545A Chapter 9545A Chapter 9

About the MathProfessional Development

About the MathProfessional Development

LESSON AT A GLANCE

Progressto Algebra

545A Chapter 9

Interactive Student Edition

Personal Math Trainer

Math on the Spot Video

iTools: Algebra

HMH Mega Math

Professional Development Videos

Progress to AlgebraTeaching for DepthIn this lesson, a time- and temperature-related activity is used to introduce students to collecting and interpreting real-world data.

During the activity, students will collect temperature data and observe a temperature change (the temperature will decrease). By recording and then graphing the data points on a coordinate grid, students can better understand the relationship between the x- and y-coordinates, and how the changes in the two sets of data are related. In this activity, students see that the x-coordinate represents time, the y-coordinate represents temperature, and that both pieces of information are represented by a single point.

In subsequent lessons, students will graph points generated by patterns, and will see the difference in what they graph when the change in every x-value causes a corresponding change in the y-value.

Investigate • Graph Data

LESSON 9.3

Learning ObjectiveCollect and graph data on a coordinate grid.

Language ObjectiveStudent pairs use a real-world example of how you can use a coordinate grid to display data collected in an experiment.

MaterialsMathBoard, paper cup, water, Fahrenheit thermometer, ice cubes, stopwatch

F C R Focus:Common Core State Standards

5.G.A.2 Represent real world and mathematical problems by graphing points in the fi rst quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation.

MATHEMATICAL PRACTICES (See Mathematical Practices in GO Math! in the Planning Guide for full text.)MP4 Model with mathematics. MP5 Use appropriate tools strategically.MP8 Look for and express regularity in repeated reasoning.

F C R Coherence:Standards Across the GradesBefore4.OA.C.54.MD.B.4

Grade 55.G.A.2

After6.EE.C.96.NS.C.8

F C R Rigor:Level 1: Understand Concepts....................Share and Show ( Checked Items)Level 2: Procedural Skills and Fluency.......On Your Own, Practice and HomeworkLevel 3: Applications..................................Think Smarter and Go Deeper

F C R For more about how GO Math! fosters Coherence within the Content Standards and Mathematical Progressions for this chapter, see page 531J.

FOCUS COHERENCE RIGOR

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ENGAGE1

Lesson 9.3 545B

Daily RoutinesCommon Core

How can you use a coordinate grid to display

data collected in an experiment ?

with the Interactive Student Edition

Essential QuestionHow can you use a coordinate grid to display data collected in an experiment?

Making ConnectionsInvite students to tell you what they know about thermometers.

What is a thermometer? A thermometer is an instrument used to measure and indicate temperature.

Learning ActivityWhat is the problem the students are trying to solve? Connect the story to the problem.

• What problem are you trying to solve? Find the set of ordered pairs that shows the data in the table.

• How did they record the temperature? used a thermometer

• When did they record the temperature? about the same time each night

• What is the title of the table? Daily Temperatures at 8 P.M.

• How many days did they record the temperature? 5 days

• What unit was the temperature measured in? Fahrenheit degrees

Literacy and MathematicsChoose one or more of the following activities.

• Have students draw a thermometer and explain in writing how to read different temperatures on the thermometer.

• Have students generate a list of situations in which temperature might be measured. Have students present their ideas.

Problem of the Day 9.3Adam is making a square on a coordinate grid. What ordered pair describes the missing point, D, if A is (2, 1); B is (2, 6); and C is (7, 6)? (7, 1)

VocabularyInteractive Student EditionMultimedia Glossary e

1 23 4 Fluency BuilderSubtract Fractions Write the following examples on the board. Have students practice subtracting fractions with like denominators, writing the difference as a mixed number, when possible.

9 __ 12 − 2 __ 12 = 7 __ 12

2 2 _ 5 − 3 _ 5 = 9 _ 5 ; 1 4 _ 5

3 1 _ 3 − 2 _ 3 = 8 _ 3 ; 2 2 _ 3

1 3 _ 8 − 6 _ 8 = 5 _ 8

EXPLORE2

Heights of Rafael’s Tomato Plants

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0 5 10 15 20 25 30Day in August

Hei

ght

(in In

ches

)

Key:CherrySan Marzano

y

x

Name

4. Stretch Your Thinking What do you notice about the two sets

of data you graphed?

1. Graph Rafael’s cherry tomato

plant data on the coordinate

grid.

