Lesson LESSON 27 Overview Make Line Plots and Interpret Data

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Lesson Overview

LESSON 27

Make Line Plots and Interpret Data

Prerequisite Skills

• Interpret data on line plots, including data displayed in fractions of a unit with like denominators.

• Use line plots to solve word problems involving addition and subtraction of fractions with like denominators.

• Order fractions from least to greatest.

• Add, subtract, and multiply fractions, including mixed numbers.

• Divide with unit fractions.

Lesson Vocabulary

There is no new vocabulary. Review the following key terms.

• scale (on a graph) the value represented by the distance between one tick mark and the next on a number line.

• line plot a data display that shows data as marks above a number line.

Lesson Objectives

Content Objectives• Make a line plot that displays

measurement data given in fractions of a unit with unlike denominators.

• Use a line plot to solve word problems about measurement data given in fractions of a unit with unlike denominators.

Language Objectives• Make a line plot to present measurement

data.

• Interpret measurement data shown on a line plot.

• Communicate precisely with others about conclusions drawn from data shown in line plots.

Learning Progression

Since Grade 2 students have been making line plots for measurement data and analyzing the data shown in line plots. In Grade 4 students solved word problems involving addition and subtraction of fractional measurement units, including measurements expressed as mixed numbers, by interpreting data shown in line plots. Students ordered fractions with unlike denominators, added and subtracted with fractions with like denominators, and multiplied fractions by whole numbers. In Grade 5 students extend their knowledge of fraction

operations to include adding and subtracting fractions with unlike denominators, multiplying fractions, and dividing with unit fractions.

In this lesson students make line plots for data expressed in fractions of a unit with unlike denominators and use their understanding of fraction operations to solve problems about data presented in line plots.

In later grades students will use their data analysis skills when they do more in-depth statistical reasoning.

CCSS FocusDomainMeasurement and Data

ClusterB. Represent and interpret data.

Standard5.MD.B.2 Make a line plot to display a

data set of measurements in fractions of

a unit ( 1 · 2 , 1 · 4 , 1 · 8 ). Use operations on fractions

for this grade to solve problems involving

information presented in line plots. For

example, given different measurements

of liquid in identical beakers, find the

amount of liquid each beaker would

contain if the total amount in all the

beakers were redistributed equally.

Additional Standards5.NF.A.1, 5.NF.A.2, 5.NF.B.6, 5.NF.B.7 (See Standards Correlations at the end of the book for full text.)

Standards for Mathematical Practice (SMP)SMPs 1, 2, 3, 4, 5, and 6 are integrated in every lesson through the Try-Discuss-Connect routine.*

In addition, this lesson particularly emphasizes the following SMPs:

1 Make sense of problems and persevere in solving them.

2 Reason abstractly and quantitatively.

5 Use appropriate tools strategically.

* See page 305m to see how every lesson includes these SMPs.

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Lesson Pacing Guide

PERSONALIZE

i-Ready Lesson*Grade 5• Line Plots with Fractions

Independent Learning

PREPARE

Ready Prerequisite LessonGrade 4• Lesson 22 Add and Subtract Fractions in

Line Plots

RETEACH

Tools for InstructionGrade 4• Lesson 22 Using Line Plots

Grade 5• Lesson 27 Solve Problems with Fractional

Measurement Data

REINFORCE

Math Center ActivitiesGrade 5• Lesson 27 Line Plot Vocabulary Match• Lesson 27 Fractions as Data

EXTEND

Enrichment ActivityGrade 5• Lesson 27 Weighing Pumpkins

Small Group DifferentiationTeacher Toolbox

Lesson MaterialsLesson (Required)

Per pair: 1 set of fraction tiles or circles

Activities Per pair: number cube Per group: index cards with one measurement on each card (see Session 2 Hands-On Activity for details), masking tape, 1 bean bag, 1 yardstick For display: copy of the Tomato Weights line plot from Session 1 Try It, copy of Keira’s data list from Session 2 Try It, copy of Activity Sheet Sticker WidthsActivity Sheet: Sticker Widths

Math Toolkit fraction tiles, fraction circles, fraction bars, number lines, rulers, sticky notes

SESSION 1

Explore45–60 min

Making Line Plots and Interpreting Data • Start 5 min• Try It 10 min• Discuss It 10 min• Connect It 15 min• Close: Exit Ticket 5 min

Additional PracticeLesson pages 555–556

SESSION 2

Develop45–60 min

Making a Line Plot • Start 5 min• Try It 10 min• Discuss It 10 min• Model Its 5 min• Connect It 10 min• Close: Exit Ticket 5 min


Fluency Making a Line Plot

SESSION 3

Develop45–60 min

Solving Problems Using Data in a Line Plot • Start 5 min• Try It 10 min• Discuss It 10 min• Picture It & Model It 5 min• Connect It 10 min• Close: Exit Ticket 5 min


Fluency Solving Problems Using Data in a Line Plot

SESSION 4

Refine45–60 min

Making Line Plots and Interpreting Data• Start 5 min• Example & Problems 1–3 15 min• Practice & Small Group

Differentiation 20 min• Close: Exit Ticket 5 min

Lesson Quiz or Digital Comprehension Check

Whole Class Instruction

* We continually update the Interactive Tutorials. Check the Teacher Toolbox for the most up-to-date offerings for this lesson.

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LESSON 27

Connect to Family, Community, and Language DevelopmentThe following activities and instructional supports provide opportunities to foster school, family, and community involvement and partnerships.

Connect to FamilyUse the Family Letter—which provides background information, math vocabulary, and an activity—to keep families apprised of what their child is learning and to encourage family involvement.

©Curriculum Associates, LLC Copying is not permitted.Lesson 27 Make Line Plots and Interpret Data552

ACTIVITY MAKING A Line plotDo this activity with your child to make line plots and interpret data.

Materials centimeter ruler

Work with your child to make a line plot of the lengths of book covers.

• Gather several books. Measure the length of the cover of each book. Measure to the nearest centimeter. Use your own centimeter ruler or cut out and use the centimeter ruler below.

• Make a list of the lengths and use the data to make a line plot.

• Use the number line below. Title the line plot “Lengths of Book Covers” and write the label “Length (in centimeters)” beneath the number line.

• Decide what scale to use based on the measurements you collect. Then mark Xs to show the data.

• Describe how the data shown on the line plot are grouped.

• Do mathematical operations with the data values to describe the data. For example, fi nd the diff erence between the length of the longest book cover and the length of the shortest book cover.

centimeters16

552©Curriculum Associates, LLC Copying is not permitted.

Make Line Plots and Interpret Data

27Dear Family,This week your child is learning about line plots and about how to interpret data on line plots.A line plot is a data display that shows data as marks above a number line. A line plot is useful for showing how data are grouped. The line plot below shows the weights of onions. Each onion is represented by an X on the line plot. Xs that are one above another represent onions that have the same weight. Weights are labeled beneath the number line.

Weight (in pounds)

Onion WeightsXXXXX X

XXX

XX

XXXX

0 118

14

38

12

58

34

78

The line plot shows how the data are grouped. You can describe the data by looking

at the line plot. Most pieces of data on this line plot are grouped between 1 ··

8

and 1 ··

2

.

You can also do mathematical operations with the data values to describe the data.

For example, you can fi nd the diff erence between the heaviest and lightest onions.

The weights vary from 1 ··

8

pound to 7 ··

8

pound. The diff erence is 6 ··

8

, or 3 ··

4

, pound.

Using line plots can help your child ask and answer complex questions about data.

Invite your child to share what he or she knows about making line plots and interpreting data by doing the following activity together.

Lesson 27 Make Line Plots and Interpret Data 551551

GoalThe goal of the Family Letter is to provide students and their families opportunities to develop understanding of line plots and interpreting data.

• Students use prior understanding of units of measurement and fractions to make line plots and then use the line plots to better understand the data provided.

ActivityIn the Making a Line Plot activity, students and family members measure different books and use the data to make and describe a line plot. Adjust the activity if necessary to connect with your students.

Math Talk at HomeEncourage students to talk about data they can gather and how they will use a line plot to represent it.

Conversation Starters Below are additional conversation starters students can write in their Family Letter or math journal to engage family members:

• Do you collect data at work? What type of data do you collect? How do you organize the data?

• What kind of data can we collect at home? How can we use this data?

Available in Spanish

Teacher Toolbox

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Connect to Community and Cultural ResponsivenessUse these activities to connect with and leverage the diverse backgrounds and experiences of all students.

Connect to Language DevelopmentFor ELLs, use the Differentiated Instruction chart to plan and prepare for specific activities in every session.

Listening/Speaking Read Connect It problem 3 aloud. Ask: What two whole

numbers of pounds are all the data between? [0 and 1] What fractions do you see on the line

plot? 3 1 ·· 4 , 1 ·· 2 , and 3 ·· 4 4 Say: The tick marks divide 1

whole on the number line into 8 equal parts.

That tells you that the scale is 1 ·· 8 . Ask: What is

the denominator of 1 ·· 8 ? [8] What is the

denominator of each fraction on the line plot? [4, 2, 4] Say: You can change the denominator

of each fraction to match the denominator of

the scale of the line plot. Ask: What number do

you need to multiply the numerator of each

fraction by? [2, 4, 2] Have students form pairs and complete the following:

1 ·· 4 5 ? ·· 8 2 ·· 4 5 ? ·· 8 3 ·· 4 5 ? ·· 8

Speaking/Writing Read Connect It problem 3 aloud. Ask: What two whole numbers of pounds are all the data between? [0 and 1] Have students form pairs and complete the following sentence frames:

• The tick marks on the line plot divide the 1 whole into equal parts.

• The scale of the line plot is .

• The denominator of 1 ·· 8 is .

• The of the fractions on the line plot are 4, 2, and 4.

Have students take turns reading the completed sentences to their partners. Then have them work together to write a sentence that answers the question. Call on students to read their sentences aloud.

Writing Have students form pairs and read Connect It problem 3 aloud. Ask pairs to write a short paragraph that tells about the information in the line plot. Provide the following terms for guidance: tick marks, scale, fractions, and denominator. Have students take turns reading the completed sentences to their partners. Then have them work together to write a sentence that answers the question. Call on students to read their sentences aloud.

