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LESSON AT A GLANCE

725A Chapter 12

Fourths

LESSON 12.10

If Children AskSome children may ask why it is important that the parts showing halves or fourths are equal parts or equal shares. Explain that equal parts or equal shares are important mathematical concepts that will help children when they learn more about fractions and division in later grades.

Discuss how being able to recognize equal parts or equal shares will help children understand real-life situations in which words such as half, fourth, or quarter are used. Point out that these words are connected to many real-life uses, such as time (half-past ten), distances (a quarter mile), dozens (a half dozen), and money (a quarter). In turn, such informal real-life applications will help children see that the work they do with shapes is related to things that people do every day.

Interactive Student Edition

Personal Math Trainer

Math on the Spot Video

Animated Math Models

iTools: Fractions

HMH Mega Math

About the Math

Learning ObjectivePartition circles and rectangles into four equal shares.

Language ObjectiveChildren use a paper cut-out shape to demonstrate how a shape can be separated into four 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

ENGAGE1Daily Routines

Common Core

1 23 4 Pages 48–49 in Strategies and Practice for Skills and Facts Fluency provide additional fluency support for this lesson.

139 + 4 4 + 9

6 + 77 + 610 + 3

3 + 108 + 5

13 13 13

Lesson 12.10 725B

How can a shape be separated into four

equal shares?

1 23 4 Fluency BuilderTarget Sums RelayOrganize the class into four teams. Have each team stand in a line facing the board. Assign a section of the board to each team.

Write a target sum on the board. At your signal, the first person in each line goes to the board and writes two addends with that sum. He or she then passes the chalk to the next person in line who does the same.

Children go to the end of the line after their turn. They may not duplicate any facts their team has written. The race continues until you say Stop.

Problem of the Day 12.10Word of the Day picture graph Ben collects 4 shells, 1 red rock, and 1 black rock at the beach. Make a picture graph to show what Ben collects. Graphs should show 4 shells, 1 red rock, and 1 black rock.

Tell children that they can make a graph with pictures. Remind them to label the parts of the graph.

Vocabulary fourth of, fourths, quarter of, quarters

Interactive Student EditionMultimedia Glossary e

with the Interactive Student Edition

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

Making ConnectionsInvite children to tell you what they know about separating a shape into parts.

• If you separate a shape into two equal parts, what are the parts called? halves

Learning ActivityDirect children to think about how to separate a shape into more than two parts.

• How many kinds of clothes are there on the line? 4

• What does Avery wonder? what it would look like if 4 piles of laundry each took up a fourth of the bench

• Another name for four equal shares is called fourths.

Literacy and MathematicsChoose one or more of the following activities.

• Have children work in small groups to write a short story about separating a rectangle into four equal parts.

• Have children write a description about shapes that are separated into equal and unequal parts.

Common Core Fluency Standard 1.OA.C.6

Draw to solve. Write how many.

Listen and DrawListen and Draw

MathTalk MATHEMATICAL PRACTICES 6

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Use what you know about halves.

FourthsEssential Question How can a shape be separated into four equal shares?

Lesson 12.10

Chapter 12 seven hundred twenty-fi ve 725

There are 4 — equal shares.

Geometry—1.G.A.3

MATHEMATICAL PRACTICESMP1, MP4, MP6

Explain How did you decide how to cut the pizza?

FOR THE TEACHER • Read the following problem. Two friends will share a pizza. Then two more friends come. Now four friends will share the pizza. How can the pizza be cut so each friend gets an equal share? How many equal shares are there?

Possible answer shown.

Math Talk: Possible answer: 4 friends share the pizza so I know there needs to be 4 pieces. First I drew a line from top to bottom to show halves, which make 2 equal shares. Then I drew another line from side to side to cut each half into 2 equal shares.

EXPLORE2

1

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Name

1 whole

4 fourths

4 fourths

1 whole

1 whole

There are 4 equal shares.

Fourths

How can you show fourths?

4 fourths or 4 quarters

Draw lines to show fourths. Write the number. 1.

2. Draw lines to show quarters. Write the number.

Lesson 12.10Reteach

Possible answers shown.

12-23 ReteachChapter Resources© Houghton Mifflin Harcourt Publishing Company

Name Lesson 12.10Enrich

From Halves to FourthsThese shapes show halves. Draw lines to make them show fourths.

Writing and Reasoning Tell how you can solve Exercise 1 in a different way.

1. 2.

3. 4.

Possible answers shown.

Possible answer: I can draw one line from

the left side to the right side.

12-24 EnrichChapter Resources© Houghton Mifflin Harcourt Publishing Company

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3 DifferentiatedInstruction

725 Chapter 12

LESSON 12.101.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 Draw Read the following aloud.

Two friends will share a pizza. Then two more friends come. Now four friends will share the pizza. How can the pizza be cut so each friend gets an equal share? How many equal shares are there?

