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Math on the Spot Video Tutor Online Assessment

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Soar to Success Math Online Intervention

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Digital ManagementCenter organizes program resources by TEKS!

Interactive Student Edition provides students

with an interactive learning environment!

Resources

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Texas Essential Knowledge and Skills

Geometry and Measurement—3.6.A Classify and sort two- and three-dimensional solids, including cones, cylinders, spheres, triangular and rectangular prisms, and cubes, based on attributes using formal geometric language 3.6.B Use attributes to recognize rhombuses, parallelograms, trapezoids, rectangles, and squares as examples of quadrilaterals and draw examples of quadrilaterals that do not belong to any of these subcategories

MATHEMATICAL PROCESSES3.1.D Communicate mathematical ideas and reasoning 3.1.F Analyze mathematical relationships

Are You Ready?Access Prior KnowledgeUse the Are You Ready? 15.1 in the Assessment Guide to assess students’ understanding of the prerequisite skills for this lesson.

Vocabularyangle, vertex, right angle, parallel

lines, quadrilateral, trapezoid,

parallelogram, rectangle, square,

rhombus

Go to Multimedia eGlossary at thinkcentral.com

15.1 Classify Quadrilaterals How can you use right angles and parallel sides to help you classify quadrilaterals?

Essential Question?

Lesson OpenerMaking 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.)

Using the Digital LessonYou may wish to have large pictures of a rectangle, rhombus, square, and trapezoid to use as visual aids when discussing the figures.

Learning TaskWhat 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.)

• Are any of the sides equal in length? (Yes)

• 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.

How can you use right angles and parallel sides

to help you classify quadrilaterals?

Lesson 15.1 481A

Essential Question?

Unlock the ProblemUnlock the Problem

endpoint

ray

Name

How can you use right angles and parallel sides to help you classify quadrilaterals?

Geometry and Measurement—3.6.A, 3.6.B

MATHEMATICAL PROCESSES3.1.D, 3.1.F

15.1 Classify Quadrilaterals

An angle is formed by two rays that share an

endpoint. Two dimensional figures have angles

formed by two line segments that share an endpoint.

The shared endpoint is called a vertex. The plural of

vertex is vertices.

Jason drew this polygon

on dot paper.

There are __ angles.

There are __ sides.

Jason’s polygon has 2 right angles. They form

square corners. You can use the corner of a sheet of

paper to tell if an angle is a right angle. Draw boxes

to show the right angles.

Look at Jason’s polygon.

How many pairs of sides

are parallel?

Lines that appear to never cross or meet and are always

the same distance apart are parallel lines.

So, Jason’s polygon has __ pair of parallel sides.

Math Idea

A polygon is a closed plane figure with straight sides that are line segments.

Think: Which sides will never cross or meet?

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English Language Learners Language SupportELLLeveled Activities ELPS

Beginning: Activity 20 1.A.1, 3.G.2, 4.C.3

Intermediate: Activity 25 1.A.2, 3.D.2, 3.H.3, 4.D

Advanced: Activity 58 2.C.2, 4.C.3, 4.F.9

Advanced High: Activity 43 4.F.8, 4.G.2, 4.G.4

Go to thinkcentral.com for the ELL Activity Guide containing these leveled activities.

Strategy: Explore Context Materials: pairs of things such as shoes, socks, gloves

• Students use prior knowledge to understand expressions.• Explain that a pair is two of something. 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

• Show students a rectangle and discuss the pairs of parallel sides. Help students see that there are two sides in each pair.

ELPS 2.C.1, 2.C.2, 2.I.3

Auditory / Visual Small Group

Unlock the Problem This lesson lays the foundation for classifying and measuring angles in later grades.

• What do we call a plane figure with straight sides that are line segments? a polygon

• How do you know that two of the angles in Jason’s polygon are right angles? You can compare the angles to the corner of a sheet of paper.

• If you rotate Jason’s figure so the square corners are both on the bottom or both on the top, are they still right angles? Explain. Yes; possible explanation: changing the position of the angle will not change the type of angle.

• How would you describe the other angles in Jason’s polygon? Possible answer: one angle is greater than a right angle and one angle is less than a right angle.

Review with students the meaning of the word parallel.

• Who can give a real-world example of parallel lines? Possible answer: railroad tracks, steps on a ladder, chains on a swingset

• Why can’t parallel lines ever cross? The lines are always the same distance apart.

• Why aren’t the blue and pink sides of Jason’s shape parallel? The lines cross or meet at a right angle.

• How could you change the shape so there would be 2 pairs of parallel sides? Make the blue side as long as the green side and the orange side as long as the pink side.

481 Module 15

ERROR AlertSome quadrilaterals cannot be classified as a trapezoid, parallelogram, rectangle, square, or rhombus.