Levels 3–5Levels 2–4Levels 1–3

ELLEnglish Language Learners:Differentiated Instruction

Prepare for Session 1Use with Connect It.

Sessions 1–4 Use anytime during these sessions.• Point out that the ability to interpret data is essential to many

professions. Weather forecasters, for example, collect and study data and then use it to predict the temperature and the weather. A sports reporter collects and studies different kinds of data—numbers from baseball and football players, for example. A reporter uses these data to help write articles and inform readers. Encourage students to mention professions they might be familiar with that involve collecting data and how that data is used. Make and display a list of students’ suggestions throughout the lesson.

Session 3 Use with Try It.• Ask students to share how their friends and family listen to music

and what they use, such as MP3 players, mobile phones, and CDs. Prompt students to discuss how knowing the length of songs helps you calculate how many songs will fit on a CD or can be played on an hour-long radio program.

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LESSON 27

SESSION 1 Explore

StartConnect to Prior KnowledgeWhy Review interpreting a line plot of whole- number data to prepare for interpreting line plots of fractional data.

How Have students record three facts they know about the data shown in the line plot. Have them share and compare their ideas with a partner.

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Start

Grade 5 Lesson 27 Session 1 | Explore Making Line Plots and Interpreting Data

Use the line plot to list three facts about Maria’s seedlings.

Height (in inches)

Maria’s SeedlingsXXXX X

XXX

0 84

XX

Possible SolutionsThe shortest seedling is 2 inches tall.There are 4 seedlings that are 6 inches tall.Half the seedlings are taller than 5 inches.

TRY ITMake Sense of the ProblemTo support students in making sense of the problem, have them identify that each X on the line plot represents a different tomato.

DISCUSS ITSupport Partner DiscussionTo reinforce measurement and data concepts, encourage students to use the terms line plot and data as they talk to each other.

Look for, and prompt as necessary for, understanding of:

• 3 ·· 4 pound as the weight of the heaviest tomato

• 1 ·· 8 pound as the weight of the lightest tomato

• 3 ·· 4 2 1 ·· 8 as the difference

Common Misconception Look for students who are not comfortable with identifying the values for the unlabeled tick marks. As students present solutions, have them specify how they determined the value for the lightest tomato.

Select and Sequence Student SolutionsOne possible order for whole class discussion:

• concrete models or drawings of visual fraction models

• number lines marked in eighths

• counting on or counting back strategies to find the difference

• equations that show subtracting using a common denominator

Support Whole Class DiscussionPrompt students to note the relationship between the numbers in each model and the numbers in the problem.

Ask How do [student name]’s and [student name]’s models show how to subtract the weight of the lightest tomato from the weight of the heaviest tomato?

Listen for The heaviest tomato weighs 3 ·· 4 pound. The lightest tomato weighs 1 ·· 8 pound. To find the difference, you can subtract 1 ·· 8 from 3 ·· 4 using a common denominator. 3 ·· 4 5 6 ·· 8 , so 3 ·· 4 2 1 ·· 8 5 6 ·· 8 2 1 ·· 8 5 5 ·· 8 . You also can count back by eighths from 3 ·· 4 to 1 ·· 8 to find a difference of 5 ·· 8 .

Purpose In this session students draw on what they know about reading line plots and subtracting fractions to solve a problem. They share models to explore how to interpret a line plot of data values expressed as fractions. They will look ahead to think about how a line plot showing fractional data values is constructed.

©Curriculum Associates, LLC Copying is not permitted. 553Lesson 27 Make Line Plots and Interpret Data

You have made and used line plots before. Now you will make line plots and use them to answer more complex questions about data. Use what you know to try to solve the problem below.

Mrs. May’s class weighs tomatoes of diff erent sizes and

types. They weigh each tomato to the nearest 1 ·· 8 pound.

The results are shown in the line plot below. What is the

diff erence between the weights of the heaviest tomato and

the lightest tomato?

Weight (in pounds)

Tomato WeightsXXXX X

XX

X

XXX

XXX

0 114

12

34

TRY IT Math Toolkit• fraction tiles• fraction circles• fraction bars• number lines

DISCUSS ITAsk your partner: Why did you choose that strategy?

Tell your partner: I knew . . . so I . . .

Learning Target• Make a line plot to display a data set

of measurements in fractions of a

unit 1 1 ·· 2 , 1 ·· 4 , 1 ·· 8 2 . Use operations on

fractions for this grade to solve

problems involving information

presented in line plots.

SMP 1, 2, 3, 4, 5, 6

LESSON 27 SESSION 1

Explore Making Line Plots and Interpreting Data

553

Possible student work:

Sample Alightest tomato: 1 ·· 8 pound heaviest tomato: 3 ·· 4 pound; 3 ·· 4 5 6 ·· 8

6 ·· 8 2 1 ·· 8 5 5 ·· 8 , so the difference is 5 ·· 8 pound.

Sample B

0 1

lightest heaviest

18

14

38

12

58

34

78

1 ·· 8 pound is 5 ·· 8 pound less than 3 ·· 4 pound.


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LESSON 27 EXPLORE

Lesson 27 Make Line Plots and Interpret Data

SESSION 1

Connect It1 LOOK BACK

What is the diff erence between the weights of the heaviest tomato and the lightest tomato? Explain how you know.

2 LOOK AHEADGraphing data on a line plot helps you get a “picture” of the data and how the data are spread out or grouped.

Weight (in pounds)

Tomato Weights XXXX X

XX

X

XXX

XXX

0 114

12

34

a. The scale of a line plot is the value represented by the distance between one tick mark and the next on the number line.

Counting up, how many tick marks does it take to get from 0 to 1?

What fraction of the whole is the distance between tick marks?

So, the scale is pound.

b. How many data values are recorded on the line plot? Explain how you know.

c. What do the four Xs above 1 ·· 8 represent?

3 REFLECTIf the scale of the line plot is 1 ·· 8 , why are the numbers 1 ·· 4 , 1 ·· 2 , 3 ·· 4 , and 1 on the line plot?

554

5 ·· 8 pound; Possible explanation: Rewrite 3 ·· 4 pound as 6 ·· 8 pound.

Then subtract 6 ·· 8 2 1 ·· 8 to find the difference.

8

1 ·· 8

1 ·· 8

14; There are 14 Xs on the line plot.

four tomatoes that each weigh 1 ·· 8 pound

Possible answer: 1 ·· 4 5 2 ·· 8 , 1 ·· 2 5 4 ·· 8 , 3 ·· 4 5 6 ·· 8 , and 1 5 8 ·· 8 .

CONNECT IT 1 LOOK BACK

Look for understanding of using the scale to identify the weights of the heaviest and lightest tomatoes, and of how to find the difference 3 ·· 4 2 1 ·· 8 , or 6 ·· 8 2 1 ·· 8 .

Visual ModelInterpret a line plot in different ways.

If . . . students are unsure about interpreting line plots,

Then . . . use this activity to practice.

Materials For display: copy of the Tomato Weights line plot from Try It

• Display the Tomato Weights line plot.

• Remind students that they just used data from the line plot to answer the question What is the difference between the weights of the heaviest and lightest tomatoes? Have a volunteer explain how to identify the weight of the heaviest tomato and the weight of the lightest tomato in the line plot.

• Tell students that the line plot can be used to answer many other questions about the same data. For example, ask: Which weight occurred most often as the class weighed the tomatoes? How do you know? 3 1 ·· 8 pound; the tick mark for 1 ·· 8 pound has the most Xs above it. 4

• Have pairs write their own questions about the tomato weight data. Select several pairs to present their questions to the class and explain how to use the line plot to answer the question. [Sample questions: How many tomatoes did the class weigh? What is the total weight of the two heaviest tomatoes? How many tomatoes weigh more than 1 ·· 2 pound?]

• Follow up by choosing additional students to ask their questions. For each question, ask a volunteer to explain how to answer the question using the line plot.

2 LOOK AHEAD Point out that line plots help you represent data visually and that the scale of a line plot helps you identify the data values from the graph. Ask volunteers to state definitions of data, line plot, and scale in their own words. Students will spend more time learning about scale in the Additional Practice.

Close: Exit Ticket3 REFLECT

Look for understanding that different, equivalent fractions can represent the same value, in this case fractions equivalent to various eighths.

Common Misconception If students think that a line plot with a scale of 1 ·· 8 should show all labels for tick marks written as eighths, then reinforce what students know about equivalent fractions, and remind them that benchmark fractions such as 1 ·· 4 , 1 ·· 2 , 3 ·· 4 are also useful for understanding the relative sizes of numbers. Tell students they can always write their own, equivalent fractions on a line plot if they wish.

Real-World ConnectionEncourage students to think about everyday places or situations in which

people might find it useful to present data on a line plot. Have volunteers share their ideas. Examples: heights of each student in a class, age of each athlete in a race, distance each employee of a company commutes to work.


LESSON 27

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Name:


LESSON 27 SESSION 1

2 Look at the line plot. What is the scale? How do you know?

Weight (in pounds)

Apple WeightsXXXX X

XX

XXXX X

0 18

14

38

12

1 Think about what you know about line plots. Fill in each box. Use words, numbers, and pictures. Show as many ideas as you can.

Word In My Own Words Example

line plot

scale

data

Prepare for Making Line Plots and Interpreting Data

555

Possible answers:

1 ··· 16 pound; Possible explanation: The first tick mark is

halfway between 0 and 1 ·· 8 . 1 ·· 8 4 2 5 1 ··· 16 .

a graph that uses Xs above a number line to show data

the change in value between one tick mark and the next on a line plot

My line plot has a scale of 1 year.

information or factsData in my line plot:

9, 10, 10, 11, 11, 12, 12

Age (in years)

My FriendsXX

XX

XXX

7 8 9 10 11 12 13

SESSION 1 Additional Practice

Solutions

Support Vocabulary Development

1 Have students say each of the terms in the first column of the graphic organizer. Ask students to work in small groups to complete the organizer. Call on volunteers to read what they wrote for In My Own Words. Correct any misconceptions and ask students to revise their graphic organizers, if necessary. Encourage students to share and explain their examples in the third column.

