LESSON AT A GLANCE

Professional Development

Professional Development Videos

Sort Two-Dimensional Shapes

LESSON 12.1

671A Chapter 12

Teaching for DepthIn this lesson about two-dimensional shapes, children distinguish between defining attributes, such as number of sides and being closed or open, and non-defining attributes, such as color, orientation, and overall size. They learn that both common and different looking two-dimensional shapes, also known as flat or plane shapes, can be sorted in more than one way.

First graders will approach this task with varying levels of geometric thinking: Levels 0–2 of the 5 levels described by Pierre and Dina Van Hiele-Geldof (1959).

• Level 0: Visualization: “I put shapes together that look alike.”

• Level 1: Analysis: “I put all the shapes with four sides into one group.”

• Level 2: Informal Deduction: “A rectangle has 4 right angles. A square has 4 right angles. So a square is also a rectangle.”

About the Math

Learning ObjectiveUse defining attributes to sort shapes.

Language ObjectiveChildren sort two-dimensional shapes into piles and describe their common attributes.

MaterialsMathBoard

F C R Focus:Common Core State Standards

1.G.A.1 Distinguish between defining attributes (e.g., triangles are closed and three-sided) versus non-defining attributes (e.g., color, orientation, overall size); build and draw shapes to possess defining attributes.

MATHEMATICAL PRACTICES (See Mathematical Practices in GO Math! in the Planning Guide for full text.)MP6 Attend to precision. MP7 Look for and make use of structure.MP8 Look for and express regularity in repeated reasoning.

F C R Coherence:Standards Across the GradesBeforeK.G.A.2

Grade 11.G.A.1

After2.G.A.1

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 667J.

FOCUS COHERENCE RIGOR

Interactive Student Edition

Personal Math Trainer

Math on the Spot Video

Animated Math Models

iTools: Geometry

HMH Mega Math

ENGAGE1Daily Routines

Common Core

Lesson 12.1 671B

How can you use attributes to classi fy and sor t

two-dimensional shapes?

with the Interactive Student Edition

Essential QuestionHow can you use attributes to classify and sort two-dimensional shapes?

Making ConnectionsInvite children to name the different shapes they know.

Have children point out the different shapes they see in the classroom.

Learning ActivityYou might have children model the lesson by using attribute blocks to draw two-dimensional shapes.

Direct children’s attention to the shapes drawn by the plane.

• How many shapes do you see? 3

• What shapes are drawn in the sky? a circle, a triangle, and a rectangle

• Name one of the ways in which the square and triangle are different from the circle. Possible answer: the rectangle and triangle have straight sides and the circle has curved sides

Literacy and MathematicsAfter viewing the digital lesson, choose one or more of the following activities.

• Have children work with a partner to make a list of real-world objects that are in the shape of a rectangle, circle, or triangle.

• Guide children in creating a poster using cutouts of circles, rectangles, and triangles.

Signs Shape Up

Literature ConnectionFrom the Grab-and-Go™ Differentiated Centers Kit

Children read the book and identify shapes of signs.

Vocabulary BuilderName Sides and VerticesMaterials Vocabulary Cards vertex and side (See eTeacher Resources)

• Give each child Vocabulary cards for side and vertex and introduce the words. Tell children a vertex is a corner on a shape where two sides meet. The word for more than one vertex is vertices.

• Draw a square on the board. Point to a side and ask if it is a side or vertex. Have children hold up the card with the correct word. Point to a vertex and do the same. Repeat with a rectangle and a triangle.

Problem of the Day 12.1Word of the Day modelThere are 3 flowers in each pot. How many flowers are in 2 pots? Make a model to solve. 6 flowers

To build fluency, have children explain how a model is different from a picture.

Vocabulary circles, rectangles, sides, square, triangles, vertices

Interactive Student EditionMultimedia Glossary e

Listen and DrawListen and Draw

MATHEMATICAL PRACTICES 6MathTalk

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Sort Two-Dimensional ShapesEssential Question How can you use attributes to classify and sort two-dimensional shapes?

Draw to sort the shapes.Write the sorting rule.

Chapter 12 • Lesson 1 six hundred seventy-one 671

FOR THE TEACHER • Read the following aloud. Devon wants to sort these shapes to show a group of triangles and a group of rectangles. Draw and write to show how Devon sorts the shapes.

Explain Are there shapes that did not go in your groups?

Geometry—1.G.A.1

MATHEMATICAL PRACTICESMP6, MP7, MP8

Lesson 12.1

Math Talk: Possible answer: The two open shapes. One has three sides, but it is not a triangle because it is open, not closed. The other has 4 sides, but is not a rectangle because it is open, not closed.