2. Complete the table above by

filling in the height of the San

Marzano plant.

3. Use the completed table.

Graph Rafael’s San Marzano

tomato plant data on the

same coordinate grid. You

may want to use a different

color than you used in

Exercise 1.

Graphing and Analyzing Tomato Plant Data

Rafael has two plants: a cherry tomato plant and a San Marzano tomato plant. Every 5 days in August, Rafael records the height of his cherry tomato plant. He knows that the San Marzano tomato plant grows exactly 2 inches every 5 days.

Day in August Cherry Plant Height (in inches)

San Marzano Plant Height (in inches)

5 6 8

10 10

15 14

20 15

25 18

30 23

Lesson 9.3Enrich

Possible answer: The cherry tomato plant was

smaller at 5 days, but taller at 30 days, so it grew at

a faster rate than the San Marzano tomato plant.

1816141210

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9-10 EnrichChapter Resources© Houghton Mifflin Harcourt Publishing Company

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x-axisTime (in minutes)

y-ax

isTo

tal P

ages

Bianca’s Writing Progress

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Time (in minutes)

Dis

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x-axis

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Distance of Bike Ride

12

10

8

6

4

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0 2 31 4 5 6

End of Week

Plant Growth

Hei

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(in in

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x-axis

y-ax

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1. Distance of Bike Ride

Time (in minutes) 30 60 90 120

Distance (in miles) 9 16 21 27

Write the ordered pair for each point.

1 , 2, 1 , 2 1 , 2, 1 , 2

2. Bianca’s Writing Progress

Time (in minutes) 15 30 45 60

Total Pages 1 3 9 11

Write the ordered pair for each point.

1 , 2, 1 , 2 1 , 2, 1 , 2

Graph the data on the coordinate grid. Label the points.

Graph Data

Graph the data on the coordinate grid.

Plant Growth

End of Week 1 2 3 4

Height (in inches) 4 7 10 11

• Choose a title for your graph and label it. You can use the data categories to name the x- and y-axis.

• Write the related pairs of data as ordered pairs.

1 , 2, 1 , 2

1 , 2, 1 , 2• Plot the point for each ordered pair.

Lesson 9.3Reteach

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Check students’ graphs.

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9-9 ReteachChapter Resources© Houghton Mifflin Harcourt Publishing Company

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DifferentiatedInstruction1

2

3

Progressto Algebra

Water Temperature

Time(in seconds)

Temperature(in 8F)

0

10

20

30

40

50

60

InvestigateInvestigate

Name

Chapter 9 545

Lesson 9.3

Graph DataEssential Question How can you use a coordinate grid to display data collected in an experiment?

Materials ■ paper cup ■ water ■ Fahrenheit thermometer

■ ice cubes ■ stopwatch

When data is collected, it can be organized in a table.

A. Fill the paper cup more than halfway with room-temperature water.

B. Place the Fahrenheit thermometer in the water and find its beginning temperature before adding any ice. Record this temperature in the table at 0 seconds.

C. Place three cubes of ice in the water and start the stopwatch. Find the temperature every 10 seconds for 60 seconds. Record the temperatures in the table.

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Geometry—5.G.A.2

MATHEMATICAL PRACTICESMP3, MP4, MP8

Data will vary. Check students’ work.

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545 Chapter 9

Reteach 9.3 Enrich 9.3

Give students an opportunity to share their ideas and explanations.

Investigate MATHEMATICAL PRACTICES

Prior to the activity:MP4 Model with mathematics.• Display a stopwatch and demonstrate how

to use it.• Separate the class into small groups. Assign

roles for timing, reading data, and recording data.

• Have students position a thermometer in each cup so that it can be read without being moved.

• Point out that the data will be displayed in a graph. Invite volunteers to predict what the graph might look like and give reasons to support their answers.

If the materials for the activity are not available, an option for collecting data would be to have students observe and record bird sightings from classroom windows or vehicle sightings in the school parking lot.MP8 Look for and express regularity in repeated reasoning.• What do you think will happen to the

temperature of the water every ten seconds? Possible answer: Since we’re adding ice to the water, I think the temperature will go down every ten seconds.

ELL Strategy: Model Language

Display the table and help students make a graph of the data.

