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LESSON AT A GLANCE

Hands On • Describe Two-Dimensional Shapes

LESSON 12.2

677A Chapter 12

Interactive Student Edition

Personal Math Trainer

Math on the Spot Video

Animated Math Models

iTools: Geometry

HMH Mega Math

Why Teach ThisExploring the attributes of shapes is a first step in developing geometrical ideas. As you work through this lesson, help children relate what they are learning to the world around them. Ask where they have seen squares, rectangles, triangles, and circles outside of school, and how those shapes are like the shapes in their math books.

As children explore the relationship between the number of sides and the number of vertices in familiar polygons, they are beginning their study of an important part of mathematics, one related to other areas of mathematics and one used in many professions.

Geometry builds on children’s spatial sense, and children who struggle with arithmetic may find geometry more satisfying and interesting.

Learning ObjectiveDescribe attributes of two-dimensional shapes.

Language ObjectiveTeams of children list the attributes they can use to describe two-dimensional shapes.

MaterialsMathBoard, models of two-dimensional shapes or Two-Dimensional Shapes (See eTeacher Resources) glue, pattern blocks, red and blue crayons

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

ENGAGE1Daily Routines

Common Core

Lesson 12.2 677B

What attributes can you use to describe

two-dimensional shapes?

with the Interactive Student Edition

Essential QuestionWhat attributes can you use to describe two-dimensional shapes?

Making ConnectionsInvite children to tell you what they know about shapes.

Have children find a shape in the classroom and describe it using language they know about shapes.

Learning ActivityHelp children to model shapes by drawing or tracing shapes as you describe their attributes. Invite children to look at the shapes on the screen.

• How are the shapes alike? Possible answer: they are all made of straight lines.

• What do we mean when we talk about the sides of a shape? Possible answer: the lines that make up the outside of the shape.

• What do we mean when we talk about the vertices of a shape? Possible answer: the corners that join the sides of the shape.

Literacy and MathematicsChoose one or both of the following activities.

• Invite children to create riddles about shapes. Provide an example. Say, I have four sides. Two of them are long and two of them are short. What am I? a rectangle

• Have children sort pattern block shapes into groups. Then have them describe the similarities and differences among the groups of shapes.

Vocabulary BuilderMore ShapesMaterials variety of two-dimensional shapes including a trapezoid and a hexagon; vocabulary cards hexagon and trapezoid (See eTeacher Resources)

Display the shapes to introduce trapezoid and hexagon. Have children share their observations about each shape. Then ask questions to generate discussion about ways these shapes are alike or different from other shapes.

Problem of the Day 12.2Number of the Day Find the secret number. Start at zero. Count by tens 4 times. Then count by ones 3 times. What is the secret number? 43

To make the problem more challenging, suggest that children start at a number other than zero.

Vocabulary hexagon, trapezoid

Interactive Student EditionMultimedia Glossary e

• How is the trapezoid like a square? How is it different? Possible answer: Both are two-dimensional shapes that have 4 sides and 4 vertices. All four sides of a trapezoid do not have to be the same length.

curved straight

Listen and DrawListen and Draw

MathTalk MATHEMATICAL PRACTICES 7

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Describe Two-Dimensional Shapes

Chapter 12 six hundred seventy-seven 677

Use two-dimensional shapes. Sort them into two groups. Draw to show your work.

Essential Question What attributes can you use to describe two-dimensional shapes?

HandsOn

Lesson 12.2HANDS ON

Geometry—1.G.A.1

MATHEMATICAL PRACTICESMP6, MP7, MP8

FOR THE TEACHER • Have children sort two-dimensional shapes into groups that are curved and straight. Have them draw the shapes to show how they sorted.

Look for Structure How did you sort the shapes into two groups? Name the shapes in each group.

Math Talk: Possible answer: I sorted shapes with a curve in one group and shapes with straight sides in another group. The shape with a curve is a circle. The shapes with straight sides are square, rectangle, and triangle.

Possible answer: Possible answer:

EXPLORE2

1

2

3

side

vertex

Name

This shape has 4 straight sides and 4 vertices.

Describe Two-Dimensional Shapes

Write the number of straight sides or vertices.

1. triangle

3 sides

2. square

4 vertices

3. hexagon

6 vertices

4. trapezoid

4 sides

5. triangle

3 vertices

6. square

4 sides

Lesson 12.2Reteach

12-7 ReteachChapter Resources© Houghton Mifflin Harcourt Publishing Company

Name Lesson 12.2Enrich

3. Sort , , , , and into two groups. Draw to show your work.

3 or 4 vertices more than 4 vertices

1. I have more than 4 vertices. I have more than 5 sides. Which shape am I?

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

Writing and Reasoning Draw a shape that has 5 vertices and 5 sides.

Riddle ShapesCircle the shape that answers the riddle.

Possible answer is shown.

