polygons of many types - tusd1.orgpolygons of many types, continued day session common core...

Common Core

I N V E S T I G AT I O N 1

Linear Measurement Teach this Investigation as is.

Day Session Common Core Adaptation Common Core Standards

1 1.1 Measurement Benchmarks

MP54.NBT.4, 4.MD.1, 4.MD.3

2 1.2 Measurement Tools MP54.NBT.4, 4.MD.1

3 1.3 Assessment: How Long Is Our Classroom?

MP54.NBT.4, 4.MD.1, 4.MD.2, 4.MD.3

4 1.4 Measuring Length MP5, MP64.NBT.4, 4.MD.1, 4.MD.3

5 1.5 Measuring Length, continued

MP54.NBT.4, 4.MD.1, 4.MD.2, 4.MD.3


Polygons of Many TypesDay Session Common Core Adaptation Common Core Standards

6 2.1 Is It a Polygon? MP64.G.1, 4.G.2

7 2.2 Making Polygons MP64.G.1

8 2.3A Identifying Geometric Figures

See p. CC16. MP5, MP64.NBT.4, 4.MD.5.a, 4.G.1, 4.G.2

9 2.3 Sorting Polygons MP5, MP64.MD.3, 4.G.1, 4.G.2

Mathematical Practices (MP)

Domains• Number and Operations in Base Ten (NBT)• Measurement and Data (MD)• Geometry (G)

Size, Shape, and Symmetry

Unit 4

CC12 UNIT 4 Size, Shape, and Symmetry

INV12_TE04_U04.indd 12 10/28/11 1:05 PM


Polygons of Many Types, continued


10 2.4 Sorting Quadrilaterals MP3, MP64.G.1, 4.G.2

MATH WORKSHOPGuess My Rule with Quadrilaterals

Teaching NoteParallel and Perpendicular Lines Suggest that students use parallel lines and perpendicular lines as rules in Guess My Rule with Quadrilaterals.

DIScuSSIONAll Quadrilaterals…Some Quadrilaterals

Teaching NoteParallel 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.

11 2.5 Assessment: What Is a Quadrilateral?

MP3, MP64.G.1, 4.G.2

MATH WORKSHOPGuess My Rule (with Power Polygons or Shape Cards)

Teaching NoteParallel and Perpendicular Lines in Guess My Rule Suggest that students use parallel lines, perpendicular lines, and right triangles as rules in Guess My Rule.


Measuring AnglesDay Session Common Core Adaptation Common Core Standards

12 3.1 Making Right Angles MP54.NBT.4, 4.MD.6, 4.MD.7

DIScuSSIONHow Many Degrees?

Teaching NoteEquations 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 ofthe angles in shape O, write on the board: “30° + 30° + 30° = 90°. “

2A

3A

Instructional Plan cc13

INV12_TE04_U04.indd 13 6/2/11 4:36 PM


Measuring Angles, continued


13 3.2 More or Less Than 90 Degrees?

MP54.NBT.4, 4.MD.6, 4.MD.7

MATH WORKSHOPHow Many Degrees?

Teaching NoteEquations 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-UPDaily Practice and Homework

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.

14 3.3 Assessment: Building Angles

MP54.NBT.4, 4.MD.6, 4.MD.7

DISCUSSIONMore Strategies for How Many Degrees

Teaching NoteAddition 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°.

DISCUSSIONHow Do You Know It Is 120 Degrees?

