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Professional Development Videos

LESSON AT A GLANCE

LESSON 10.3

587A Chapter 10

Interactive Student Edition

Personal Math Trainer

Math on the Spot Video

Teaching for DepthA picture graph uses a picture or a symbol to represent each thing, and children need to count the pictures or symbols in a row to determine the number. A bar graph uses shaded bars to represent data, and children need to look at the length of the bar to determine the number.

In order to analyze and interpret data on a bar graph, it is important for children to correctly label the parts of a graph.

• Each bar graph needs to have a title reflecting the data that has been collected.

• Each axis of the bar graph needs to be labeled. After identifying the categories of data, each category should be labeled with a word or a picture. The number of items needs to be labeled on the other axis, starting with 0.

Read Bar Graphs

Learning ObjectiveAnalyze and compare data shown in a bar graph.

Language ObjectiveChildren use a bar graph to point out to another child how to read a bar graph to find the number that a bar shows.

MaterialsMathBoard, two-color counters

F C R Focus:Common Core State Standards

1.MD.C.4 Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another.

MATHEMATICAL PRACTICES (See Mathematical Practices in GO Math! in the Planning Guide for full text.)MP3 Construct viable arguments and critique the reasoning of others. MP4 Model with mathematics. MP5 Use appropriate tools strategically.

F C R Coherence:Standards Across the GradesBeforeK.MD.B.3

Grade 11.MD.C.4

After2.MD.D.10

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 571J.

FOCUS COHERENCE RIGOR

ENGAGE1Daily Routines

Common Core

Lesson 10.3 587B

with the Interactive Student Edition

Essential QuestionHow can you read a bar graph to find the number that a bar shows?

Making ConnectionsInvite children to tell you what they know about graphs. Have them talk about the different places they have seen graphs.

Why is information sometimes presented in a graph? Possible answer: Graphs make information easier to see and compare.

Learning ActivityGuide children in reading and interpreting the information displayed in the bar graph.

• What do the bars on the bar graph show? the number of tomatoes, peppers, and carrots the gardener planted

• Which vegetable did the gardener plant the most of? The gardener planted more peppers.

Literacy and MathematicsChoose one or more of the following activities.

• Display a number of crayons of different colors. Invite children to write a paragraph explaining how a bar graph can be used to show information about the crayons.

• Invite children to write one question about the bar graph from the lesson. Select a few questions to read aloud. Call on volunteers to answer.

1 23 4 Fluency BuilderMaking TensWrite the following number sentences.

Ask children to explain how they can use the make a ten strategy to rewrite and solve each number sentence.

9 + 6 = _____ 9 + 1 + 5 = 15

8 + 7 = _____ 8 + 2 + 5 = 15

9 + 8 = _____ 9 + 1 + 7 = 17

Children can draw a ten frame if necessary to find the sums.

Problem of the Day 10.3Calendar Math Place adhesive notes on different numbers of days for each week of

this month. Which week has the most notes? Which week has the fewest notes? Answers will vary.

Vocabulary bar graph

How can you read a bar graph to f ind the number that

a bar shows?

Common Core Fluency Standard 1.OA.C.6

Interactive Student EditionMultimedia Glossary e

1 23 4 Pages 50–51 in Strategies and Practice for Skills and Facts Fluency provide additional fluency support for this lesson.

Type of Sneaker We Are Wearing

Each stands for 1 child.

no laces

laces

ListenListen

MATHEMATICAL PRACTICES 3MathTalk

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Chapter 10 fi ve hundred eighty-seven 587

Write a question about the graph.Use to help solve the problem.

Read Bar GraphsEssential Question How can you read a bar graph to find the number that a bar shows?

Lesson 10.3

HandsOn

FOR THE TEACHER • Read the following problem. Emma’s class made this picture graph. What question could Emma’s class answer using the graph? Write the question and the answer.

Apply Describe how the class made this picture graph.

Measurement and Data—1.MD.C.4

MATHEMATICAL PRACTICESMP3, MP4, MP5

Math Talk: Possible answer: Each child drew a circle in the graph to show if he or she was wearing sneakers with laces or with no laces.

Possible question: How many children are wearing sneakers with laces?

