LESSON 27 Make Line Plots and Interpret Data. Lesson Objectives. Content Objectives

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Overview

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 Focus

Domain

Measurement and Data

Cluster

B. Represent and interpret data.

Standard

5.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 Standards

5.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

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Lesson Pacing Guide

PERSONALIZE

i-Ready Lesson*

Grade 5

• Line Plots with Fractions

Independent Learning

PREPARE

Ready Prerequisite Lesson

Grade 4

• Lesson 22 Add and Subtract Fractions in Line Plots

RETEACH

Tools for Instruction

Grade 4

• Lesson 22 Using Line Plots Grade 5

• Lesson 27 Solve Problems with Fractional Measurement Data

REINFORCE

Math Center Activities

Grade 5

• Lesson 27 Line Plot Vocabulary Match • Lesson 27 Fractions as Data

EXTEND

Enrichment Activity

Grade 5

• Lesson 27 Weighing Pumpkins

Small Group Differentiation

Teacher Toolbox

Lesson Materials

Lesson

(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 Widths

Activity Sheet: Sticker Widths

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

SESSION 1

Explore

45–60 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 Practice Lesson pages 555–556

SESSION 2

Develop

45–60 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

Additional Practice Lesson pages 561–562 Fluency

Making a Line Plot

SESSION 3

Develop

45–60 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

Additional Practice Lesson pages 567–568 Fluency

Solving Problems Using Data in a Line Plot

SESSION 4

Refine

45–60 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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Connect to

Family, Community, and Language Development

The following activities and instructional supports provide opportunities to foster school, family, and community involvement and partnerships.

Connect to

Family

Use 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 Data

552

ACTIVITY MAKING A Line plot

Do 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.

centimeters

16

552

Make Line Plots and Interpret Data

27 Dear 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 Weights X X X X X X X X X X X X X X X 0 1 1 8 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 _··₂1 .

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 _··₈1 pound to _··7 ₈ pound. The diff erence is _··₈6 , 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 551

551

Goal

The 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.

Activity

In 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

Math Talk at Home

Encourage 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 Responsiveness

Use these activities to connect with and leverage the diverse backgrounds and experiences of all students.

Connect to

Language Development

For 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 , ₂_··1 , 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 3–5

Levels 2–4

Levels 1–3

ELL

English 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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SESSION 1

Explore

Start

Connect to Prior Knowledge

Why 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.

©Curriculum Associates, LLC Copying is permitted.

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 Seedlings X X X X X X X X 0 4 8 X X Possible Solutions

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

TRY IT

Make Sense of the Problem

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

DISCUSS IT

Support Partner Discussion

To 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 _··1₈ 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 Solutions

One 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 Discussion

Prompt 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 ₈_··1 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. Lesson 27 Make Line Plots and Interpret Data 553

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 Weights X X X X X X X X X X X X X X 0 1 1 4 1 2 3 4

TRY IT

_{Math Toolkit}

• fraction tiles • fraction circles • fraction bars • number lines

DISCUSS IT

Ask 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 , ₄_··1 , _··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 A

lightest 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 1 8 1 4 3 8 1 2 5 8 3 4 7 8 1

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554

LESSON 27 EXPLORE

SESSION 1

Connect It

1 LOOK BACK

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

2 LOOK AHEAD

Graphing 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 X X X X X X X X X X X X X X 0 1 1 4 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 REFLECT

If 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 Model

Interpret 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 Ticket

3 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 Connection

Encourage 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.

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©Curriculum Associates, LLC Copying is not permitted. 555

Name:

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

Weight (in pounds) Apple Weights X X X X X X X X X X X X 0 1 8 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 _···₁₆1 .

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 facts Data in my line plot: 9, 10, 10, 11, 11, 12, 12

Age (in years) My Friends X X X X X X X 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

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Levels 1–3

Levels 2–4

Levels 3–5

English Language Learners: Differentiated Instruction

ELL

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 _···₁₆1 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 Weights X X X X X X X X X X X X 0 1 8 14 38 12 Solution

4 Check your answer. Show your work.

556

Possible student work using an equation: lightest apple: _···₁₆1 pound

heaviest apple: _··1 ₂ pound, or _···₁₆8 pound 8

···

16 2 ··· 16 1 5 ··· 16 7

0 lightest heaviest 1 16 1 8 3 16 1 4 1 2 5 16 3 8 7 16 1 ···

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

The difference is _···₁₆7 pound.

