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LESSON AT A GLANCE

711A Chapter 12

LESSON 12.5

Interactive Student Edition

Personal Math Trainer

Math on the Spot Video

Animated Math Models

iTools: Graphs

HMH Mega Math

Teaching for DepthLearning to make and read concrete graphs is an important mathematical skill. Children need much practice at the concrete level in order to better understand more abstract graphs that they will learn about in later grades.

In this lesson, children read graphs to find how many counters are in each row and then write the numbers. They compare the numbers and tell which color counter there is more or fewer of on the graph.

According to the National Research Council, it is important as children are graphing that they communicate their actions and thoughts. Encourage them to talk about the graphing using comparison language, such as more and fewer. It is important that they describe how they find their answers.

Read a Graph

Learning ObjectiveRead a graph to count objects that have been classified into categories.

Language ObjectivePairs of children use a graph to count objects that have been classified into categories.

MaterialsMathBoard, two-color counters

F C R Focus:Common Core State Standards

K.MD.B.3 Classify objects into given categories; count the numbers of objects in each category and sort the categories by count.

Also K.CC.C.6

MATHEMATICAL PRACTICES (See Mathematical Practices in GO Math! in the Planning Guide for full text.)MP2 Reason abstractly and quantitatively. MP6 Attend to precision. MP8 Look for and express regularity in repeated reasoning.

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

After1.MD.C.4

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 683H.

ENGAGE1Daily Routines

Common Core

Lesson 12.5 711B

How can you read a graph to count objects that have been

classif ied into categories?

with the Interactive Student Edition

Essential QuestionHow can you read a graph to count objects that have been classified into categories?

Making ConnectionsAsk children to tell you what they know about graphs.

• What is a graph? Possible answer: a picture that shows information in an organized way

• What can a graph show you? Possible answers: which of two groups has more of something; how many objects are in a group

Learning ActivityDirect children towards understanding the different parts of a graph.

• What kind of festival is going on at the farm? a hot air balloon festival

• How many different color balloons are there? 2

• What does Scout plan to use to keep track of the balloons? a graph

Literacy and MathematicsView the lesson opener with children. Then complete this activity.

• As a class, write a story about taking hot air balloon rides. Create a graph to show information from the story.

1 23 4 Fluency BuilderSort and Count by ColorMaterials connecting cubes, 10 each of three colors per pair of children (see eTeacher Resources), paper bag

Have partners put the cubes in a paper bag and shake the bag to mix up the cubes. Then have each child take out a handful of the cubes and lay them on a table. Have partners work together to sort and count each color of cubes.

• How many red cubes are there?

• How many blue cubes are there?

Repeat for each color. Ask children to explain how they found the answers.

Children can repeat the activity by returning the cubes to the bag, shaking, and drawing a new handful of cubes from the bag.

Problem of the Day 12.5Word of the Day Which is greater, 3 or 6? 12 or 18? Which is less, 6 or 4? 14 or 16? 6; 18; 4; 14

Have children explain how they know that one number is greater or less than another. Possible answer: When I count, the number that is greater comes after the other number. The number that is less comes before the other number.

Vocabulary

Interactive Student EditionMultimedia Glossary e

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Red and Yellow Counters

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DIRECTIONS Erin made a graph of her counters. How many counters are in each category? Trace the numbers. Trace the circle to show which category has more counters.

Problem Solving • Read a GraphEssential Question How can you read a graph to count objects that have been classified into categories?

Lesson 12.5PROBLEM SOLVING

Measurement and Data—K.MD.B.3 Also K.CC.C.6

MATHEMATICAL PRACTICESMP2, MP6, MP8

Check children’s work.

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Problem Solving • Read a Graph

DIRECTIONS 1. Color the counters to show the categories. R is for red, and Y is for yellow. How many counters are in each category? Draw a dot on each counter on the graph as you count. Trace or write the numbers. 2. Trace the circle around the category that has fewer counters on the graph.

Lesson 12.5Reteach

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12-13 ReteachChapter Resources© Houghton Mifflin Harcourt Publishing Company

Name Lesson 12.5Enrich

DIRECTIONS 1. Count how many of each type of fruit is in the crate. Color the fruit and write the number. 2. Draw your own fruit in the crate. Count how many of each type of fruit is in the crate. Color the fruit and write the number.

Crates of Fruit

Check children’s work.

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711 Chapter 12

LESSON 12.5

Enrich 12.5Reteach 12.5

Unlock the ProblemRead the problem aloud as children listen.

Erin’s graph shows red and yellow counters. How can Erin read the graph to know whether there are more red counters or more yellow counters?