12-8 EnrichChapter Resources© Houghton Mifflin Harcourt Publishing Company

11

222

3333

1

2

3 DifferentiatedInstruction

677 Chapter 12

LESSON 12.21.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 Materials models of two-dimensional shapes or Two-Dimensional Shapes (see eTeacher Resources), glue

Read the following directions aloud. Sort two-dimensional shapes into two groups. One group should have shapes that are curved. The other group should have shapes with straight sides.

• Describe a curved side. Curved sides are rounded.

• Describe a straight side. Straight sides are not rounded.

Have children use two-dimensional shapes to explore sorting by the defining attribute of curved or straight sides. If children have difficulty drawing the shapes, guide them to trace the shapes on the page or glue down the cutouts. Have volunteers share their drawings and observations.• How are the shapes in the curved group

alike? They are all circles; they have no straight sides.

• What do you notice about the shapes in the straight group? Possible answers: There are more shapes in this group. All the shapes have sides and vertices (corners), but they do not all have the same number of sides and vertices.

• Are the shapes you drew closed or open? They are all closed. All the sides touch each other.

MathTalk

MP7 Look for and make use of structure. Use Math Talk to focus on children’s understanding of how to classify two-dimensional shapes.

ELL Strategy: Restate

Restate the word vertex to help children learn how to describe attributes of two-dimensional shapes. Draw a triangle. Point to the vertex.• In math we call this a vertex. What does it

look like to you? Build from the children’s language to teach the word vertex.

• A vertex is also a corner. Repeat by pointing to other vertices on the triangle.

• Triangles have three vertices or corners.Repeat with a square and a rectangle.

HandsOn

Enrich 12.2Reteach 12.2

side

(corner)vertex

trapezoid hexagon

Model and DrawModel and Draw

Share and ShShare and ShShare and Show MATHBOARDMATHBOARD

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Some shapes have straight sides and vertices (corners).

ShapeDraw the

shape.Number of

Straight Sides

Number of Vertices (Corners)

1. hexagon 6 6

2. rectangle 4 4

3. square 4 4

4. trapezoid 4 4

5. triangle 3 3

678 six hundred seventy-eight

Use two-dimensional shapes. Draw and write to complete the chart.

Possible drawings shown.Orientation may vary.

Accept any triangle.

COMMON ERRORS

Quick Check

If

Rt I RR1

2

3

Then

EXPLAIN3

Advanced Learners

Lesson 12.2 678

Error Children may identify only the vertices on the trapezoid that have acute angles.

Example In Exercise 4, children write 2 for the number of vertices on the trapezoid. Springboard to Learning Remind children that a vertex (corner) is the point where two sides of a polygon meet.

a child misses the checked exercises

Differentiate Instruction with • Reteach 12.2

• Personal Math Trainer 1.G.A.1

• RtI Tier 1 Activity (online)

Model and Draw MATHEMATICAL PRACTICES

MP6 Attend to precision. Work through the model together and say the names for trapezoid and hexagon as you define these shapes with children.• How are the hexagon and the trapezoid

alike? How are they different? Both shapes have straight sides and vertices. They are both closed shapes. The hexagon has more sides and vertices than the trapezoid.

Share and Show MATHBOARDMATHBOARDMBMMMBBBMATHABOARDMMMAAATHATHTHHAAAAAAAAATTAAAABOARDBOARDBOARD

Have children complete Exercises 1–5.• What do you notice about the number

of sides and vertices (corners) for each shape? Each shape has the same number of sides as it has vertices.

• How do you know that your answers are correct? Possible answer: the shape should have sides and corners; the number of sides and vertices should be the same.

Use the checked exercises for Quick Check. Children should use the MathBoards to show their solutions.

VisualIndividual / Partners

Materials magazines, catalogs, scissors, glue, construction paper, crayons

• Have groups cut out pictures of objects that model various two-dimensional shapes. They might find doors for rectangles, yield signs for triangles, and so on.

• Have children make a poster for each shape by gluing the pictures on a sheet of construction paper. They can also draw objects. Each poster should be titled with the name of the shape, the number of sides, and the number of vertices.

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6. 4 — sides

4 — vertices

7. 4 — sides

4 — vertices

8.

3 — sides

3 — vertices

9.

3 — sides

3 — vertices

10.

6 — sides

6 — vertices

11.

4 — sides

4 — vertices

On Your OwnOn Your Own

Use to trace each straight side. Use to circle each vertex (corner).Write the number of sides and vertices (corners).

Chapter 12 • Lesson 2 six hundred seventy-nine 679

12. I am a shape with 3 straight sides and 3 vertices.

13. I am a shape with 4 straight sides that are the same length and 4 vertices.

SMARTER Draw a picture to solve.

All straight sides should be traced blue. All vertices should be circled red.

Also accept a rhombus.

Triangle may vary in type and in orientation.

4 ELABORATE

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

679 Chapter 12

On Your OwnMP6 Attend to precision. If children answered Exercises 4 and 5 correctly, assign Exercises 6–13. Remind children that shapes can be in different positions and still be the same shape.