Teaching NoteEquations for Angles That Make 120 Degrees As 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 Lines and Angles See p. CC21. MP54.NBT.4, 4.MD.5.a, 4.MD.5.b, 4.MD.6, 4.G.1

2A

CC14 UNIT 4 Size, Shape, and Symmetry

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Finding AreaDay Session Common Core Adaptation Common Core Standards

16 4.1 Symmetry MP54.MD.3, 4.G.2, 4.G.3TEN-MINUTE MATH

Quick Images: 2-DAlso ask students:• Are there parallel lines, perpendicular lines, or right

triangles in this image? If so, where are they?17 4.2 Symmetry and Area MP5

4.MD.3 , 4.G.2, 4.G.3TEN-MINUTE MATHQuick Images: 2-D

Also ask students:• Are there parallel lines, perpendicular lines, or right

triangles in this image? If so, where are they?18 4.3 Finding Halves of

Crazy CakesMP54.MD.3, 4.G.2, 4.G.3

TEN-MINUTE MATHQuick Images: 2-D

Also ask students:• Are there parallel lines, perpendicular lines, or right

triangles in this image? If so, where are they?SESSION FOLLOW-UPDaily Practice and Homework

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.

19 4.4 Decomposing Shapes MP54.MD.3, 4.G.2, 4.G.3TEN-MINUTE MATH

Quick Images: 2-DAlso ask students:• Are there parallel lines, perpendicular lines, or right

triangles in this image? If so, where are they? 20 4.5 Area of Rectangles MP5

4.NBT.4, 4.MD.321 4.6 Area of Polygons MP5

4.NBT.4, 4.MD.3, 4.G.322 4.7 End-of-Unit Assessment MP1, MP2, MP6

4.NBT.4, 4.MD.3, 4.G.1, 4.G.2

Instructional Plan CC15

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s e s s i o n 2 . 3 A

Activity

Parallel and Perpendicular Lines 30 Min clAss PAirs

• Student Activity Book, p. 22A orc9, Parallel and Perpendicular lines Make copies. (as needed)• Power Polygons™

Activity

Kinds of Angles15 Min clAss PAirs

• Power Polygons

Activity

Right Triangles15 Min clAss PAirs

• Student Activity Book, p. 22B orc10, Angles and right triangles Make copies. (as needed)• T47• Power Polygons

session FolloW-UP

Daily Practice • Student Activity Book, p. 22D orc11, sorting shapes Make copies. (as needed)

Ten-Minute MathToday’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)

pointlinerayline segmentperpendicular

lines

parallel linesangleright angleacute angleobtuse angleright triangle

today’s Plan Materials

Identifying Geometric FiguresMath Focus Points

Identifying parallel lines and perpendicular lines

Identifying right angles, acute angles, and obtuse angles

Identifying right triangles

vocabulary

cc16 investiGAtion 2 Polygons of Many types

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Point Line Ray Line Segment

Perpendicular Lines Parallel Lines

1 Activity 2 Activity 3 Activity 4 Session Follow-Up

A C T I V I T Y

Parallel and Perpendicular Lines

pAIrSClASS30 MIn

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.

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.

Session 2.3A Identifying Geometric Figures CC17

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Right Angle Acute Angle Obtuse Angle

DateNameSize, Shape, and Symmetry

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Unit 4 Session 2.3A

Parallel and Perpendicular LinesIn 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.

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.

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Can you describe examples of some things in the real world that look like perpendicular lines or parallel lines?

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.”

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.

A C T I V I T Y

Kinds of AnglespAIrSClASS15 MIn

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.

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: Obser ving Student s at Work

• Do students recognize right angles, acute angles, and obtuse angles? DotheyuseasquarecorneronaPowerPolygonorthecornerofasheetofpapertocheck?

▲ Student Activity Book, Unit 4, p. 22A; resource Masters, C9

Teaching note1 WorkingWithAngles Right, acute, and

obtuse angles are studied further in Investigation 3.

CC18 InVeSTIgATIOn 2 polygons of Many Types

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Sessions 2.3, 2.4, 2.5 Unit 4

Shape Cards (page 1 of 2)

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22B

Angles and Right TrianglesIn 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.

Session 2.3A Unit 4

INV12_SE04_U4.indd 2 6/2/11 4:07 PM


A C T I V I T Y

Right TrianglespAIrSClASS15 MIn

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?

Students should recognize both shapes as triangles, and notice the differences in the angles.

[Derek] said Shape 1 has a right angle. A triangle that has a right angle in it is called a right triangle.

