For the student For the teacher

Teacher Edition

Math on the Spot Video Tutor Online Assessment

System

Soar to Success Math Online Intervention

iTools Virtual Manipulatives

Digital ManagementCenter organizes program resources by TEKS!

Interactive Student Edition provides students

with an interactive learning environment!

Resources

e

Texas Essential Knowledge and Skills

Number and Operations—3.2.D Compare and order whole numbers up to 100,000 and represent comparisons using the symbols >, <, or =MATHEMATICAL PROCESSES3.1.A Apply mathematics to problems 3.1.E Create and use representations 3.1.G Display, explain, and justify mathematical ideas and arguments

Are You Ready?Access Prior KnowledgeUse the Are You Ready? 1.5 in the Assessment Guide to assess students’ understanding of the prerequisite skills for this lesson.

Vocabularygreater than >, less than <, equal to =

Go to Multimedia eGlossary at thinkcentral.com

1.5 Compare and Order Whole Numbers What are some ways you can compare and order whole numbers?

Essential Question?

Lesson OpenerMaking ConnectionsInvite students to talk about clouds. Pose the following questions.

What kinds of clouds have you seen? Can you describe them? Have you ever looked for shapes in a cloud? What shapes have you seen?

Using the Digital LessonThe problem in the lesson opener compares the heights of two clouds. When discussing the kinds of clouds students may have seen, describe what each of three common types of clouds means in terms of the weather. For example, puffy white clouds [cumulus] are fair weather clouds; thin, wispy clouds [cirrus] indicate a coming change in the weather; gray clouds that cover the sky [stratus] indicate light rain.

Learning Task• Ask students to explain what it means to compare two numbers.

• Have students explain how they can decide whether one number is greater than another. Is there a model they can use?

• Ask students to read each number in the problem aloud.

Literacy and Mathematics• Have students write a short story about two trips they’ve either taken or they would

like to take one day. Provide students with an atlas to find the approximate distance of each trip from where they live to the destination.

• Have students illustrate their stories showing how distances of the two trips compare.

What are some ways you can compare and order

whole numbers?

Lesson 1.5 29A

Unlock the ProblemUnlock the Problem

32,000 33,000 34,000 35,000 37,00036,000

32,102 34,373

32,000 33,000 34,000 35,000 37,00036,000

36,96032,102 34,373

Essential Question?

1.5Name

What are some ways you can compare and order whole numbers?

Compare and Order Whole Numbers

Number and Operations—3.2.D

MATHEMATICAL PROCESSES3.1.A, 3.1.E, 3.1.G

The Sunshine Skyway bridge is 34,373 feet

long. The W. K. Wilson bridge is 32,102 feet

long. Which bridge is shorter?

You can use symbols to compare numbers.

> < = greater than less than equal to

Use a number line. Compare 34,373 and 32,102.

32,102 is to the left of 34,373. 32,102 ● 34,373

So, the W. K. Wilson bridge is shorter.

To find the longest bridge in the table, look for the

bridge with the greatest length.

One Way Use a number line. Order 34,373; 32,102; and 36,960.

Which number is greatest? Explain how you know.

________

Which bridge is the longest?

________

Bridges in the United States

Bridge State Length (in feet)

Sunshine Skyway FL 34,373

W. K. Wilson AL 32,102

San Mateo-Hayward CA 36,960

RememberWhen you write numbers in order, you write them from greatest to least or from least to greatest.

<

36,960; it is to the right of the other numbers.

San Mateo-Hayward

Module 1 29

© H

ough

ton

Miff

lin H

arco

urt P

ublis

hing

Com

pany

English Language Learners Language SupportELL

4, 25, 46

ELPS 2.C.4, 2.I.3, 3.B.3Leveled Activities ELPS

Beginning: Activity 2 2.I.4, 3.C.4, 3.G.2

Intermediate: Activity 24 3.D.1, 3.F.2, 4.F.9

Advanced: Activity 12 2.I.4, 3.F.1, 3.F.2

Advanced High: Activity 6 2.I.5, 3.G.2, 4.G.2

Go to thinkcentral.com for the ELL Activity Guide containing these leveled activities.