Outdoor Temperatures

Time Temp. (in °F)

6:00 am 38°

8:00 am 41°

10:00 am 49°

12:00 pm 59°

2:00 pm 62°

• Ask questions about the graph students made. For example:

The title tells what the graph is about. Let’s read the title. What does the title do?

The labels name the parts of the graph. Point to the labels as I read them. What do the labels do?

Hands

On

LESSON 9.35.G.A.2 Represent real world and mathematical problems by graphing points in the fi rst quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation.

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

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252015105

0 10 20 40 50 6030x-axis

Time (in seconds)

Water Temperature

Te

mp

era

ture

(in

8F)

y-ax

is

Make ConnectionsMake Connections

MathTalk MATHEMATICAL PRACTICES 4

546

STEP 2 Construct a coordinate grid and write a title for it. Label each axis.

STEP 3 Plot a point for each ordered pair.

STEP 1 Write the related pairs of data as ordered pairs.

(0, _ ) (20, _ ) (40, _ )

(10, _ ) (30, _ ) (50, _ )

(60, _ )

You can use a coordinate grid to graph and analyzethe data you collected in the experiment.

1. Explain why you would record the beginning temperature

at 0 seconds.

2. Describe what happens to the temperature of the water in

60 seconds, during the experiment.

3. MATHEMATICALPRACTICE 8 Draw Conclusions Analyze your observations of the

temperature of the water during the 60 seconds, and explain what you

think would happen to the temperature if the experiment continued

for 60 seconds longer.

Draw ConclusionsDraw Conclusions

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Use Graphs What is the ordered pair that you recorded for the data at 10 seconds? Explain what each coordinate represents.

Possible explanation: The beginning temperature is recorded at 0 seconds because the

ice has not been put in the cup and the experiment has not started yet.

Possible description: The temperature decreases rapidly for the fi rst 30 seconds and then

decreases but not as rapidly, for the remaining time.

Possible explanation: Since the temperature decreases quickly at fi rst and then slows,

I believe the temperature would continue to decrease more and more slowly until it did

not decrease any longer.

Data will vary. Check students’ graphs.

x-coordinate: 10; y-coordinates will vary, but will be less than the recorded temperature at 0 seconds. Possible explanation: The x-coordinate represents the length of time the ice was in the water. The y-coordinate represents the temperature of the water at 10 seconds.

COMMON ERRORS Advanced Learners

Lesson 9.3 546

Error Students reverse the ordered pairs when plotting points.

Example In Make Connections, students also see multiples of 10 on the y-axis and record the ordered pair using the vertical axis first.Springboard to Learning Have students label the first row or column of the data table x and label the second row or column y. Or have them write (x, y) at the top of their list of ordered pairs.

Draw ConclusionsGive several students the opportunity to verbalize their answers to the questions.

MP8 Look for and express regularity in repeated reasoning. Exercise 3 requires students to use higher order thinking skills. Tell students that this involves predicting. A variety of answers are possible.

Make Connections Discuss Step 2.

• The graph has an x-axis and a y-axis. Why is the label Time (in seconds) placed on the x-axis and not on the y-axis? The first coordinates of the ordered pairs in the table represent time, and the first coordinate of any ordered pair is x. So, the x- or horizontal axis will be labeled Time (in seconds).

Make sure students understand that the y-axis of a graph could be labeled Time. However, for this problem the x-axis was labeled Time because of how the ordered pairs were written.

• Why isn’t the temperature recorded every 5 seconds? Possible answer: The temperature doesn’t change much in 5 seconds. So recording the temperature every 5 seconds would be unnecessary.

MathTalk Use Math Talk to help students

interpret the meaning of coordinate values in the context of the experiment.

• What is the ordered pair you recorded at 60 seconds? What do these coordinates tell you about the change in the water’s temperature? Data will vary. Possible answer: The x-coordinate is 60. The y-coordinate is also 60. These coordinates show that in 60 seconds, the temperature of the water decreased by 15 degrees.

HandsOn

KinestheticIndividuals

• Have students collect data through observations made at 0, 3, 6, 9, 12, and 15 minute intervals. Possible observations are the number of birds seen out the classroom window and the number of pages read in a library book.

• Have students record their observations in a two-column table. Students should then graph the data they recorded using a coordinate grid. Make sure students include a title for their graph and appropriate labels and scales for the axes.

• Then ask students to choose one point, write the ordered pair that describes its location, and explain how the coordinates in the ordered pair are related.