Discuss the different parts of the graph. Make sure children understand that a row goes across. Ask children to describe the graph on the page. Read the title. • What are the categories of this graph? red

counters and yellow counters

• How many counters are there in the category for red counters? 3 How can you tell? I can count the red counters in the top row. Trace the number to show how many.

• How many counters are there in the category for yellow counters? 4 Trace the number.

MP2 Reason abstractly and quantitatively.• Which category has more counters? yellow

How do you know? The graph shows 4 yellow counters and 3 red counters. 4 is more than 3.

• Trace the circle to show which has more. Reread the problem about Erin.

MP6 Attend to precision.• What does Erin’s graph show her?

Possible answer: There are more yellow counters than red counters.

ELL Strategy: Develop Meanings

Children can develop meaning by relating a concrete graph and its features to their definitions.Draw a two-row graph. Draw a shape to the left of each row. Draw a few of each shape in each row. Label the graph. Have children take turns explaining the graph using more and fewer. Have children explain how they know there are more or fewer. Possible answer: I counted how many in each row.

K.MD.B.3 Classify objects into given categories; count the numbers of objects in each category and sort the categories by count.

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DIRECTIONS 1. Billy made a graph showing his counters. Color the counters to show his categories. How many counters are in each category? Write the numbers. 2. Circle the category that has more counters on the graph.

Try Another ProblemTry Another Problem

Check children’s work.

COMMON ERRORS

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Lesson 12.5 712

Error Children may not identify which category has more counters.

Example Children circle red as the category with more counters.Springboard to Learning Make sure children realize that the category with more counters is the one that goes out farther than the other one. The greater number is the one with more.

Try Another ProblemDirect children’s attention to the graph in Exercise 1. Read the title of the graph.• How do you know the categories on this

graph? The counters at the beginning of each row are the categories.

• What are the categories? red counters and yellow counters

• How many counters are in the category for red counters? 4 Write the number and color the counter.

• How many counters are in the category for yellow counters? 5 Write the number and color the counter.

Direct attention to Exercise 2.• Are there more red or yellow counters on

the graph? yellow How do you know? Possible answers: I can count the counters in each row and compare the numbers. The row of counters with more is longer than the row with fewer.

• Circle the category that has more counters on the graph. yellow

MP8 Look for and express regularity in repeated reasoning.• Look at the graph of yellow and red

counters. How did it help you fi nd the number of each color counter? Possible answer: I could count the number of counters in each row of the graph. That number tells the number of each color counter.

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KinestheticIndividual / Partners

Materials 2-Row Graph, Numeral Cards (0–7) (see eTeacher Resources)

Give partners numeral cards 1 to 6 and a two-row graph. Have children place cards face down. One row should show a red counter label and the other row should show a yellow counter label. Have children place numeral cards facedown.One child turns over the top card and draws that number of red counters in the top row. The other child turns over the next card and draws that number of yellow counters in the second row. Using the graph, children write the number of red and yellow counters and write more or fewer by each category.

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4 ELABORATECounter Colors

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DIRECTIONS 3. Rong made a graph of her counters. Color the counters to show her categories. How many counters are in each category? Write the numbers.4. Circle the category that has fewer counters on the graph.

Check children’s work.

Quick Check

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

713 Chapter 12

Share and ShowDirect children’s attention to the graph and have them identify the categories. red counters and yellow counters Read the title.In Exercise 3, have children color the counters to show the categories and write the numbers.• Which category has fewer counters? red

Circle it in Exercise 4.

Use the checked exercise(s) for Quick Check.

SMARTER

Read this problem to children.• If you add one red counter to the graph,

does your answer change? Write how many red counters. If you add two more red counters, what happens to your answer? Write how many red counters.

DEEPER

MP3 Construct viable arguments and critique the reasoning of others. Children should recognize that if one red counter is added, there would still be fewer red counters. If two red counters are added, there would be an equal number of red and yellow counters.• What would happen to your answer if you

added three more red counters? There would be more red counters than yellow counters.

a child misses the checked exercise(s)

Differentiate Instruction with • Reteach 12.5

• Personal Math Trainer K.MD.B.3

• RtI Tier 1 Activity (online)

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

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Differentiated Centers Kit

DIFFERENTIATED INSTRUCTION INDEPENDENT ACTIVITIES

Cube Colors

MATHEMATICAL PRACTICES

WRITEWRITEMathMath

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HOME ACTIVITY • Have your child tell about the graph he or she made on this page. Ask him or her which category has more cubes and which category has fewer cubes.

DIRECTIONS 5. Brian has more blue cubes than red cubes. Draw and color to show his cubes on the graph. Count how many in each category. Write the numbers.

On Your OwnOn Your Own

Check children’s work.