2 Read the problem. Have students form pairs and discuss the scale. Ask: What is the first labeled tick mark after 0? 3 1 ·· 8 4 How many tick marks are between that tick mark and 0? [1] Encourage students to think about what that tells them about the scale. Have students work with their partners to develop an answer. Listen to the conversations and provide guidance as needed.

Supplemental Math Vocabulary• tally mark

• graph

• facts


Levels 1–3 Levels 2–4 Levels 3–5

English Language Learners:Differentiated InstructionELL

Speaking/Writing Have students form pairs and read Connect It problem 6 aloud. Provide the following terms to students: data, greatest, order, least, and value. Have students work with their partners to explain how they use a line plot to organize measurement data. Ask them to write complete sentences and to use the terms provided as needed. Have pairs work with other pairs and take turns reading their explanations to each other. Encourage students to discuss whether the explanations are valid and to say why or why not.

Speaking/Writing Read Connect It problem 6 aloud. Ask: What can you organize using a line plot? [data or measurement data] The line plots you have worked with in this lesson show data from 0 to 1. Is 1 greater than or less than 0? [greater than] Provide the following sentence frames:

• I organize on a line plot.

• A line plot shows data from value to value.

• The marks on a line plot tell you its .

Have students form pairs and complete the sentences in writing. Then ask them to write a sentence that explains how they use a line plot to organize data. Call on students to read their sentences.

Speaking/Writing Read Connect It problem 6 aloud. Say: A line plot contains information. What can you organize using a line plot? [data or measurement data] The line plots you have worked with in this lesson show data from 0 to 1. The data have been organized from least value to greatest value. Provide the following sentence frames:

• I organize on a line plot.

• A line plot shows data from value to value.

• The marks on a line plot tell you its .

Have students form pairs and complete the sentences in writing. Then have them take turns reading the sentences to each other.

556 Lesson 27 Make Line Plots and Interpret Data

LESSON 27 SESSION 1

3 Solve the problem. Show your work.

Mr. Lee’s class weighs apples of diff erent sizes and types. They weigh

each apple to the nearest 1 ··· 16 pound. The results are shown in the line

plot below. What is the diff erence between the weights of the heaviest

apple and the lightest apple?

Weight (in pounds)

Apple WeightsXXXX X

XX

XXXX X

0 18

14

38

12

Solution

4 Check your answer. Show your work.

©Curriculum Associates, LLC Copying is not permitted.

556

Possible student work using an equation:

lightest apple: 1 ··· 16 pound

heaviest apple: 1 ·· 2 pound, or 8 ··· 16 pound

8 ··· 16 2 1 ··· 16 5 7 ··· 16


0

lightest heaviest

116

18

316

14

12

516

38

716

1 ··· 16 pound is 7 ··· 16 pound less than 1 ·· 2 pound.

The difference is 7 ··· 16 pound.


3 Assign problem 3 to provide another look at interpreting data from a line plot.

This problem is very similar to the problem about finding the difference between the weights of the heaviest tomato and the lightest tomato. In both problems, students are given a line plot with data. The question asks for the difference between the weights of the heaviest apple and the lightest apple.

Students may want to use number lines or fraction bars.

Suggest that students read the problem three times, asking themselves one of the following questions each time:

• What is this problem about?

• What is the question I am trying to answer?

• What information is important?

Solution:

The lightest apple weighs 1 ·· 16 pound. The heaviest apple weighs 1 ·· 2 pound, or 8 ·· 16 pound. 8 ·· 16 2 1 ·· 16 5 7 ·· 16 . The difference between the heaviest weight and lightest weight is 7 ·· 16 pound.

Medium

4 Have students solve the problem a different way to check their answer.


LESSON 27


LESSON 27


TRY IT

SESSION 2

Develop Making a Line Plot

Read and try to solve the problem below.

Keira bought 12 diff erent types of stickers to decorate her scrapbook. She measured the width, in inches, of each type of sticker and wrote down the results. Make a line plot to organize and display Keira’s data.

Math Toolkit• fraction tiles or circles• fraction bars• number lines• rulers• sticky notes

Sticker Widths (in inches)14

34

38

34

14

58

18

12

12

12

1 1

DISCUSS ITAsk your partner: How did you get started?

Tell your partner: I started by . . .

557


Sample A

1 ·· 8 , 1 ·· 4 , 1 ·· 4 , 3 ·· 8 , 1 ·· 2 , 1 ·· 2 , 1 ·· 2 , 5 ·· 8 , 3 ·· 4 , 3 ·· 4 , 1, 1

Width (in inches)

Keira’s StickersXXX

XX

XX

XXXX X

0 1

Sample B

Width (in inches)

18

14

38

12

58

34

78

Sticker WidthsXXX

XX

XX

XXXX X

0 1

Start Connect to Prior Knowledge

Materials For each pair: 1 set of fraction tiles or circles

Why Review ordering fractions and counting the number of times a data value occurs in preparation for making a line plot with fractional data.

How Have students use fraction tiles or circles to show and find the greatest fraction in a list of data in halves, fourths, and eighths. Have students count how many times the data value occurs.


Start

What is the greatest value in the list of data below?

How many Xs would a line plot show for that value?

3 ·· 4 , 1 ·· 2 , 5 ·· 8 , 3 ·· 4 , 4 ·· 8 , 1 ·· 2

Grade 5 Lesson 27 Session 2 | Develop Making a Line Plot

Solution 3 ·· 4 ; 2

Develop LanguageWhy Reinforce the meaning of the terms narrowest and widest.

How Explain that narrowest and widest are words used to compare. Say: The ending “-est” means “more than all the others in the group.” Have students find the terms in the first Model It. Point out that Keira is measuring the widths of different stickers. Ask: Which sticker is more narrow than all the others, or narrowest? Which sticker is more wide than all the others, or widest?

TRY ITMake Sense of the ProblemTo support students in making sense of the problem, help them recognize the data on Keira’s paper as a list of lengths.

Ask What data are you given? What is the meaning of each number on Keira’s paper?

DISCUSS ITSupport Partner DiscussionEncourage students to use the terms line plot, data, and scale as they discuss.

Support as needed with questions such as:

• How did you get started?

• How did the data values affect how you chose the scale in your line plot?

Common Misconception Look for students who omit some of the data values on their line plot, showing only one X for each different value that is present in Keira’s list. As students present solutions, have them specify where each of the 12 numbers shown on Keira’s paper appears in their graph.


• evidence of checking off data values one by one

• evidence of sorting data values before graphing

• variety in labeling tick marks: all tick marks labeled as eighths; tick marks labeled as halves, fourths, and eighths; only a few tick marks labeled to establish the scale

Purpose In this session students solve a problem that requires making a line plot given data that includes fractions with unlike denominators. Students model the data in the problem to develop strategies for choosing a scale for a line plot, plotting points, and labeling a line plot so that it captures and communicates information about the data.

SESSION 2 Develop



LESSON 27 DEVELOP


Explore diff erent ways to understand making a line plot.

Keira bought 12 diff erent types of stickers to decorate her scrapbook. She measured the width, in inches, of each type of sticker and wrote down the results. Make a line plot to organize and display Keira’s data.

Model ItList what you know and plan how to make the line plot.

• The fractions are in eighths, fourths, and halves.

• The narrowest sticker is 1 ·· 8 inch. The widest sticker is 1 inch.

• The line plot will start at 0 and go up to 1 inch.

• The line plot will show an X for each of the 12 stickers.

• The line plot will have a title and scale label.

Model ItUse your plan to start labeling and marking the line plot to display the data.

Draw a number line from 0 to 1. Choose an appropriate scale for the data.

Graph each data value. The line plot below shows the fi rst row from Keira’s list of sticker widths.

X X X

0 1

Sticker Widths (in inches)14

34

38

34

14

58

18

12

12

12

1 1

558

Final line plot is shown, with possible labels.

Width (in inches)

Sticker Widths

X X XX

XXXX X

12

Support Whole Class DiscussionCompare and connect the different representations and have students identify how they are related.

Ask How does your model show the sticker width data? What title did you give your line plot? What scale did you choose and how did you label your scale with units?

Listen for Students should recognize that accurate line plots include all 12 points, each plotted above the tick mark that represents its value. Line plots should include a title appropriate for sticker widths, a label showing the widths are in inches, and a scale of 1 ·· 8 to allow points to be plotted with accuracy.

MODEL ITsIf no student presented these models, connect them to the student models by pointing out the ways they each represent:

• the least and greatest data values

• the need for a scale in eighths

Ask What information listed in the plan is used to set the scale on the number line in the line plot?

Listen for The fact that the fractions are in eighths, fourths, and halves tells you that you need to show eighths on the number line.

For planning the line plot, prompt students to consider how to work with the data to gather the information listed in the plan.

• Why might it be good to put Keira’s list of data in order from least to greatest?

• How would you order the fractions from least to greatest? Would a common denominator help?

For the line plot model, prompt students to think about how the line plot follows from the plan in the first Model It.

• How is each part of the plan reflected in the partially completed line plot?

• What are the blanks above and below the line plot for? Why is this information important?

Deepen UnderstandingOrganize Data for a Line PlotSMP 1 Make sense of problems.

Materials For each student: Activity Sheet Sticker Widths; For display: Keira’s data list from the Student Worktext page, copy of Activity Sheet Sticker Widths

When discussing the planning process, prompt students to consider using a table to organize the data and count how many times each data value occurs.

• Display the table and Keira’s list. Have students look at the table’s first column.

• Ask: Is every width in Keira’s list shown in the table? [yes] Why are only 7 widths listed, not 12? [Some widths occur more than once in Keira’s list.] What do you notice about the order the data is listed in? [from least to greatest width]

• Have a volunteer put a tally mark for each fraction in the first row of Keira’s data in the appropriate row of the Tally column. Have other volunteers do the same for the remaining data. All students tally the data in their own table.

• Finally, use the tally marks to fill in the third column. Ask: How can the information in the third column help you draw your line plot? [It tells you how many Xs to place above each data value.]


LESSON 27


SESSION 2

Connect ItNow you will use the problem from the previous page to help you understand how to make a line plot.