Strategy: Restate• Restate key vocabulary to make sure students can work on the lesson.• Tell students that the greatest number in a set is the number that is

greater than all other numbers in the set. Say and write: 4, 25, 46. Ask: Is 46 greater than 4 and 25? yes Which is the greatest number? 46

• Tell students that the least number in a set is the number that is less than all other numbers in the set. Is 4 less than 25 and 46? yes Which is the least number? 4

• Have students repeat the steps to compare other sets of numbers aloud.

Verbal / LinguisticSmall Group

Unlock the Problem Discuss the problem. Tell students that they must compare the lengths of two bridges in the table in order to determine which is shorter.

In previous grades, students have learned to compare 3- and 4-digit numbers using base-ten blocks, number lines, and place value. Review with them the greater than (>), less than (<), and equal to (=) symbols.

• How is using a number line to compare numbers helpful? If two numbers are on a number line, the lesser number is on the left and the greater number is on the right.

One WayStudents use the number line and the information in the first problem to order the lengths of the bridges.

• How is using a number line to order numbers helpful? Explain. Possible explanation: The numbers on a number line are in order from least to greatest, with the least number on the left and the greatest number on the right. This makes seeing the order easy.

• If you are ordering three numbers from greatest to least or least to greatest, does the number in the middle change? Explain. No. Possible answer: the number in the middle is always greater than the least number and less than the greatest number.

29 Module 1

Share and ShowShare and Show

Mathematical ProcessesMath Talk

7. 32,090; 31,390; 32,009

__ ; __ ; __

8. 68,006; 47,891; 24,962

__ ; __ ; __

Another Way Use place value.

Order 34,373; 32,102; and 36,960 from greatest to least.

STEP 1

34,373

32,102

36,960

Compare the ten thousands. They are the same.

So, look at the thousands.

STEP 2

34,373

32,102

36,960

Compare the thousands.

● > ● > ●.

So, the order from greatest to least is __; __; __.

Compare the numbers. Write <, >, or = in the ●.

1. 897 ● 1,321

3. 13,751 ● 13,766

2. 1,604 ● 1,604

4. 64,007 ● 46,007

Write the numbers in order from greatest to least.

Write the numbers in order from least to greatest.

5. 685; 3,482; 1,907

_, _, _

6. 2,597; 4,698; 4,689; 3,851

_ ; _ ; _ ; _

When you compare numbers with the same

number of digits, why do you compare the digits

with greatest value first? Explain.

32,00931,390 32,090 24,962 47,891 68,006

36,960 34,373 32,102

<

6 4 2

< >

=

Possible explanation: if the digits of greatest value are in the same place but are not the same, then you can compare the numbers without having to look at the other place values.

3,482 1,907 685 4,698 4,689 3,851 2,597

30

© H

ough

ton

Miff

lin H

arco

urt P

ublis

hing

Com

pany

Go to Go to thinkcentral.com for additional enrichmentactivities in the Enrich Activity Guide.

Enrich

Materials: number cube, Place-Value Charts (see Teacher Resources)

• Have each student toss a number cube five times and use the numbers on the cubes to make a 5-digit number. Have them record the number in a place-value chart.

• Have students repeat this process until they have recorded six different 5-digit numbers in their place-value charts.

• Have students use the place-value charts to help them write the six numbers in order from least to greatest.

• Encourage students to share the methods they used to order the numbers.

VisualIndividual / Partners

Math Talk Use Math Talk to focus on students’ understanding of place value. Point out that any 4-digit whole number will always be greater than any 3-digit whole number, and any number with fewer than three digits.

Mathematical Processes

Another Way • Why do you need to compare the digits in the ten

thousands place first? The ten thousands place is a greater place value position than the thousands, hundreds, tens, or ones.

• In what order will you compare the remaining digits? thousands, hundreds, tens, then ones

• How would the order change if you were ordering the lengths of the bridges from shortest to longest? Possible answer: they would be written in the opposite order.

Share and ShowUse the checked exercises for Quick Check. Students should show their answers for the Quick Check on the MathBoard.

1

2

3

a student misses the checked exercises

Quick Check

IF

THENDifferentiate Instruction withRtI Tier 1 Lesson 5

COMMON ERRORSError Students compare numbers by digit rather than place value.