SMARTER

Exercises 12 and 13 require children to solve attribute riddles. For Exercise 13, they need to analyze several shapes with 4 sides and 4 vertices (corners) to determine which shapes also have all sides the same length. Although children have not been taught rhombuses, they may already know the shape.

DEEPER

MP8 Look for and express regularity in repeated reasoning. To extend learning, have children identify each shape in Exercises 6–11. Have them tell which attributes of each drawing helped them identify the shape.To continue discussion about defining attributes of different shapes, draw a rhombus on the board.• How many sides does this shape have?

4 sides

• How many vertices does this shape have? 4 vertices

• How is this shape different from a rectangle? Possible answer: The vertices are not all the same. All the vertices in a rectangle are the same.

Continue discussing defining attributes with shapes such as a trapezoid, a pentagon, and a hexagon.MP7 Look for and make use of structure.• What do you notice about the numbers

of sides and vertices in these figures? The number of sides and the number of vertices is always the same.

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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14. Jake draws a shape that has fewer than 5 sides. It has 3 vertices.

15. Meg draws a shape with 4 sides. She labels it as a trapezoid.

MATHEMATICALPRACTICE 6 Use Math Vocabulary

Draw shapes to match the clues.

680 six hundred eighty

17. SMARTER Circle the number that makesthe sentence true.

A has 2

3

4

vertices (corners).

TAKE HOME ACTIVITY • Have your child draw a square, a trapezoid, and a triangle. For each shape, have him or her show you the sides and vertices and tell how many of each.

16. DEEPER Ben draws two different shapes. They each have only 4 vertices.

Children should draw any kind of triangle.

Children should draw a trapezoid.

Possible answer: square and non-square rectangle. Accept any two different quadrilaterals.

EVALUATE5 Formative Assessment

Differentiated Centers Kit

DIFFERENTIATED INSTRUCTION INDEPENDENT ACTIVITIESD

MATHEMATICAL PRACTICES

Lesson 12.2 680

Have children read Exercises 14 and 15. In these exercises, children follow the clues and draw the matching shape.

DEEPER

MP6 Attend to precision. Exercise 16 has more than one possible answer. To extend thinking, ask children to name each shape that they drew.

SMARTER

Exercise 17 requires children to describe two-dimensional shapes by their attributes. Children who incorrectly choose 2 or 4 may not understand the meaning of vertices or corners. Have children draw a triangle and circle the corners to check their answers.

Essential QuestionReflect Using the Language Objective Have teams list and describe to answer the Essential Question.What attributes can you use to describe two-dimensional shapes? Possible answer: I can describe shapes by the number of sides and vertices, by being open or closed, and by having curved or straight sides.

Math Journal Math

Use pictures and words to show the attributes of a hexagon.

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 blue Activity Card 10 by showing the number of sides and corners for various shapes.

ActivitiesOn the Corner

Problem Solving • Applications

Extend the Math Activity

Problem SolvingProblem Solving

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Describe Two-Dimensional Shapes

Chapter 12 six hundred eighty-one 681

Use to trace each straight side. Use to circle each vertex. Write the number of sides and vertices.

1.

6 sides

6 vertices

2.

4 sides

4 vertices

3.

4 sides

4 vertices

4.

3 sides

3 vertices

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

Lesson 12.2Practice and Homework

Draw a shape to match the clues.

5. Ying draws a shape with 4 sides. She labels it as a rectangle.

6. Math Use pictures and words to show the attributes of a hexagon.

Children should draw a rectangle.

All straight sides should be traced blue. All vertices should be circled red.

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.

681 Chapter 12

Use a Chart to SortMaterials Two-Dimensional Shapes (see eTeacher Resources), construction paper, glue

Investigate Give each pair of children a piece of construction paper and an assortment of two-dimensional shapes. Have pairs fold their paper in half to make a two-column chart. Have them choose which attributes they will use to sort the shapes and then label each section with the attributes they chose. Pairs glue each shape to the correct section.Tell children that they may choose an attribute that some shapes may not have. Explain that their chart does not need to include every shape. You may wish to have children explain why one or more shapes could not be sorted by their chosen attributes.

Math Talk Ask children the following questions.• How did you decide which kind of shape to place in

each section?• How can you decide if all the shapes in a section

belong there?• Which shapes, if any, can also be added to your

chart?• Is there another way to label your chart?

Accept all reasonable answers

Summarize Children can sort the shapes in any way to show classifications of two-dimensional shapes. Have them justify their reasoning for the way they sorted.

Personal Math Trainer

FOR MORE PRACTICE GO TO THE

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682 six hundred eighty-two

3. Circle the greater addend.Count on to find the sum.

4. Corey measures a crayon box with his paper clip ruler. Abouthow long is the box?

about 4 —

Spiral Review (1.OA.C.5, 1.MD.A.2)

1. How many vertices does a triangle have?

3 — vertices

2. How many vertices does a have?

4 — vertices

Lesson Check (1.G.A.1)

2 + 9

]

11

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 12.2 682