Mathematical ProcessesMath Talk

rectangle

_ pairs of opposite

sides that are parallel

_ pairs of sides that

are of equal length

_ right angles

square

_ pairs of opposite

sides that are parallel

_ sides that are of

equal length

_ right angles

rhombus

_ pairs of opposite

sides that are parallel

_ sides that are of

equal length

Classify Quadrilaterals Quadrilaterals are

named by their sides and their angles.

Describe quadrilaterals.

quadrilateral

__ sides

__ angles

parallelogram

__ pairs of opposite sides that are parallel

__ pairs of sides that are of equal length

trapezoid

exactly __ pair of opposite sides that are parallel

lengths of sides could be the same

Explain why a square can also be named

a rectangle or a rhombus.

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.

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Go to Go to thinkcentral.com for additional enrichmentactivities in the Enrich Activity Guide.

Enrich

Classify QuadrilateralsDiscuss with students the meaning of opposite. Ask them to use the word as they would in everyday life. Then discuss the meaning of the word as it pertains to sides of quadrilaterals.

• Draw a quadrilateral on the board and indicate opposite sides by drawing arrows that point to each side. Draw an arrow that points to an adjacent side as well.

• Ask students to identify the pair of opposite sides and to explain their choice.

Have students make connections to what they have learned 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 or the same number of pairs of parallel sides.

Have students look at each quadrilateral to complete the descriptions of the quadrilaterals. Then ask:

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

• Which quadrilaterals are also parallelograms? Explain. square, rectangle, and rhombus because opposite sides are parallel and of equal length

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

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.

Visual / SpatialIndividual

Math Talk Use Math Talk to focus on students’ understanding of why a square is a special type of rectangle and rhombus.

Mathematical Processes

COMMON ERRORSError Students may not identify a square as a rectangle or a rhombus.

Example Students may not remember the attributes of a rectangle or a rhombus when identifying possible names for a square.

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.

CE

Lesson 15.1 482

Problem SolvingProblem Solving

Share and ShowShare and Show

rhombus

parallelogram

square

rectangle

rectangle

rhombus

square

parallelogram

a c

b

d

Name

4. 5.

6. The opposite sides of _

rectangles are parallel.

8. _ rhombuses are squares.

7. _ sides of a rhombus are the

same length.

9. _ trapezoids have 1 pair of

opposite sides that are parallel.

Look at the quadrilateral at the right.

1. How many right angles are in the quadrilateral?

__ right angles

2. Which sides appear to be parallel? ____

3. Name the quadrilateral. ____

Circle all the words that describe the quadrilateral.

10. Communicate I am a quadrilateral that has no right angles

and 4 sides that are of equal length. What figure am I?

11. Multi-Step I am a polygon that has 4 sides

and 4 angles. All of my angles are right angles. Circle all the

figures that I could be.

Analyze Write all or some to complete the sentence for 6–9.

quadrilateral rectangle square rhombus

trapezoid parallelogram

4

a and c, b and d

rectangle

all All

AllSome

rhombus

Module 15 • Lesson 1 483

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square rectangle

rhombus

trapezoid

parallelogram

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Name

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

How can you classify the quadrilateral?

It has only 1 pair of sides that are parallel.The lengths of all 4 sides are not equal.So, the quadrilateral is a trapezoid.

Circle all the words that describe the quadrilateral.

1. 2. 3.

Classify QuadrilateralsOBJECTIVE Describe, classify, and compare quadrilaterals based on their sides and angles.

LESSON 72

• 2 pairs of opposite sides that are parallel

• 2 pairs of opposite sides that are of equal length

• 4 right angles

• 2 pairs of opposite sides that are parallel

• 4 sides that are of equal length• 4 right angles

• 2 pairs of parallel sides• 2 pairs of equal sides

• 2 pairs of opposite sides that are parallel

• 4 sides that are of equal length

• 1 pair of opposite sides that are parallel; lengths of sides could be the same

square

rhombus

trapezoid

square

rectangle

parallelogram

square

rectangle

rhombus

3.6.A, 3.6.B

Geometry and Measurement 143 © Houghton Mifflin Harcourt Publishing Company

Name

E69Enrich

Enrich 69

Quadrilateral Riddles

Read the riddles and name the plane fi gure 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 with 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 plane figure and described it as a square. Kayla described it as a rectangle. Luis described it as a rhombus. Can they all be correct? Explain.

rectangle

Yes; possible answer: a square is also a rhombus because it has 4 sides of equallength. 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.

quadrilateral

trapezoidPossible answers: square, rhombus,

rectangle

Enrich 69RtI Tier 1 Lesson 72

Problem SolvingProblems

Exercises 6–9 require students to analyze attributes of quadrilaterals.