30

40

50

60

20

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0 1 2 4 5 6 7 8 93x-axis

Age (in years)

He

igh

t (in

inch

es)

y-ax

is

Ryan’s Height

Ryan’s HeightAge (in years) 1 2 3 4

Height (in inches) 30 35 38 41

5

44

Share and ShShare and ShShare and Show MATHBOARDMATHBOARD

Name

Chapter 9 • Lesson 3 547

1. Write the ordered pairs for each point.

2. What does the ordered pair (3, 38) tell you about

Ryan’s age and height?

3. Why would the point (6, 42) be nonsense?

For items 1–3, graph the data on the coordinate grid.

4. SMARTER Th e table shows the depth of the Dakota River at

diff erent times during a rainstorm.

Graph the ordered pairs from the tiles on the coordinate grid.

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Dakota RiverTime (hours) 1 2 3 4

Depth (feet) 7 8 10 12

5

15

1210

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2

8

6

0 1 2 4 5 6 7 83Time (hours)

De

pth

(fe

et)

River Depth

y

x

(1, 7)(2, 8)

(3, 10)

(4, 12)

(5, 15)

(1, 7)

(2, 8)

(3, 10)

(4, 12)

(5, 15)

Possible answer: Because it would mean

that at the age of 6, Ryan’s height would

be less than his height at the age of 5; he

would have gotten shorter as he got older

instead of taller.

(1, 30); (2, 35); (3, 38); (4, 41); (5, 44)

Possible answer: At the age of 3, Ryan’s

height was 38 inches.

Check students’ graphs.

EXPLAIN3

Quick Check

If

Rt I RR1

2

3

Then

ELABORATE4

547 Chapter 9

SMARTER

This item assesses a student’s ability to graph data from a table on a coordinate grid. If students have difficulty graphing the y-coordinate of each ordered pair, point out that the interval of the vertical axis is 2 feet. So, a depth of 7 feet should be plotted halfway between 6 feet and 8 feet on the vertical axis.

Share and Show MATHBOARDMATHBOARDMBMMMBBBMATHABOARDMMMAAATHATHTHHAAAAAAAAATTAAAABOARDBOARDBOARD

The first problem connects to the learning model. Have students use the MathBoard to explain their thinking.Before graphing the data in each table, have students explain how to plot a point on a coordinate grid.Use the checked exercises for Quick Check. Students should show their answers for the Quick Check on the MathBoard.

a student misses the checked exercises

Differentiate Instruction with • Reteach 9.3

• Personal Math Trainer 5.G.A.2

• RtI Tier 1 Activity (online)

Problem Solving • Applications

Differentiated Centers Kit

DIFFERENTIATED INSTRUCTION INDEPENDENT ACTIVITIES

Miniature Car’s Speed

Speed

(in miles per hour)

Distance

(in feet)

0

1

2

3

4

0

4

8

6

3

6

8

10

4

2

0 2 31 4 5 86 7Distance (in feet)

Miniature Car’s Speed

Sp

ee

d (

in m

iles

pe

r h

ou

r)

0 2 31 4 5 86 7Distance (in feet)

Miniature Car’s Speed

Spee

d (in

mile

s pe

r hou

r)6

8

10

4

2

MATHEMATICAL PRACTICES M

548

6. MATHEMATICALPRACTICE 3 Verify the Reasoning of Others Describe the error Mary made.

7. DEEPER At what distance do you think the car will stop? Explain and write the ordered pair.

Look at Mary’s graphed data. Find her error.

Graph the data and correct the error.

SMARTER What’s the Error?

5. Mary places a miniature car onto a track with

launchers. The speed of the car is recorded every

foot. Some of the data is shown in the table. Mary

graphs the data on the coordinate grid below.

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Possible description: Mary’s error is that she reversed her x-coordinates and

y-coordinates for the data, so that Distance is on the y-axis and Speed is on the x-axis.

Possible answer: The car will stop at 5 feet, because it slows down more for each foot.

The ordered pair will be (5, 0).

EVALUATE5 Formative Assessment

Differentiated Centers Kit

DIFFERENTIATED INSTRUCTION INDEPENDENT ACTIVITIESD

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

Lesson 9.3 548

GamesIt’s a Toss-Up

LiteratureIs This a Career for You?

ActivitiesWhat’s the Point?

Students toss beanbags and express the results as ordered pairs on the coordinate plane.