Answer for possible question: 10 children

EXPLORE2

Kin

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f S

nacks

Number of Children

Our Favorite Snack

0

apple

pretzel

yogurt

1 2 3 4 5 6

Name

The longest bar shows the

snack most children chose.

Read Bar Graphs

A bar graph uses a bar to show how many.

This graph shows 6 children chose .

Use the bar graph to answer the question.

1. How many children chose ? 2 children

2. How many children chose ? 4 children

3. Circle the snack the most children chose.

4. Circle the snack the fewest children chose.

Lesson 10.3Reteach

10-9 ReteachChapter Resources© Houghton Mifflin Harcourt Publishing Company

Acti

vit

ies

Number of Children

dance

soccer

music

Our Favorite After-School Activity

0 1 2 3 4 5 6 7 8 9

Name

Bar Graph CluesUse the bar graph to complete each sentence.

1. 3 more children chose soccer than dance.

2. 2 fewer children chose music than soccer.

3. 11 children chose dance or music.

4. If 3 more children chose dance, then the bar graphwould show 8 children for dance.

Writing and Reasoning How can you tell without counting if more children chose soccer than music? Explain.

Lesson 10.3Enrich

than the bar for music.

Possible answer: The bar for soccer is longer

10-10 EnrichChapter Resources© Houghton Mifflin Harcourt Publishing Company

DifferentiatedInstruction1

2

3

587 Chapter 10

LESSON 10.3

Enrich 10.3Reteach 10.3

ListenMaterials two-color countersRead the following problem aloud to the class.

Emma’s class made this picture graph. What question could Emma’s class answer using the graph?

• What do you need to write? a question about the graph

• What information does the picture graph show? Possible answer: The graph shows the numbers of children wearing laces or no laces on their shoes.

• What is one thing you learned from this graph? Possible answer: There are more children wearing laces than no laces on their shoes in Emma’s class.

After writing their questions, have children exchange papers with a classmate. Have the classmate answer the question, and then have the child check the answer.

MathTalk

MP3 Construct viable arguments and critique the reasoning of others. Use Math Talk to focus on children’s understanding of how to make and read a picture graph.• How could you change this graph to show

other kinds of shoes you and your friends wear? Possible answer: Children can suggest shoes to add to the graph, such as sandals or boots.

ELL Strategy: Model Language

Direct children’s attention to one of the graphs illustrated in the text.Explain that graphs provide information.• What information can we get from

this graph?Model questions and answers about the graph. Write sentence frames on the board as you model: How many _____? How many more _____? How many fewer _____?Direct children’s attention to another graph in the text. Encourage children to ask questions about the graph.

1.MD.C.4 Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another.

HandsOn

Art

To

ols

Number of Children 0 1 2 3 4 5 6

markers

paintbrushes

crayons

Possible answer: Art Tool We Like

Model and DrawModel and Draw

Share and ShShare and ShShare and Show MATHBOARDMATHBOARD

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Use the bar graph to answer the question.

In a bar graph, each bar shows information. You can compare the lengths of the bars. What title describes this graph?

1. How many children chose ?

6 —

children

2. How many childrenchose ?

2 — children

4. Which art tool did the fewest children choose? Circle.

5. Which art tool did the most children choose? Circle.

Touch the end of a bar. Look down to see the number of

children.

3. How many more children chose than ? 4 — more children

EXPLAIN3

Quick Check

If

Rt I RR1

2

3

Then

COMMON ERRORS

MATHEMATICAL PRACTICES

Advanced Learners

0 1 2 3 4 5 6 7 8 9 10

At the Aquarium

sea star

fish

eel

crab

At the Aquarium

sea star

fish

eel

crab

Lesson 10.3 588

Model and Draw MP4 Model with mathematics. Point out the bar graph and guide children through the model with the following questions.• How can you tell the length of the bar for

markers? I find the line at the end of the red bar and follow it down to the number 5.

• What does the red bar tell you? Possible answer: It tells how many children chose markers.

• What clues help you write a title for the graph? I use the labels for the rows and numbers.

• How can you tell your answer is correct? It describes the information in the graph.

