hands on • make bar graphs€¦ · it in the graph. make a bar graph to show each animal in the...

About the MathProfessional Development

Professional Development Videos

Hand We Use to Write

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Each stands for 1 child.


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Number of Children

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LESSON AT A GLANCE

593A Chapter 10

LESSON 10.4

Using Connecting Cubes to Make Bar GraphsWhen making bar graphs in this lesson, children may find it helpful to represent the data with connecting cubes before recording in the grid. This model is illustrated for the survey question: Do you write with your left hand or your right hand? Suppose children found that 3 of their classmates write with their left hand and 7 classmates write with their right hand.

• To graph this problem, children can use the data in the picture graph to make a cube train with 3 cubes in one color and 7 cubes in another color. They can use this model to create the bar graph.

• Children can compare the lengths of the cube trains or the bars to compare quantities. They can see that there are more children who write with their right hand than with their left hand because the red bar and cube train are longer than the blue bar and cube train.

Hands On • Make Bar Graphs

Learning ObjectiveMake a bar graph and interpret the information.

Language ObjectivePartners discuss and share two ways that a bar graph helps you compare information.

MaterialsMathBoard, connecting cubes, crayons

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.MP8 Look for and express regularity in repeated reasoning.

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 10.4 593B

with the Interactive Student Edition

Essential QuestionHow does a bar graph help you compare information?

Making ConnectionsInvite children to tell you what they know about bar graphs.

Have children describe a bar graph and compare it to a picture graph. What do the bars in a bar graph show? Possible answer: how many of each item there are What does the longest bar in a bar graph show? Possible answer: the item with the greatest number

Learning ActivityLead children in a discussion about graphs and how to read them.

• How can Avery keep track of the yellow, red, and purple balloons? Possible answer: by making a bar graph

• How might Avery use the information in the bar graph? Possible answer: to count and compare the balloons

Literacy and MathematicsChoose one or more of the following activities.

• Arrange volunteers in three rows, aligned on the left, to represent the number of yellow, red, and purple balloons from the story. Have the rest of the class describe the rows.

• Have children write a paragraph explaining how to read a bar graph. Encourage them to include a simple drawing of a bar graph with the different parts labeled.

<

=

>

>

1 23 4 Fluency BuilderMake Ten and SubtractReview step-by-step how to use the strategy, subtract to ten. Then solve.

15 − 7 = ? Think: 7 − 5 = 2

15 − 5 − 2 = 10 − 2 = 8

Then display a selection of subtraction facts like the ones below. For each fact, have children explain how they can take apart the smaller number to subtract back to ten and then solve.

Share each solution step-by-step.

12 − 5 = ? Think: 5 = 2 + 3 12 − 2 − 3 = 10 − 3 = 7

14 − 6 = ? Think: 6 = 4 + 2 14 − 4 − 2 = 10 − 2 = 8

15 − 8 = ? Think: 8 = 5 + 3 15 − 5 − 3 = 10 − 3 = 7

13 − 7 = ? Think: 7 = 3 + 4 13 − 3 − 4 = 10 − 4 = 6

16 − 7 = ? Think: 7 = 6 + 1 16 − 6 − 1 = 10 − 1 = 9

Problem of the Day 10.4Word of the Day compare

Complete each number sentence to compare two numbers. Write <, >, or =.

1. 42 42 2. 75 57

3. 23 32 4. 65 61

Have children justify their answers and explain how to compare two-digit numbers.

Vocabulary

How does a bar graph help you

compare information?

Common Core Fluency Standard 1.OA.C.6

Interactive Student EditionMultimedia Glossary e

1 23 4 Pages 103–104 in Strategies and Practice for Skills and Facts Fluency provide additional fluency support for this lesson.

EXPLORE2

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Number of Food Items Sold

Food Sold at the Soccer Game

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Listen and DrawListen and DrawHands

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MATHEMATICAL PRACTICES 4MathTalk

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Chapter 10 fi ve hundred ninety-three 593

FOR THE TEACHER • Read the following problem. Dan keeps track of the food he sells at the soccer game. He sells all of the food on the table. Make a bar graph to show the food Dan sells.