1 Look at the fi rst Model It. Why is it a good plan to go from 0 up to 1 inch for the line plot?

2 What scale is used for the line plot in the second Model It? Explain.

3 Why does this scale make sense for the data?

4 The tick marks in the second Model It are not labeled with fractions. Do they have to be? How can you locate data points with Xs when the tick marks are not labeled with numbers?

5 Complete the line plot in the second Model It. Include the rest of the data, a title above the line plot, and a label for the scale below the line plot.

6 How do you use a line plot to organize measurement data?

7 REFLECTLook back at your Try It, strategies by classmates, and Model Its. Which models or strategies do you like best for making line plots? Explain.

559

Possible answer: All the stickers are from 0 to 1 inch in width.

1 ·· 8 inch; Possible explanation: There are eight equal sections from 0 to 1.

Possible answer: The scale makes sense because all of the stickers can be shown in eighths using equivalent fractions.

Possible answer: You do not need to label all the tick marks. You can count

eighths to locate the data points. For example, 1 ·· 4 is equivalent to 2 ·· 8 , so you

plot an X on the second tick mark after 0.

Possible answer: A line plot shows the data in order from least to greatest value. The Xs show how the data are distributed among the different measures.

See second Model It.

Some students may like making a list of facts about the data to help them

plan their line plot. They may use facts to determine key characteristics of

their line plot, such as maximum, minimum, and scale.

CONNECT IT• Remind students that the models show how to

plan and make a line plot to represent data.

• Explain that on this page they will look closely at how to choose a scale and set up the number line for a line plot.

Monitor and Confirm

1 – 4 Check for understanding that:

• the least and greatest data values determine where to start and end tick marks on a line plot

• the scale refers to the value represented by the distance between consecutive tick marks

• the scale should be chosen in a way that allows each data value to be plotted above a tick mark

• not all tick marks need to be labeled as long as enough are labeled to clearly establish the scale

Support Whole Class Discussion

5 Have students compare their completed line plot in Model It to the plots they made in Try It.

Ask Did you do anything differently in your two line plots? Are there ways in which your new line plot is a clearer presentation of the data?

Listen for Responses may include using more precise titles that make the meaning of the data clearer and using more or fewer labels for tick marks. Some students may feel fewer labels makes the display less cluttered and easier to read, while others may feel that including all the labels makes it easier to identify each data value.

Ask Suppose Keira has 10 of each type of sticker.

She puts all the stickers of width 1 ·· 4 inch in a row so

they touch but do not overlap. How long is the row?

Listen for The line plot shows she has 2 types of stickers 1 ·· 4 inch wide, so the row has 20 stickers; 20 3 1 ·· 4 = 20 ·· 4 , or 5; the row is 5 inches long.

6 Look for the idea that a line plot gives a visual representation of how data values are distributed across a range of values from least to greatest.

7 REFLECTHave all students focus on the strategies used to solve this problem. If time allows, have students share their preferences with a partner.

SESSION 2 Develop

Hands-On ActivityMake a human line plot.

If . . . students are unsure about graphing data on a line plot,

Then . . . use this activity to have them make a human line plot with classmates.

Materials For each group: index cards with one measurement on each card (use data values 1 ·· 8 , 1 ·· 4 , 3 ·· 8 , 1 ·· 2 , 5 ·· 8 , 3 ·· 4 , 7 ·· 8 , repeating some values in various amounts until there is one card per student), masking tape

• Find a space large enough for a human line plot. Use masking tape to make a number line from 0 to 1 with a scale of 1 ·· 8 and tick mark labels at 0, 1 ·· 4 , 1 ·· 2 , 3 ·· 4 , and 1.

• Ask: What is the scale of this line plot? How do you know? [ 1 ·· 8 ; there are eight sections between 0 and 1, so you count up by eighths.]

• Distribute one index card (with a pre-labeled measurement) to each student.

• Have students line up one at a time at the corresponding tick mark on the number line. Have each student explain how they knew where to stand.



LESSON 27 DEVELOP


SESSION 2

Apply ItUse what you just learned to solve these problems.

8 Shawn records the lengths in inches of several bugs he collects for a science project. Complete the line plot of the data.

1 5 ·· 8 , 3 1 ·· 4 , 1 3 ·· 4 , 2 7 ·· 8 , 1 3 ·· 4 , 3 1 ·· 4 , 1 5 ·· 8 , 2 3 ·· 8 , 1, 1 3 ·· 4

1 2 3 4

9 Dolores trains for a 5-mile race. She keeps track of the distances she runs each day, in miles, in a training log. Use the data to make a line plot. Show your work.

Distance Run Each Day (miles)

Mon Tues Wed Thurs Fri Sat Sun

Week 1 7 1 ·· 4 5 6 1 ·· 2 5 1 ·· 2 5 7 6

Week 2 4 1 ·· 4 6 1 ·· 2 5 1 ·· 2 5 7 1 ·· 4 6 1 ·· 4 4 3 ·· 4

560



Length (in inches)

Bug Lengths

XXX

XX

XXX XX

141 1

21 341 1

42 122 3

42 143 1

23 343

4 5 86 7

Distance (in miles)

Daily Running DistancesXXX

X

XX

XX

XXX X X X

144 1

24 344 1

45 125 3

45 146 1

26 346 1

47 127 3

47

APPLY ITFor both problems, encourage students to make a plan for their line plot before beginning, including listing the fractions involved from least to greatest, identifying start and end points for their line plots, and an appropriate scale to determine tick marks.

You may also want to encourage students to use the type of table presented in Deepen Understanding (called a frequency table) to order the data values and count the number of times each data value occurs.

8 See line plot on the Student Worktext page; Students’ line plots should show a scale of 1 ·· 8 inch per tick mark, an X above a tick mark for each time the corresponding length appears in the list, and appropriate title and scale label, including the unit inches. Students may include additional tick mark labels for halves, fourths and/or eighths.

Close: Exit Ticket

9 See line plot on the Student Worktext page; Students’ line plots should show a scale of 1 ·· 4 mile per tick mark, an X above a tick mark for each occurrence of the corresponding distance in the table, and appropriate title and scale label, including the unit miles.

Students’ solutions should indicate understanding of:

• how to choose a correct scale for given data

• how to plot data points

• how to title the line plot as a whole and label the scale, including the unit

Error Alert If students forget to provide a title above the line plot or a label for the scale, then review why these elements are important. Ask students how someone not seeing the problem or the original data could interpret the line plot without a title or label for the scale. Have students re-read the problem before they add the missing items.


LESSON 27


Name:


Practice Making Line PlotsStudy the Example showing how to make a line plot. Then solve problems 1–4.

ExampleRosa’s grandfather gives her a box of old foreign coins. She measures the diameter of each coin. Then she makes a list that shows the diameters. How can Rosa show the data in a line plot?

Begin making the line plot by marking a number line from 0 to 1 in eighths.

Make one X to stand for each coin in the table. The line plot below shows three of the 12 data values in Rosa’s list.

Diameter (inches)

Coin Diameters

XXX

0 1

1 Which data values do the three Xs Rosa draws represent?

2 Graph the rest of the data from the list in the Example on the line plot.

LESSON 27 SESSION 2

Coin Diameters (inches)

3 ·· 8 3 ·· 4 7 ·· 8 5 ·· 8 3 ·· 8 3 ·· 4

7 ·· 8 7 ·· 8 5 ·· 8 7 ·· 8 3 ·· 8 7 ·· 8

561

Answer is shown in the line plot above.

the 3 coins that each have a diameter of 3 ·· 8 inch

XXXXX

XX

XX

Solutions

1 the 3 coins with a diameter of 3 ·· 8 inch Basic

2 See the completed line plot in the Example box on the student page. Basic


Fluency & Skills Practice Teacher Toolbox

Assign Making a Line Plot

In this activity students make line plots involving fractions. They also reflect on how they chose a scale for two line plots. This activity helps students represent and identify patterns in data, and preparing them for situations in which they must determine the median, mode(s), and range of data sets.

©Curriculum Associates, LLC Copying is permitted for classroom use.

Name:

Fluency and Skills Practice

Making a Line Plot

1 1 __ 2 1 __ 8 5 __ 8 7 __ 8 3 __ 8

1 __ 4 5 __ 8 1 __ 8 5 __ 8 3 __ 4

3 __ 8 3 __ 4 3 __ 8 5 __ 8

2 1 __ 4 1 __ 2 1 __ 4 3 __ 4 3 __ 4 7 __ 8

1 __ 2 7 __ 8 1 __ 4 1 __ 4 1 __ 8 1 __ 2

3 3 3 1 __ 2 3 1 __ 2 4 2 1 __ 4 3 1 __ 2

3 3 __ 4 3 1 __ 2 2 1 __ 4 3 3 2

4 7 5 __ 8 7 1 __ 8 8 7 3 __ 4 8 7 __ 8

8 1 __ 4 7 3 __ 4 7 5 __ 8 8 7

7 3 __ 4 8 1 __ 2 7 3 __ 8 8 1 __ 2

5 How did you choose a scale for each line plot? Give two examples.

Make a line plot for each data set.




Speaking/Writing Read Connect It problem 6 aloud. Have students form pairs and ask them to review the strategies used in the Try It, Model It, and Picture It sections. Then provide the following terms: line plot, tick mark, equation, labeling. Have students write about why they like one or more of the models and strategies. Ask them to use complete sentences and encourage them to use the terms provided.

Ask partners to read their sentences to each other and to discuss ways each model or strategy is useful.

Speaking/Writing Read Connect It problem 6 aloud. Say: You have used different models and strategies to find the length of songs. What is one model or strategy you used? Have students write about the strategy. Provide sentence frames:

• The line plot has . Each tick mark is .

• The first equation shows . The letter m represents .

Have students compare strategies with a partner and tell why they used that strategy.

• My strategy is .

• I used this strategy because .

Speaking/Writing Read Connect It problem 6 aloud. Ask students to look back at the Picture It and Model It sections. Have them talk about the strategies with a partner. Then ask them to write about one of the strategies. Provide the sentence frames below:

Picture It: • The line plot has .

• Each tick mark is .

• The line plot shows .

Model It:• The first equation shows the of the

songs.

• The letter m means .


