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LESSON AT A GLANCE

695A Chapter 12

Interactive Student Edition

Personal Math Trainer

Math on the Spot Video

Animated Math Models

HMH Mega Math

If Children AskSome children may wonder why they need to solve problems about geometry. Tell children that real-life problems are solved with all kinds of mathematics. Using an understanding of how shapes may be composed or decomposed is an important skill in life and in many careers.

Explain that if architects did not know how to put shapes together and take them apart, they could not make plans for buildings or bridges. Understanding of shapes is needed to plan structures so people can work and drive safely.

Ask children to look at houses and other structures between home and school to find where shapes may have been put together to form a design. Children can also look for composite shapes in cars, toys, packages, and clothes.

Problem Solving • Make New Two-Dimensional Shapes

LESSON 12.5

Learning ObjectiveMake new shapes from composite two-dimensional shapes using the strategy act it out.

Language ObjectivePartners explain to the class and demonstrate how acting it out can help them make new shapes from combined shapes.

MaterialsMathBoard, Two-Dimensional Shapes (to combine) (See eTeacher Resources), tape

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.)MP1 Make sense of problems and persevere in solving them. MP4 Model with mathematics.

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

8 – 6 = 286

10 10 10 10 10

10 10 10 10 10

1 23 4 Pages 88–89 in Strategies and Practice for Skills and Facts Fluency provide additional fluency support for this lesson.

Lesson 12.5 695B

How can acting it out help you make new shapes

from combined shapes?

1 23 4 Fluency BuilderClap and Subtract• Tell children that you will clap from 1 to

10 times. Have them count the claps and write the number on a sheet of paper.

• Clap a lesser number of times. Have children count the claps and write the number under the first number of claps.

• Have children write a subtraction number sentence that tells the difference between the first and second set of claps.

• Repeat with other sets of claps to subtract within 10.

Problem of the Day 12.5Word of the Day hundredNicole and Anil collected cans for recycling. They put them in bags of ten. Nicole had 10 bags. Anil had 9 bags and 6 extra cans. Who collected one hundred cans? Nicole

Invite children to represent 100 in other ways, such as 10 tens blocks, or 9 tens and 10 ones blocks. Then invite children to find places where they see the number 100 or see about 100 things around the classroom.

VocabularyInteractive Student EditionMultimedia Glossary e

with the Interactive Student Edition

Essential QuestionHow can acting it out help you make new shapes from combined shapes?

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

Why could you not combine a circle with another shape to make a rectangle? Possible answer: a rectangle has only straight sides. I can only combine shapes with straight sides to make a rectangle.

Learning ActivityFocus children’s attention on the new shapes made by combining triangles.

• What shapes were left in the sand? triangles

• How many shapes are combined to make the first new shape? 2

• What do you notice about the second new shape? Possible answer: The second new shape is made by combining 2 of the first new shape.

• How are the shapes combined? Possible answer: The triangles switch from right side up to upside down, and are joined at the sides.

Literacy and MathematicsChoose one or both of the following activities.

• Invite children to make up a story about combining shapes. Have them describe the shapes in the story.

• Have children combine pattern blocks to make a composite shape, then make that shape several times. Children should then combine the composite shapes they made into a new shape to create a setting for a story.

Common Core Fluency Standard 1.OA.C.6

Step 1

Step 2

Unlock the ProblemUnlock the Problem

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Chapter 12 six hundred ninety-fi ve 695

Show how to solve the problem.

Use shapes. Combine to make a new shape.

and

Then use the new shape.

and

What information do I need to use?

Cora uses this shape.

What do I need to fi nd?

how Cora can make a

Cora wants to combine shapes to make a circle. She has . How can Cora make a circle?

Problem Solving • Make New Two-Dimensional ShapesEssential Question How can acting it out help you make new shapes from combined shapes?

circle

make

make

Lesson 12.5PROBLEM SOLVING

Geometry—1.G.A.2

MATHEMATICAL PRACTICESMP1, MP4

HOME CONNECTION • Recognizing how shapes can be put together and taken apart provides a foundation for future work with fractions.

EXPLORE2

1

2

3

Name

2

Problem Solving • Make New Two-Dimensional ShapesLuis wants to use to make a .How many does he need?

Unlock the Problem

What do I need to find?

how Luis can make a

using

What information do I need to use?

Luis uses

Show how to solve the problem.

make a .

Use shapes to solve. 1. Meg wants to use

to make a . 3 make a .

Lesson 12.5Reteach

Check children’s drawings. 3 triangles make a trapezoid.

12-13 ReteachChapter Resources© Houghton Mifflin Harcourt Publishing Company

Name Lesson 12.5Enrich

1. Use 2 .

Use . Show how the makes the .Draw lines. Then show how the makes the . Draw lines.

2. Use 3 .

Writing and Reasoning How many

do you need to make 2 ?

12

Shapes in a ShapeUse . Show how the makes the . Draw lines. Then show how the makes the . Draw lines.

12-14 EnrichChapter Resources© Houghton Mifflin Harcourt Publishing Company

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1

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3 DifferentiatedInstruction

695 Chapter 12

LESSON 12.51.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.

