LESSON AT A GLANCE

About the MathProfessional Development

Professional Development Videos

719A Chapter 12

LESSON 12.9

Halves

Learning ObjectivePartition circles and rectangles into two equal shares.

Language ObjectiveChildren select a shape and explain to a partner how it can be separated into two equal shares.

MaterialsMathBoard

F C R Focus:Common Core State Standards

1.G.A.3 Partition circles and rectangles into two and four equal shares, describe the shares using the words halves, fourths, and quarters, and use the phrases half of, fourth of, and quarter of. Describe the whole as two of, or four of the shares. Understand for these examples that decomposing into more equal shares creates smaller shares.

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. MP6 Attend to precision.

F C R Coherence:Standards Across the GradesBeforeK.G.B.4

Grade 11.G.A.3

After2.G.A.3

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

Teaching for DepthIn the previous lesson, children identified shapes with equal and unequal parts. This lesson builds on the important concepts of equal and unequal parts by introducing a kind of equal part—the half. But for children to understand halves, they must understand that a shape in itself is a whole. When a whole has two equal parts, these equal parts are called halves.

Folding a two-dimensional shape helps children see one whole and two halves. Without measuring and counting, children can tell if the parts made by folding are fair shares or not.

In classroom exchanges, encourage children to use words such as fair shares, one whole or one, and the fraction name halves. Using the language of fractions with geometric models helps children establish their understanding of fractional parts.

Interactive Student Edition

Personal Math Trainer

Math on the Spot Video

Animated Math Models

iTools: Fractions

HMH Mega Math

ENGAGE1

How can a shape be separated into two equal shares?

Daily RoutinesCommon Core

half past 5 7 o’clock 2:30

Lesson 12.9 719B

1 23 4 Fluency BuilderSay the Same TimeMaterials index cards

On index cards, write times to the hour and half hour from 12:00 to 11:30. Write some times in digital and analog form, and some using the words o’clock or half past.

As you hold up each card, ask children to say or write the time in a different way. For example, if you hold up a card that shows “6 o’clock,” a volunteer may write 6:00 on the board.

• What is another way to say 8:30? half past 8

• What is another way to say half past 10? 10:30

Continue until children have said or written each time in a different way.

Problem of the Day 12.9Number of the DayHow many vertices does a trapezoid have? How many sides does a trapezoid have? 4; 4

Ask children to name another two-dimensional shape that has 4 vertices and 4 sides. square or rectangle

Vocabulary half of, halves

Interactive Student EditionMultimedia Glossary e

with the Interactive Student Edition

Essential QuestionHow can a shape be separated into two equal shares?

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

• What does it mean if a shape has two equal parts? Possible answer: Both parts are the same size.

Learning ActivityDirect children to think about how to separate a shape into equal parts.

• What shape is the seesaw? a rectangle

• If you separated a rectangle into parts that were not equal, what would they look like? Possible answer: One would be bigger than the other.

Have children look for classroom objects that have two parts.

• Do these objects have two equal parts or two parts that are not equal? Answers will vary.

Literacy and MathematicsChoose one or both of the following activities.

• Have children cut shapes out of paper and then fold and cut each shape into two equal parts. Have them write a sentence or two about what they did.

• Have children write a brief story about the shapes they see on a playground. Encourage them to think about which shapes can be separated into two equal parts.

Listen and DrawListen and Draw

MathTalk MATHEMATICAL PRACTICES 1

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Draw to solve.

Lesson 12.9HalvesEssential Question How can a shape be separated into two equal shares?

Geometry—1.G.A.3

MATHEMATICAL PRACTICESMP1, MP4, MP6

Analyze Will all four friends get the same amount of sandwich?

FOR THE TEACHER • Have children draw to solve this problem: Two friends share the sandwich on the left. How can they cut the sandwich so each gets an equal share? Then have children solve this problem: Two other friends share the sandwich on the right. How could this sandwich be cut a different way so each friend gets an equal share?

Possible answers shown.

Math Talk: Possible answer: Yes. Both sandwiches are cut into 2 pieces that are equal shares, so each friend has the same amount even though they look different.

EXPLORE2

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Name

Halves

How can you show halves?

1 whole 2 equal shares or 2 halves

Draw a line to show halves. Write the numbers. Possible answers shown.1.

2.

2 halves

2 halves

1 whole

1 whole

Lesson 12.9Reteach

12-21 ReteachChapter Resources© Houghton Mifflin Harcourt Publishing Company

Name Lesson 12.9Enrich

Missing HalvesThe picture shows half of the whole. Draw the other half.

