, acute angles, and obtuse angles. Ask
students to classify the angles you drew.
Right Angle
Acute Angle
Obtuse Angle
Have students complete Student Activity Book page 51A or C13.
CC22 Investigation 3 Measuring Angles
INV12_TE04_U04_S3.4A.indd 22
6/3/11 1:17 PM
1 Activity 2 Activity 3 Session Follow-Up
AC TIVIT Y
Using a Protractor
40 Min
class
Pairs
In this activity, students relate circular arcs to angle measures before
they use a protractor to measure angles. Give each student a paper
circle. Ask students to fold the circle in half and crease the paper.
Then have them fold it in half again.
Open your circle. What kind of angles do the creases make?
What’s the measure of each of those angles? How many degrees
is the sum of the four angles?
Students might say:
“The creases look perpendicular, so those
are right angles. Each right angle measures
90 degrees. So all four of them add up to
360 degrees.”
Let’s pretend your circle is a clock. Draw
the 12, 3, 6, and 9 on your clock. Then
draw two rays on your circle pointing
straight up like the hands of a clock
pointing to the 12.
12
9
3
6
If one of the rays turns all the way around the circle, it has gone
through the four right angles, so it has gone 360 degrees. Suppose
it only goes halfway around and stops at the 6. How many
degrees is that? … What about a quarter of the way around? …
1    ​of the way around? Can you describe
Suppose it goes only ​ ___
360
what kind of angle this would make? How many degrees would it
have? Talk to a partner about your ideas.
Students might say:
1    ​of the way around is a really teensy
___
“​ 360
part of the whole way around. It’s like a
little sliver.”
1    ​of the way around is ​ ___
1    ​of 360
___
“​ 360
360
degrees. So, it’s only 1 degree.”
Session 3.4A Lines and Angles INV12_TE04_U04_S3.4A.indd 23
CC23
10/26/11 3:31 PM
1 Activity 2 Activity 3 Session Follow-Up
Name
That’s right. It has a very tiny opening. When we measure angles,
we find how many degrees are in them. How many degrees would
be in a right angle? Look at your circle. If the ray travels ​ 41_ ​of the
way around the circle, it has traveled 90°. The creases in the
paper show a right angle. A right angle has a measure of 90°.
Date
Size, Shape, and Symmetry
Using a Protractor
In Problems 1–4, use a protractor to measure each angle.
1.
2.
degrees
3.
Give each student a protractor and explain that it is used to
measure an angle in degrees. Point out that each tick mark
represents one degree. Demonstrate how to measure an angle.
Discuss the two scales and be sure students understand which scale
to use.
degrees
4.
degrees
degrees
5. How many degrees are in a full circle?
6. What fraction of a circle does the
angle in Problem 3 turn through?
Have students complete Student Activity Book page 51B or C14.
51B
Unit 4
© Pearson Education 4
7. The angle at the right cuts off _18 of
the circle. Without using a protractor,
give the measure of the angle.
Ongoing Assessment: Observing Students at Work
Session 3.4A
▲ Student Activity Book, Unit 4, p. 51B;
Resource Masters, C14
INV12_SE04_U4.indd
2
6/1/11
9:04 AM
Students determine the degree measures of angles.
• Do students understand that an angle that turns through
n one-degree angles is said to have an angle measure of
n degrees?
Differentiation: Supporting the Range of Learners
Some students may have difficulty reading the
correct scale on the protractor. Encourage them to identify the
angle they are measuring as acute, right, or obtuse before they
measure it. Then have them measure the angle and check to see
whether their numerical answer agrees with the type of angle
they identified. If it does not, they likely used the wrong scale.
Challenge students to use a protractor to draw
angles with given measures.
CC24 Investigation 3 Measuring Angles
INV12_TE04_U04_S3.4A.indd 24
6/3/11 1:20 PM
1 Activity 2 Activity 3 Session Follow-Up
Name
SESSION FOLLOW-UP
Daily Practice
Lines and Angles
Daily Practice
Date
Size, Shape, and Symmetry
note Students draw geometric figures and use a protractor to measure angles.
In Problems 1–3, draw an example
of the figure.
2.
1.
Daily Practice: For reinforcement of this unit’s content,
have students complete Student Activity Book page 51C or
C15.