EVALUATE5 Formative Assessment

Differentiated Centers Kit

DIFFERENTIATED INSTRUCTION INDEPENDENT ACTIVITIESD

Lesson 12.5 714

Children interpret and organize information by constructing a graph.

Children read the book and construct a graph to show the number of large and small shells.

Children complete blue Activity Card 10 by sorting, counting, and graphing objects.

GamesSpill the Counters

LiteratureShells! Shells!

ActivitiesSort and Graph

Essential QuestionReflect Using the Language Objective Have children work in pairs and use a graph to answer the Essential Question.How can you read a graph to count objects that have been classified into categories? I can count how many are on each row to see how many are in each category.

On Your Own MP1 Make sense of problems and persevere in solving them. Read the title of the graph in Exercise 5 with children. Ask children to explain how they will solve the problem.

Math Journal Math

MP2 Reason abstractly and quantitatively. Before children draw, discuss how the number of blue cubes should compare to the number of red cubes, no matter what the number of red cubes is. Guide them to understand that the number of blue cubes should be more than the number of red cubes. Some children may wish to place cubes on the page before they draw.• Draw and color to show the cubes in

each category.• How many red cubes are there? Possible

answers: 1 to 4, but should be fewer than the number of blue cubes

• How many blue cubes are there? Possible answers: 2 to 5 but should be more than the number of red cubes

Have children write the numbers.MP4 Model with mathematics. Have small groups compare their answers. Have children discuss why different models and answers can be correct and explain why.

Mathematical Practices in Your Classroom PROFESSIONALDEVELOPMENT

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DIRECTIONS 1. Color the counters to show the categories. R is for red, and Y is for yellow. How many counters are in each category? Write the numbers. 2. Circle the category that has more counters on the graph.

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COMMON CORE STANDARD—K.MD.B.3 Classify objects and count the number of objects in each category.

Lesson 12.5Practice and Homework

Read a Graph

Check children’s work.

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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 and begin using critical thinking skills as they complete the practice items.

CCSS.Math.Practice.MP3 Construct viable arguments and critique the reasoning of others. Mathematically proficient children are able to communicate their ideas. They are able to listen to the arguments of others and decide whether they make sense. As they answer questions and listen to others’ responses, they begin to recognize that more than one approach can lead to the correct answer.

• When asked “Which category of counters has more on a graph?” one child might reason that the longest row of counters is the one with more. Another child might argue that it is better to count the counters in each row and compare the numbers, the greater number being the category with more. When both children have their answers, they can see that the answer is the same, no matter which way they used to find it.

Provide opportunities for children to communicate their approaches and ideas as they read and compare objects on a graph.

• What can you find out by looking at a graph? Possible answer: I find out which category has more and which has fewer.

• How can you find out if there are fewer red counters or yellow counters on a graph? Possible answers: I can count how many are in each row and compare the numbers. The number that is less is the one with fewer counters; I can look at the graph and see which row of counters is shorter.

• Do you think one way is better than another when finding which is fewer? Why? Accept reasonable answers.

Counter Colors

Personal Math Trainer

FOR MORE PRACTICE GO TO THE

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DIRECTIONS 1. How many counters are in each category? Write the numbers. Circle the category that has more counters. 2. Complete the addition sentence to show the numbers that match the cube train. 3. Make a cube train that is about the same length as the cube train shown. Draw and color the cube train.

Spiral Review (K.OA.A.3, K.MD.A.2)

Lesson Check (K.MD.B.3)

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Check children’s work.

Monitoring Common Core Success

Maintaining Focus on the Major WorkThe major work of Grade K includes counting to tell the number of objects (K.CC.B). In Lessons 12.4 and 12.5, children create and read concrete graphs, using their counting skills to determine the number of each type of object. Children are also asked in some exercises to compare the two groups (K.CC.C) to determine which group has a greater number of objects.

Connecting Content Across Domains and ClustersIn Lessons 12.4 and 12.5, a connection is made between the Domain Counting and Cardinality (K.CC) to Clusters K.CC.B and K.CC.C, and Measurement and Data (K.MD) to Cluster K.MD.B. As children make and read concrete graphs, their ability to count and compare (K.CC.B and K.CC.C) is applied to data, sorting a group of objects, and counting to determine which group has more objects.

Focus on Mathematical Practices In Lessons 12.4 and 12.5, children are required to look for and express regularity in repeated reasoning, MP8. When children make and read concrete graphs, they use the structure of the graph to solve problems. Children internalize and understand that the number of items in each category is found by counting the number of items in each row. The Share and Show exercises 1 and 2 on TE page 706, and Exercises 1 and 2 on TE page 712 are examples of exercises completed by children that attend to the full meaning of this mathematical practice.

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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