Example Students may say that 897 is greater than 1,321 because 8 is greater than 1.

Springboard to Learning Have students write 1,321 above 897 so that the digits in each place align. Remind students that when they compare numbers they must compare digits in the same value place.

CE

Lesson 1.5 30

Problem SolvingProblem Solving

40,00038,00036,00034,00032,000

35,81733,254 39,65038,297

Name

Use the number line for 13–15.

Algebra Write <, >, or = in the ●.

Write two numbers so that the numbers are in order.

9. 1,385 ● 1,300 + 30 + 105 10. 20,104 ● 20,000 + 4 + 100

11. _ ; 6,010; _ ; 5,060 12. 13,005 ; __; 16,475 ; __

13. Multi-Step There were 35,817 visitors at an aquarium

in March; 39,650 in April; 38,297 in May; and 33,254 in

June. In which month did the least number of visitors

go to the aquarium? Use the number line to solve

the problem.

14. What if there were 39,475 visitors in July?

Compare the number of visitors in July to the number of

visitors in April.

15. Pose a Problem Look back at Problem 14. Write

a similar problem by comparing two different

numbers of visitors.

< =

7,054 5,871 13,821 18,397

Possible answers given.

June

39,475 < 39,650

Possible answer: Compare the number of visitors in March to

the number of visitors in May. 35,817 < 38,297

Module 1 • Lesson 5 31

© H

ough

ton

Miff

lin H

arco

urt P

ublis

hing

Com

pany

Enrich© Houghton Mifflin Harcourt Publishing Company

Name Enrich 5

E5

Comparing Roman Numerals

Roman numerals use letters to stand for numbers.

Add the value of each letter to fi nd the values of the Roman

numerals below.

XVI 5 10 1 5 1 1 5 16

Compare the Roman numerals. Write ,, ., or 5 in the .

1.

I II

2.

X V

3.

XIII XII

4.

C M

5.

C X

6.

CC XX

7.

M CCC

8.

I V

9.

XV C

10.

VII X

11.

CV CI

12.

VI MV

13. Explain how many Cs are equal to one M.

14. Stretch Your Thinking The symbol # means is less than or equal to. The symbol $ means is greater than or equal to. Use the same Roman numeral to make each of the following comparisons true.

$ C # C

M 5 1,000 C 5 100 X 5 10 V 5 5 I 5 1

10 Cs; there are 10 hundreds in 1 thousand, so 10 Cs 5 1 M.

C C

.

.

.

.

, ,

.

.

,

,

, ,

1

© H

ou

gh

ton

Mif

flin

Har

cou

rt P

ub

lish

ing

Co

mp

any

Name

LESSON 5 3.2.D

You compare two numbers to decide whether one number is greater than (> ), is less than (< ), or is equal to (= ) the other number.

Use a place-value chart to compare 54,237 and 54,537.

Step 1 The ten thousands digits are the same. The thousands digits are the same.

Step 2 Compare hundreds.

2 hundreds are less than 5 hundreds.

So, 54,237 < 54,537.

You can order three numbers by deciding which number is the greatest or least. Then compare the remaining two numbers.

Order 237, 451, and 405 from least to greatest. 237, 405, 451

Compare the numbers. Write < , > , or = in the .

1. 378 387 2. 3,275 3,257

3. 2,078 989 4. 64,367 67,251

Write the numbers in order from greatest to least.

5. 421, 197, 724

, ,

6. 1,946; 5,632; 8,105

, ,

7. 246, 190, 249

, ,

8. 94,531; 94,852; 94,850

, ,

Compare and Order Whole NumbersOBJECTIVE Use place value to compare multi-digit numbers.

Ten Thousands

Thousands Hundreds Tens Ones

54,237 5 4, 2 3 7

54,537 5 4, 5 3 7

54, 2 37

54, 5 372 < 5

>

>

<

<

8,105

94,852249

724 5,632

94,850246

421 1,946

94,531190

197

Number and Operations 9

Enrich 5RtI Tier 1 Lesson 5

Problem SolvingProblems

Exercises 9–10 and 11–12 require students to evaluate given information. For Exercises 9–10, they must compare pairs of numbers when one of the numbers is written in expanded form. For Exercises 11–12, students apply what they know about ordering numbers to write numbers greater than or less than the given numbers.

