Describe Plane Shapes - €¦ · 697A Chapter 12 About the Math Professional Development LESSON AT...

697A Chapter 12

About the MathProfessional Development

LESSON AT A GLANCE

LESSON 12.1

Interactive Student Edition

Personal Math Trainer

Math on the Spot

Animated Math Models

iTools: Geometry

Professional Development Videos

Why Teach This Plane geometry is the study of figures in a plane or flat surface. Students need to understand the following geometric terms because other geometric concepts and terms are built upon them.

A plane is a flat, continuous, unending surface. Planes can contain points (exact locations in space), lines (straight, continuous, unending collections of points), line segments (parts of lines with two endpoints), and rays (parts of lines with one endpoint that continues in one direction without end).

Plane shapes are two-dimensional. A closed shape, such as a circle or square, starts and ends at the same point. An open shape does not start and end at the same point.

Describe Plane Shapes

Learning ObjectiveIdentify and describe attributes of plane shapes.

Language ObjectiveStudent pairs brainstorm then check the textbook to list some ways to describe two-dimensional shapes.

MaterialsMathBoard

F C R Focus:Common Core State Standards3.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 PRACTICESMP5 Use appropriate tools strategically. MP6 Attend to precision. MP7 Look for and make use of structure.

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 OwnLevel 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

Multimedia and Technology

ENGAGE1

Lesson 12.1 697B

with the Digital Lesson

Essential QuestionTE_BdyTxt

Making ConnectionsTE_BdyTxt

zTE_Bold

Learning TaskTE_BdyTxtTE_BdyTxtTE_BdyTxt

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• TE_BullLst

Literacy and Mathematics• TE_BdyTxt

Problem of the Day X.XBasic Facts Use counters. Add.

1.NumList

2.NumList

3.NumList

Vocabulary

How do you make a ten to help you

subtract ?

Daily RoutinesCommon Core

Daily RoutinesCommon Core

Lesson 12.1 697B

ENGAGE1

Vocabulary BuilderWord Pictures Listthevocabularywordsontheboardwithanumbernexttoeachword.Randomlydrawpicturestoillustrateeachword.Havestudentsholdupfingerstomatchthenumbernexttothewordthatyouhaveillustrated.

Problem of the Day 12.1Frankmadeafruitsalad.Heused1_4cupofgrapes,3_4cupofstrawberries,and1_2cup

ofmelon.Listthefractions1_4,3_4,and1_2inorderfromleasttogreatest.

______

Vocabulary closed shape,endpoint,line,line segment,open shape,plane shape,point,ray,two-dimensional shape

• Interactive Student Edition• Multimedia Glossary e

with the Interactive Student Edition

Essential QuestionWhataresomewaystodescribetwo-dimensionalshapes?

Making ConnectionsAskstudentstotellwhattheyknowaboutshapes.

• Look around the room. Name some shapes you see. Answers will vary.

• What is different between a triangle and a square? A triangle has 3 sides. A square has 4 sides.

• How are a square and a rectangle alike? Both have 4 sides. How are they different? A square has all sides the same length.

Learning ActivityWhatistheproblemthestudentsaretryingtosolve?Connectthestorytotheproblem.

Askthefollowingquestions.

• What shape is Lucia wondering about? the stop sign

• What does she want to know about the shape? how many line segments it would take to draw it

Literacy and MathematicsViewthelessonopenerwiththestudents.Then,chooseoneormoreofthefollowingactivities:

• Havestudentsdrawashapeongridpaper.Havethemusemathtermstodescribetheirshape.

• Havestudentswriteabouttheshapestheyseeintheclassroomorinaphoto.Havestudentsusemathtermstodescribewhattheysee.

1 _ 4 , 1 _ 2 , 3 _ 4

What are some ways to describe two-dimensional

shapes?

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EXPLORE2

1

2

3

point

endpoints

Unlock the ProblemUnlock the Problem

Name

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Some plane shapes are made by connecting line segments at their endpoints. One example is a square.Describe a square using math words.

A square has _ line segments. The line

segments meet only at their ___.

Think: How many line segments and endpoints does a square have?

Describe Plane ShapesEssential Question What are some ways to describe two-dimensional shapes?

An architect draws plans for houses, stores, offices, and other buildings. Look at the shapes in the drawing at the right.