Use to model the problem. Color 1 box for each food item to complete the graph.

Make Bar GraphsEssential Question How does a bar graph help you compare information?

Lesson 10.4

Model How do you know that you counted each food in the picture?

Measurement and Data—1.MD.C.4MATHEMATICAL PRACTICES

MP3, MP4, MP8

Math Talk: Possible answer: I can place a cube on each food so I know which ones I counted.

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sheep

chicks

Number of Animals

Animals at the Farm

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Desks and Doors in Our Classroom

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desks

doors

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Cross out each animal as you show

it in the graph.

Make a bar graph to show each animal in the picture.

Make Bar Graphs

Are there more or in your classroom?1. Make a bar graph to find out.

2. How many are in your classroom?

3. Are there more or in your classroom? Circle.

Lesson 10.4Reteach

Check children’s work.

Answers will vary based on the graph.

10-11 ReteachChapter Resources© Houghton Mifflin Harcourt Publishing Company

Num

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Lett

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6 letters

5 letters

4 letters

3 letters

2 letters

The Number of Letters in Our Names

Number of Children0 1 2 3 4 5 6 7 8 9 10

Name

Compare the LettersSome children are comparing the number of letters in their names. 1. Write the names of 10 friends.

Count how many letters are ineach name.

2. Make a bar graph of the information. Show how many names have different numbers of letters.

3. How many letters are in the most names?

Writing and Reasoning How would the graph change if you added your name? Explain.

Lesson 10.4Enrich

Check children’s work. Answers will vary.


10-12 EnrichChapter Resources© Houghton Mifflin Harcourt Publishing Company

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593 Chapter 10

LESSON 10.4

Enrich 10.4Reteach 10.4

Listen and DrawMaterials connecting cubes, crayons

Read the following problem aloud to the class.Dan keeps track of the food he sells at the soccer game. He sells all of the food on the table. Make a bar graph to show the food Dan sells.

• What do you need to do? Make a bar graph showing the number of each kind of food in the picture.

• How can you use connecting cubes to help solve the problem? Possible answer: I can put red cubes on all of the hot dogs in the picture. I can put yellow cubes on the tacos. I can put green cubes on the slices of pizza. Then I can connect the cubes by color.

After children color the grid to match their cube trains, ask the following questions.• What does your graph show about the

food Dan sold? Possible answer: Hot dogs sold the most.

• How does the graph show that? Possible answer: The row with hot dogs is longest, so that sold the most.

MathTalk

MP4 Model with mathematics. Use Math Talk to focus on children’s understanding of how to represent and interpret data in bar graphs.• Did Dan sell more tacos or more pizza?

How do you know? Dan sold more tacos. Possible explanation: There are more squares filled in for tacos than pizza.

ELL Strategy: Cooperative Grouping

Pair fluent English speakers with English Language Learners. Have pairs work together to make a bar graph and talk about the information on the graph.Give each pair some connecting cubes of three different colors.Have the children connect the like colored cubes together and use the cubes to form a bar graph. Have children write a title and labels for their graphs.Then encourage children to take turns asking and answering questions about the information on the bar 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

EXPLAIN3

Flowers in the Garden

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1. Which hand do more children use to write?


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Number of Children0 1 2 3 4 5 6 7 8 9 10

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Model and DrawModel and Draw

Share and ShShare and ShShare and Show MATHBOARDMATHBOARD

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Do more children write with their left hand or right hand? Ask 10 friends which hand they use. Make a bar graph.

Are there more or in the garden? Make a bar graph to fi nd out.Shade 1 box for each fl ower in the picture.

There are more sunfl owers in the garden.


COMMON ERRORS

Quick Check

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MATHEMATICAL PRACTICES

Advanced Learners

Lesson 10.4 594

Error Children may color the wrong number of cells for a bar in the graph.