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.

Have students complete Student Activity Book page 22B or C10.

DIFFerenTIATIon: Suppor ting the range of lear ner s

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.

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.

▲ Transparencies, T47

▲ Student Activity Book, Unit 4, p. 22B;resource Masters, C10

Session 2.3A Identifying Geometric Figures CC19

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22D

Sorting ShapesWrite the numbers of all the shapes that belong in each category.

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?

Session 2.3A Unit 4

note Students identify parallel sides, perpendicular sides, and obtuse angles in polygons.

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DateNameSize, Shape, and Symmetry Daily Practice

INV12_SE04_U4.indd 4 5/4/11 1:30 PM


S E S S I O N F O L L O W - U P

Daily Practice Daily Practice:Forreinforcementofthisunit’scontent,

havestudentscompleteStudent Activity Bookpage22Dor C11.

▲ Student Activity Book, Unit 4, p. 22D; Resource Masters, C11

CC20 INVESTIGATION 2 Polygons of Many Types

INV12_TE04_U04_S2.3A.indd 20 6/2/11 5:24 PM

s e s s i o n 3 . 4 A

Ten-Minute MathToday’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)

Vocabularyprotractor

Today’s Plan Materials

Lines and AnglesMath Focus Points

Drawinglines,partsoflines,andangles

Understandingtherelationshipbetweenthedegreemeasureofanangleandcirculararcs

Measuringanglesusingaprotractor

AcTiViTy

Drawing Lines and Angles20 Min clAss indiViduAls

•Student Activity Book,p.51Aorc13, drawing lines and Angles Makecopies.(asneeded)

AcTiViTy

Using a Protractor40 Min clAss PAirs

•Student Activity Book,p.51Borc14, using a Protractor Makecopies.(asneeded)

•6-inchpapercircles(1perstudent)•Protractors(1perstudent)

session Follow-uP

Daily Practice •Student Activity Book,p.51Corc15, lines and Angles Makecopies.(asneeded)

•Student Math Handbook,pp.111–112

session 3.4A lines and Angles cc21

INV12_TE04_U04_S3.4A.indd 21 6/3/11 1:17 PM

Line Ray Line Segment

Perpendicular Lines Parallel Lines

Right Angle Acute Angle Obtuse Angle

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51ASession 3.4A Unit 4

Drawing Lines and AnglesDraw an example of the figure.

1.

Line Segment

2.

Line

3.

Ray

4.

Perpendicular Lines

5.

Parallel Lines

6.

Angle

7.

Right Angle

8.

Acute Angle

9.

Obtuse Angle

INV12_SE04_U4.indd 1 5/4/11 1:31 PM

1 Activity 2 Activity 3 Session Follow-Up

A C T I V I T Y

Drawing Lines and AnglesClASS20 MIn 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.

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.

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.

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.

Have students complete Student Activity Book page 51A or C13.

▲ Student Activity Book, Unit 4, p. 51A;Resource Masters, C13

CC22 InVeSTIgATIon 3 Measuring Angles

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A C T I V I T Y

Using a ProtractorPAIrSClASS40 MIn

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.

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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? … Suppose it goes only 1 ___ 360 of the way around? Can you describe what kind of angle this would make? How many degrees would it have? Talk to a partner about your ideas.

Students might say:

“ 1 ___ 360 of the way around is a really teensy part of the whole way around. It’s like a little sliver.”

“ 1 ___ 360 of the way around is 1 ___ 360 of 360 degrees. So, it’s only 1 degree.”

Session 3.4A lines and Angles CC23

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51B Unit 4 Session 3.4A

Using a ProtractorIn Problems 1–4, use a protractor to measure each angle.

1.

degrees

2.

degrees

3.

degrees

4.

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 1 _ 8 of the circle. Without using a protractor, give the measure of the angle.

INV12_SE04_U4.indd 2 6/1/11 9:04 AM

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 1 _ 4 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°.

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.

Have students complete Student Activity Book page 51B or C14.

