Classify Quadrilaterals€¦ · Classify Quadrilaterals Learning Objective Describe, classify, and compare quadrilaterals based on their sides and angles. Language Objective Students

723A Chapter 12

LESSON AT A GLANCE

Ch t 12

About the MathProfessional Development

LESSON 12.5

Interactive Student Edition

Personal Math Trainer

Math on the Spot Video

Animated Math Models

iTools: Geometry

HMH Mega Math

Professional Development Videos

Why Teach This Students learned how to describe sides of polygons and about types of angles earlier in this chapter. Those topics provide students with a foundation to describe, classify, and compare quadrilaterals.Quadrilaterals can be described by the types of sides and by the lengths of the sides that they have. A rectangle has two pairs of opposite sides that are parallel, two pairs of sides of equal length, and four right angles. A rhombus has two pairs of opposite sides that are parallel, four sides of equal length, and could have right angles. A square has two pairs of opposite sides that are parallel, four sides of equal length, and four right angles. The term “trapezoid” may have two different meanings. One meaning is that a trapezoid is a quadrilateral with exactly one pair of parallel sides. Another meaning is that it is a quadrilateral with at least one pair of parallel sides. In this book, the latter definition is used.These different meanings will result in different classifications. For example, according to the first meaning, a rectangle is not a trapezoid and according to the second meaning, a rectangle is a trapezoid.

Classify Quadrilaterals

Learning ObjectiveDescribe, classify, and compare quadrilaterals based on their sides and angles.

Language ObjectiveStudents demonstrate and explain how to use the sides and angles to describe quadrilaterals.

MaterialsMathBoard

F C R Focus:Common Core State Standards

3.G.A.1 Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories.

MATHEMATICAL PRACTICES (See Mathematical Practices in GO Math! in the Planning Guide for full text.)MP2 Reason abstractly and quantitatively. MP4 Model with mathematics. MP6 Attend to precision.

F C R Coherence:Standards Across the GradesBefore2.G.A.1

Grade 3 3.G.A.1

After4.G.A.2

F C R Rigor:Level 1: Understand Concepts....................Share and Show ( Checked Items)Level 2: Procedural Skills and Fluency.......On Your Own, Practice and HomeworkLevel 3: Applications..................................Think Smarter and Go Deeper

F C R For more about how GO Math! fosters Coherence within the Content Standards and Mathematical Progressions for this chapter, see page 695J.

FOCUS COHERENCE RIGOR

Lesson 12.5 723B

ENGAGE1Daily Routines

Common Core

Lesson 12.5 723B

How can you use sides and angles to help you

describe quadrilaterals?

with the Interactive Student Edition

Essential QuestionHow can you use sides and angles to help you describe quadrilaterals?

Making ConnectionsInvite students to tell you what they know about figures.

What figures do you remember learning about? Triangle, square, circle, etc.

What do squares, rectangles, rhombuses, and trapezoids have in common? They have 4 sides and 4 angles.

Learning ActivityWhat is the problem the students are trying to solve? Connect the story to the problem.

• What do you know about the shape of the sign? It has 4 sides and 4 angles.

• What are other characteristics about the figure that you notice? Answers may vary.

Literacy and MathematicsChoose one or more of the following activities.

• Have students use dot paper to draw 5 to 10 four-sided figures. Have them write about the characteristics that they notice about their figures.

• Have students draw as many road signs as they can. Have students describe the characteristics of each sign.

Vocabulary Builder• Write each of the vocabulary words on

the board.

• Draw a picture of a square, a rectangle, a rhombus, a trapezoid, and a quadrilateral that is none of these.

• Have students come up to the board and write an appropriate vocabulary word under each of the pictures.

• Note that more than one of the vocabulary words may be used to describe a square.

Problem of the Day 12.5The area of a county is 578 square miles. What is 578 rounded to the nearest hundred?

