About the MathProfessional Development

Professional Development Videos

I see one square with 4 straight sides.

I see two triangles. Each has 3 sides.

LESSON AT A GLANCE

707A Chapter 12

Interactive Student Edition

Personal Math Trainer

Math on the Spot Video

Animated Math Models

iTools: Geometry

HMH Mega Math

MP7 Look for and make use of structure.As children explore geometric concepts, it is important that they are able to describe and recognize the attributes of two-dimensional shapes. Children use these skills when they decompose shapes by drawing lines to create new shapes within a given shape.

• Help children recognize that each line they draw will be a side in the new shapes they create.

• Encourage children to step back and look at the whole shape from a different perspective—as a sum of its parts. They can adjust their focus and identify either the single shape or an assemblage of more than one shape.

Take Apart Two-Dimensional Shapes

LESSON 12.7

Learning ObjectiveDecompose two-dimensional shapes into parts.

Language ObjectivePartners design a step-by-step poster to explain how to take apart two-dimensional shapes.

MaterialsMathBoard, orange and purple crayons

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. MP7 Look for and make use of structure.

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.

ENGAGE1Daily Routines

Common Core

Lesson 12.7 707B

How can you take apart two-

dimensional shapes?

1 23 4 Fluency BuilderHundred Chart RiddlesMaterials Hundred Chart (See eTeacher Resources), two-color counters

Display a Hundred Chart. Have children identify numbers on the chart using riddles such as the following:

• I am 6 tens and 3 more. What number am I? 63

• I am 10 tens. What number am I? 100

After you say each riddle, invite a volunteer to find the number on the Hundred Chart. The volunteer can cross out the number.

Problem of the Day 12.7Word of the Day squareStan builds a square with toothpicks and clay. How many sides does Stan’s square have? How many vertices? Draw what Stan’s square might look like. 4 sides; 4 vertices; Children’s drawings should show a shape with 4 straight sides of equal length and 4 vertices.

VocabularyInteractive Student EditionMultimedia Glossary e

with the Interactive Student Edition

Essential QuestionHow can you take apart two-dimensional shapes?

Making ConnectionsHave children tell what they know about taking apart two-dimensional shapes.

Display a rectangle and draw a line through it to show 2 squares. Have children describe what they see. Repeat to show 2 rectangles.

Learning ActivityWhat is the problem the children are trying to solve? Connect the story to the problem. Ask the following questions.

• If you separated a square into two parts, what would you see? Possible answers: two rectangles, two triangles

• If you separated a rectangle into two parts, what would you see? Possible answers: two rectangles, two squares, two triangles

Literacy and MathematicsView the Digital Lesson. Then choose one or more of the following activities.

• Give children cutouts of Two-Dimensional Shapes (See eTeacher Resources). Have children cut each shape into two parts. Have them write a few sentences about what they did and the new shapes that resulted.

• Have each child pick a shape and make a list of the different shapes he or she can make from the original shape.

Listen and DrawListen and Draw

MathTalk MATHEMATICAL PRACTICES 7

Name

© H

ough

ton

Miff

lin H

arco

urt

Pub

lishi

ng C

ompa

ny

Color rectangles orange.Color triangles purple.

Take Apart Two-DimensionalShapesEssential Question How can you take apart twodimensional shapes?

Lesson 12.7

Chapter 12 seven hundred seven 707

Geometry—1.G.A.2

MATHEMATICAL PRACTICESMP1, MP7

FOR THE TEACHER • Read the following aloud. Angelina put some triangles and rectangles together. She drew pictures to show what she made. Color to show how Angelina put the shapes together.

Look for Structure What shapes did Angelina make?

Check children’s coloring.

Math Talk: Possible answer: Angelina made a trapezoid and a hexagon. The trapezoid is made from two triangles and one rectangle. The hexagon is also made from two triangles and one rectangle.

EXPLORE2

1

2

3

Name

Take Apart Two-Dimensional ShapesUse pattern blocks to help you find the parts of a shape.

Use 2 to find parts of .

Draw a line to show the parts.

Use pattern blocks. Draw a line to show the parts.

1. Show 2 . 2. Show 2 .

3. Show 2 . 4. Show 2 .

Lesson 12.7Reteach

12-17 ReteachChapter Resources© Houghton Mifflin Harcourt Publishing Company

Name Lesson 12.7Enrich

Writing and Reasoning How did you find the triangles in Exercise 2? Explain.

1. 2.

3. 4. triangles in all

Use the picture above. Find as many triangles as you can. Write how many.

How Many Triangles?

13

3

1

9

Possible answer: I looked for an upside

down triangle. Then I looked around it for

the other 3 triangles.