Unlock the Problem Materials Two-Dimensional Shapes (to combine) (see eTeacher Resources)Prepare four quarter-circles for each child using Two-Dimensional Shapes (to combine). Then read the following aloud to the class.

Cora wants to combine shapes to make a circle. She has this shape. How can Cora make a circle?

Work through the Problem Solving graphic organizer together. Guide children to solve the problem by asking these questions.• What does Cora want to do? Cora wants to

make a circle by putting shapes together.

Give children one quarter-circle.• Describe the shape Cora has. Possible answer:

The shape has two straight sides and one curved side.

• What do you know about the sides of a circle? A circle is curved. It does not have any straight sides.

Give children a second quarter-circle. Have them use the two shapes to make the half-circle shown on their page. Then give children the other two quarter-circles to make another half-circle. • When you combine your two new shapes,

what shape do you make? a circle

• How many small shapes did you need to use to make a circle? 4

ELL Strategy: Illustrate Understanding

Have children illustrate their understanding of making new shapes from other shapes.Give children two two-dimensional shapes. Ask the children to trace each shape. Then ask children to put the two shapes together to form a new shape. Have the children trace around the new shape.Help children organize into pairs. Encourage the pairs to trade shapes and the outlines they drew. Challenge the children to put the two shapes together to make the new shape.

Enrich 12.5Reteach 12.5

MATHEMATICAL PRACTICES

Step 1

Step 1

Step 2

Step 2

Try Another ProblemTry Another Problem

MathTalk MATHEMATICAL PRACTICES 4

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696 six hundred ninety-six

1. Use to make a larger .

2. Use to make a .

Use shapes to solve. Draw to show your work.

Combine shapes to make a new shape.

and

Combine shapes to make a new shape.

and

Then use the new shape.

and

Then use the new shape.

and

make

make

make

make

Model How did you make the rectangle in Exercise 2?

• What do I need to find?

• What information do I need to use?

Lines drawn may vary.

Math Talk: Possible answer: First, I put the longest sides of the two triangles together to make a square. I made a second square the same way. Then I put the two squares together to make the rectangle.

COMMON ERRORS

EXPLAIN3

Advanced Learners

MATHEMATICAL PRACTICES

Lesson 12.5 696

Error Children may not draw the line in the correct place for the first step of the process.

Example In Exercise 2, children draw a straight line down the middle of the square. Springboard to Learning Model how to put together two right triangles to make a square. Have children trace with their finger the line where the two triangles meet. Then have children draw the same line in the new shape on the page.

Try Another Problem

MP1 Make sense of problems and persevere in solving them. Guide children through Exercise 1. Use similar questions to guide them through Exercise 2.• What do you need to do in Exercise 1?

I need to use squares to make a larger square.

• Look at the new shape in Step 1. How can you use your squares to make that new shape? I can put one square on top of the other.

Have children use two squares to make the rectangle and tape the squares together. • What is the name of that shape? rectangle

• Where will you draw a line on the rectangle to show it is made with two squares? across the middle of the rectangle.

Have children draw the line on the rectangle.• What do you need to do in Step 2? I need to

use two of the rectangles to make a square.

Have children use two more squares to make a second rectangle, and then combine their rectangles to make the square.• Where will you draw a line on the new

square to show that it is made with two rectangles? down the middle of the square.

Have children draw the line on the square.

MathTalk

MP4 Model with mathematics. Use Math Talk to focus on children’s descriptions of how they use shapes to combine two shapes and then use that composite shape to make a new shape.

Materials pattern blocks

• Distribute pattern blocks to pairs. Each pair should have several copies of the same pattern block.

• Have one partner combine the blocks to make a new shape. Then the other partner makes the same new shape. Partners work together to combine their two new shapes into a larger new shape.

• Partners draw their new shape, including lines to show the shapes that make it.

• Have children compare their drawings with pairs who used the same pattern blocks. Have them describe how the same blocks may be combined in different ways.

Logical / MathematicalPartners

Step 1

Step 1

Step 2

Step 2

and

Share and ShShare and ShShare and Show MATHBOARDMATHBOARD

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Chapter 12 • Lesson 5 six hundred ninety-seven 697

MATHEMATICALPRACTICE 1 Analyze Relationships Use

shapes to solve. Draw to show your work.

Combine shapes to make a new shape.

and

Then use the new shape.

and

make

make

make

and

Combine shapes to make a new shape.

3. Use to make a .

Then use the new shape.

4. SMARTER Use and to make a .

TAKE HOME ACTIVITY • Have your child explain how he or she solved Exercise 3.

make

Lines drawn may vary.

Quick Check

If

Rt I RRR1

2

3

Then

EVALUATE5 Formative Assessment

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

697 Chapter 12

Share and Show MATHBOARDMATHBOARDMBMMMBBBMATHABOARDMMMAAATHATHTHHAAAAAAAAATTAAAABOARDBOARDBOARD

MP1 Make sense of problems and persevere in solving them. Have children complete these exercises in the same way that Exercises 1 and 2 were solved.