Example Children count all of the responses in the graph, and they find that they colored more than 10.Springboard to Learning It is helpful for children to collect their data in a list and then display that data in the graph. Then they have something to check if there are questions about the original data.

a child misses the checked exercise

Differentiate Instruction with • Reteach 10. 4

• Personal Math Trainer 1.MD.C.4

• Rtl Tier 1 Activity (online)

Model and Draw MP4 Model with mathematics. Guide children through the model at the top of the page with the following questions.• What do you use to make the bar graph?

I use the picture of the flowers in the garden.

• How do you know that you have counted each flower in the picture? I mark each flower with an X after I record it in the graph.

• What information does the graph show? There are more sunflowers than daisies.

• How do you know your answer is correct? The bar showing the number of daisies is shorter.

Share and Show MATHBOARDMATHBOARDMBMMMBBBMATHABOARDMMMAAATHATHTHHAAAAAAAAATTAAAABOARDBOARDBOARD

Have children work in groups of 10 to collect data on the MathBoards and record it in the graph on their pages.Use the checked exercise for Quick Check.

Children should use MathBoards to show their solutions.

Materials 1-Inch Grid Paper (see eTeacher Resources), markers, connecting cubes in three colors

• Give children a mixture of three different colors of cubes (1 to 5 of each). Have partners make horizontal bar graphs on Grid Paper by drawing and coloring a cube as a label for each row. Have them label the scale horizontally.

• Have children repeat the activity with the same cubes but with a new sheet of Grid Paper for a vertical bar graph. Explain that this time children should draw and color a cube as the label for each column. Have them label the scale vertically.

• Discuss the ways in which the graphs are alike and different.

Logical / Mathematical Individual / Partners

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3. Which toy did the most children choose? Circle.

children

TAKE HOME ACTIVITY • Your child has learned how to make picture graphs and bar graphs. Ask your child to explain how bar graphs are different from picture graphs.

MATHEMATICALPRACTICE 8 Draw Conclusions

Do children like , , or best?Ask 10 friends which toy they like best.

2. Make a bar graph. Write a title and labels for your graph.

5. SMARTER How are picture graphs and bar graphs alike?

4. How many children chose ?


Possible answer: Picture graphs and bar graphs both show information in an organized way.

4 ELABORATE

EVALUATE5 Formative Assessment

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

595 Chapter 10

On Your OwnMP8 Look for and express regularity in repeated reasoning. If children answered Exercise 1 correctly, assign Exercises 2–5.Children ask 10 classmates which toy they like best. Then children represent the data they gathered in a bar graph.

SMARTER

Exercise 5 requires children to compare picture graphs and bar graphs. Point out that picture graphs and bar graphs can show the same information but in different ways.

Essential QuestionReflect Using the Language Objective Have child pairs discuss and share two ways to answer the essential question.How does a bar graph help you compare information? Possible answer: You can see the answer without counting since the longer row has more.

Math Journal Math

Use words and pictures to show how to make a bar graph about favorite storybooks.

DEEPER

MP3 Construct viable arguments and critique the reasoning of others. To extend learning, have children share their graphs with the class. You may wish to display the pages on a class bulletin board.• Are your graphs exactly alike? Why or why

not? Possible answer: no because we asked different people.

• Look at the bar graphs. How could they be turned into picture graphs? Encourage children to think of ways that pictures can represent information.

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

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Do you wear glasses?

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Personal Math TrainerOnline Assessment and InterventionMid-Chapter Checkpoint

SMARTER Use the bar graph to answer the questions. (1.MD.C.4)

3. How many children take the bus to school?

Name

596 fi ve hundred ninety-six Chapter 10

1. How many children do not wear glasses?

2. How many children wear glasses? 8 —

8 —

3 —

Concepts and SkillsConcepts and Skills

Use the picture graph to answer the questions. (1.MD.C.4)

Yes No Yes No Yes No

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4. SMARTER Is the sentence true? Choose Yes or No. 5 children ride in a car or ride a bike.More children go by car than by bus.Fewer children go by bike than by car.