OngOing Assessment: Obser ving student s at Work

Studentsdeterminethedegreemeasuresofangles.

• Dostudentsunderstandthatananglethatturnsthroughnone-degreeanglesissaidtohaveananglemeasureofndegrees?

DifferentiAtiOn: suppor ting the range of Lear ner s

Somestudentsmayhavedifficultyreadingthecorrectscaleontheprotractor.Encouragethemtoidentifytheangletheyaremeasuringasacute,right,orobtusebeforetheymeasureit.Thenhavethemmeasuretheangleandchecktoseewhethertheirnumericalansweragreeswiththetypeofangletheyidentified.Ifitdoesnot,theylikelyusedthewrongscale.

Challengestudentstouseaprotractortodrawangleswithgivenmeasures.

1 Activity 2 Activity 3 session follow-Up

▲ student Activity Book, Unit 4, p. 51B;resource masters, C14

CC24 investigAtiOn 3 measuring Angles

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DateNameSize, Shape, and Symmetry Daily Practice

51CSession 3.4A Unit 4

Lines and AnglesIn Problems 1–3, draw an example of the figure.

1.

Line Segment

2.

Parallel Lines

3.

Obtuse Angle

In Problems 4 and 5, use a protractor to measure the numbered angle.

4.

1

degrees

5.

2

degrees

note Students draw geometric figures and use a protractor to measure angles.

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S E S S I O N F O L L O W - U P

Daily Practice Daily Practice:Forreinforcementofthisunit’scontent,

havestudentscompleteStudent Activity Bookpage51CorC15.

Student Math Handbook:StudentsandfamiliesmayuseStudent Math Handbookpages111–112forreferenceandreview.Seepages170–174inthebackofUnit4.

▲ Student Activity Book, Unit 4, p. 51C;Resource Masters, C15

Session 3.4A Lines and Angles CC25

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C9 © Pearson Education, Inc., or its affiliates. All Rights Reserved. 4Unit 4 Session 2.3A

Parallel and Perpendicular LinesIn 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.



For Problems 7 and 8, use the map below.

7. Name a pair of parallel streets.

8. Name a pair of perpendicular streets.


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Angles and Right TrianglesIn Problems 1–3, write right angle, acute angle, or obtuse angle.

1. 2. 3.







INV12_BLM04_U4.indd 10 6/22/11 4:56 PM


Sorting ShapesWrite the numbers of all the shapes that belong in each category.

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?


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notE Students identify parallel sides, perpendicular sides, and obtuse angles in polygons.

Daily Practice

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C12 © Pearson Education, Inc., or its affiliates. All Rights Reserved. 4Unit 4 Session 3.2

Sides and AnglesFor Problems 1 and 2, use the polygon at the right.









NOtE Students identify parallel sides, perpendicular sides, and special types of angles in polygons, and they identify right triangles.

1

2

3

4

Daily Practice

INV12_BLM04_U4.indd 12 6/23/11 3:54 PM


Drawing Lines and AnglesDraw an example of the figure.

1.

Line Segment

2.

Line

3.

Ray

4.

Perpendicular Lines

5.

Parallel Lines

6.

Angle

7.

Right Angle

8.

Acute Angle

9.

Obtuse Angle


INV12_BLM04_U4.indd 13 6/22/11 5:00 PM


Using a ProtractorIn Problems 1–4, use a protractor to measure each angle.

1.

degrees

2.

degrees

3.

degrees

4.

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 1 _ 8 of the circle. Without using a protractor, give the measure of the angle.


INV12_BLM04_U4.indd 14 6/22/11 5:02 PM

Daily Practice

C15 © Pearson Education, Inc., or its affiliates. All Rights Reserved. 4

Size, Shape, and Symmetry

Unit 4 Session 3.4A

Lines and AnglesIn Problems 1–3, draw an example of the figure.

1.

Line Segment

2.

Parallel Lines

3.

Obtuse Angle

In Problems 4 and 5, use a protractor to measure the numbered angle.