A plane shape is a shape on a flat surface. It is formed by points that make curved paths, line segments, or both.

point• is an exact position

or location

endpoints• points that are used

to show segments of lines

line• is a straight path

• continues in both directions

• does not end

line segment• is straight

• is part of a line

• has 2 endpoints

Lesson 12.1

ray• is straight • is part of a line • has 1 endpoint • continues in one direction

Geometry—3.G.A.1

MATHEMATICAL PRACTICESMP1, MP3, MP6

MathTalk MATHEMATICAL PRACTICES 3

Apply Why can you not measure the length of a line?

4

endpoints

Possible explanation: because a line goes on forever in both directions

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ray

line segment

line

point

endpoints

Name

Circle all the words that describe the shape.

1.

linelinesegment

2.

pointray

3.

closedshapeopenshape

4.

closedshapeopenshape

Write whether the shape is open or closed.

5.

6.

7.

8.

You can use math words to describe plane shapes.

an exact position or location

a straight path that goes in two directions without end

points that are used to show segments of lines

part of a line and has 2 endpoints

part of a line that has 1 endpoint and continues in one direction

A plane shape is a shape on a flat surface. It is formed by points that make curved paths, line segments, or both. Plane shapes can be open or closed.

A closed shape starts and An open shape does not startends at the same point. and end at the same point.

Look at this plane shape called a triangle.

It is a closed shape.

It has 3 line segments.

The line segments meet at the endpoints.


Lesson 12.1Reteach

openclosedclosedopen

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12-5 ReteachChapter Resources© Houghton Mifflin Harcourt Publishing Company

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Name

Shape Up!

Read the description. Then draw the shape. If the shape cannot be drawn, write the word impossible.

1. a ray with two endpoints 2. a closed shape with 6 line segments

3. a part of a line with two endpoints 4. an open triangle

5. an open shape with 7 line segments

6. a closed shape with 3 line segments and a curved path

7. Nick says we cannot see any true lines in the real world. He thinks everything we call a line is really a line segment. Do you agree or disagree? Explain.

Lesson 12.1Enrich

Check students’ drawings. Possible shapes are given.

I agree; Possible explanation: all the straight lines we

see have a beginning and an end. They do not go on without ending.

impossible

impossible

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12-6 EnrichChapter Resources© Houghton Mifflin Harcourt Publishing Company

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1

2

3 DifferentiatedInstruction

697 Chapter 12

LESSON 12.1

Unlock the Problem MATHEMATICAL PRACTICES

Have students read the introduction to make connections between mathematics and the real world. Discuss that the architect uses plane shapes to represent what will become the roof, walls, windows, and doors of the building. MP6 Attend to precision. Review the highlighted math words with students.

• Look at the picture of the line. What do the arrows mean? that the line continues in both directions and does not end

• How are a line and line segment alike? How are they different? Alike: both are straight. Different: a line segment has two endpoints, but a line continues forever in both directions.

• Why does a ray only have one arrow? It continues in only one direction.

MathTalk Use Math Talk to check students’

understanding of the definition of a line.

• Could you measure a ray? a line segment? Explain. Possible answers: You could not measure a ray since it goes on forever in one direction, but you could measure a line segment because it has two end points.

ELL Strategy: Frontload

Frontload essential vocabulary including point, line, endpoints, line segment and ray to build understanding of the properties of plane shapes.

• Explain the definitions of point, line, endpoints, line segment, and ray with words and pictures.

• Have students rephrase the definitions in their own words. Prompt students by asking questions. What do you know about a line segment? A line segment is part of a line. A line segment does not go on forever.

• Have students record the vocabulary with a drawing and labels in their Math Journal.

MP2 Reason abstractly and quantitatively. • What plane shape can be formed with

three line segments? triangle

Enrich 12.1Reteach 12.1

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.


Meeting Individual Needs

DifferentiatedInstruction

width

length

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• Is the plane shape at the right a closed shape

or an open shape? Explain how you know.

Plane shapes have length and width

but no thickness, so they are also called

two-dimensional shapes.

Try This! Draw plane shapes.

A closed shape starts and ends at the same point.

In the space below, draw more examples of closed shapes.

An open shape does not start and end at the same point.

In the space below, draw more examples of open shapes.

Plane shapes can be open or closed.


Explain whether a shape with a curved path must be a closed shape, an open shape, or can be either.

Possible explanation: it can be either closed

or open. The letter B above is a shape with

a curved path that is closed. The letter S is

a shape with a curved path that is open.

Check students’ drawings.


