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LESSON AT A GLANCE

Hands On • Combine Two-Dimensional Shapes

LESSON 12.3

683A Chapter 12

Interactive Student Edition

Personal Math Trainer

Math on the Spot Video

Animated Math Models

iTools: Geometry

HMH Mega Math

Teaching for DepthAn effective way to teach lessons that introduce the ideas of informal geometry is to let children explore and experiment. In addition to the explorations in composing shapes presented in this lesson, encourage children to find other ways to use the triangles and rhombuses to build trapezoids and hexagons and to use the pattern blocks to make other shapes.

Have children record what they learn and look for relationships among the shapes. Some may discover relationships among the pattern blocks. For example, a hexagon may be composed with 6 green triangles, 3 blue rhombuses, or 2 red trapezoids, or with a combination, such as 2 rhombuses and 2 triangles. Activities that focus on relationships also help build problem-solving skills.

Learning ObjectiveUse objects to compose new two-dimensional shapes.

Language ObjectiveChildren demonstrate to a partner how you can put two-dimensional shapes together to make new two-dimensional shapes.

MaterialsMathBoard, pattern blocks

F C R Focus:Common Core State Standards

1.G.A.2 Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, and quarter-circles) or three-dimensional shapes (cubes, right rectangular prisms, right circular cones, and right circular cylinders) to create a composite shape, and compose new shapes from the composite shape.

MATHEMATICAL PRACTICES (See Mathematical Practices in GO Math! in the Planning Guide for full text.)MP5 Use appropriate tools strategically. MP6 Attend to precision.

F C R Coherence:Standards Across the GradesBeforeK.G.B.6

Grade 11.G.A.2

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

Two-Dimensional Shapes

window door

Lesson 12.3 683B

How can you put two-dimensional shapes

together to make new two-dimensional shapes?

with the Interactive Student Edition

Essential QuestionHow can you put two-dimensional shapes together to make new two-dimensional shapes?

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

Show children a pattern or design in a fabric or artwork. Have children describe the shapes used within the pattern.

Learning ActivityEncourage children to identify the shapes in the sandbox.

• What shapes did the children make in the sandbox? rectangles

• What new shape did the children make by combining the other shapes? a square

• How is the new shape different from the shapes used to make it? The square has four sides of the same length. The rectangles are smaller than the square and have 2 long sides and 2 short sides.

Literacy and MathematicsChoose one or both of the following activities.

• Have children trace pattern blocks, combining shapes to create a border design for the classroom. Have them name the shapes they use, then color and decorate the border.

• Have children use pattern blocks to create rectangles, squares, and triangles in as many different ways as they can.

1 23 4 Fluency BuilderWeb of ShapesOn the board, draw a word web with four spokes. Write Two-Dimensional Shapes in the center. Provide shape clues for drawing a two-dimensional shape (circle, square, rectangle, triangle) at the end of each spoke. Have children use the clues to identify each shape. Then draw the shape.

Challenge children to point out objects in the classroom that resemble each shape. Write the names of the objects in the web.

Problem of the Day 12.3Calendar Math One week has 7 days. How many days are in 3 weeks? 21 days

Have children describe their solution strategies.

VocabularyInteractive Student EditionMultimedia Glossary e

Listen and DrawListen and Draw

MathTalk MATHEMATICAL PRACTICES 5

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Combine Two-Dimensional Shapes Essential Question How can you put two-dimensional shapes together to make new two-dimensional shapes?

Chapter 12 six hundred eighty-three 683

HandsOn

Lesson 12.3HANDS ON

Geometry—1.G.A.2

MATHEMATICAL PRACTICESMP5, MP6

FOR THE TEACHER • Have children use pattern blocks to act out the following problem. Karen has some pattern blocks. She puts two triangles together. Draw a new shape Karen could make.

Use Tools Describe the new shape Karen made.

Use pattern blocks. Draw to show your work.

Math Talk: Possible answer: Karen put two triangles together and made a new shape that has 4 sides.

Orientation of drawing may vary.

EXPLORE2

1

2

3

Name

2 make a .

3 make a .

3 make

a .

Combine Two-Dimensional Shapes

You can put shapes together to make a new shape.

Use pattern blocks. Draw to show the blocks. Write how many blocks you used.

1. How many make a ?

2. How many make a ?

Lesson 12.3Reteach

12-9 ReteachChapter Resources© Houghton Mifflin Harcourt Publishing Company

Name Lesson 12.3Enrich

1. Use . 2. Use .

3. Use . 4. Use .

Writing and Reasoning Draw lines to show

how this can be made from 3 and 1 .

Shape MakerUse pattern blocks. Draw lines to show how to make each shape.

Possible answer is shown.