______

Vocabulary rectangle, rhombus, square, trapezoid

Interactive Student EditionMultimedia Glossary e

600

DifferentiatedInstruction1

2

3 DDDDDDDiDiDiDiDiDiDD fff erentiatedIInInnnIInststruructctioionn

Unlock the ProblemUnlock the Problem

Some quadrilaterals cannot be classified as a trapezoid, rectangle, square, or rhombus.

Name

Chapter 12 723

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NameLesson 12.5

Classify QuadrilateralsEssential Question How can you use sides and angles to help you describe quadrilaterals?

Quadrilaterals are named by their sides and

their angles.

quadrilateral

__ sides

__ angles

trapezoid

at least __ pair of opposite sides that are parallel lengths of sides could be the same

rectangle

_ pairs of opposite sides that are parallel

_ pairs of sides that are of equal length

_ right angles

square


_ sides that are of equal length

_ right angles

rhombus


_ sides that are of equal length

Describe quadrilaterals.

Geometry—3.G.A.1

MATHEMATICAL PRACTICESMP1, MP6, MP8

MathTalk MATHEMATICAL PRACTICES 8

Generalize Why can a square also be named a rectangle or a rhombus?

4

2

2

Possible explanation: a square is a rectangle because it

has 2 pairs of opposite sides that are parallel, 2 pairs of

sides of equal length, and 4 right angles. A square is a rhombus

because it has 2 pairs of opposite sides that are parallel and

4 sides of equal length.

4

4

2

4

4

2

4

1

EXPLORE2

rhombustrapezoid

rectanglesquare

Name

2 pairs of opposite sides that are parallel

4 sides that are of equal length

at least 1 pair of opposite sides that are parallel

lengths of sides could be the same


2 pairs of sides that are of equal length

4 right angles


4 sides that are of equal length

4 right angles

Circle all the words that describe the quadrilateral.

1. 2. 3.

square

rhombus

trapezoid

square

rectangle

quadrilateral

square

rectangle

rhombus

You can classify quadrilaterals by their sides and by their angles.

How can you classify the quadrilateral?

It has only 1 pair of opposite sides that are parallel.

The lengths of all 4 sides are not equal.

So, the quadrilateral is a trapezoid.


Lesson 12.5Reteach

12-13 ReteachChapter Resources© Houghton Mifflin Harcourt Publishing Company

Name

Quadrilateral Riddles

Read the riddles and name the shape that is

being described.

1. I am a quadrilateral with exactly 1 pair of opposite sides that are parallel. What shape am I?

2. I am a quadrilateral that always has 4 sides that are of equal length and 4 right angles. What shape am I?

3. I am a quadrilateral with 2 pairs of opposite sides that are parallel, 2 pairs of sides that are of equal length, and 4 right angles. I am not a square. What shape am I?

4. I am a polygon with 4 sides and 4 angles. I do not have any pairs of opposite sides that are parallel. What shape am I?

5. Jerome drew a shape and described it as a square. Kayla described it as a rectangle. Luis described it as a rhombus. Can they all be correct? Explain.

Lesson 12.5Enrich

squaretrapezoid

quadrilateral

Yes; possible answer: a square is also

a rhombus because it has 4 sides of equal

length. A square is also a rectangle because

it has 2 pairs of opposite sides that are

parallel and 2 pairs of sides that are of

equal length.

Possible answers: rectangle, trapezoid

12-14 EnrichChapter Resources© Houghton Mifflin Harcourt Publishing Company

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3333

1

2

3 DifferentiatedInstruction

723 Chapter 12

LESSON 12.5

Enrich 12.5Reteach 12.5

Unlock the ProblemMATHEMATICAL PRACTICES

MP6 Attend to precision. Have students make connections to what they already know about quadrilaterals.

• What is true about all quadrilaterals? They all have four sides and four angles.

• How might quadrilaterals be different? Possible answer: they might have different kinds of angles, and not every quadrilateral will have the same number of sides of equal length.