12-18 EnrichChapter Resources© Houghton Mifflin Harcourt Publishing Company

11

222

3333

1

2

3 DifferentiatedInstruction

707 Chapter 12

LESSON 12.71.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 orange and purple crayons Read aloud the following problem.

Angelina put some triangles and rectangles together. She drew pictures to show what she made. Color to show how Angelina put the shapes together.

Guide children through the solution process.• How do you know which shapes are

rectangles? They have 4 straight sides and 4 vertices.

Have children identify the rectangle in both drawings. Encourage them to trace the rectangles with their fingers. Then have children use an orange crayon to outline and color each rectangle.Have children identify the triangles the same way, coloring them purple.• Why are these shapes in both drawings

triangles even though they look different? They all have 3 straight sides and 3 vertices.

• How is the first picture like the second picture? It has the same number of triangles and rectangles.

• How is the first picture different from the second picture? Possible answer: It has 4 sides and the second one has 6 sides.

MathTalk

MP7 Look for and make use of structure. Use Math Talk to focus on children’s understanding of how shapes are composed of other shapes.

ELL Strategy: Scaffold Language

Scaffold language to help children understand how shapes can be taken apart to make other shapes. Draw a square. Draw a diagonal line from one vertex to the opposite vertex.

• When I draw a line in this square, what two shapes do I make? 2 triangles

Draw another square.

• How can I draw another line in the square to make two rectangles?

Help children see that by drawing a line from one side of a square to the other, they create two rectangles.

Enrich 12.7Reteach 12.7

Model and DrawModel and Draw

© H

ough

ton

Miff

lin H

arco

urt

Pub

lishi

ng C

ompa

ny

1. Show 2 . 2. Show 2 .

3. Show 2 . 4. Show 2 .

You can draw to showparts of a shape.

shows and

708 seven hundred eight

Share and ShShare and ShShare and Show MATHBOARDMATHBOARD

Draw a line to show the parts.Possible answers shown.

EXPLAIN3

Quick Check

If

Rt I RR1

2

3

Then

COMMON ERRORS Advanced Learners

Lesson 12.7 708

Model and Draw MATHEMATICAL PRACTICES

MP1 Make sense of problems and persevere in solving them. Work through the model with children. Have them trace the line in the circle. Explain that this line shows how two shapes can be made from the circle.• If you put the two parts together again,

what shape do you make? a circle

• Will you always get the same two shapes if you draw the line in a different place? Why or why not? Possible answer: No. You can draw a line near the bottom of the circle and you would get a big shape and a small shape.

Share and Show MATHBOARDMATHBOARDMBMMMBBBMATHABOARDMMMAAATHATHTHHAAAAAAAAATTAAAABOARDBOARDBOARD

Have children complete Exercises 1–4. Suggest that children first use their MathBoards to copy the shapes and draw lines before marking their answers. Explain that the two shapes they create may or may not be the same size. For example, in Exercise 1 children could draw a line that creates two rectangles of different sizes.Use the checked exercises for Quick Check.

a child misses the checked exercises

Differentiate Instruction with • Reteach 12.7

• Personal Math Trainer 1.G.A.2

• RtI Tier 1 Activity (online)

Error Children may draw a line that makes two shapes different from what the directions show.

Example In Exercise 3, children draw a line that shows two rectangles instead of two squares.Springboard to Learning Provide children with a cutout of the rectangle shown in Exercise 3. Children can practice folding the shape until they make two squares. Then have children draw a line down the correct fold to show the two shapes.

Materials Two-Dimensional Shapes (see eTeacher Resources), scissors, crayons, poster board

• Prepare cutouts from Two-Dimensional Shapes using sturdy paper, such as poster board. Have partners create and solve shape-outline puzzles.

• One child chooses a cutout of a shape and draws one or two lines on the cutout to make new shapes. The partner cuts along those lines to make puzzle pieces.

• Partners exchange puzzles with another pair. Each pair then puts the pieces together to make a shape they can name.

Kinesthetic / LogicalIndividual / Partners

Name

© H

ough

ton

Miff

lin H

arco

urt

Pub

lishi

ng C

ompa

ny •

Imag

e C

redi

ts: ©

Viri

naflo

ra/S

hutt

erst

ock

Chapter 12 • Lesson 7 seven hundred nine 709

7. Show 1 and 1 . 8. Show 1 and 1 .

9. Show 3 . 10. Show 2 and1 .

5. Show 2 . 6. Show 2 .

On Your OwnOn Your Own

MATHEMATICALPRACTICE 7 Identify Relationships

Draw a line to show the parts.

SMARTER Draw two lines to show the parts.Possible answers shown.