Share and Show MATHBOARDMATHBOARDMBMMMBBBMATHABOARDMMMAAATHATHTHHAAAAAAAAATTAAAABOARDBOARDBOARD

Have children complete Exercises 1 and 2 by following the line down from the end of the bar for that tool to read the number. Have children explain how they solved Exercise 3.Use the checked exercises for Quick Check. Have children use MathBoards to show their solutions.

a child misses the checked exercises

Differentiate Instruction with • Reteach 10.3

• Personal Math Trainer 1.MD.C.4

• RtI Tier 1 Activity (online)

Error Children may have difficulty finding the value for a given bar in a bar graph.

Example For Exercise 1, they follow the line at the end of the blue bar and write 5.Springboard to Learning Some children may be distracted by all the elements in the bar graph and may be unable to focus on the one line to trace down to the bottom. Encourage children to hold a straightedge along the line at the end of a given bar to identify the corresponding number.

Logical / MathematicalIndividual / Partners

Materials 1-Inch Grid Paper (see eTeacher Resources), crayons

• Draw a bar graph on the Grid Paper as shown.

• Read aloud the following riddle.

I am thinking of a sea creature from the aquarium. I saw more of these than the number of eels. I saw fewer of these than the number of crabs. What creature am I thinking of? sea star

• Have children write similar riddles that can be solved with the graph. Have them trade with a partner and solve each other’s riddles.

Favorite Vehicle

Kinds of Vehicles

Num

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car truck dumptruck

0

1

2

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Chapter 10 • Lesson 3 fi ve hundred eighty-nine 589

6. How many children

chose ?

2 — children

7. How many children

chose

How many children

?

6 — children

8. How many children in all

chose and

ow many children in all

?

8 — children

10. Which vehicle did the most children choose? Circle.

11. SMARTER Order the vehicles from least to most votes. Write 1 for the least votes and 3 for the most votes.

MATHEMATICALPRACTICE 4 Use Graphs Use the

bar graph to answer the question.

1 —

2 —

3 —

9. How many more children

chose

How many more children

than ? 3 — more children

On Your OwnOn Your Own

DO NOT EDIT--Changes must be made through “File info”CorrectionKey=A

1_MNLESE341944_C10L03.indd 589 3/12/14 7:18 PM

ELABORATE4

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

PROBLEM TYPE SITUATIONS

589 Chapter 10

On Your OwnMP4 Model with mathematics. If children answered Exercises 4 and 5 correctly, assign Exercises 6–11. This bar graph is in vertical orientation, and children have worked only with horizontal graphs so far. Point out that the number of children is now shown on the vertical axis and the kinds of vehicles are shown on the horizontal axis.

SMARTER

Exercise 11 requires children to use higher order thinking skills as they order the vehicles to show the results of the bar graph. Make sure that children use number 1 for the vehicle chosen by the fewest children.

DEEPER

To extend learning, have children write the three numbers showing the results of the bar graph. Ask them to write the numbers in order from least to greatest. Then ask children to write the numbers from greatest to least.• What is a quick way to reverse the order?

Possible answer: I can change the fi rst and third numbers and leave the middle number the same.

• Why does the middle number stay the same? Possible answer: The middle is still the middle in either order.

MP3 Construct viable arguments and critique the reasoning of others.• How could you use “greater than” and “less

than” to describe the middle number? Possible answer: The middle number is greater than one number and less than the other number.

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

Addition and Subtraction

Compare • Difference Unknown Exercises: 3, 9, 13

Put Together/Take Apart • Total Unknown Exercise: 8

DO NOT EDIT--Changes must be made through “File info”CorrectionKey=D

Differentiated Centers Kit

DIFFERENTIATED INSTRUCTION INDEPENDENT ACTIVITIESD

Math

How Our Jackets Are Fastened

Fast

ener

s

Number of Jackets1 2 3 4

zippers

buttons

0 5

TAKE HOME ACTIVITY • Have your child look through newspapers and magazines for examples of bar graphs. Talk about what information is shown in each graph you find.

Math

MATHEMATICAL PRACTICES

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12. Kim puts on a jacket with .Add her jacket to the graph. Now how many jackets have ? 3 — jackets

3 — jackets

13. DEEPER Ed adds a row to the graph to show jackets with snaps. 2 fewer jackets have snaps than have zippers. How many jackets have snaps?