Have students look at each quadrilateral.

• Which quadrilaterals can have two pairs of opposite sides that are parallel? square, rectangle, trapezoid, and rhombus

• Are all quadrilaterals also rectangles? Explain. No; possible explanation: a trapezoid is a quadrilateral, but it may not a rectangle.

• Are all rectangles also trapezoids? Explain. Yes; possible explanation: trapezoids have at least 1 pair of opposite sides that are parallel and rectangles have 2 pairs of opposite sides that are parallel.

MathTalk Use Math Talk to focus on students’

understanding of why a square is a special type of rectangle and rhombus.

In Grade 4, students will learn that a rectangle, a square, and a rhombus can also be classified as a parallelogram.

ELL Strategy: Understand Context

Students use prior knowledge and context to understand the concept of a pair.

• Explain that a pair is two of something, not a fruit (like pear). Point out things that come in pairs: a pair of shoes, a pair of socks, or a pair of gloves.

• Show two gloves. Here is one pair of gloves. How many gloves are there? 2

• Add two more gloves. Here are two pairs of gloves. How many gloves are there now? 4

• Repeat the activity with other pairs of objects they suggest.

MP2 Reason abstractly and quantitatively. • How can you check if two sides of a

quadrilateral are parallel? Possible answer: The sides are parallel if they never cross.

3.G.A.1 Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories.

On Your OwnOn Your Own

Share and ShShare and ShShare and Show MATHBOARDMATHBOARD

724

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4.

rectangle

rhombus

square

trapezoid

5.

rhombus

quadrilateral

square

rectangle

6.

rectangle

rhombus

trapezoid

quadrilateral


7.

rectangle

trapezoid

quadrilateral

rhombus

8.

rectangle

rhombus

trapezoid

square

9.

quadrilateral

square

rectangle

rhombus

Look at the quadrilateral at the right.

1. Outline each pair of opposite sides that are parallel

with a different color. How many pairs of opposite sides

appear to be parallel? __

2. Look at the parallel sides you colored.

The sides in each pair are of __ length.

3. Name the quadrilateral in as many ways as you can.

____


Think: All the angles are right angles.

MathTalk MATHEMATICAL PRACTICES 1

Analyze How can you have a rhombus that is not a square?

2 pairs

equal

rectangle, trapezoid

See below.

Check students’ drawings.

Math Talk: Possible explanation: a rhombus has 4 sides of

equal length, like a square. But a rhombus may not have 4 right angles, like a square.

COMMON ERRORS

Quick Check

If

Rt I RR1

2

3

Then

EXPLAIN3

Advanced Learners

Lesson 12.5 724

Error Students may not identify a square as a rectangle or a rhombus.

Example Students may not circle rectangle or rhombus in Exercise 9.Springboard to Learning Review the properties of a square, a rectangle, and a rhombus. Point out that a square is a special kind of rectangle and a special kind of rhombus.

Share and Show MATHBOARDMATHBOARDMBMMMBBBMATHABOARDMMMAAATHATHTHHAAAAAAAAATTAAAABOARDBOARDBOARD

The first three problems connect to the learning model. Have students use the MathBoard to explain their thinking.Use the checked exercises for Quick Check.

MathTalk Use Math Talk to focus on

comparing properties of quadrilaterals to classify them.

Suggest students use a ruler to determine if sides are or are not equal in length. Students may also use the corner of a piece of paper to help decide if an angle is a right angle.

On Your OwnWhen students have finished Exercises 7–9, ask:

• How can you prove that the quadrilateral in Exercise 7 is NOT a rhombus or a square? All 4 sides are not equal in length.

• How can you prove that the shape in Exercise 8 is a trapezoid? It has at least one pair of parallel sides.

a student misses the checked exercises

Differentiate Instruction with • Reteach 12.5

• Personal Math Trainer 3.G.A.1

• RtI Tier 1 Activity (online)

Visual / SpatialIndividual

Materials ruler, Dot Paper (see eTeacher Resources)

• Write the following directions on the board and have students draw each shape on square dot paper.