Prepare for Session 2

Use with Connect It.

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 _··₁₆1 pound. The heaviest apple weighs 1 _··₂ pound, or _··₁₆8 pound. 8

··

16 2 ·· 16 1 5 ·· 16 7 . The difference between the heaviest weight and lightest weight is _··₁₆7 pound.

Medium

4

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

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LESSON 27

Lesson 27 Make Line Plots and Interpret Data 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)

1 4 34 38 3 4 14 58 1 8 1 2 1 2 1 2 1 1 DISCUSS IT

Ask your partner: How did

you get started?

Tell your partner: I started

by . . .

557

Sample A 1

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

Width (in inches)

Keira’s Stickers X X X X X X X X X X X X 0 1 Sample B

1 8 1 4 3 8 1 2 5 8 3 4 7 8 Sticker Widths X X X X X X X X X X X 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 , 4 ·· 3 , 4 ·· 8 , 1 ·· 2

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

Solution 3 ·· 4 ; 2

Develop Language

Why 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 IT

Make Sense of the Problem

To 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 IT

Support Partner Discussion

Encourage 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.

Select and Sequence Student Solutions

One possible order for whole class discussion: • 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.

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558

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 It

List 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 It

Use 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)

1 4 3 4 3 8 3 4 14 58 1 8 1 2 1 2 1 2 1 1

558

Final line plot is shown, with possible labels.

Sticker Widths X X X X X X X X X 1 2

Support Whole Class Discussion

Compare 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 ITs

If 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 Understanding

Organize Data for a Line Plot

SMP 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

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©Curriculum Associates, LLC Copying is not permitted. Lesson 27 Make Line Plots and Interpret Data 559

SESSION 2

Connect It

Now 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 REFLECT

Look 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 REFLECT

Have 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 Activity

Make 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 , _··₄3 , 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

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560

LESSON 27 DEVELOP

SESSION 2

Apply It

Use 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 _··₈5 , 3 1 _··₄ , 1 ₄3 _·· , 2 7 _··₈ , 1 ₄_··3 , 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 ₂_··1 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 X X X X X X X X X X 1 4 1 11₂ 13₄ 21₄ 2₂1 23₄ 31₄ 31₂ 33₄ 4 5 6 7 8

Distance (in miles)

Daily Running Distances

X X X X X X X X X X X X X X 1 4 4 41₂ 43₄ 5₄1 51₂ 53₄ 6₄1 61₂ 63₄ 71₄ 71₂ 73₄

APPLY IT

For 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.

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Name:

Practice Making Line Plots

Study the Example showing how to make a line plot. Then solve problems 1–4.

Example

Rosa’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 X X X 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.

Coin Diameters (inches)

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

X X X X X X X X X

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

SESSION 2

Additional Practice

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.

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.}

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Levels 1–3

Levels 2–4

Levels 3–5

English Language Learners: Differentiated Instruction

ELL

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 .

562 Lesson 27 Make Line Plots and Interpret Data

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

Vocabulary

scale (on a graph) the value

represented by the distance between one tick mark and the next on a number line.

562

Widths (in inches)

1 2 1 4 3 4 Stamp Widths X X X X X X X X X X 0 1 1 2 4 1 11₂ 13₄

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 X X X X X X X X X X X X X X 0 1 1 2 3 2 112 212

Prepare for Session 3

Use with Connect It.

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.

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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 X X X X X X X X 2 3 4 5

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 IT

Ask 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 ₁2 1 _··₂ 1 4 1 _··₂ ₂ 1 ₁ 2 _··3₄ 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 Knowledge

Materials 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 Language

Why 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 IT

Make Sense of the Problem

To 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 IT

Support Partner Discussion

Encourage 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.

Select and Sequence Student Solutions

One possible order for whole class discussion:

• 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.