Problem 11 requires students to visualize which quadrilaterals can be named, given the properties listed.

Go DeeperTo 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 figure. Then have volunteers read their descriptions while other volunteers identify the figures.

Share and ShowThe first three problems connect to the learning model. Have students use the MathBoard to explain their thinking.

Use the checked exercises for Quick Check.

1

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a student misses the checked exercises

Quick Check

IF

THENDifferentiate Instruction withRtI Tier 1 Lesson 72

Math on the Spot Video Tutor

Through the Math on the Spot Video Tutor, students will be guided through an interactive solving of this type of H.O.T. problem. Use this video to also help students solve the H.O.T. problem in the Interactive Student Edition. With these videos and the H.O.T. problems, students will build skills needed in the TEXAS assessment.

MV

Math on the Spot videos are in theInteractive Student Edition and atthinkcentral.com.

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483 Module 15

Daily Assessment TaskDaily Assessment Task

Mathematical Processes

TEXAS Test Prep 15. What is a true statement about the quadrilateral

at the right?

A There is 1 right angle.

B There are 4 right angles.

C There are no right angles.

D There are 2 right angles.

Fill in the bubble for the correct answer choice.

12. While playing football after school, Jesse notices

that the distance marker contains a quadrilateral

with one pair of opposite sides that are parallel.

What type of quadrilateral is it?

A rectangle

B trapezoid

C square

D rhombus

13. Dean makes a pattern using 10 square tiles. How many

pairs of opposite sides are parallel in the 10 square tiles?

A 20 C 40

B 10 D 0

14. Multi-Step Carina is using scraps of fabric

to make a quilt. How many of the fabric

scraps are in the shape of rhombuses?

A 1 C 0

B 2 D 3

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Daily Assessment Task 1

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• Soar to Success MathWarm-Up 38.31

• Enrich 69

• Homework and Practice Lesson 15.1

Differentiated Centers Kit

ActivitiesWhat Figure? Students complete purple Activity Card 18 by identifying and defining two-dimensional figures by playing a game.

Can students use right angles and parallel sides to classify quadrilaterals?

TEXAS Test Prep CoachTest Prep Coach helps teachers to identify common errors that students can make.

In the Test Prep exercise, if students selected:

A They do not see the second right angle in the trapezoid.

B They think all 4 angles are right angles in the trapezoid.

C They are unable to identify the 2 right angles in the trapezoid.

Essential Question? WriteMathWriteMath

How can you use right angles and parallel sides to help you classify quadrilaterals? All quadrilaterals have 4 sides and 4 angles, and have special names if the opposite sides are parallel or equal in length, or if the angles are right angles.

ActivitiesClassification ActStudents complete orange Activity Card 18 by classifying two-dimensional figures based on their attributes.

Lesson 15.1 484

TEXAS Test PrepLesson CheckLesson Check

9. Lily makes an art poster that has

exactly one pair of opposite sides

that are parallel and 2 sides that are

the same length. What figure is Lily’s

poster?

A trapezoid

B rectangle

C rhombus

D parallelogram

10. Desmond draws a polygon that has

4 sides that are the same length and

no right angles. How can Desmond

classify the polygon he drew?

A square

B rhombus

C rectangle

D parallelogram

11. Kara makes the kite shown at the

right from 4 triangles. What is the

shape of Kara’s kite?

A square

B parallelogram

C rhombus

D quadrilateral

12. Multi-Step Ben is making cutouts

to use in an art design. How many

of the cutouts have the shape of

a rectangle?

A 5

B 2

C 4

D 3

Fill in the bubble completely to show your answer.

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Problem SolvingProblem Solving

Homeworkand Practice

Name

Circle all the words that describe the quadrilateral.

1. 2.

3. __ rectangles are squares.

5. __ parallelograms have

all 4 sides that are equal in length.

4. __ angles of a rectangle

are right angles.

6. __ trapezoids have

2 sides that are equal in length.

Classify Quadrilaterals15.1

Geometry and Measurement—3.6.A, 3.6.BMATHEMATICAL PROCESSES 3.1.D, 3.1.F

parallelogram

trapezoid

rhombus

rectangle

square

quadrilateral

rectangle

parallelogram

trapezoid

rhombus

parallelogram

trapezoid

rhombus

rectangle

Write all or some to complete the sentence for 3–6.

7. I am a polygon that has 2 pairs of opposite sides that are

parallel. Circle all of the figures that I could be.

8. I am a quadrilateral that has 4 right angles. My opposite

sides are parallel and of equal length. What figure am I?

Some

square

Some Some

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Homework and PracticeUse the Homework and Practice pages to provide students with more practice on the concepts and skills of this lesson.

485-486 Module 15