1. Draw a quadrilateral with 2 right angles and exactly 1 pair of opposite sides that are parallel.

2. Draw a quadrilateral with 2 pairs of opposite sides that are parallel and 2 angles that are greater than a right angle.

• Then have students draw another quadrilateral and write directions for how to draw it. Possible directions: Draw a quadrilateral with 4 right angles and all sides of equal length.

AB

D

C

F

E

Chapter 12 • Lesson 5 725

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NameName

10. Which quadrilaterals appear to have

4 right angles?

11. Which quadrilaterals appear to have

2 pairs of opposite sides that are parallel?

12. Which quadrilaterals appear to have no right

angles?

Use the quadrilaterals at the right for 10–12.

13. The opposite sides of _ rectangles

are parallel.

15. _ squares are rectangles.

17. _ quadrilaterals are polygons.

14. _ sides of a rhombus are the

same length.

16. _ rhombuses are squares.

18. _ polygons are quadrilaterals.

Write all or some to complete the sentence for 13–18.

19. MATHEMATICALPRACTICE 6 Circle the shape at the

right that is not a quadrilateral. Explain

your choice.

20. SMARTER I am a polygon that has 4 sides and 4 angles. At

least one of my angles is less than a right angle. Circle all

the shapes that I could be.

quadrilateral rectangle square rhombus trapezoid

B, C

B, C, D

D, E, F

Possible explanation: I circled the pentagon

because it has 5 sides and 5 angles. All

quadrilaterals have 4 sides and 4 angles.

all All

All Some

SomeAll

ELABORATE4

Math on the Spot videos are in the Interactive Student Edition and at www.thinkcentral.com.

725 Chapter 12

Explain to students that in Exercises 10–12, they should write the letter names of the quadrilaterals that answer each question. Point out that each exercise has more than one answer.MP6 Attend to precision. Discuss the definition of quadrilaterals with students. Help students understand that a quadrilateral has 4 sides and 4 angles. Guide students to count the number of sides and angles in each shape. Then, ask:

• If the shape in Exercise 19 is not a quadrilateral, what shape is it? It is a pentagon.

• Can a trapezoid have exactly two right angles? Explain. Yes; it can have exactly two right angles and still have one pair of opposite sides that are parallel. For example, quadrilateral A is a trapezoid with two right angles.

SMARTER

Exercise 20 requires students to visualize a polygon that is drawn based on the properties of quadrilaterals.

To extend students’ thinking, have students write the name of a quadrilateral and then write a description of it in their own words. Tell them to be sure to write enough information so that if anyone draws it using the description, they will draw the correct shape. Then have volunteers read their descriptions while other volunteers identify the shapes.

Math on the Spot Video TutorUse this video to help students model and solve this type of Think Smarter problem.

Problem Solving • Applications

Differentiated Centers Kit

DIFFERENTIATED INSTRUCTION INDEPENDENT ACTIVITIES

WRITE Math Show Your Work

MATHEMATICAL PRACTICES ANALYZE

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Compare and ContrastWhen you compare, you look for

ways that things are alike. When

you contrast, you look for ways

that things are different.

Mr. Briggs drew some shapes on

the board. He asked the class to

tell how the shapes are alike and

how they are different.

DEEPER Complete the sentences.

• Shapes _ , _ , _ , _ , _ , _ , and _ are polygons.

• Shapes _ , _ , and _ are not polygons.

• Shapes _ , _ , _ , and _ are quadrilaterals.

• Shapes _ , _ , and _ appear to have only 1 pair of opposite sides that are parallel.

• Shapes _ , _ , and _ appear to have 2 pairs of opposite sides that are parallel.

• All 4 sides of shapes _ and _ appear to be the same length.

• In these polygons, all sides do not appear to be the same length. ____

• These shapes can be called rhombuses. ____

• Shapes _ and _ are quadrilaterals but cannot be called rhombuses.