Have students use the information and number line from Problem 13 to complete Problems 14 and 15.

Math on the Spot Video Tutor

Through the Math on the Spot Video Tutor, students will be guided through an interactive solving of this type of H.O.T. problem. Use this video to also help students solve the H.O.T. problem in the Interactive Student Edition. With these videos and the H.O.T. problems, students will build skills needed in the TEXAS assessment.

MV

Math on the Spot videos are in theInteractive Student Edition and atthinkcentral.com.

1

2

3

31 Module 1

Mathematical Processes

Daily Assessment TaskDaily Assessment Task

TEXAS Test Prep 19. The dolphin exhibit had 5,346 visitors in the winter;

4,437 in the spring; 6,107 in the summer; and 5,275 in

the fall. In which season did the most visitors go to

the exhibit?

A winter C summer

B spring D fall

Fill in the bubble for the correct answer choice.

16. Apply During a football game, fans bought 8,542 bags

of popcorn. They bought 5,398 pieces of fruit. They also

bought 7,208 sandwiches. Which shows the snacks in

order from the least number to the greatest number?

A fruit, sandwiches, popcorn

B sandwiches, fruit, popcorn

C fruit, popcorn, sandwiches

D popcorn, sandwiches, fruit

17. Evaluate Nina needs to know which is greater, 41,381 or

35,927. Which place should she look at first to compare

the numbers?

A the hundreds place C the thousands place

B the tens place D the ten thousands place

18. Multi-Step Luke’s book has 182 pages. Elena’s book has

208 pages. Corey’s book has more pages than Luke’s and

fewer pages than Elena’s. Which could be the number of

pages in Corey’s book?

A 179 C 194

B 224 D 210

32

© H

ough

ton

Miff

lin H

arco

urt P

ublis

hing

Com

pany

Games

THENIF

YES

NO

Daily Assessment Task 1

2

3

Differentiated Centers Kit

• Soar to Success MathWarm-Up 7.32; 7.33

ActivitiesRoll to 100!Students complete orange Activity Card 1 by finding the sum of three numbers.

LiteratureConcert Halls of the WorldStudents read about and compare the number of seats in the great music centers of the world.

GamesBuilding NumbersStudents practice comparing numbers using a place-value chart.

TEXAS Test Prep CoachTest Prep Coach helps teachers to identify common errors that students can make.

In the Test Prep exercises, if students selected:

A, D They chose a season that was between the least and greatest number of visitors.

B They chose the season with the least number of visitors.

Essential Question? WriteMathWriteMath

What are some ways you can compare and order whole numbers? Use a number line, or use place value.

• Enrich 5

• Homework and Practice Lesson 1.5

Can students compare and order whole numbers up to 100,000 in different ways?

Lesson 1.5 32

TEXAS Test PrepLesson CheckLesson Check

673518 7295,078 6,147?

13. Martine puts number cards in the

order shown below.

Which number can Martine put on

the empty card?

A 659

B 821

C 722

D 584

14. Daryl writes these numbers on a

number line.

Which number can Daryl write to fill

in the blank?

A 5,780

B 5,049

C 6,417

D 6,704

15. At the state fair, visitors bought 3,671

vanilla yogurts, 4,032 blueberry

yogurts, and 2,978 strawberry

yogurts. Which show the flavors in

order from least to greatest?

A vanilla, blueberry, strawberry

B strawberry, vanilla, blueberry

C vanilla, strawberry, blueberry

D blueberry, strawberry, vanilla

16. An airplane travels 45,890 miles. The

next week it travels 37,604 miles.

The following week it travels 40,098

miles. Which shows the miles in

order from greatest to least?

A 40,098; 37,604; 45,890

B 45,890; 37,604; 40,098

C 37,604; 40,098; 45,890

D 45,890; 40,098; 37,604

17. Multi-Step Marco has 342 photos

in an album. Rosa has 297 photos.

Hideki has more photos than both

Marco and Rosa. Which shows how

many photos Hideki could have?

A 189 C 287

B 382 D 314

18. Multi-Step A company ships

35,809 pears and 21,790 plums.

It also ships more apples than

plums, but fewer apples than pears.