Guide children to share the pizza for two friends first by asking these questions. • How can you share the pizza for two

friends to have equal shares? I could draw a line to make 2 parts that are the same size.

• What is each part called? a half

Have children draw a line to show halves.• How can you change your drawing so that

four friends can each have an equal share? I can draw another line to make 4 equal parts.

Guide children to draw a second line to show fourths.• Who gets a smaller equal share, two friends

who share a pizza or four friends who share a pizza? Explain. Four friends get a smaller share because their equal shares are smaller than halves.

MathTalk

MP6 Attend to precision. Use Math Talk to focus on children’s understanding of four equal shares.• Why can’t you cut this round pizza into

four strips? The pieces would not be equal.

ELL Strategy: Illustrate Understanding

Have children illustrate their understanding of four equal shares by dividing circles and squares.Ask children to draw a circle. Have them draw a line to make two equal shares. Then ask children to draw a second line to make four equal shares. Check to see that all the children have drawn four equal shares.Repeat, asking children to draw a square and two lines to make four equal shares.

Enrich 12.10Reteach 12.10

Model and DrawModel and Draw

Share and ShShare and ShShare and Show MATHBOARDMATHBOARD

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The 4 equal shares make 1 whole.

4 equal shares

1 whole 4 fourths, or4 quarters

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How can you describe one of the

4 equal shares?

Color a fourth of the shape.

4. 5. 6.

Color a quarter of the shape.

1. 2. 3. Possible answers shown.

Possible answers shown.

COMMON ERRORS

EXPLAIN3

Quick Check

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Advanced Learners

Lesson 12.10 726

Error Children may color more than one part of the shape.

Example For Exercise 5, children color all four parts.Springboard to Learning Ask children how many fourths make a whole. Together, read the directions again. Point out that they are to color a fourth of the shape, or one of the four equal shares of the shape.

Model and Draw MATHEMATICAL PRACTICES

MP6 Attend to precision. Work through the model with children, emphasizing the different names for the equal shares.• What are two different names for 4 equal

parts? fourths or quarters

• How many fourths make a whole? 4• How many quarters make a whole? 4

Share and Show MATHBOARDMATHBOARDMBMMMBBBMATHABOARDMMMAAATHATHTHHAAAAAAAAATTAAAABOARDBOARDBOARD

As children color one equal share of each shape, tell them that fourth of and quarter of have the same meaning.• Does it matter which fourth you color?

Explain. Possible answer: It does not matter because any one share will show one of the four equal shares.

• How do you know you colored one fourth of the shape? Possible answer: the shape is divided into four equal parts and I colored one of them.

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

a child misses the checked exercises

Differentiate Instruction with • Reteach 12.10

• Personal Math Trainer 1.G.A.3

• RtI Tier 1 Activity (online)

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

• Copy squares from Two-Dimensional Shapes. Give each pair four squares.

• Have each partner take a square and draw a line to show halves. Then have partners exchange squares and draw a second line to show fourths. Have children compare the equal parts they made.

• Extend the activity by having partners draw more than two lines on their remaining squares to show fourths. Have children compare the equal parts they made.

Visual / VerbalIndividual / Partners

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On Your OwnOn Your Own

MATHEMATICALPRACTICE 4 Use Diagrams Circle the shapes

that show fourths.

7. 8. 9.

10. 11. 12.

13. 14. 15.

16. DEEPER Draw three different ways to show fourths.Possible answer shown.

727 Chapter 12

On Your OwnMP4 Model with mathematics. If children answered Exercises 3 and 6 correctly, assign Exercises 7–16.• How can you tell if a shape shows fourths?

It must have 4 parts that are all the same size or amount.

DEEPER

MP6 Attend to precision. Exercise 16 requires children to use higher order thinking skills as they represent multiple ways of showing fourths. To extend thinking, ask these questions about the relationship between fourths and wholes.• When you cut a whole into fourths, how

many fourths are there? 4

• Which is smaller, the whole or a fourth? Explain. Possible answer: A fourth is smaller. If you cut a whole, you separate it into parts that have to be smaller than the shape you started with.

• Which is larger, the whole or a fourth? Explain. Possible answer: The whole is larger. To get a fourth, you cut the whole in 4 equal parts.

MP1 Make sense of problems and persevere in solving them.• Suppose you had 8 game tokens. How could

you give one fourth of your tokens to a friend? Possible answer: I could make 4 equal shares. That is 2 tokens in each share. So one fourth of my game tokens is 2 tokens.

4 ELABORATE

Differentiated Centers Kit

DIFFERENTIATED INSTRUCTION INDEPENDENT ACTIVITIES

MathMath

MATHEMATICAL PRACTICES COMMUNICA C

Personal Math Trainer

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17. Write halves, fourths, or quarters to name the equal shares.

Solve.