3.
Line Segment
Parallel Lines
Obtuse Angle
In Problems 4 and 5, use a protractor to measure the
numbered angle.
5.
4.
2
Student Math Handbook: Students and families may use
Student Math Handbook pages 111–112 for reference and
review. See pages 170–174 in the back of Unit 4.
1
degrees
degrees
© Pearson Education 4
Session 3.4A
Unit 4
51C
▲ Student Activity Book, Unit 4, p. 51C;
Resource Masters, C15
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Name
Date
Size, Shape, and Symmetry
Parallel and Perpendicular Lines
In Problems 1–4, write point, line, ray, or line segment.
1.
2.
3.
4.
For Problems 5 and 6, use the
polygon at the right.
2
3
1
4
5
5. Give the numbers for a pair of parallel sides.
6. Give the numbers for a pair of perpendicular
sides.
For Problems 7 and 8, use the map below.
7. Name a pair of parallel streets.
Law
ren
Lincoln
Ford
Howard
ce
8. Name a pair of perpendicular streets.
Evans
Unit 4 Session 2.3A
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Name
Date
Size, Shape, and Symmetry
Angles and Right Triangles
In Problems 1–3, write right angle, acute angle, or obtuse angle.
1.
2.
3.
4. Complete the chart.
Number of
Right Angles
Number of
Acute Angles
Number of
Obtuse Angles
5. Circle each right triangle.
Unit 4 Session 2.3A
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Name
Date
Size, Shape, and Symmetry
Daily Practice
Sorting Shapes
notE Students identify
parallel sides, perpendicular sides,
and obtuse angles in polygons.
Write the numbers of all the shapes that belong in
each category.
1
4
3
2
9
6
5
10
8
7
14
11
13
12
1. Which shapes have at least one pair of parallel sides?
2. Which shapes have at least one pair of perpendicular
sides?
3. Which shapes have at least one obtuse angle?
Unit 4 Session 2.3A
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Name
Date
Size, Shape, and Symmetry
Daily Practice
Sides and Angles
For Problems 1 and 2, use the
polygon at the right.
2
3
1
notE Students identify parallel sides,
perpendicular sides, and special types
of angles in polygons, and they identify
right triangles.
4
1. Give the numbers for a pair of parallel sides.
2. Give the numbers for a pair of perpendicular sides.
3. Circle each right triangle.
4. Complete the chart.
Number of
Right Angles
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Number of
Acute Angles
Number of
Obtuse Angles
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6/23/11 3:54 PM
Name
Date
Size, Shape, and Symmetry
Drawing Lines and Angles
Draw an example of the figure.
1.
2.
3.
Line Segment
4.
Line
5.
Perpendicular Lines
7.
6.
Angle
Parallel Lines
8.
Right Angle
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Ray
9.
Acute Angle
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Obtuse Angle
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6/22/11 5:00 PM
Name
Date
Size, Shape, and Symmetry
Using a Protractor
In Problems 1–4, use a protractor to measure each angle.
1.
2.
degrees
degrees
3.
4.
degrees
degrees
5. How many degrees are in a full circle?
6. What fraction of a circle does the
angle in Problem 3 turn through?
7. The angle at the right cuts off ​ _18 ​ of
the circle. Without using a protractor,
give the measure of the angle.
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Name
Date
Size, Shape, and Symmetry
Daily Practice
Lines and Angles
notE Students draw geometric
figures and use a protractor to
measure angles.
In Problems 1–3, draw an example
of the figure.
1.
2.
3.
Line Segment
Parallel Lines
Obtuse Angle
In Problems 4 and 5, use a protractor to measure the
numbered angle.
5.
4.
2
1
degrees
degrees
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Name
Date
Size, Shape, and Symmetry
Daily Practice
More Lines and Angles
notE Students draw geometric
figures and use a protractor to
measure angles.
In Problems 1–3, draw an example of the figure.
1.
2.
3.
Perpendicular Lines
Ray
Acute Angle
4. Use a protractor to measure each numbered angle.
Angle 1
degrees
Angle 2
degrees
Angle 3
Angle 4
4
3
degrees
degrees
1
2
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Nombre
Fecha
Tamaño, forma y simetría
Rectas paralelas y perpendiculares
En los Problemas 1 a 4, escribe punto, recta, semirrecta o
segmento de recta.