Writing and Reasoning Do any of your whole shapes match? Explain.

1. 2.

3. 4.

Possible answer: Yes. My last two shapes are

squares. Half of a square can be either a

triangle or a rectangle.12-22 EnrichChapter Resources

© Houghton Mifflin Harcourt Publishing Company

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719 Chapter 12

LESSON 12.91.G.A.3 Partition circles and rectangles into two and four equal shares, describe the shares using the words halves, fourths, and quarters, and use the phrases half of, fourth of, and quarter of. Describe the whole as two of, or four of the shares. Understand for these examples that decomposing into more equal shares creates smaller shares.

Listen and DrawRead the following problem aloud.

Two friends share the sandwich on the left. How can they cut the sandwich so each gets an equal share?

• How many equal shares do you need? 2

Have children draw a line to divide the sandwich into two equal shares. • Now look at the whole sandwich. How can

you describe its shares? The whole sandwich is made up of two equal shares.

Continue by reading the following problem.Two other friends share the sandwich on the right. How could this sandwich be cut a different way so each friend gets an equal share?

If children drew a vertical line in the first sandwich, encourage them to draw a horizontal line or a diagonal line to show equal shares in the second sandwich.• When you cut a shape into equal shares,

is each share bigger or smaller than the whole? Explain. Possible answer: Each share is smaller than the whole because you are cutting it up to share.

MathTalk

MP1 Make sense of problems and persevere in solving them. Use Math Talk to focus on children’s understanding of making two equal shares.• Do parts of the sandwich have to be the

same shape to be equal? Explain. No. Explanations will vary.

ELL Strategy: Illustrate Understanding

Have children illustrate their understanding of two equal shares by dividing circles and squares.Ask children to draw a circle. Have them draw a line to make two equal shares.When children have drawn their lines, ask them to show you. Check to see that all the children have drawn a line to make two equal shares. Repeat, asking children to draw a square and a line that makes equal shares. Talk about the different ways a line can be drawn to make equal shares.

Enrich 12.9Reteach 12.9

Model and DrawModel and Draw

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1. 2.

3. 4.

The 2 equal shares make 1 whole. 2 equal shares

1 whole 2 halves

Is half of the circle larger or smaller than the

whole circle?

Share and ShShare and ShShare and Show MATHBOARDMATHBOARD

Draw a line to show halves.Possible answers shown.

COMMON ERRORS

EXPLAIN3

Quick Check

If

Rt I RR1

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Then

Advanced Learners

Lesson 12.9 720

Error Children may draw a line that makes two unequal parts.

Example In Exercise 4, children draw a line so that one part is smaller than the other.Springboard to Learning Draw the same line children drew on a rectangle. Cut out the parts of the rectangle to show that the parts are unequal. Then demonstrate equal parts by guiding children to draw a line on a rectangle and to cut the rectangle into its equal parts.

Model and Draw MATHEMATICAL PRACTICES

MP6 Attend to precision. Work through the model with children.• How many equal shares are shown? 2• How many halves are shown? 2• How many halves make 1 whole? 2Emphasize that when a shape has two equal shares, the equal shares are called halves, and each individual share is called a half.

Share and Show MATHBOARDMATHBOARDMBMMMBBBMATHABOARDMMMAAATHATHTHHAAAAAAAAATTAAAABOARDBOARDBOARD

Have children notice that the same shape is shown in Exercises 1 and 2, and the same shape is shown in Exercises 3 and 4.• Is there more than one way to show halves

on a shape? Explain. Possible answer: Yes. As long as the two parts are equal, the line can go in different places.

• How do you know the lines you drew are correct? Possible answer: the two shapes are the same.

Use the checked exercises for Quick Check.

a child misses the checked exercises

Differentiate Instruction with • Reteach 12.9

• Personal Math Trainer 1.G.A.3

• RtI Tier 1 Activity (online)

Materials Two-Dimensional Shapes (see eTearcher Resources), glue, crayons, drawing paper

• Give each child a copy of the square, rectangle, and circle from Two-Dimensional Shapes.

• Have children draw lines or fold the shapes to show halves.

• Then have children cut out the halves from the shapes and create a picture by gluing the halves on drawing paper and coloring the shapes.

Visual / KinestheticIndividual / Partners

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5. 6. 7.

8. 9. 10.

11. 12. 13.

The picture shows halves.

The equal shares make whole.

On Your OwnOn Your Own

MATHEMATICALPRACTICE 1 Analyze Relationships

Circle the shapes that show halves.