• Shape _ is a rhombus and can be called a square.

21. SMARTER Identify the quadrilateral that can have two pairs

of parallel sides and no right angles.

A rhombus B square C rectangle

A, B, G, H, I

E, F

A

C

A B E F G H I

E

A

F

B

G

I

E

D

F

J

G

E F

F

A G

EVALUATE5 Formative Assessment

Differentiated Centers Kit

DIFFERENTIATED INSTRUCTION INDEPENDENT ACTIVITIESD

Lesson 12.5 726

Essential QuestionUsing the Language ObjectiveReflect Have students demonstrate and explain to a partner to answer the Essential Question. How can you use sides and angles to help you describe quadrilaterals? All quadrilaterals have 4 sides and have special names if the sides are parallel or perpendicular, or equal in length.

Math Journal WRITE MathExplain how a trapezoid and rectangle are different.

Students complete purple Activity Card 18 by identifying

and defining two-dimensional shapes by playing a game.

Students complete orange Activity Card 18 by

classifying two-dimensional shapes based on their attributes.

ActivitiesClassification Act

ActivitiesWhat Figure?

MATHEMATICAL PRACTICES

SMARTER

This item assesses a student’s ability to classify a quadrilateral based on its sides and angles. Students should recognize that both a square and a rectangle have 4 right angles, and therefore know that the rhombus is the only shape that could fulfill both conditions.

Connect to ReadingStudents will learn the reading skill compare and contrast by considering the attributes of the polygons shown.

Practice and HomeworkUse the Practice and Homework pages to provide students with more practice of the concepts and skills presented in this lesson. Students master their understanding as they complete practice items and then challenge their critical thinking skills with Problem Solving. Use the Write Math section to determine student’s understanding of content for this lesson. Encourage students to use their Math Journals to record their answers.

727 Chapter 12

A B C ED

Problem SolvingProblem Solving

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Lesson 12.5Practice and Homework



Use the quadrilaterals below for 4–6.

7. A picture on the wall in Jeremy’s

classroom has 4 right angles,

4 sides of equal length, and 2 pairs

of opposite sides that are parallel.

What quadrilateral best describes

the picture?

8. WRITE Math Explain how a

trapezoid and a rectangle are different.

Chapter 12 727

1.

square

rectangle

rhombus

trapezoid

2.

square

rectangle

rhombus

trapezoid

3.

square

rectangle

rhombus

trapezoid

4. Which quadrilaterals

appear to have no right

angles?


appear to have 4 right

angles?


appear to have 4 sides

of equal length?

COMMON CORE STANDARD—3.G.A.1 Reason with shapes and their attributes.

square

B, D, and E A and C B, C, and D

Possible explanation: a rectangle

has 2 pairs of parallel sides, where a

trapezoid has at least 1 pair of parallel

sides.

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Com

pany

Continue concepts and skills practice with Lesson Check. Use Spiral Review to engage students in previously taught concepts and to promote content retention. Common Core standards are correlated to each section.

Lesson 12.5 728

Personal Math Trainer

FOR MORE PRACTICE GO TO THE

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Lesson Check (3.G.A.1)

1. What word describes the

quadrilateral?

2. Which quadrilaterals appear to

have 2 pairs of opposite sides that

are parallel?

A B C

Spiral Review (3.G.A.1)

5. What word describes the dashed

sides of the shape shown? Write

intersecting, perpendicular, or

parallel.

6. How many right angles does this

shape have?

3. Aiden drew the the polygon shown.

What is the name of the polygon

he drew?

4. How many pairs of parallel sides

does this shape appear to have?

trapezoid

decagon

parallel

A and B

2 pairs

0 right angles

Documents

Classify Quadrilaterals€¦ · Classify Quadrilaterals Learning Objective Describe, classify, and compare quadrilaterals based on their sides and angles. Language Objective Students