Students read about careers that require reading coordinate grids.

Students complete purple Activity Card 19 by locating a specific ordered pair using the guess-and-check method.

Essential QuestionUsing the Language ObjectiveReflect Have student pairs use a real-world example to answer the essential question. How can you use a coordinate grid to display data collected in an experiment? Possible answer: If my data are measured in two ways, such as time and temperature, I can write my recorded data as ordered pairs and then graph them.

Math Journal WRITE MathGive an example of some data you could collect and display on a coordinate grid.

SMARTER

MP3 Construct viable arguments and critique the reasoning of others. If students need help recognizing that there is an error, have them begin at zero and use a pencil to connect consecutive points from left to right. Then say:

• Describe the speed of the car as the distance increases using Mary’s graph. The speed increases, decreases, increases, and then decreases.

• Describe the speed of the car as the distance increases using the table. The speed increases and then decreases.

• Is the speed of the car the same in Mary’s graph and in the table? no

• What conclusion can you draw? There is an error in the graph because the graph is not displaying the data correctly.

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

Outdoor Temperature Hour

Temperature (°F)

1

61

3

65

5

71

7

75

9

77

60

70

80

50

40

30

20

10

0 2 31 4 5 7 8 9 106

Outdoor Temperature

Time (hours)

Tem

pera

ture

(°F)

x

y

Windows RepairedDay

Total Number Repaired

1

14

2

30

3

45

4

63

5

79

60

70

80

50

40

30

20

10

0 2 31 4 5 6 7 8 9 10

Windows Repaired

Days

Tota

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x

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Problem SolvingProblem Solving

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Practice and HomeworkLesson 9.3

COMMON CORE STANDARD—5.G.A.2 Graph points on the coordinate plane to solve real-world and mathematical problems.

Graph Data

Graph the data on the coordinate grid.

Chapter 9 549

1.

a. Write the ordered pairs for each point.

b. How would the ordered pairs be different if the

outdoor temperature were recorded every hour

for 4 consecutive hours?

2.

a. Write the ordered pairs for each point.

b. What does the ordered pair (2, 30) tell you about

the number of windows repaired?

Possible graph is shown.

(1, 61), (3, 65), (5, 71), (7, 75), (9, 77)

(1, 14), (2, 30), (3, 45), (4, 63), (5, 79)

Possible answer: After 2 days, a total

of 30 windows had been repaired.

Possible answer: There would be 4 ordered pairs;

the ordered pairs would record the outdoor temperature at hours 1, 2, 3, and 4.

549 Chapter 9

Practice and HomeworkUse the Practice and Homework pages to provide students with more practice of the concepts and skills presented in this lesson. Students master their understanding as they complete practice items and then challenge their critical thinking skills with Problem Solving. Use the Write Math section to determine student’s understanding of content for this lesson. Encourage students to use their Math Journals to record their answers.

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PREPTEST

607080

5040302010

0 2 31 4 5 7 86 9 10

Amount of Dog Food Consumed

Weeks

Am

ount

of D

og F

ood

Con

sum

ed (I

b)

x

y

Personal Math Trainer

FOR MORE PRACTICE GO TO THE

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550

Spiral Review (5.OA.A.2, 5.NBT.B.6, 5.NF.A.2)

Lesson Check (5.G.A.2)

1. About how many weeks did it take for the dog to

consume 45 pounds of food?

2. By the end of Week 8, how much food had the

dog consumed?

3. A restaurant chain ordered 3,940 pounds of rice

in 20-pound bags. About how many 20-pound

bags of rice did the chain order?

4. The population of Linton is 12 times as great

as the population of Ellmore. The combined

population of both towns is 9,646 people. What

is the population of Linton?

5. Timothy needs 1 _ 2 cup of bread crumbs

for a casserole and 1 _ 3 cup of bread crumbs for

the topping. How many cups of bread crumbs

does Timothy need?

6. Jessie bought 3 T-shirts for $6 each and

4 T-shirts for $5 each. What expression can you

use to describe what Jessie bought?

about 6 weeks

60 pounds

8,904 people

(3 × 6) + (4 × 5)

about 200 bags

5 _

6 cup

Lesson 9.3 550

Continue concepts and skills practice with Lesson Check. Use Spiral Review to engage students in previously taught concepts and to promote content retention. Common Core standards are correlated to each section.