14. SMARTER Use the picture. Write numbers to solve.

THINKHalves are equal

shares.

2

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

721 Chapter 12

On Your OwnMP1 Make sense of problems and persevere in solving them. If children answered Exercises 2 and 4 correctly, assign Exercises 5–14. Make sure children understand that halves are two equal parts and not just any two parts.

SMARTER

Exercise 14 requires children to use higher order thinking skills as they explain the relationships between halves and a whole.

DEEPER

MP6 Attend to precision. To extend thinking, have children explore the relationship between the parts and the whole. Direct their attention to Exercise 8.• How many halves make one whole? 2• Are the halves larger or smaller than the

whole? They are smaller.

• Is a whole larger or smaller than its halves? Explain. The whole is always larger because the halves are smaller pieces of the whole.

MP4 Model with mathematics.• How could you use pattern blocks to show

equal shares? Possible answers: I coould use two triangles to make a rhombus. Each triangle is half of the rhombus. I could use two trapezoids to make a hexagon.Each trapezoid is half of a hexagon.

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 ACTIVITIESD

Math

MATHEMATICAL PRACTICES

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15. Color half of each shape.

16. Linus cut a circle into equal shares. He traced one of the parts. Write half of or halves to name the part.

Draw or write to solve.

a circle

17. DEEPER Draw three different ways to show halves.

18. SMARTER Circle the shapes that show halves.

TAKE HOME ACTIVITY • Draw a rectangle on a piece ofpaper. Ask your child to draw a line to show halves.

Check children’s work.

half of

EVALUATE5 Formative Assessment

MATHEMATICAL PRACTICES

Lesson 12.9 722

MP1 Make sense of problems and persevere in solving them. For Exercises 15 and 16, have children recall that halves are two equal shares that make up a whole. Make sure children understand that halves means “two equal parts” and half of means “one half, or one of two equal parts.”

DEEPER

Exercise 17 requires children to use higher order thinking skills as they visualize and show multiple ways to separate a rectangle into halves.

SMARTER

Exercise 18 requires children to classify figures as those that do or do not show halves. Some children may misunderstand and choose all figures that show two parts. Ask children to explain their answers to assess errors in thinking or visualization processes. Have children use pattern blocks, drawings, or folded shapes to check their answers.

Essential QuestionReflect Using the Language Objective Have children select a shape and explain to a partner to answer the Essential Question.How can a shape be separated into two equal shares? I can draw a line on the shape to make two parts that are the same size.

Math Journal Math

Draw a circle and separate it into halves. Color each half a different color.

Children complete blue Activity Card 19 by dividing two-dimensional shapes into two equal parts.

ActivitiesHalf Math

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

GamesOn the Water

Problem Solving • Applications

Mathematical Practices in Your Classroom PROFESSIONALDEVELOPMENT

Problem SolvingProblem Solving

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Halves

Circle the shapes that show halves. 1. 2. 3.

4. 5. 6.

Draw or write to solve.

7. Kate cut a square into equal shares. She traced one of the parts. Write half of or halves to name the part.

Chapter 12 seven hundred twenty-three 723

a squarehalf of

COMMON CORE STANDARD—1.G.A.3 Reason with shapes and their attributes.

Lesson 12.9Practice and Homework

8. Math Draw a circle and separate it into halves. Color each half a different color.

Possible answer shown.

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.

723 Chapter 12

CCSS.Math.Practice.MP4 Model with mathematics. As children create geometric models, previous work with shapes helps them recognize two equal parts as halves. They can apply this knowledge to solve fraction problems in everyday life.

Children identify that two equal parts are equal shares of a whole. Encourage them to demonstrate this relationship with tools such as diagrams, paper models, and pattern blocks.

In the context of a real-world problem, help children analyze the mathematical relationships and reflect on the results.

Jill wants to share a slice of bread with Mara. How can she cut the bread to make halves?

• How many cuts does Jill need to make in the bread? Explain. Jill needs to make 1 cut because two equal parts make halves.

• How many pieces of bread does Jill need? Explain. Jill needs 2 pieces since there are 2 people.

Personal Math Trainer

FOR MORE PRACTICE GO TO THE

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2. Circle the new shape you can make.

3. Circle the shape that has both flat and curved surfaces.

Spiral Review (1.G.A.1, 1.G.A.2)

1. Circle the shape that shows halves.

Lesson Check (1.G.A.3)

Combine and .

4. How many do you use to make a ?Draw to show your answer.

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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