SMARTER

Exercise 4 requires children to complete all parts of the item to find the composite shape. Children who answer incorrectly may have trouble recognizing the same shape when it is rotated. Have these children use cut-outs to to help develop this spatial reasoning.

Use the checked exercise for Quick Check.

4 ELABORATE

a child misses the checked exercise

Differentiate Instruction with • Reteach 12.5

• Personal Math Trainer 1.G.A.2

• RtI Tier 1 Activity (online)

Essential QuestionReflect Using the Language Objective Have partners explain to the class and demonstrate to answer the Essential Question.How can acting it out help you make new shapes from combined shapes? Possible answer: I can use shapes to make a new shape. Then I can copy the new shape and put those two together to make a different new shape.

Math Journal Math

Use pictures to show how you can make a new shape using a combined shape made from two trapezoids.

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

Mid

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Mid-Chapter Checkpoint Personal Math TrainerOnline Assessment and Intervention

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Concepts and SkillsConcepts and Skills

Write the number of sides and vertices (corners). (1.G.A.1)

1. 2.

3.

Circle the shapes that can combine to make the new shape. (1.G.A.2)

Step 1

Combine and to make .

Step 2 Then use and .

698 six hundred ninety-eight Chapter 12

4 — sides 6 — sides

4 — vertices 6 — vertices

4. SMARTER Which new shape can you make? (1.G.A.2)

1

2

3

Data-Driven Decision Making

Mid-Chapter Checkpoint 698

Formative AssessmentUse the Mid-Chapter Checkpoint to assess children’s learning and progress in the first half of the chapter. The formative assessment provides the opportunity to adjust teaching methods for individual or whole class instruction.

SMARTER

Children must complete all parts of Exercise 4 to find the composite shape. Children who answer incorrectly may focus only on the pieces having curved sides or straight sides. Have these children draw each smaller shape to experiment with different ways to combine them.

LESSONS 12.1 TO 12.5

Based on the results of the Mid-Chapter Checkpoint, use the following resources to strengthen individual or whole class instruction.

Key: R—Reteach (in the Chapter Resources)

Item Lesson Standard Common ErrorPersonal

Math TrainerIntervene with

1, 2 12.2 1.G.A.1 May miscount the number of sides and vertices 1.G.A.1 R—12.2

3 12.4 1.G.A.2 May have difficulty recognizing shapes in a different orientation 1.G.A.2 R—12.4

4 12.5 1.G.A.2 May not recognize that the final shape should have both curved and straight sides. 1.G.A.2 R—12.5

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Problem Solving • Make New Two-Dimensional Shapes

Use shapes to solve. Draw to show your work.

Chapter 12 six hundred ninety-nine 699

1. Use to make a .Step 1. Combine shapes to make a new shape.

Step 2. Then use the new shape.

make

make

and

and

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

Lesson 12.5Practice and Homework

2. Math Use pictures to show how you can make a new shape using a combined shape made from two trapezoids.

Lines drawn may vary.

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.

699 Chapter 12

Personal Math Trainer

FOR MORE PRACTICE GO TO THE

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700 seven hundred

2. Circle the shape that has no flat surfaces.

3. Which flat surface does a cylinder have?Circle your answer.

Spiral Review (1.G.A.1)

Follow the steps.

1. Which new shape could you make?Circle your answer.

Lesson Check (1.G.A.2)

Step 1.

Combine and to make .

Step 2.

Then use and .

Monitoring Common Core Success

Maintaining Focus on the Major WorkIn Grade 1, the major work includes extending the counting sequence (1.NBT.A). In Lesson 12.1, children use defining attributes to sort and describe shapes based on the number of sides and vertices (1.G.A.1). In Lessons 12.3–12.5, children combine two-dimensional shapes to compose new shapes. They count the number of sides and vertices a shape has to identify the shape. Children must have a firm grasp of the counting sequence when working with shapes and their attributes.

Connecting Content Across Domains and ClustersIn Lessons 12.1–12.5, children work within Cluster 1.G.A, reason with shapes and their attributes. Children learn the attributes of two-dimensional shapes (1.G.A.1) and compose two-dimensional shapes to create a composite shape (1.G.A.2). In Lesson 12.2, children count the number of sides and vertices of shapes to identify the shape. This work connects to Cluster 1.NBT.A in which children use the counting sequence. Lessons 12.3–12.5

have children compose two-dimensional shapes to create a composite shape. Children recognize that the number of sides and vertices may change as you combine two-dimensional shapes.

Focus on Mathematical Practices In Chapter 12, children frequently look for and make use of structure (MP7). While working in Lesson 12.1, children learn the characteristics of two-dimensional shapes and sort groups of shapes according to these characteristics. They notice that any shape with a certain number of sides is in the same shape category. In Lesson 12.2, children make a connection between the models of shapes and the attributes of the shapes. In both lessons, children recognize common characteristics in a group of shapes and use this structure to classify shapes. The suggested questions found on TE pages 672 and 677 can be used to help children address the full meaning of this standard.

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 12.5 700