3 Gabe has a collection of stamps. He records the heights of the stamps in inches.

1 ·· 2 , 1, 1 1 ·· 2 , 2 1 ·· 2 , 3, 2, 2, 1 ·· 2 , 1, 1, 2 1 ·· 2 , 2, 1 1 ·· 2 , 1, 2 1 ·· 2

Complete a line plot of Gabe’s data. Label each tick mark for this line plot.

Height (in inches)

Stamp Heights

4 Gabe also records the widths of some of the stamps in inches.

3 ·· 4 , 1, 1 1 ·· 2 , 1 1 ·· 4 , 1 1 ·· 2 , 1, 1 3 ·· 4 , 1 3 ·· 4 , 1 1 ·· 2 , 1 ·· 2

Make a line plot of Gabe’s data.

What scale did you use to make your line plot? Explain.

LESSON 27 SESSION 2

Vocabularyscale (on a graph) the value represented by the distance between one tick mark and the next on a number line.

562



Widths (in inches)

12

14

34

Stamp WidthsXXX

XX

XXXX X

0 21 141 1

21 341

Possible answer: 1 ·· 4 inch; The stamp widths include

measurements to the nearest 1 ·· 4 inch. So, using a 1 ·· 4 -inch

scale allows you to plot the data accurately.

X

XXXX

XX

XX

XXX

XXX

0 1 2 312

121 1

22


3 See the completed line plot on the student page; Students should label tick marks from 0 to 3 with a scale of 1 ·· 2 inch per tick mark and draw an X above a tick mark for each time the corresponding height appears in the list of stamp heights. Medium

4 See the line plot on the student page; Students may show tick marks from 0 to 2 with a scale of 1 ·· 4 inch per tick mark and draw an X above a tick mark for each time the corresponding width appears in the list of stamp widths. They should also include an appropriate title and scale label, with the unit inches. Challenge


LESSON 27


LESSON 27


SESSION 3

Develop Solving Problems Using Data in a Line Plot

Read and try to solve the problem below.

The line plot shows the lengths of songs, in minutes, on Ron’s playlist.

Length (in minutes)

Song Lengths

XXX

XXX XX

2 543

Ron adds two new songs to his playlist. His new playlist is now 34 minutes in length. What are two possible lengths for the new songs?

TRY IT Math Toolkit• fraction tiles• fraction circles• fraction bars• number lines

DISCUSS ITAsk your partner: Do you agree with me? Why or why not?

Tell your partner: I disagree with this part because . . .

563


Sample A

Ron’s songs: 2 1 ·· 2 1 2 3 ·· 4 1 3 1 3 1 3 3 ·· 4 1 4 1 4 1 4 1 ·· 2

2 1 2 1 3 1 3 1 3 1 4 1 4 1 4 5 25 1 ·· 2 1 3 ·· 4 1 3 ·· 4 1 1 ·· 2 5 10 ··· 4

25 1 10 ··· 4 5 25 1 2 1 ·· 2 5 27 1 ·· 2

34 2 27 1 ·· 2 5 6 1 ·· 2 The new songs could be 3 and 3 1 ·· 2 minutes.

Sample B

2 1 ·· 2 1 2 3 ·· 4 1 3 1 3 1 3 3 ·· 4 1 4 1 4 1 4 1 ·· 2

5 (3 1 3) 1 (4 1 4) 1 1 2 1 ·· 2 1 4 1 ·· 2 2 1 1 2 3 ·· 4 1 3 3 ·· 4 2 5 6 1 8 1 7 1 5 6 ·· 4 5 26 6 ·· 4 5 27 2 ·· 4 , or 27 1 ·· 2

34 2 27 1 ·· 2 = 6 1 ·· 2

Ron added 6 1 ·· 2 minutes. The new songs could be 2 and 4 1 ·· 2 minutes.

Start

Connect to Prior KnowledgeMaterials For each pair: 2 sets of fraction tiles or circles

Why Review fraction operations with mixed numbers to prepare for solving problems with mixed numbers based on data in a line plot.

How Have each pair share fraction tiles to show and find the value of each expression.


Start

Grade 5 Lesson 27 Session 3 | Develop Solving Problems Using Data in a Line Plot

Use fraction tiles to find the value of each expression.

2 3 1 1 ·· 4 5 ?

2 1 ·· 2 2 1 3 ·· 4 5 ?

Solutions

2 3 1 1 ·· 4 = 2 1 ·· 2 , or 2 2 ·· 4

2 1 ·· 2 – 1 3 ·· 4 = 3 ·· 4

Develop LanguageWhy Clarify the meaning of the term length as it relates to durations of time.

How Review what students know about the term. Students probably know that length describes the distance from one point to another. Explain that length can also describe the amount of time something lasts. Have students find the term in Try It. Ask: What unit does Ron use to show the lengths of the songs in the line plot?

TRY ITMake Sense of the ProblemTo support students in making sense of the problem, have them analyze the given information and identify that there can be more than one correct answer.

Ask Does the line plot represent Ron’s original playlist or his playlist after he adds two songs?

DISCUSS ITSupport Partner DiscussionEncourage students to use the Discuss It question and sentence starter on the Student Worktext page as part of their discussion.

Support as needed with questions such as:

• What did you have to do first to start solving the problem?

• Did you and your partner find the same lengths for the new songs?

Common Misconception Look for students who include 3 minutes and 4 minutes only once when finding the length of Ron’s original playlist. As students present solutions, have them match each X in the line plot with an addend in their sum.


• concrete models used to support part of the problem, such as adding fractions

• drawings to represent part or all of the problem

• variations of using properties of operations to find the sum of the song lengths

• equations that use letters to represent unknowns

Purpose In this session students use data from a line plot to solve a multi-step problem requiring operations with mixed numbers. The purpose of this problem is to have students interpret data on a line plot and use that data to solve a real-world problem as they apply previously learned knowledge of fraction operations.

SESSION 3 Develop



LESSON 27 DEVELOP


Explore diff erent ways to understand solving a problem using data from the line plot.

The line plot shows the lengths of songs, in minutes, on Ron’s playlist.

Length (in minutes)

Song Length

XXX

XXX XX

2 543

Ron adds two new songs to his playlist. His new playlist is now 34 minutes in length. What are two possible lengths for the new songs?

Picture ItYou can use a picture to help understand the data in the problem.

Label the tick marks in the line plot to show the song lengths.

Length (in minutes)

Song Lengths

XXX

XXX XX

2 543142

122

342

143

123

343

144

124

344

Model ItYou can use equations to help understand the problem.

Write an equation to fi nd m, the length in minutes of Ron’s original playlist.

m 5 2 1 ·· 2 1 2 3 ·· 4 1 3 1 3 1 3 3 ·· 4 1 4 1 4 1 4 1 ·· 2

Write an equation that shows how to fi nd the total number of minutes, t, that the new songs add to the length of Ron’s playlist.

t 5 34 2 m

Find two songs that add to the number of minutes, t.

564

Support Whole Class DiscussionCompare and connect the different strategies used and have students identify how they are related.

Ask How did you use the line plot to find the length of Ron’s original playlist? How does your model find the total length of the two songs Ron adds to his playlist?

Listen for Students should recognize that accurate responses explain how to add the value represented by each X on the line plot to show that Ron’s original playlist is 27 1 ·· 2 minutes long. Responses should also include that you can add up from 27 1 ·· 2 to 34 or subtract 27 1 ·· 2 from 34 to determine the total length of the two additional songs. Students may choose different lengths that add to this amount.

PICTURE IT & MODEL ITIf no student presented these models, connect them to the student models by pointing out the ways they each represent:

• the number of songs in Ron’s original playlist

• the length of each song in Ron’s original playlist

Ask How do the line plot and the equation show the number of songs on Ron’s original playlist?

Listen for The line plot shows 8 data points and the equation shows 8 addends, so Ron’s original playlist has 8 songs.

For the number line model, prompt students to consider the benefit of labeling tick marks.

• How does the scale of the line plot help you determine the label for each tick mark?

• Why might it be a good idea to label the tick mark values between the whole numbers?

For the equation model, prompt students to consider other possible equations to write.

• What do the letters t and m represent?

• Compare the following equations to the equations shown in Model it. How do they show the same relationships in a different way?

m 5 2 1 ·· 2 1 2 3 ·· 4 1 (2 3 3) 1 3 3 ·· 4 1 (2 3 4) 1 4 1 ·· 2

34 5 m 1 t

Deepen UnderstandingEquation ModelsSMP 2 Reason abstractly and quantitatively.

Discuss that the equations in Model It represent relationships among quantities in the problem and that the equations use letters for unknown quantities.

Have students brainstorm questions that can be answered using data from Ron’s line plot. Ask students to decide which questions they can model with equations. Have students use letters to represent the unknowns. Examples:

How much longer is Ron’s longest song than his shortest song? [This question can be modeled with the equation d 5 4 1 ·· 2 2 2 1 ·· 2 , where d is the difference between the lengths of the longest and shortest songs.]

How many of Ron’s songs are longer than 4 minutes? [This question is not modeled by an equation; it is answered by counting data points.]

If all the songs in Ron’s original playlist were the same length, how long would they be? [This question can be modeled with two equations, the equation for m shown in Model It and the equation s = m 4 8, where s is the song length if all songs on the original playlist are the same length.]


LESSON 27


SESSION 3

Connect ItNow you will use the problem from the previous page to help you understand how to solve a problem using data in a line plot.

1 How many minutes, m, is Ron’s original playlist? Explain how you know.

2 How many minutes, t, do the two new songs add to Ron’s playlist? Explain.

3 What are two possible lengths for the new songs? Is more than one correct answer possible? Explain.

4 How did the line plot help you solve the problem?

5 How did you use operations with fractions to solve the problem?

6 REFLECTLook back at your Try It, strategies by classmates, and Picture It and Model It. Which models or strategies do you like best for solving problems using data in a line plot? Explain.

565

27 1 ·· 2 minutes; Possible explanation: Add the song lengths to find the total time.

6 1 ·· 2 minutes; Possible explanation: Subtract the length of Ron’s playlist from

34 to find the total length of the two songs he added. 34 2 27 1 ·· 2 5 6 1 ·· 2 .