Possible sorting is shown.

triangles rectangles

blue

redblue

red

blue

red

EXPLORE2

1

2

3

Name

Rectangles have 4 sides and 4 vertices.

Triangles have 3 sides and 3 vertices.

Circles are curved and closed.

A square is a special kind of

rectangle.

Sort Two-Dimensional Shapes

Read the sorting rule. Circle the shapes that follow the rule.

1. 4 sides

2. curved and closed

3. 3 vertices

Lesson 12.1Reteach

12-5 ReteachChapter Resources© Houghton Mifflin Harcourt Publishing Company

Name Lesson 12.1Enrich

Draw a shape to solve.

3. I have 3 vertices.I have 3 sides.

4. I have 4 sides. I have 4 vertices. My sides are not all the same length.

1. We have 4 vertices. We have 4 sides. All of our sides are the same length.

2. We have more than 2 sides. We do not have 4 sides.

Writing and Reasoning Draw two different shapes that have 4 vertices and 4 sides.

Shape GroupsCross out the shapes that do not belong.

Accept any quadrilateral with unequal sides.

Accept any triangle.

Possible answer is shown.

12-6 EnrichChapter Resources© Houghton Mifflin Harcourt Publishing Company

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3333

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3 DifferentiatedInstruction

671 Chapter 12

LESSON 12.11.G.A.1 Distinguish between defining attributes (e.g., triangles are closed and three-sided) versus non-defining attributes (e.g., color, orientation, overall size); build and draw shapes to possess defining attributes.

Listen and Draw Read the following problem aloud to the class.

Devon wants to sort these shapes to show a group of triangles and a group of rectangles. Draw and write to show how Devon sorts the shapes.

Point out that these are two-dimensional shapes, and are also known as flat shapes or plane shapes. • How are the shapes alike and different?

number of sides/vertices, color, size, open or closed

• How can you sort these shapes into two groups? Possible answers: rectangles/triangles, red/blue, 3 sides/4 sides, open/closed, big/small

• Are there some shapes that are not triangles or rectangles? How do you know? Possible answer: Yes. The open shapes are not triangles or rectangles because their sides are not closed.

• Can you sort by color to show a group of triangles and a group of rectangles? Explain. No. Rectangles and triangles would be in both groups.

• Can you sort by size to show a group of triangles and a group of rectangles? Explain. No. Rectangles and triangles would be in both groups.

• How can you sort a group of triangles and a group of rectangles? by the shape

MathTalk

MP6 Attend to precision. Use Math Talk to focus on children’s understanding of the defining attributes of two- dimensional shapes.

ELL Strategy: Illustrate Understanding

Have children illustrate their understanding of two-dimensional shapes. Draw a triangle. • This is a triangle. It has 3 sides and

3 vertices. Ask children to draw triangles. Ask them to count the three sides of the triangles they drew.

• Yes, that is a triangle; it has 3 sides and 3 vertices. If the child did not draw a triangle, repeat the directions and show an example. Repeat with other shapes.

Enrich 12.1Reteach 12.1

Model and DrawModel and Draw

Share and ShShare and ShShare and Show MATHBOARDMATHBOARD

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Here are some ways to sort two-dimensional shapes.

triangles rectangles

curved —— and closed shapes

closed shapes with 3 — sides

closed shapes with 4 — vertices

1. 4 vertices (corners) 2. not curved

3. only 3 sides 4. more than 3 sides

672 six hundred seventy-two

A square is a special kind of

rectangle.

Read the sorting rule. Circle the shapes that follow the rule.

circles

THINKVertices (corners)

are where the sides meet.

COMMON ERRORS

Quick Check

If

Rt I RR1

2

3

Then

EXPLAIN3

Advanced Learners

Lesson 12.1 672

Error Children may misidentify a turned square as a triangle.

Example In Exercise 1, children do not circle the purple square.Springboard to Learning Have children draw a dot on each vertex (or side) as they count to help them keep track. Remind children that even though a shape is turned, the number of its sides/vertices does not change.

a child misses the checked exercises

Differentiate Instruction with • Reteach 12.1

• Personal Math Trainer 1.G.A.1

• RtI Tier 1 Activity (online)

Model and Draw MATHEMATICAL PRACTICES

MP7 Look for and make use of structure. Work through the model with children. Point out that a square is a special kind of rectangle because it has four sides that are all the same length.• What do you notice about all of the shapes

in the first group? They are all curved and closed.