12-10 EnrichChapter Resources© Houghton Mifflin Harcourt Publishing Company

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3333

1

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3 DifferentiatedInstruction

683 Chapter 12

LESSON 12.31.G.A.2 Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, and quarter-circles) or three-dimensional shapes (cubes, right rectangular prisms, right circular cones, and right circular cylinders) to create a composite shape, and compose new shapes from the composite shape.

Listen and Draw Materials pattern blocks

For this lesson, you may wish to show each pattern block to children and name it, thereby introducing the name rhombus. Alternatively, you can refer to each block by its color. (For clarity, discussion is written using the shape names of the pattern blocks.)Present the following problem to the class.

Karen has some pattern blocks. She puts two triangles together. Draw a new shape Karen could make.

• What is the color of the triangle pattern block? green

• How many triangles does Karen put together? 2

Have children use two triangle pattern blocks to form a shape. Then have children trace the triangles to record their new shape. Have volunteers share their drawings with the class.• How are your drawings the same? They all use

two triangles.

• How are your drawings different? Children will likely observe that their drawings show different ways to put the triangles together.

MathTalk

MP5 Use appropriate tools strategically. Use Math Talk to focus on children’s understanding of combining two-dimensional shapes to make new shapes.

ELL Strategy: Identify Relationships

Provide children with pattern blocks. Allow time to manipulate the blocks. As children are using the blocks, ask informal questions about the relationships of the blocks.• How many triangles make a hexagon? 6• How many trapezoids make a hexagon? 2Take time to talk about the relationships among pattern blocks with the children. Ask children to tell a partner about the relationship between two pattern blocks.

HandsOn

Enrich 12.3Reteach 12.3

Model and DrawModel and Draw

Share and ShShare and ShShare and Show MATHBOARDMATHBOARD

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How many do you need to make a ?

2 — make a .

1.

3 — make a .

2.

3 — make a .

How many make a ? How many make a ?

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Use pattern blocks. Draw to show the blocks. Write how many blocks you used.

COMMON ERRORS

Quick Check

If

Rt I RR1

2

3

Then

EXPLAIN3

Advanced Learners

Lesson 12.3 684

Error Some children may be unable to visualize how to combine the smaller blocks into the larger shape.

Example In Exercise 1, children cannot figure out how to combine the rhombuses to make a hexagon.Springboard to Learning Have children place a rhombus block on top of a hexagon and move it around until it matches one part of the hexagon. Have them continue adding rhombuses until the hexagon is covered.

a child misses the checked exercise

Differentiate Instruction with • Reteach 12.3

• Personal Math Trainer 1.G.A.2

• RtI Tier 1 Activity (online)

Model and Draw MATHEMATICAL PRACTICES

MP6 Attend to precision. Work through the model with the class. Have children use two trapezoid pattern blocks to model the hexagon as shown.• How can you describe the way you put the

trapezoids together? The long sides go together.

• What do you notice about the sides and vertices? A trapezoid has 4 sides and 4 vertices. When I put two trapezoids together to make a hexagon, the hexagon has 6 sides and 6 vertices.

Share and Show MATHBOARDMATHBOARDMBMMMBBBMATHABOARDMMMAAATHATHTHHAAAAAAAAATTAAAABOARDBOARDBOARD

Before beginning Exercises 1 and 2, encourage children to turn the blocks over and around to help visualize the shape they need to make.• How can you tell that the shape you made

is correct? Possible answers: I can count the sides and corners. I can place the smaller shapes on top of the larger shape.

Use the checked exercise for Quick Check. Have children use their MathBoards to show the solution.

KinestheticIndividual / Partners

Materials pattern blocks, Tangram Pattern cut apart (see eTeacher Resources), drawing paper

• Give each partner a set of pattern blocks and the tangram pieces.

• Have partners build larger two-dimensional shapes with pattern blocks and tangram pieces. Children should trace the outside of the shape they make.

• Then have partners give each other the outline and the shapes that they used. Partners should try to reconstruct the two-dimensional shapes traced by their partners.

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3. How many make a ?

6 — make a .

4. How many make a ?

2 — make a .

On Your OwnOn Your Own

MATHEMATICALPRACTICE 5 Use a Concrete Model Use pattern

blocks. Draw to show the blocks. Write how many blocks you used.

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5. SMARTER Use me two times to make this shape. Which block am I? Circle a block to show your answer.

6. DEEPER Use these pattern blocks to make the shape. Write how manytimes you used each block.

6 — 3 — 2 —

4 ELABORATE

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

685 Chapter 12

On Your OwnMP5 Use appropriate tools strategically. If children answered Exercise 2 correctly, assign Exercises 3–6.