Use the bar graph to answer the question.

14. SMARTER Use the graph. How many more jackets have than

? Circle the answer.

7

5

3

more jackets have than .

EVALUATE5 Formative Assessment

MATHEMATICAL PRACTICES

Lesson 10.3 590

Children practice making and reading bar graphs in this game.

Children read the book and learn how to gather and compare data by making tally tables and graphs.

Children complete blue Activity Card 8 by making a bar graph.

GamesGraph Game

LiteratureMiss B’s Class Makes Tables and Graphs

ActivitiesPass the Bar

Essential QuestionReflect Using the Language Objective Have children use a bar graph to point out to another child how to answer the Essential Question.How can you read a bar graph to find the number that a bar shows? Possible answer: I match the end of a bar to the number below.

Math Journal Math

Use numbers and pictures to compare two items in a bar graph.

MP5 Use appropriate tools strategically. For Exercise 12, make sure children understand that the bar graph shows how many jackets are fastened with zippers or buttons.

DEEPER Multi-Step

For Exercise 13, children solve a multi-step problem by reading a graph and then comparing that data with information given in the problem. Children must first determine that 5 jackets have zippers. Then guide children to solve 5 − 2 to find how many jackets have snaps.

SMARTER

For Exercise 14, children interpret the information given in a bar graph to answer the question. If children choose 7, they may have added rather than compared the information in the graph. An answer of 5 indicates the number of zippers rather than an interpretation of the compared data. Children may need a reminder that a comparison often involves subtraction.

Problem Solving • Applications

COMMON CORECOMMCOMMCOMMCOMMON CON CON CON COREOREOREORE

PROFESSIONALDEVELOPMENT Math Talk in Action

Problem SolvingProblem Solving

Our Favorite Breakfast

Num

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What We Use in the Rain

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Practice and HomeworkLesson 10.3

COMMON CORE STANDARD—1.MD.C.4 Represent and interpret data.

Use the bar graph to answer the question.

3. Claudette uses an . Add her to the graph. Now how many more children use an than a ?

2 — more children

Chapter 10 fi ve hundred ninety-one 591

Read Bar Graphs

Use the bar graph to answer the question.

1. How many children chose ?

3 — children

2. How many more children chose than ?

3 — more childrenmuffin egg pancakes

4. Math Use numbers and pictures to compare two items in a bar graph.

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.

591 Chapter 10

Have children discuss the strategy they used to interpret the data in Exercise 2.

Teacher: For Exercise 2, which two bars do you need to look at?

Dawn: I look at the pancakes bar for pancakes and the egg bar for eggs.

Teacher: How do you know how many votes pancakes have?

Nikki: I found the top of the pancakes bar and followed it across to the number of children. They have 6 votes.

Teacher: How do you know how many votes eggs have?

Cal: The egg bar touches the third line, so they have 3 votes.

Teacher: These are both good ways to read the bars on the graph. How did you find how many more children chose pancakes than eggs?

Mel: I just looked at the pancakes bar and the egg bar together because the egg is next to the pancakes. If I look at the egg bar first, I see that it ends at 3. Then I count up from 3 to where the pancakes bar ends. It ends at 6. So I counted up 3.

Teacher: Yes, Mel, counting up is a good way to find the difference. Is there another way to find the difference?

Troy: I know 6 children voted for pancakes and 3 voted for eggs. So I found 6 – 3, which equals 3.

Teacher: Yes, these are all different ways you can compare the votes. You can use whichever way is easiest for you.

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Number of Children

Our Favorite Activity for a Rainy Day

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1 2 3 4 5 6 7 8 9 10

Personal Math Trainer

FOR MORE PRACTICE GO TO THE

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Lesson Check (1.MD.C.4)

Spiral Review (1.OA.B.4, 1.OA.D.8)

2. Write a subtraction sentence you can solve by using 9 + 7 = 16.

_ − _ = _

3. How many fewer are there ? Subtract to compare.

1. How many more children chose than ?

5 _ more children

592 fi ve hundred ninety-two

Use the bar graph to answer the question.

7 − 5 = 2 _

2 _ fewer

Possible answers:

16 − 7 = 9

16 − 9 = 7

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 10.3 592