Possible answers shown.

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

709 Chapter 12

On Your OwnMP7 Look for and make use of structure. If children answered Exercises 3 and 4 correctly, assign Exercises 5–10.

SMARTER

Exercises 9 and 10 require children to use higher order thinking skills as they draw two lines to make the requested shapes. You may provide children with copies of Two-Dimensional Shapes (to combine) to help them model the trapezoid in Exercise 9 and the rectangle in Exercise 10. Children can use their models to help them determine where to draw the lines.

DEEPER

MP3 Construct viable arguments and critique the reasoning of others. To extend thinking, have children draw a picture of a common kind of food with an identifiable shape. For example, children may draw a square slice of cheese, a triangular tortilla chip, a circular pancake, or a rectangular cracker. Then have children swap drawings with a partner and draw two lines on the shape to make new shapes. Have volunteers share the drawings and identify the shapes they made by drawing lines.MP8 Look for and express regularity in repeated reasoning.• Why is a slice from a round pizza not a

triangle? One side is curved. A triangle has all straight sides.

4 ELABORATE

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 COMMUNICA C

© H

ough

ton

Miff

lin H

arco

urt

Pub

lishi

ng C

ompa

ny

710 seven hundred ten

squares

11. SMARTER How many squares are there?

12. SMARTER Draw a line to show the parts. Show 2 .

TAKE HOME ACTIVITY • Ask your child to explain howhe or she solved Exercise 11.

4 small squares (1 × 1)1 large square (2 × 2)

Possible answer is shown.

5

EVALUATE5 Formative Assessment

Differentiated Centers Kit

DIFFERENTIATED INSTRUCTION INDEPENDENT ACTIVITIESD

MATHEMATICAL PRACTICES

Lesson 12.7 710

Have children read Exercise 11.

SMARTER

MP1 Make sense of problems and persevere in solving them. As children complete Exercise 11, they may need help visualizing all the squares, including the one large square that holds all the parts.

DEEPER

To extend learning, challenge children to find all the squares in a 3-by-3 grid. There are 14 possible squares: 9 small, 4 medium, and 1 large.

SMARTER

Exercise 12 requires children to look for structure to take apart two-dimensional shapes. Incorrect answers may include parts that are not the same size. Intervene with additional practice using drawings or pattern blocks. Children also may use paper cutout models to fold into parts.

Essential QuestionReflect Using the Language Objective Have partners design a step-by-step poster to answer the Essential Question.How can you take apart two-dimensional shapes? Possible answer: I can draw lines to show parts of the shape.

Math Journal Math

Draw a shape. Then draw one or two lines to show parts of the shape.

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

ActivitiesBuilding Blocks

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

GamesOn the Water

Problem Solving • Applications

COMMON CORECOMMCOMMCOMMCOMMON CON CON CON COREOREOREORE

PROFESSIONALDEVELOPMENT Math Talk in Action

Problem SolvingProblem Solving

Name

© H

ough

ton

Mif

flin

Har

cour

t Pub

lishi

ng C

omp

any

Take Apart Two-Dimensional Shapes

Draw a line to show the parts.

1. Show 2 . 2. Show 2 .

3. How many triangles are there?

5 _ triangles

Chapter 12 seven hundred eleven 711

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

Lesson 12.7Practice and Homework

4. Math Draw a shape. Then draw one or two lines to show parts of the shape.

Possible answers are shown.

4 small triangles.1 large triangle.

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.

Some children can see shapes within shapes more readily than others, but practice can help.

Teacher: Who can draw a line on a trapezoid to make two triangles?

Fatima: I can! I go from vertex to vertex.

Teacher: The shapes are not alike. How do you know they are both triangles?

Darius: They both have 3 sides and 3 vertices.

Teacher: Very good! Now, who can draw two lines on a trapezoid to show 2 triangles and 1 rectangle?

Jimet: I can! I go straight up from each bottom vertex to the top of the shape.

Teacher: Good work, class! Now you see that there can be different ways to find parts on a trapezoid.

711 Chapter 12

s?

Our Favorite Sport

soccer

baseball

tennis

Each stands for 1 child.

Personal Math Trainer

FOR MORE PRACTICE GO TO THE

© H

ough

ton

Mif

flin

Har

cour

t Pub

lishi

ng C

omp

any

712 seven hundred twelve

2. Use the graph. How many children chose ?

2 _ children

3. Which new shape can you make?Circle your answer.

Spiral Review (1.MD.C.4, 1.G.A.2)

1. Look at the picture. Circle the pair that shows the parts.

Lesson Check (1.G.A.2)

Combine and .

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 12.7 712