Possible answer: 3 minutes and 3 1 ·· 2 minutes; Students’ explanations should

show an understanding that any pair of fractions or whole numbers with a

sum of 6 1 ·· 2 minutes is a possible correct answer.

Possible answer: The line plot gave the length of each of the songs on Ron’s original playlist. You need those data to find the length of the two new songs.

Possible answer: I added mixed numbers to find the length of the original

playlist. I subtracted this total from 34 minutes. Then I added two numbers,

3 and 3 1 ·· 2 , to find a sum of 6 1 ·· 2 minutes.

Students may say labeling tick marks helps them identify data values. They

may also say using letters to represent unknown quantities helps them keep

track of the quantities that they need to find in a multi-step problem.

SESSION 3 Develop

CONNECT IT• Remind students that one thing that is alike about

the representations is that they represent the data from Ron’s original playlist.

• Explain that on this page they will describe how to use the line plot data as part of the solution to the problem.

Monitor and Confirm1 – 3 Check for understanding that:

• you add the song lengths to find the length of the original playlist, 27 1 ·· 2 minutes

• the two new songs add 6 1 ·· 2 minutes

• any two times with a sum of 6 1 ·· 2 minutes could be the lengths of the two new songs

Support Whole Class Discussion

1 Prompt students to compare a variety of strategies for finding the value of m, the sum of the song lengths from the original playlist.

Ask What are some different ways you can carry out adding the 8 song lengths?

Listen for Students may describe a variety of strategies, such as the following.

You can group whole numbers and mixed numbers:

(2 1 ·· 2 1 2 3 ·· 4 1 3 3 ·· 4 1 4 1 ·· 2 ) 1 (3 1 3 1 4 1 4)

You can break apart the mixed numbers and then group whole numbers and fractions:

(2 1 2 1 3 1 3 1 3 1 4 1 4 1 4) 1 1 1 ·· 2 1 3 ·· 4 1 3 ·· 4 1 1 ·· 2 2 With the whole number parts, you can look for groups of ones that add to make 10, and with the fractions you can look for fractions that sum to 1.

4 – 5 Look for the ideas that you interpret each X on the line plot to get the data you need to solve the problem. Then you use fraction operations to add and/or multiply as you combine song lengths to find the length of the original playlist. You can add, subtract, or divide to find the length of the two new songs. Students may choose to use different operations to complete each step in the problem.

6 REFLECTHave all students focus on the strategies used to solve this problem. If time allows, have students share their preferences with a partner.

Hands-On ActivityMake a line plot and solve problems.

If . . . students are struggling with solving problems involving fraction operations on a line plot,

Then . . . use this activity for additional practice with line plots.

Materials For each pair: number cube

• Write the following song lengths (in minutes) on the board: 2 3 ·· 4 , 3, 3 1 ·· 8 .

• Have pairs roll a number cube for each song length to tell how many times the length occurs on a playlist. Then have pairs make a line plot of their data.

• Ask: How could you write an equation to find the difference in song length between the shortest and longest song? Use m to represent the difference, in minutes. 3 m 5 3 1 ·· 8 2 2 3 ·· 4 4

• Have pairs use any method to find the value of m. 3 m 5 3 ·· 8 minute 4 • Ask additional questions about the playlist and have pairs use an equation to

solve the problem. For example: What is the difference in song length between the most common song length and the shortest song length? What is the sum of all the song lengths?



LESSON 27 DEVELOP


SESSION 3

Apply ItUse what you just learned to solve these problems.

Renaldo collects 10 shells at the beach and weighs each of them. He uses the line plot below to display the data.

Weight (in ounces)

Shell WeightsXXX

XXX X X X X

9 10 11 12149

129

349

1410

1210

3410

1411

1211

3411

7 What is the diff erence between the weights of the lightest and heaviest shells Renaldo collected?Show your work.

Solution

8 What is the total weight of the shells Renaldo collected that weigh less than 10 1 ·· 2 ounces? Show your work.

Solution

9 What is the total weight of the shells Renaldo collected most often?

� 11 3 ·· 4 ounces � 22 1 ·· 4 ounces

� 33 3 ·· 8 ounces � 33 3 ·· 4 ounces

566


11 3 ·· 4 2 9 1 ·· 8 5 d;

11 6 ·· 8 2 9 1 ·· 8 5 2 5 ·· 8

10 1 ·· 4 5 10 2 ·· 8

9 1 9 1 10 1 10 5 38

1 ·· 8 1 5 ·· 8 1 2 ·· 8 1 2 ·· 8 5 10 ··· 8 38 1 10 ··· 8 5 38 1 1 2 ·· 8 5 39 2 ·· 8

2 5 ·· 8 ounces

39 2 ·· 8 , or 39 1 ·· 4 , ounces


APPLY ITFor all problems, encourage students to use fraction operation strategies from past lessons.

Be sure that students understand that all three problems refer to the data in the Shell Weights line plot at the top of the page.

7 2 5 ·· 8 ounces; Students may identify the lightest shell’s weight as 9 1 ·· 8 ounces and the heaviest shell’s weight as 11 3 ·· 4 ounces from the leftmost and rightmost tick marks on the line plot. They may then write an equation to find the difference as shown on the Student Worktext page, or they may use a counting up by eighths strategy from the leftmost tick mark to the rightmost tick on the number line.

8 39 2 ·· 8 or 39 1 ·· 4 ounces; Students identify the weights less than 10 1 ·· 2 ounces as the Xs to the left of 10 1 ·· 2 , on the line plot: 10 1 ·· 4 , 10 1 ·· 4 , 9 5 ·· 8 , and 9 1 ·· 8 ounces. They may then add the whole number and fractional parts of each mixed number and then combine these sums. Students may also use multiplication to find the weight of the two 10 1 ·· 4 ounce shells and then add the product to sum of the 9 1 ·· 8 and 9 5 ·· 8 ounce shells.

Close: Exit Ticket

9 C; Students may use addition or multiplication to find the total weight of the three 11 1 ·· 8 ounce shells.

Error Alert If students choose A or B, then have them identify the weight that has the most Xs above it on the line plot. Remind students that each X represents a shell of that weight, so they must include three addends of 11 1 ·· 8 (or multiply 11 1 ·· 8 by 3).


LESSON 27


Name:


LESSON 27 SESSION 3

Practice Solving Problems Using Data in a Line PlotStudy the Example showing how to solve a problem using data in a line plot. Then solve problems 1–6.

ExampleMiguel has strips of colored tape that he uses to decorate his model planes. The line plot shows how many strips he has in several diff erent lengths.

If Miguel places all of

the 1 ·· 4 -inch strips in a row,

how long is the line that

he would make?

The tick marks divide the distance from 0 to 1 into eighths. The second tick mark to

the right of 0 is 2 ·· 8 , or 1 ·· 4 .

There are six 1 ·· 4 -inch strips, and 6 3 1 ·· 4 5 6 ·· 4 , or 1 1 ·· 2 . The line would be 1 1 ·· 2 inches long.

1 How long a line can Miguel make using all the 3 ·· 8 -inch strips? Show your work.

Solution

2 What is the diff erence in length between a line made with all the 3 ·· 8 -inch strips and

a line made with all the 3 ·· 4 -inch strips? Show your work.

Solution

Length (in inches)

Tape Strip Lengths

XXXXXX

XXXXX

XXXXXXX

XXXXXXXX

XXXXXXXX

0 1

567

Possible work: 7 3 3 ·· 8 5 21 ··· 8 , and 21 ··· 8 5 2 5 ·· 8 .

2 5 ·· 8 inches long

Possible student work: 3 ·· 8 3 7 5 2 5 ·· 8 ; 3 ·· 4 3 8 5 6; 6 2 2 5 ·· 8 5 3 3 ·· 8

3 3 ·· 8 inches


Solutions

1 2 5 ·· 8 inches long; See possible work on the student page. Basic

2 3 3 ·· 8 inches; See possible work on the student page. Medium

Fluency & Skills Practice Teacher Toolbox

Assign Solving Problems Using Data in a Line Plot

In this activity students solve problems by interpreting data displayed in a line plot. Understanding data displays is an essential skill in everyday life, particularly in a media environment that often displays information in graphs. Students may make line plots in science classes, particularly in life-science classes that involve recording and representing variations in the heights and masses of plants and animals.

©Curriculum Associates, LLC Copying is permitted for classroom use.

Name:

Fluency and Skills Practice

Solving Problems Using Data in a Line Plot

Sheila weighs some strawberries of different sizes. She weighs each strawberry to the

nearest 1 __ 8 ounce. The results are shown in the line plot below.

Weight (in ounces)

Strawberry Weights

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

180 11

438

12

58

34

78

1 What is the diff erence of the weights of the heaviest and lightest strawberries?

2 What is the total weight of the strawberries that weigh 3 __ 4 ounce or more?

3 What is the total weight of the strawberries that weigh less than 1 __ 2 ounce?

4 What is the diff erence in weight between all the strawberries

that weigh 7 __ 8 ounce and all the strawberries that weigh 1 __ 2 ounce?

Answer the questions about each line plot.




Speaking/Listening Have students form pairs and read Apply It problem 2 aloud. Ask pairs to discuss the process they will use to make the line plot. Encourage them to use complete sentences.

Have pairs take turns explaining their process to other pairs of partners. Then have them work together to make the line plot. Call on students to share their line plots and explain their process. Encourage students to say whether they agree with the processes shared and why.

Speaking/Listening Read Apply It problem 2 aloud.

Ask: What is the least weight in the problem? [14 1 ·· 4 pounds] What is the greatest weight?

[17 1 ·· 2 pounds] Have students form pairs and discuss the process they will use to make the line plot. Encourage them to use complete sentences.

Have students take turns explaining their process to their partners. Then have them work together to make the line plot. Call on students to share their line plots and explain their process.

Speaking/Listening Read Apply It problem 2 aloud and have students repeat after you. Ask: What is the least weight in the

problem? [14 1 ·· 4 pounds] What is the greatest

weight? [17 1 ·· 2 pounds] Say: Let’s start and end

the line plot with whole numbers. Draw the line plot from 14 to 18. Now ask students to use the fractions they see in the data to decide how many parts to break each whole into by drawing more ticks marks. [4] Mark the tick marks on the line plot and an X for each of the weights. Then, display the weights. Point to an X and ask the students to say the corresponding weight. As you say the weight, cross it out. Then have students make their own line plots.