18. SMARTER Circle the shape that shows quarters.

19. SMARTER Alano has a small pizza. He wants to share the pizza with friends. He cuts the pizza into fourths. Draw lines to show how he cuts the pizza.

How many equal shares did you draw? 4 —

How many halves can you show in a circle? 2 —

Tell how you can solve this problem in a different way.

TAKE HOME ACTIVITY • Draw a circle on a piece ofpaper. Ask your child to draw lines to show fourths.

halves ——

Possible answer: I can draw lines from top left to bottom

right and from top right to bottom left.

fourths or quarters —————

Possible answer is shown.

EVALUATE5 Formative Assessment

Differentiated Centers Kit

DIFFERENTIATED INSTRUCTION INDEPENDENT ACTIVITIESD

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

MATHEMATICAL PRACTICES

Lesson 12.10 728

For Exercises 17 and 18, encourage children to use what they know about halves and fourths to help them find the answer.

SMARTER

MP6 Attend to precision. Exercise 18 requires children to use higher order thinking skills as they analyze the similarities and differences between the triangles shown within each rectangle.

Personal Math Trainer SMARTER

Be sure to assign Exercise 19 to children in the Personal Math Trainer. It features a video to help them model and answer the problem. Children need to look for structure and separate a shape into fourths. Children who answer incorrectly may not understand that fourths refer to four equal parts or four quarters. Provide prompts for children who struggle to show fourths of a circle in more than one way by asking how the shape looks different if it is turned slightly.

Essential QuestionReflect Using the Language Objective Have children use a paper cut-out shape to demonstrate and answer the Essential Question.How can a shape be separated into four equal shares? Possible answer: I can draw lines to make 4 parts that are all the same size.

Math Journal Math

Draw two squares. Draw lines to show fourths. Color a fourth of the first square. Color the second square to show a whole.

GamesOn the Water

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.

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

Problem Solving • Applications

Extend the Math Activity

Problem SolvingProblem Solving

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7. Chad drew a picture to show a quarter of a circle. Which shape did Chad draw? Circle it.

Fourths

Circle the shapes that show fourths.

1. 2. 3.

4. 5. 6.

Chapter 12 seven hundred twenty-nine 729

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

Lesson 12.10Practice and Homework

8. Math Draw two squares. Draw lines to show fourths. Color a fourth of the first square. Color the second square to show a whole.

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.

729 Chapter 12

Which Part is Smallest?Materials Circles (halves and fourths) (see eTeacher Resources), green, red, and yellow crayons, drawing paper

Investigate Have children explore the relative sizes of wholes, halves, and fourths. Give each child three unmarked circles. Then give them the following three scenarios. At a class pizza party, a whole spinach pizza was left. Use green to color one circle to show a whole pizza. Check children’s work. A half of a pepperoni pizza was left. Use red to color another circle to show a half of a pizza. Check children’s work. A fourth of a cheese pizza was left. Use yellow to color another circle to show a fourth of a pizza. Check children’s work.

Math Talk After children complete their drawings, discuss the results.

• Which circle shows the most pizza left: a whole, a half, or a fourth? A whole is the most.

• Which circle shows the least pizza: a whole, a half, or a fourth? A fourth is the least.

• Are a fourth and a half less than a whole or greater than a whole? less than

Summarize Ask children to say whole, half, and fourth in order from least to greatest. Then have them arrange their circles to show this order.

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Personal Math Trainer

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2. What shapes did Leila use to build the wall? Circle the shapes she used.

3. Use the graph to answer the question. How many fewer children answered yes than no?

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

1. Circle the shape that shows fourths.

Lesson Check (1.G.A.3)

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Monitoring Common Core Success

Maintaining Focus on the Major WorkThe major work in future grades includes solving problems involving fractions. In Lessons 12.8–12.10, children identify equal and unequal parts in two-dimensional shapes. They work to recognize that equal parts, when combined, make a whole. Their work with halves and fourths connects to fractions as they partition a shape into equal parts.

Connecting Content Across Domains and ClustersIn Lessons 12.6—12.10, children work within Cluster 1.G.A, reason with shapes and their attributes. Children continue to learn how to compose two or more shapes into a larger composite shape, and conversely to decompose shapes into smaller components. Children extend this knowledge to build an understanding of equal parts, partitioning circles and rectangles into two or four equal parts, and naming these parts as halves or quarters. Work in this cluster connects to developing an understanding of fractions.

Focus on Mathematical Practices Children construct viable arguments and critique the reasoning of others (MP3). Children draw shapes to decompose them into smaller shapes. They make reasonable arguments as to what shapes can be decomposed to form other shapes. Then justify their conclusions by communicating them to classmates. This process can be extended to partitioning circles and rectangles into two and four equal shares. Children draw a shape and construct an argument as to how and why the shape can be partitioned equally. Children listen to the arguments of others, decide whether they make sense, and ask questions to clarify their understanding.

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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