4.

1

degrees

5.

2

degrees

DateName

notE Students draw geometric figures and use a protractor to measure angles.

INV12_BLM04_U4.indd 15 6/22/11 6:08 PM

Daily Practice

C16 © Pearson Education, Inc., or its affiliates. All Rights Reserved. 4Unit 4 Session 4.3

More Lines and AnglesIn Problems 1–3, draw an example of the figure.

1.

Perpendicular Lines

2.

Ray

3.

Acute Angle

4. Use a protractor to measure each numbered angle.

Angle 1 degrees

Angle 2 degrees

Angle 3 degrees

Angle 4 degrees


notE Students draw geometric figures and use a protractor to measure angles.

4

3

2

1

INV12_BLM04_U4.indd 16 6/22/11 6:08 PM

C9 © Pearson Education, Inc., or its affiliates. All Rights Reserved. 4Unidad 4 Sesión 2.3A

Rectas paralelas y perpendicularesEn los Problemas 1 a 4, escribe punto, recta, semirrecta o segmento de recta.

1. 2. 3. 4.

En los Problemas 5 y 6 usa el polígono de la derecha.

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.

FechaNombreTamaño, forma y simetría

2

5

3

1 4

Ford

Linc

oln

Howard

Evans

Lawrence

AYUNTAMIENTO

INV12_SP_BLM04_U4.indd 9 6/20/11 8:29 PM


Ángulos y triángulos rectángulosEn 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.




Agrupar figurasEscribe los números de todas las figuras que pertenecen a cada categoría.

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?

12 3 4

6

11

12

7

8

14

13

9

5

10

notA Los estudiantes identifican lados paralelos, lados perpendiculares y ángulos obtusos en polígonos.

FechaNombreTamaño, forma y simetría Práctica diaria


C12 © Pearson Education, Inc., or its affiliates. All Rights Reserved. 4Unidad 4 Sesión 3.2

Lados y ángulosEn los Problemas 1 y 2, usa el polígono de la derecha.

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

Número de ángulos agudos

Número de ángulos obtusos

notA Los estudiantes identifican lados paralelos, lados perpendiculares y tipos de ángulos en polígonos e identifican triángulos rectángulos.

1

2

3

4




Dibujar rectas y ángulosDibuja un ejemplo de cada figura.

1.

Segmento de recta

2.

Recta

3.

Semirrecta

4.

Rectas perpendiculares

5.

Rectas paralelas

6.

Ángulo

7.

Ángulo recto

8.

Ángulo agudo

9.

Ángulo obtuso




Usar un transportadorEn los Problemas 1 a 4, usa un transportador para medir cada ángulo.

1.

grados

2.

grados

3.

grados

4.

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 1 _ 8 del círculo. Sin usar un transportador, da la medida del ángulo.


INV12_SP_BLM04_U4.indd 14 7/21/11 7:18 AM


Rectas y ángulosEn los Problemas 1 a 3, dibuja un ejemplo de cada figura.

1.

Segmento de recta

2.

Rectas paralelas

3.

Ángulo obtuso

En los Problemas 4 y 5, usa un transportador para medir el ángulo numerado.

4.

1

grados

5.

2

grados

notA Los estudiantes dibujan figuras geométricas y usan un transportador para medir ángulos.



C16 © Pearson Education, Inc., or its affiliates. All Rights Reserved. 4Unidad 4 Sesión 4.3

Más rectas y ángulosEn los Problemas 1 a 3, dibuja un ejemplo de cada figura.

1.

Rectas perpendiculares

2.

Semirrecta

3.

Ángulo agudo

4. Usa un transportador para medir los ángulos numerados.

Ángulo 1 grados

Ángulo 2 grados

Ángulo 3 grados

Ángulo 4 grados

notA Los estudiantes dibujan figuras geométricas y usan un transportador para medir ángulos.

4

3

2

1



polygons of many types - tusd1.orgpolygons of many types, continued day session common core...

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