1.
2.
3.
4.
2
En los Problemas 5 y 6 usa el
polígono de la derecha.
3
1
4
5
5. Da los números de un par de lados paralelos.
6. Da los números de un par de lados perpendiculares.
En los Problemas 7 y 8, usa el mapa de abajo.
7. Nombra un par de calles paralelas.
8. Nombra un par de calles perpendiculares.
Law
ren
Lincoln
Ford
Howard
ce
AYUNTAMIENTO
Evans
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Nombre
Fecha
Tamaño, forma y simetría
Ángulos y triángulos rectángulos
En los Problemas 1 a 3, escribe ángulo recto, ángulo agudo o
ángulo obtuso.
1.
2.
3.
4. Completa la tabla.
Número de
ángulos rectos
Número de
ángulos
agudos
Número de
ángulos
obtusos
5. Encierra en un círculo cada triángulo rectángulo.
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Nombre
Fecha
Tamaño, forma y simetría
Práctica diaria
Agrupar figuras
notA Los estudiantes identifican
lados paralelos, lados perpendiculares
y ángulos obtusos en polígonos.
Escribe los números de todas las figuras que
pertenecen a cada categoría.
1
4
3
2
9
6
5
10
8
7
14
11
12
13
1. ¿Qué figuras tienen por lo menos un par de lados
paralelos?
2. ¿Qué figuras tienen por lo menos un par de lados
perpendiculares?
3. ¿Qué figuras tienen por lo menos un ángulo obtuso?
Unidad 4 Sesión 2.3A
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Nombre
Fecha
Tamaño, forma y simetría
Práctica diaria
Lados y ángulos
En los Problemas 1 y 2, usa el
polígono de la derecha.
2
3
1
notA Los estudiantes identifican
lados paralelos, lados perpendiculares
y tipos de ángulos en polígonos e
identifican triángulos rectángulos.
4
1. Da los números de un par de lados paralelos.
2. Da los números de un par de lados perpendiculares.
3. Encierra en un círculo cada triángulo rectángulo.
4. Completa la tabla.
Número de
ángulos rectos
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Número de
ángulos
agudos
Número de
ángulos
obtusos
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Nombre
Fecha
Tamaño, forma y simetría
Dibujar rectas y ángulos
Dibuja un ejemplo de cada figura.
1.
2.
3.
Segmento de recta
5.
4.
Rectas
perpendiculares
7.
6.
Ángulo
Rectas paralelas
8.
Ángulo recto
9.
Ángulo agudo
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Semirrecta
Recta
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Ángulo obtuso
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7/13/11 1:59 PM
Nombre
Fecha
Tamaño, forma y simetría
Usar un transportador
En los Problemas 1 a 4, usa un transportador para medir cada ángulo.
1.
2.
grados
grados
3.
4.
grados
grados
5. ¿Cuántos grados hay en un círculo completo?
6. ¿Qué fracción de un círculo atraviesa el ángulo
del Problema 3?
7. El ángulo de la derecha corta ​ _18 ​ del
círculo. Sin usar un transportador, da la
medida del ángulo.
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Nombre
Fecha
Tamaño, forma y simetría
Práctica diaria
Rectas y ángulos
notA Los estudiantes dibujan
figuras geométricas y usan un
transportador para medir ángulos.
En los Problemas 1 a 3, dibuja un ejemplo
de cada figura.
1.
2.
3.
Segmento de recta
Rectas paralelas
Ángulo obtuso
En los Problemas 4 y 5, usa un transportador para medir el
ángulo numerado.
5.
4.
2
1
grados
grados
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Nombre
Fecha
Tamaño, forma y simetría
Práctica diaria
Más rectas y ángulos
notA Los estudiantes dibujan
figuras geométricas y usan un
transportador para medir ángulos.
En los Problemas 1 a 3, dibuja un ejemplo de
cada figura.
2.
1.
Rectas
perpendiculares
3.
Semirrecta
Ángulo agudo
4. Usa un transportador para medir los ángulos
numerados.
4
Ángulo 1
grados
Ángulo 2
grados
3
Ángulo 3
grados
1
Ángulo 4
grados
2
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