LESSON 27 SESSION 3

Use the data in the line plot to solve problems 3–6.

3 If Miguel uses 2 of each strip length that he has to make a line, how long would the line be? Show your work.

Solution

4 Miguel adds another data value so that the diff erence between

the longest and shortest strip lengths is 3 ·· 4 inch. What tape length

did Miguel add? Explain.

5 If Miguel makes a line with all of the 5 ·· 8 -inch strips, what is the

total length in inches? Show your work.

Solution

6 How could Miguel use strips of diff erent lengths to make a 4-inch line?

Length (in inches)

Tape Strip Lengths

XXXXXX

XXXXX

XXXXXXX

XXXXXXXX

XXXXXXXX

0 118

14

38

12

58

34

78

568

Possible work: 2 3 1 ·· 4 5 2 ·· 4 ;

2 3 3 ·· 8 5 6 ·· 8 ; 2 3 1 ·· 2 5 1; 2 3 5 ·· 8 5 10 ··· 8 ;

2 3 3 ·· 4 5 6 ·· 4

Write all fractions in eighths and

add: 4 ·· 8 1 6 ·· 8 1 8 ·· 8 1 10 ··· 8 1 12 ··· 8 5 40 ··· 8 ,

or 5

5 inches

1 inch; Possible explanation: 1 5 4 ·· 4 , and 4 ·· 4 2 1 ·· 4 5 3 ·· 4 .


5 ·· 8 3 5 5 25 ··· 8 ; 25 ··· 8 5 3 1 ·· 8

Answers will vary. Possible answer: He could use six 1 ·· 2 -inch strips and

four 1 ·· 4 -inch strips: 6 3 1 ·· 2 5 3; 4 3 1 ·· 4 5 1; 3 1 1 5 4.

3 1 ·· 8 inches

Prepare for Session 4Use with Apply It.

3 5 inches; See possible equations on the student page. Medium

4 1 inch; See possible explanation on the student page. Medium

5 3 1 ·· 8 inches; See possible work on the student page. Medium

6 Answers will vary; See possible lengths on the student page. Challenge


LESSON 27


LESSON 27


Complete the Example below. Then solve problems 1–7.

ExampleThe line plot shows the weights of the burgers Mel made for a cookout. How many pounds of meat did she use to make all the burgers?

Weight (in pounds)

Burger WeightsXXXXX

XX

XXXXX

0 112

Look at how you could use the data in the line plot.

One 1 ·· 8 -lb burger: 1 ·· 8 Five 1 ·· 4 -lb burgers: 5 3 1 ·· 4 5 1 1 ·· 4

Four 1 ·· 2 -lb burgers: 4 3 1 ·· 2 5 2 Two 3 ·· 4 -lb burgers: 2 3 3 ·· 4 5 1 1 ·· 2

Total: 1 ·· 8 1 1 1 ·· 4 1 2 1 1 1 ·· 2

Solution

SESSION 4

Refine Making Line Plots and Interpreting Data

The student multiplied the number of burgers of each weight by the weight and then added the amounts to � nd the total.

PAIR/SHARECheck your partner’s answer using addition instead of multiplication.

PAIR/SHAREDraw a picture to show how Mel cut the burger.

Apply It1 Use the line plot in the Example. Mel cuts the smallest burger in

half. What is the weight of the meat in each half? Show your work.

Solution

What operations could you use to solve the problem?

569

4 7 ·· 8 pounds

1 ··· 16 pound

Possible work: 1 ·· 8 4 2; 1 ·· 8 3 1 ·· 2 5 1 ··· 16

Start

Check for UnderstandingWhy Confirm understanding of using fraction operations to solve a problem about data presented in a line plot.

How Have students find the total weight of the strawberry weights shown in the line plot using any strategy they want.


Start

Grade 5 Lesson 27 Session 4 | Refi ne Making Line Plots and Interpreting Data

How many ounces of strawberries were picked?

Weight (in ounces)

Strawberries Picked

XX

0 1

XX

XXXX

XXX

XXXX

XXX

Solution10 7 ·· 8 ounces

Purpose In this session students solve word problems involving constructing and interpreting line plots. They then discuss and confirm their answers with a partner.

Before students begin to work, use their responses to the Check for Understanding to determine those who will benefit from additional support.

As students complete the Example and problems 1–3, observe and monitor their reasoning to identify groupings for differentiated instruction.

SESSION 4 Refine

If the error is . . . Students may . . . To support understanding . . .

4 3 ·· 8 ouncesnot have multiplied each weight by the number of strawberries.

Ask students how many strawberries were weighed. [18] Ask them if their answer represents the weight of all 18 strawberries. Explain that they need to multiply each weight by the number of strawberries at that weight.

9 7 ·· 8 ouncesnot have included the strawberry that weighs 1 ounce in the total.

Ask students how many strawberries were weighed. [18] Have them check to be sure that they included the weights of all 18 strawberries weighed.

Error Alert



LESSON 27 REFINE


2 An animal doctor’s scale weighs animals to the nearest 1 ·· 4 pound.

The list below shows the weights, in pounds, of the last 10 dogs

the animal doctor saw.

14 1 ·· 2 , 17 1 ·· 2 , 15 1 ·· 4 , 17 1 ·· 4 , 17 1 ·· 2 , 15 1 ·· 4 , 14 1 ·· 4 , 16, 14 3 ·· 4 , 15 1 ·· 4

Create a line plot to show the data.

3 Look at the line plot for problem 2. Which statement about the data is true?

� The heaviest dog is 4 1 ·· 4 pounds heavier than the lightest dog.

� The three lightest dogs weigh 43 1 ·· 2 pounds combined.

� The three heaviest dogs weigh 52 1 ·· 2 pounds combined.

� The 16-pound dog is closer in weight to the lightest dog than

to the heaviest dog.

Michelle chose � as the correct answer. How did she get that answer?

PAIR/SHAREHow is your line plot the same as your partner’s? How is it diff erent?

PAIR/SHAREDoes Michelle’s answer make sense?

How should the line plot’s scale be labeled to show these data?

Read each statement carefully and check it against the data to see if it is true.

570

Possible answer: Michelle subtracted the weight of the

lightest dog from the weight of the heaviest dog, but she

subtracted incorrectly. 17 1 ·· 2 2 14 1 ·· 4 5 3 1 ·· 4 , not 4 1 ·· 4 .

Possible line plot:

Weight (in pounds)

Dog WeightsXXX

XXXX X X X

14 171615 18

Example4 7 ·· 8 pounds; the equations shown are one way to solve the problem. Students could also solve the problem by adding all burger weights.

Look for To find the sum, write the mixed numbers as fractions and use 8 as a common denominator: 1 ·· 8 1 10 ·· 8 1 16 ·· 8 1 12 ·· 8 5 3 9 ·· 8 , or 4 7 ·· 8 pounds.

APPLY IT1 1 ·· 16 pound; Students could solve the problem

by dividing the least weight, 1 ·· 8 pound, by 2 or multiplying 1 ·· 8 by 1 ·· 2 . DOK 2

Look for You can divide the unit fraction 1 ·· 8 by 2 or multiply 1 ·· 8 by 1 ·· 2 .

2 See the line plot on the Student Worktext page; Students may show tick marks from 14 to18 with a scale of 1 ·· 4 pound per tick mark and draw an X above a tick mark for each time the corresponding weight appears in the list of data. They should also include an appropriate title and scale label, with the unit pounds. DOK 2

Look for Use a scale of 1 ·· 4 pound per tick mark because the data shown are in halves and fourths.

3 B; Students could solve the problem by identifying the weights for the three leftmost data points and then finding their sum: 14 1 ·· 4 1 14 1 ·· 2 1 14 3 ·· 4 5 43 1 ·· 2 .

Explain why the other two answer choices are not correct:

C is not correct because the three heaviest dogs have a combined weight of 52 1 ·· 4 pounds.

D is not correct because 16 pounds

is 1 1 ·· 2 pounds less than 17 1 ·· 2 pounds

and 1 3 ·· 4 pounds more than 14 1 ·· 4 pounds.

DOK 3


LESSON 27


SESSION 4

4 Juan drives a race car. The race tracks vary in length. To prepare for racing season, he records the lengths, in miles, of the tracks in the list shown below. Which line plot correctly shows the track data?

1 ·· 4 , 1 ·· 2 , 3 ·· 8 , 1 ·· 2 , 1 ·· 4 , 1 ·· 2 , 1, 1 1 ·· 4 , 3 ·· 4 , 1 ·· 2 , 7 ·· 8 , 1 ·· 2 , 3 ·· 4

�

Length (in miles)

XXXXXX

XX

XXXXX

38

34

14

12

78

1411

Track Lengths

�

Length (in miles)

XX XXX

XXX

XXXXX

58

14

38

12

34

78

181

1411

Track Lengths

�

Length (in miles)

XXX XXX

XX

XXXXX

14

12

34

78

1411

Track Lengths

�

Length (in miles)

XX XXX

XX X

XXXXX

58

14

38

12

34

78

181

1411

Track Lengths

5 Look at the data for problem 4. Choose True or False for each statement.

True False

The longest track is 6 times the length of the shortest track. � �

The combined length of the three shortest tracks is 4 ·· 8 mile. � �

The combined length of the three longest tracks is 3 1 ·· 8 miles. � �

Half the length of the shortest track is 1 ·· 8 mile. � �

571

4 D; Identify which line plot lists the lengths in order from least to greatest and has the correct number of Xs above each length. DOK 1

Error Alert Students may choose the wrong answer because they do not match data to the line plot carefully. Encourage those students to first make a frequency table (see Deepen Understanding for Session 2) using the given data before identifying the correct line plot.

5 B (False);D (False);E (True);G (True) DOK 2

SESSION 4 Refine

Differentiated Instruction

RETEACH EXTEND

Hands-On ActivityGather, plot, and interpret data.

Students struggling with concepts around problem solving with data and line plots

Will benefit from additional work with line plots and problem solving

Materials For each group: 1 bean bag, 1 yardstick, masking tape

• Form groups of at least 8 students. Use masking tape to mark a target on the floor about 5 feet away.