Possible explanation: it is a closed shape because it starts and

ends at the same point.

COMMON ERRORS

Lesson 12.1 698

Error Students might confuse lines, line segments, and rays.

Example Students may name a line segment as a line when describing the square on page 697.Springboard to Learning Draw a line and remind students that it continues in both directions. Then draw two points on the line. Explain that a segment is part of the line, so it has endpoints. Then point to and explain that a ray has only one endpoint.

Try This!Read about the two types of plane shapes—closed shapes and open shapes.

• How can you tell if a shape is closed? It starts and ends at the same point; the lines or curved paths are connected, with no opening.

• Is a three-sided shape always closed? Explain. No; possible explanation: because two sides may not be connected

• How could you change an open shape so that it is a closed shape? Connect the starting and ending points.

• Is a cardboard box a two-dimensional shape? Why or why not? No, because it has 3 dimensions—length, width, and height or thickness

• The answer to this question is yes: “Is a ____ a closed shape?” What could go in the blank? Answers will vary. Possible answers: a circle or any polygon students name such as a triangle, rectangle, square, pentagon.

• How can you describe the paths in the shapes on this page? Some are straight and others are curved.

• Which shapes have both kinds of paths? the “B” and the “pie” with a missing piece

Tell students that their books describe some shapes having straight paths or curved paths. That is because in geometry, a shape can be made up of one, the other, or both.Point out that when we talk about shapes we may use line to mean something different. We may use it to mean a line segment or even a curved path.

MathTalk Use Math Talk to focus on

students’ understanding of shapes with curved paths.

HandsOn

Advanced Learners

• Draw the following shapes on the board.

• Which plane shape is formed by only line segments? triangle by only curved paths? circle by both? letter D

• Then have students print uppercase letters in their name and describe each with respect to whether it has line segments or curved paths.

VisualIndividual

DifferentiatedInstruction

On Your OwnOn Your Own

Share and ShowShare and ShowShare and ShowShare and ShowShare and ShowShare and ShowShare and ShowShare and ShowMATHBOARDMATHBOARDMATHBOARDMATHBOARDMATHMATHMATHMATHBOARDBOARDBOARDBOARD

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Chapter 12 • Lesson 1 699

1. Write how many line segments

the shape has. ___

Circle all the words that describe the shape.


Write how many line segments the shape has.


2.

ray

point

3.

open shape

closed shape

4.

open shape

closed shape

5.

line

line segment

6. 7. 8. 9.

10.

__ line segments

11.

__ line segments

12.

__ line segments

13.

__ line segments

14. 15. 16. 17.


Describe How do you know whether a shape is open or closed?

3 line segments

closedopen open closed

44 6 8

closed closedclosedopen

Possible explanation: An open shape does not begin and end at the same point. A closed shape does.


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EXPLAIN3

Quick Check

If

Rt I 1

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Quick Check

If

Rt I 1

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Then

699 Chapter 12

On Your Own If students complete the checked exercises correctly, they may continue with the On Your Own section. Then ask:

• How are a ray and a line segment alike? Possible answer: they are both straight and are part of a line.

Share and Show MATHBOARDMATHBOARD

The first problem connects to the learning model. Have students use the MathBoard to explain their thinking. Use the checked exercises for Quick Check. Students should show their answers for the Quick Check on the MathBoard.

MathTalk Use Math Talk to focus on students’

understanding of the definition of open and closed shapes.

• Name two letters of the alphabet that represent a closed shape with a curved path and two letters that represent an open shape with a curved path. Possible answers: closed : B, D, O, open: S, C, U, J

a student misses the checked exercises

Differentiate Instruction with • Reteach 12.1

• Personal Math Trainer 3.G.A.1

• RtI Tier 1 Activity (online)


ELABORATE4

Differentiated Centers Kit

DIFFERENTIATED INSTRUCTION INDEPENDENT ACTIVITIES

MATHEMATICAL PRACTICES M

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18. What’s the Error? Brittany says there are two

endpoints in the shape shown at the right. Is she

correct? Explain.

19. MATHEMATICALPRACTICE 6 Explain how you can make the shape at

the right a closed shape. Change the shape so it is a

closed shape.

20. DEEPER Look at Carly’s drawing at the right.

What did she draw? How is it like a line? How is

it different? Change the drawing so that it

is a line.

21. SMARTER Draw a closed shape in the

workspace by connecting 5 line segments

at their endpoints.