• To be a triangle, does the size define the shape? Does the color define the shape? Explain. No. A triangle can be any size or color, but it always has 3 sides and 3 vertices (corners).

Share and Show MATHBOARDMATHBOARDMBMMMBBBMATHABOARDMMMAAATHATHTHHAAAAAAAAATTAAAABOARDBOARDBOARD

Have children complete Exercises 1–4. Have them draw a dot on each side or vertex to help keep track of what has been counted.• How can you tell that you circled the

correct shapes? Possible answer: I can mark the parts that follow the sorting rule.

Use the checked exercises for Quick Check.

Kinesthetic Individual / Partners

Materials models of two-dimensional shapes

• Give each pair a set of two-dimensional shapes.

• Have children sort the shapes in different ways.

• How many groups did you make? Children will likely say two, three, or four groups.

• How did you sort the shapes? Possible answer: I sorted the shapes by the number of sides and vertices.

• Have children draw or write to record each sorting.

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5. curved 6. only 3 vertices (corners)

7. 4 sides 8. 4 sides are the same length

9. 3 sides and 3 vertices (corners)

10. 2 sides are long and 2 sides are short

MATHEMATICALPRACTICE 6 Use Math Vocabulary

Circle the shapes that follow the rule.

Chapter 12 • Lesson 1 six hundred seventy-three 673

On Your OwnOn Your Own

SMARTER Draw 2 different two-dimensional shapes that follow both parts of the sorting rule.

REMEMBERRead the sorting

rule first.

Possible answers shown.

4 ELABORATE

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

673 Chapter 12

On Your OwnMP6 Attend to precision. If children answered Exercises 3 and 4 correctly, assign Exercises 5–10. Point out that the shapes in Exercises 7 and 8 are the same, but children must use different sorting rules to circle the correct shapes. In Exercise 7, children circle the shapes with four sides. In Exercise 8, children use the same group of shapes to circle those that have four sides of the same length. Tell children that these exercises show that they can sort a group of shapes in more than one way.

SMARTER

Exercises 9 and 10 require children to use higher order thinking skills as they interpret the sorting rule and draw 2 different two-dimensional shapes.

DEEPER

MP8 Look for and express regularity in repeated reasoning. Have children identify the kind of shapes that they sorted in Exercise 5.• What shapes matched the rule in Exercise 5?

Possible answer: only the circles

• What shapes did not match the rule? triangles, squares, and other rectangles

Repeat with similar questions for Exercises 6–8. Guide children to notice that each exercise sorted a type of shape (circles, triangles, rectangles, or squares). Discuss how each sorting rule is a defining attribute of these two-dimensional shapes.MP7 Look for and make use of structure.• What shapes have curved sides? circles

• What shapes have straight sides? triangles, rectangles, squares

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

Differentiated Centers Kit

DIFFERENTIATED INSTRUCTION INDEPENDENT ACTIVITIES

Math

MATHEMATICAL PRACTICES

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Ted sorted these shapes three different ways. Write sorting rules to tell how Ted sorted.

11.

12.

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TAKE HOME ACTIVITY • Gather some household objects such as photos, buttons, and napkins. Ask your child to sort them by shape.

14. SMARTER Which shapes have more than 3 sides? Choose all that apply.

● ● ● ● ●

13. SMARTER

4 vertices

closed

3 sides

Many sorting rules will apply.Possible rules are shown.

EVALUATE5 Formative Assessment

Differentiated Centers Kit

DIFFERENTIATED INSTRUCTION INDEPENDENT ACTIVITIESD

MATHEMATICAL PRACTICES

Lesson 12.1 674

MP8 Look for and express regularity in repeated reasoning.For Exercises 11−12, point out to children that each exercise contains a different group of shapes. For Exercise 11, if children write triangles as the sorting rule, ask them to tell what they notice about the numbers of sides and vertices of each shape.

SMARTER

Exercise 13 requires children to apply a sorting rule that includes all the shapes in the original group.

SMARTER

Exercise 14 requires children to be able to sort and classify the shapes by the ones that have 3 sides and the ones that have more than 3 sides. Children who answer incorrectly may miscount the number of sides on each shape. If children do not select all of the shapes that have more than 3 sides, have them place a small mark on each side of each shape and then count the marks.

Essential QuestionReflect Using the Language Objective Have children sort two-dimensional shapes into piles to answer the Essential Question.How can you use attributes to classify and sort two-dimensional shapes? I can sort by the number of sides or vertices, by straight or curved sides, or by closed or open shapes.

Math Journal Math

Explain how you would name a sorting rule for 1 square, 1 rectangle, and 1 triangle.