• Have each student in a group toss the bean bag at the target. After each toss, have students measure the distance from where the bean bag lands to the target. Students should measure to the nearest 1 ·· 4 inch.

• Tell students to list the data for their group in a table and then transfer the data to a line plot. Ask each group to use the line plot to describe their data. Have the groups answer questions such as, What is the difference in length between the toss closest to the target and the one farthest from the target? Follow up with additional questions about the data.

Challenge ActivityInterpret related line plots.

Students who have achieved proficiency

Will benefit from deepening understanding of line plots

• Display the heights, in feet, of two teams:

Team A: 5 3 ·· 4 , 6 1 ·· 4 , 5 7 ·· 8 , 6 1 ·· 2 , 6, 6 1 ·· 4 , 6 1 ·· 8 , 5 5 ·· 8 , 6 1 ·· 2

Team B: 5 5 ·· 8 , 6 1 ·· 2 , 5 3 ·· 4 , 6 1 ·· 8 , 5 7 ·· 8 , 6 1 ·· 2 , 5 5 ·· 8 , 6 1 ·· 4 ,

5 7 ·· 8 , 6 1 ·· 2 , 5 5 ·· 8 , 6 3 ·· 8

• Tell students to make a line plot for each set of data. Have students write and justify statements about relationships between the two data sets.



LESSON 27 REFINE


SESSION 4

6 Sara owns Sara’s Hardware. She made the line plot below to compare the fuel tank capacity of several lawn mowers she sells.

Capacity (in gallons)

Tank Capacity of Lawn MowersXXXX

XXX

XXX X

1 2 3121

122

Part A What is the most common capacity of the mowers she sells?

Part B Marc buys the lawn mower with the smallest tank capacity. He uses 3 full tanks of gas mowing in the summer. How much fuel does he use? Show your work.

Solution

7 MATH JOURNALJordan looks at the line plot above. He says the diff erence between the most

common capacity and the least capacity is 1 ·· 4 gallon. He says he knows the

diff erence without subtracting. Explain Jordan’s mistake. Then fi nd the actual

diff erence between the measurements.

SELF CHECK Go back to the Unit 4 Opener and see what you can check off .572

1 5 ·· 8 gallons

Possible student work: 3 3 1 1 ·· 2 5 (3 3 1) 1 1 3 3 1 ·· 2 2 5 3 + 3 ·· 2

5 4 1 ·· 2

Marc uses 4 1 ·· 2 gallons of fuel.

Possible answer: He thinks that the scale is 1 ·· 4 , because there are labels once

every four tick marks. Each whole is divided into eighths, so the next tick

mark after 1 1 ·· 2 represents 1 5 ·· 8 and the difference between the measurements is 1 ·· 8 .

1 1 ·· 2 5 1 4 ·· 8 ; 1 5 ·· 8 2 1 4 ·· 8 5 1 ·· 8 .

6 Part A

1 5 ·· 8 gallons; Use the line plot to identify which column of Xs is the tallest.

Part B

4 1 ·· 2 gallons; Use the X farthest left on the line plot to identify the smallest tank capacity. Multiply 1 1 ·· 2 gallons by 3. DOK 2

Close: Exit Ticket7 MATH JOURNAL

Student responses should indicate understanding of using data from line plots, identifying the scale of line plots, and subtracting mixed numbers.

Error Alert If students say Jordan is correct, then review how to determine the scale of a line plot. Have students identify the number of sections between two consecutive whole numbers on the line plot. Ask What fraction of the whole is each tick mark as you count up from 1 to 2?

REINFORCE PERSONALIZE

Problems 4–7Make line plots and interpret data.

All students will benefit from additional work with showing and interpreting data in line plots by solving problems in a variety of formats.

• Have students work on their own or with a partner to solve the problems.

• Encourage students to show their work.

Provide students with opportunities to work on their personalized instruction path with i-Ready Online Instruction to:

• fill prerequisite gaps

• build up grade-level skills

SELF CHECK Have students consider whether they feel they are ready to check off any new skills on the Unit 4 Opener page.

©Curriculum Associates, LLC Copying is not permitted.572a Lesson 27 Make Line Plots and Interpret Data

LESSON 27

Lesson Quiz Teacher Toolbox

Short Response Scoring Rubric

Points Expectations

2

Response contains the following:• Correct computations, solutions, and/or calculations.

(1 point)• Well-organized, clear, and concise work that

demonstrates thorough understanding of math concepts and/or procedures. (1 point)

1

Response contains the following:• Mostly correct solution(s). • Shows partial or good understanding of math

concepts and/or procedures.

0

Response contains the following:• Incorrect solution(s).• No attempt at find a solution.• No effort to demonstrate an understanding of

mathematical concepts and/or procedures.

1©Curriculum Associates, LLC

Copying permitted for classroom use.Grade 5 Lesson 27 Make Line Plots and Interpret Data

Name ___________________________________________________________ Date ____________________

Lesson 27 Quiz

Solve the problems.

Al practices the standing long jump. He records the distance, in feet, of each of his jumps. His results are shown on the line plot below.

Use this line plot to answer questions 1 – 3.

Distance (feet)

Standing Long Jump Distances

65

X X X XX XX XXX

145 1

25 345

1 What scale did Al use to make his line plot? Write your answer in the blank.

Al used a scale of foot.

2 Find the jump length that Al made most often. What is the total distance of the jumps of this length?

� 12 1 ·· 4 feet � 16 1 ·· 2 feet

� 17 5 ·· 8 feet � 18 1 ·· 4 feet

3 What is the diff erence between Al’s shortest and longest jumps? Show your work.

feet

(1 point)

1 ·· 8

(1 point)

(2 points)


6 1 ·· 8 2 5 1 ·· 4 5 6 1 ·· 8 2 5 2 ·· 8

5 5 9 ·· 8 2 5 2 ·· 8

5 7 ·· 8

7 ·· 8

Tested SkillsAssesses 5.MD.B.2

Problems on this assessment form require students to be able to use the scale of a line plot to identify data values, to solve multi-step word problems about measurement data involving fractional units, and to make line plots to display measurement data using fractional units. Students will also need to be familiar with computing with fractions and the meaning of each operation in order to answer questions about the data.

Alternately, teachers may assign the Digital Comprehension Check online to assess student understanding of this material.

Error Alert Students may:

• not interpret the scale of a line plot correctly.

• miscalculate when solving problems involving fractions and mixed numbers represented on a line plot.

• only count a data value once instead of counting the number of Xs.

Choice Matrix Scoring Rubric

2 points 1 point 0 points

All answers are correct

1 incorrect answer 2 or more incorrect answers

Graphing Scoring Rubric

2 points 1 point 0 points

Response contains the following: • All data points are

correctly plotted.• Well-organized,

clear, and concise work that demonstrates thorough understanding of math concepts and/or procedures.

Response contains the following:• Most data points

are correctly plotted.

• Shows partial or good understanding of math concepts and/or procedures.

Response contains the following:• Data points are

incorrectly plotted. • No effort to

demonstrate an understanding of mathematical concepts and/or procedures.

©Curriculum Associates, LLC Copying is not permitted. 572bLesson 27 Make Line Plots and Interpret Data

Differentiated Instruction

RETEACH REINFORCE EXTEND

Teacher Toolbox

Enrichment ActivitiesStudents who have achieved proficiency with concepts and skills and are ready for additional challenges

Will benefit from group collaborative games and activities that extend understanding

Math Center ActivitiesStudents who require additional practice to reinforce concepts and skills and deepen understanding

Will benefit from small group collaborative games and activities (available in three versions—on-level, below-level, and above-level)

Tools for InstructionStudents who require additional support for prerequisite or on-level skills

Will benefit from activities that provide targeted skills instruction

2©Curriculum Associates, LLC

Copying permitted for classroom use.Grade 5 Lesson 27 Make Line Plots and Interpret Data

Name ___________________________________________________________ Date ____________________

Lesson 27 Quiz continued

4 The line plot below shows the weight, in pounds, of each bean bag for a tossing game.

Weight (pounds)

1

XX X

XXXX X XXX

1411

234

121

Bean Bag Weights

Decide if each statement is true.

Choose True or False for each statement.

True False

The total weight of all the bean bags is 10 1 ·· 2 pounds. � �

The combined weight of the three lightest bags is 2 pounds. � �

The combined weight of the three heaviest bags is 4 pounds. � �

The difference between the weights of the lightest bag and the heaviest bag is 1 pound.

� �

5 Claire and her family cook meals on a camping stove on their camping trips. Claire recorded the number of canisters of cooking fuel they used on diff erent camping trips. The list of the data Claire recorded is shown below.

2 1 ·· 8 , 1 1 ·· 2 , 1 3 ·· 4 , 2 3 ·· 4 , 2 7 ·· 8 , 1 1 ·· 4 , 1 3 ·· 4 , 2 3 ·· 8 , 2 3 ·· 4 , 1 3 ·· 4

Graph Claire’s data on the line plot.

Cooking Fuel Used (canisters)

Canisters of Cooking Fuel Used

1 2 3141

121

341

142

122

342

(2 points)

(2 points)

Cooking Fuel Used (canisters)

Canisters of Cooking Fuel Used

1 2 3141

121

341

142

122

342

X X X X XXX

X XX

Solutions1 Al used a scale of 1 ·· 8 foot.

1 point 5.MD.B.2, DOK 1

2 C; Students could use addition or multiplication to find the total distance of the three jumps measuring 5 7 ·· 8 feet each. A is not correct because it represents the total distance of the two longest jumps. B is not correct because the scale was misinterpreted as three jumps measuring 5 1 ·· 2 feet each instead of 5 7 ·· 8 feet each.

D is not correct because it represents the total distance of the three longest jumps instead of the jumps that occurred most often. 1 point 5.MD.B.2, DOK 1

3 7 ·· 8 feet; See possible student work on the student page. 2 points 5.MD.B.2, DOK 2

4 B (False); C (True); E (True); H (False) 2 points 5.MD.B.2, DOK 2

5 See completed line plot on the student page. 2 points 5.MD.B.2, DOK 2

Documents

Lesson LESSON 27 Overview Make Line Plots and Interpret Data