SMARTER

Exercise 5 requires children to use higher order thinking skills. Children use clues to decide how to make a given shape with two of the same blocks. Encourage children to think about the blocks to decide, and then use blocks to check their work before circling their answer. Ask volunteers to share their solutions and explain their reasoning.

DEEPER

MP8 Look for and express regularity in repeated reasoning. Exercise 6 helps children understand that they can make the same shape in different ways. To extend learning, have children work with a partner to rewrite the clues for Exercise 5 using a different pattern block as the answer. You may give children this example: Use me four times to make this shape. Which block am I? triangle

Have children trade clues with a partner and solve.MP3 Construct viable arguments and critique the reasoning of others.• Is there more than one way to make a shape

that matches a set of clues? How do you know? Possible answer: Yes but the shape you get may not be a triangle, a hexagon, or a trapezoid.

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

Personal Math Trainer

MATHEMATICAL PRACTICES COMMUNICA C

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7. 2 make a .

How many make 3 ?

6 —

make 3 .

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DEEPER Use pattern blocks. Draw to show your answer.

8. SMARTER How many make a ?

Use pattern blocks. Draw to show the blocks you used.

TAKE HOME ACTIVITY • Have your child explain how he or she solved Exercise 7.

3; Possible drawing is shown. Orientation of drawing may vary. EVALUATE5 Formative

Assessment

Differentiated Centers Kit

DIFFERENTIATED INSTRUCTION INDEPENDENT ACTIVITIESD

MATHEMATICAL PRACTICES

Lesson 12.3 686

Have children read Exercise 7.

DEEPER

MP6 Attend to precision. Children apply what they know about the number of triangles that make one rhombus to determine the number of triangles that would make 3 rhombuses. To extend learning, have children find the total number of triangles needed to make 4, 5, and 6 rhombuses.

Personal Math Trainer SMARTER

Be sure to assign Exercise 8 to children in the Personal Math Trainer. It features an animation to help them model and answer the problem. Children use two-dimensional shapes to make combined two-dimensional shapes. Children who answer incorrectly may be unable to visualize the smaller shapes in the larger shape. Have these children practice with pattern blocks to find solutions.

Essential QuestionReflect Using the Language Objective Have children demonstrate to a partner to answer the Essential Question.How can you put two-dimensional shapes together to make new two-dimensional shapes? I can put shapes together by matching some sides and vertices to make a new shape.

Math Journal Math

Draw the shapes you could put together to make a rectangle.

ActivitiesBuilding Blocks

Children complete purple Activity Card 10 by combining two-dimensional shapes to create new shapes.

Problem Solving • Applications

Cross-Curricular

Problem SolvingProblem Solving

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Combine Two-Dimensional Shapes

Use pattern blocks. Draw to show the blocks. Write how many blocks you used.

Chapter 12 six hundred eighty-seven 687

1. How many make a ?

3 make a .

2. How many make a ?

2 make a .

COMMON CORE STANDARD—1.G.A.2 Reason with shapes and their attributes.

Lesson 12.3Practice and Homework

Use pattern blocks. Draw to show your answer.

3. 2 make a .

How many make 4 ?

8 make 4 .

4. Math Draw the shapes you could put together to make a rectangle.

Check children’s drawings.

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.

687 Chapter 12

Materials Two-Dimensional Shapes (see eTeacher Resources), poster board, flashlight• Prepare Two-Dimensional Shapes ahead of time by

cutting out each shape, tracing it on a piece of poster board, and cutting the shape out of the poster board.

• Tell children that outside on a sunny day, they can see shadows. They can also see shadows inside when light shines. Tell children that a shadow forms when an object blocks light.

• Dim the lights in the classroom and hold up a shape so children can see. Then shine the flashlight on the shape so that its shadow appears on the wall. Have children discuss the shape of the shadow. Repeat the activity with different shapes.

Materials pictures of various traffic signs

• Discuss the idea that all citizens are responsible for following the laws of the community. Point out that some laws, such as wearing seat belts and observing speed limits, are designed to keep people safe.

• Display pictures of signs children might see in their neighborhood, such as a stop sign, a yield sign, or a school-crossing sign. Discuss what each sign means, and have children describe the attributes and shape of each sign.

SOCIAL STUDIES

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7 6 54

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Personal Math Trainer

FOR MORE PRACTICE GO TO THE

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3. Use . Which string is about 5 long?Circle the string that is about 5 long.

4. Look at the hour hand. Write the time.

5:00

Spiral Review (1.MD.A.2, 1.MD.B.3)

Lesson Check (1.G.A.2)

1. How many do you use to make a ?

6 make a .

2. How many do you use to make a ?

3 make a .

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.

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