Children practice describing the attributes of two-dimensional shapes to win the game.

GamesOn the Water

Children read the book and identify the shapes of signs.

LiteratureSigns Shape Up

Children complete orange Activity Card 10 by sorting shapes by the number of sides.

ActivitiesMore Alike Than Not

Problem Solving • Applications

COMMON CORECOMMCOMMCOMMCOMMON CON CON CON COREOREOREORE

PROFESSIONALDEVELOPMENT Math Talk in Action

A B C D E

Problem SolvingProblem Solving

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Sort Two-Dimensional Shapes

Read the sorting rule. Circle the shapes that follow the rule.

1. not curved 2. 4 vertices

Chapter 12 six hundred seventy-fi ve 675

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

Lesson 12.1Practice and Homework

3. Katie sorted these shapes. Write a sorting rule to tell how Katie sorted.

4. Math Explain how you would name a sorting rule for 1 square, 1 rectangle, and 1 triangle.

Possible answers: 3 sides; 3 vertices

Check children’s work.

Practice and HomeworkUse the Practice and Homework pages to provide children with more practice of the concepts and skills presented in this lesson. Children 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 children’s understanding of content for this lesson. Encourage children to use their Math Journals to record their answers.

To help children think more deeply about attributes, present this set of shapes.

Teacher: What is the name of shape A?

Delia: It is a triangle.

Teacher: How do you know that?

Delia: It has 3 sides and 3 vertices.

Teacher: Do shapes A and B belong together?

Asaf: Yes. They are both triangles.

Teacher: What about shape D? Is it a triangle, too?

Elena: Well, if you turn it around, it might be.

Teacher: Why is that?

Elena: Triangles always point up.

Teacher: Triangles get their name because they have 3 sides and 3 vertices. They can point in any direction. Are shapes C and E triangles, too?

Elena: Yes. They each have 3 sides and 3 vertices, so I guess they have to be triangles too.

675 Chapter 12

Personal Math Trainer

FOR MORE PRACTICE GO TO THE

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676 six hundred seventy-six

Solve. Draw or write to explain.

3. Clue 1: A black line is shorter than a white line. Clue 2: The white line is shorter than a gray line.Is the black line longer or shorter than the gray line?

Spiral Review (1.MD.A.1)

1. Circle the shape that would not be sorted into this group.

2. Circle the shape that has fewer than 4 sides.

Lesson Check (1.G.A.1)

shorter

Connecting Math and Science

Active ReadingActive Reading

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So SaltySo SaltyYou can find water in oceans too.

An ocean is a large body of salty water. Most of Earth’s water is in oceans.

A detail is a fact about a main idea. Draw one line under a detail. Draw an arrow to the main idea it tells about.

Identify the body of water you see on the page. Circle the name of it. Describe the body of water by writing a sentence about it.

An ocean is a large body of salty water.

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In Chapter 12, children develop their understanding of two-dimensional geometry by making equal parts and making fourths. These same topics are used often in the development of various science concepts and process skills.

Help children make the connection between math and science through the S.T.E.M. activities and activity worksheets found at www.thinkcentral.com. In Chapter 12, children connect math and science with the S.T.E.M. Activity So Salty and the accompanying worksheets (pages 113 and 114).

Through this S.T.E.M. Activity, children will connect the GO Math! Chapter 12 concepts and skills with various facts about ocean water, including showing how much of the Earth is covered by land and how much is covered by ocean water. It is recommended that this S.T.E.M. Activity be used after Lesson 12.10.

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S.T.E.M. Activity

S.T.E.M. Activity one hundred thirteen 113

Chapter 12So SaltyDevelop Vocabulary1. Write the definition using your own words.

ocean:

Develop Concepts2. Identify and describe the body of water on pages 206–207.

3. Should we drink ocean water? Why do you think animals that live in the ocean cannot live in lakes?

Use with ScienceFusion pages 206–207.

No. Ocean water is salty. We live by drinking fresh water, not salt water.

The animals that live in the ocean need to live in salt water to stay alive.

They could not live in fresh water.

An ocean is a large body of salty water.

The body of water is an ocean. It is a large body of water. Its water is salty.

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114 one hundred fourteen

Do the Math!4. Color the part of the circle that shows how much of Earth

is covered with land.

5. Does the circle show equal shares? Explain.

6. Draw two more ways to make fourths.

Summarize

6. What is the main idea on pages 206–207?

Possible answer: The circle does show equal shares because all of the

four parts are equal size.

An ocean is a large body of water.

Check children’s work.

Children should color 1 of the 4 parts shown.

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

Lesson 12.1 676