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Mid-Chapter Checkpoint 596

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

In Exercise 4, children must interpret several combinations or comparisons in the bar graph in order to answer each Yes/No question correctly. If children answer No to the first sentence, help them understand that the sentence calls for a combination. For the other two statements, make sure children understand the meanings of more and fewer.

LESSONS 10.1 TO 10.4

Key: R—Reteach (in the Chapter Resources)

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

Item Lesson Standard Common ErrorPersonal

Math TrainerIntervene with

1, 2 10.1 1.MD.C.4 May miscount the pictures in the picture graph 1.MD.C.4 R—10.1

3, 4 10.3 1.MD.C.4 May not understand how to read a bar graph 1.MD.C.4 R—10.3

Problem SolvingProblem Solving

Our Favorite Meal

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breakfast

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Practice and HomeworkLesson 10.4

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

Make Bar Graphs

Which is your favorite meal?

1. Ask 10 friends which meal they like best. Make a bar graph.

Chapter 10 fi ve hundred ninety-seven 597

2. How many children chose breakfast?

— children

3. Which meal was chosen by the most children?

4. What if 10 children chose breakfast? How many children could choose lunch or dinner? 0 — children

5. Math Use words and pictures to show how to make a bar graph about favorite storybooks.

Answers will vary based on the graph.



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.

597 Chapter 10

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How Do You Like to Travel?

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Personal Math Trainer

FOR MORE PRACTICE GO TO THE

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Lesson Check (1.MD.C.4)

Spiral Review (1.OA.C.6, 1.NBT.C.4)

1. How many more children chose than ?

2 _ more children

598 fi ve hundred ninety-eight

3. What is the sum? Use tens and ones to add.

43 + 21

]

64

4 tens + 3 ones

2 tens + 1 one

6 _ tens + 4 _ ones

60 _ + 4 _ = 64 _

2. Write the number sentence that completes the related facts.

7 + 8 = 15 15 − 8 = 7 8 + 7 = 15

B 15 − B 7 = B 8

Use the bar graph to answer the question.

Monitoring Common Core Success

Maintaining Focus on the Major WorkIn Grade 1, part of the major work includes applying addition and subtraction concepts and skills to representing and interpreting data (1.MD.C). In Lessons 10.1 and 10.3, children are asked questions based on numbers they interpret from picture graphs and bar graphs. Children’s addition and subtraction skills within 20 are supported by these problems, which ask children to answer questions about the total number of data points and how many more or less are in one category than in another. In Lessons 10.2 and 10.4, children learn to make picture graphs and bar graphs to organize and interpret data.

Connecting Content Across Domains and ClustersThroughout Lessons 10.1–10.4, children work within Cluster 1.MD.C, represent and interpret data. They connect this work to Cluster 1.OA.D, work with addition and subtraction equations. By interpreting values from picture graphs or bar graphs and then adding and subtracting within 20 using equations, children make a connection between Cluster 1.MD.C and Cluster 1.OA.D.

In Lesson 10.2, children build picture graphs; and in Lesson 10.4, children build bar graphs. The practice of collecting and clearly representing information connects to Cluster 1.OA.A in which children must represent problems involving addition and subtraction.

Focus on Mathematical PracticesIn Lessons 10.1–10.4, children repeatedly reason abstractly and quantitatively, MP2. They represent data by decontextualizing it and representing it in picture graphs and bar graphs. In Lessons 10.2 and 10.4, children must successfully build picture and bar graphs and use the graphs to answer questions and attend to the meaning of the data. Emphasize MP2 by having children explain why the data quantities they used in the graph make sense. In Lessons 10.1 and 10.3, children are required to contextualize data read from picture graphs and bar graphs to answer questions and solve problems. This practice of data interpretation helps children build a meaningful understanding of MP2.

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 10.4 598

hands on • make bar graphs€¦ · it in the graph. make a bar graph to show each animal in the...

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