22. SMARTER Draw each shape where it belongs in the table.

Closed Shape Open Shape

No; possible explanation: the shape is a ray. So, there is

1 endpoint and the ray continues in the other direction.


Ray; possible answer: a ray is like a line because they are

both straight. While a line continues in both directions,

a ray continues in only one direction.

Possible explanation: draw a sixth line segment,

so the shape starts and ends at the same point.

Check students’

drawings. Possible drawing is shown.


Differentiated Centers Kit

DIFFERENTIATED INSTRUCTION INDEPENDENT ACTIVITIESD

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

EVALUATE5 Formative Assessment

MATHEMATICAL PRACTICES

Lesson 12.1 700

Essential QuestionUsing the Language ObjectiveReflect Have student pairs brainstorm then check the textbook to answer the Essential Question. What are some ways to describe two-dimensional shapes? Two-dimensional shapes have length and width but no thickness.

Math Journal WRITE MathDraw an open shape and a closed shape. Label your shapes.

MP6 Attend to precision. Exercise 19 assesses students’ understanding of open and closed shapes. Guide students to understand that closed shapes start and end at the same point. Have pairs brainstorm ways to create a closed shape from the shape given.

SMARTER

For Exercise 21, students need to visualize a five-sided closed shape with no sides crossing.To extend their thinking about Exercise 21, show students a concave pentagon and have them compare and contrast the drawing to theirs.

Students complete blue Activity Card 18 by identifying

two-dimensional shapes by their attributes.

Students complete orange Activity Card 18 by

classifying two-dimensional shapes based on their attributes.

ActivitiesFigure It Out

ActivitiesClassification Act

SMARTER

This item assesses a student’s ability to identify whether a two-dimensional shape is closed or open. Students who draw the semicircle with the open shapes might be confusing the open or closed property with whether a shape is a polygon instead.

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

Meeting Individual Needs

Problem Solving • Thinking

nt

Extend the Math Activity

radius

center

diameter

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.

Materials large paper clip, 2 pencils, ruler

Discuss these vocabulary words with students. A circle is a closed plane shape made of points that are the same distance from the center. The center is the point in the middle of the circle. A radius is a line segment. One endpoint is always the center of the circle. The other endpoint is on the circle. A diameter is a line segment that passes through the center of the circle and has its endpoints on the circle.

Investigate Students will draw a circle and label its parts.

• Draw a point on a sheet of paper.

• Place a pencil in each end of a paper clip. Place one pencil on the point you drew. Move the first pencil around to draw a circle.

• Use a ruler. Draw a radius and a diameter.

• Label the parts of your circle.

Math Talk Why does the paper clip represent the radius of your circle? It is the distance from the center of the circle to the outside of the circle.

Summarize Can a square have a point in the center so that all the points on the sides of the square are the same distance from it? No; if you draw a shape so that all the points are the same distance from one point, it is a circle. So, it will not be a square.

701 Chapter 12

Problem SolvingProblem Solving

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Lesson 12.1Practice and Homework


Write how many line segments the shape has.


5. Carl wants to show a closed

shape in his drawing. Show and

explain how to make the drawing

a closed shape.

6. The shape of a fish pond at a park

is shown below. Is the shape open

or closed?

_______

Chapter 12 701

1.

_ line segments

2.

_ line segments

3.

_____

4.

_____

4

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

7. WRITE Math Draw an open shape and a closed

shape. Label your shapes.

Add a fourth line segment, so the shape

starts and ends at the same point.

open

6

closed

closed

Check students’ work.

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 12.1 702


Personal Math Trainer

FOR MORE PRACTICE GO TO THE

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Lesson Check (3.G.A.1)

1. How many line segments does this shape have?

2. What is part of a line, has one endpoint, and continues in one direction?

Spiral Review (3.OA.A.3, 3.OA.C.7, 3.NF.A.3a)

3. What multiplication sentence does the array show?

4. What is the unknown factor and quotient?

9 × = 27

27 ÷ 9 =

5. What fraction is equivalent

to 4 _ 8 ?

6. Mr. MacTavish has 30 students from his class going on a field trip to the zoo. He puts 6 students in each group. How many groups of students will he make?

5 line segments

4 × 8 = 32 or 8 × 4 = 32

Possible answers: 1 _ 2 or 2 _

4

3

5 groups of students

ray


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Describe Plane Shapes - €¦ · 697A Chapter 12 About the Math Professional Development LESSON AT...

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