Which shows how many apples

could have been shipped?

A 35,908 C 34,118

B 21,097 D 40,055

Fill in the bubble completely to show your answer.

© H

ough

ton

Miff

lin H

arco

urt P

ublis

hing

Com

pany

34

Problem SolvingProblem Solving

Homeworkand Practice

Name

Compare the numbers. Write <, >, or = in the ●.

1. 467 ● 381 2. 4,167 ● 4,590 3. 718 ● 7,180

4. 1,970 ● 1,970 5. 2,398 ● 736 6. 5,067 ● 567

Write <, >, or = in the ●.

7. 592 ● 500 + 80 + 7 8. 3,724 ● 3,000 + 800 + 30 + 9

9. There are 29,148 people at the

baseball game on Saturday. On

Sunday, 25,974 people are at the

game. Compare the number of

people at each game.

10. A great white shark weighs

5,038 pounds. A blue fin tuna

weighs 1,759 pounds. Compare

the weight of the fish.

11. Four students play a video game.

Luke scores 5,789 points, Janell scores

3,980 points, Rashid scores 5,067

points, and Dara scores 4,690 points.

Who scores the most points?

12. A car company makes 5,689 red cars,

3,607 blue cars, 5,968 black cars, and

3,706 white cars. Which color is the

least number of cars?

Number and Operations—3.2.D MATHEMATICAL PROCESSES 3.1.A, 3.1.E, 3.1.G

1.5 Compare and Order Numbers

Luke

1,759 < 5,03829,148 > 25,974

blue

<

>

=

>

> >

< <

© H

ough

ton

Miff

lin H

arco

urt P

ublis

hing

Com

pany

Module 1 • Lesson 5 33

555555555

Homework and PracticeUse the Homework and Practice pages to provide students with more practice on the concepts and skills of this lesson.

33-34 Module 1

Module 1 Assessm

entName

Module 1 Assessment

Vocabulary

expanded form

standard form

word form

VocabularyVocabulary

Choose the best term from the box to complete the sentence.

1. The _____ of a number

is a way to write a number by showing the value of

each digit. (p. 11)

2. The _____ of a number

is a way to write a number by using words. (p. 11)

Concepts and SkillsConcepts and Skills

Complete the chart to show three forms of the number. q TEKS 3.2.A

Round to the nearest hundred. q TEKS 3.2.C

Round to the nearest thousand. q TEKS 3.2.C

Compare the numbers. Write <, >, or = in the ●. q TEKS 3.2.D

5. 409 __ 6. 876 __ 7. 399 __

8. 4,397 __ 9. 8,222 __ 10. 7,656 __

11. 891 ● 5,902 12. 6,812 ● 6,812 13. 18,001 ● 17,897

3.

4.

Standard Form Expanded Form Word Form

32,706 _ + 2,000 + __ thousand, __ hundred six

800,034 800,000 + 30 + 4 __ thousand, __

expanded form

word form

400

4,000 8,000 8,000

900 400

thirty-two seven

eight hundred

700 + 630,000

thirty-four

>=<

© H

ough

ton

Miff

lin H

arco

urt P

ublis

hing

Com

pany

Module 1 35

Based on the results of the Module 1 Assessment, use the following resources to strengthen individual or whole class instruction.

i

1

2

3

Data-Driven Decision Making

*TEKS—Texas Essential Knowledge and Skills; RtI—Response to Intervention

Item Lesson TEKS* Common Error Intervene With RtI* Tier 1 Lessons

Soar to Success Math

3, 4 1.2 3.2.A May confuse the different forms of writing numbers 2 2.25

5–10 1.4 3.2.C May not identify correct multiples of 100 or 1,000 4 35.17

11–13 1.5 3.2.D May incorrectly place number on a number line 5 7.32; 7.33

Formative AssessmentUse the Module Assessment to assess students’ learning and progress in the module. The formative assessment provides the opportunity to adjust teaching methods for individual or whole class instruction.

Module 1 Assessment 35

Mod

ule

1 As

sess

men

tTEXAS Test Prep

80 907060

Fill in the bubble for the correct answer choice. You may use models to solve.

14. Anorderfor875,380toysisbeingshippedtoawarehouseintheUnitedStates.Howmanytenthousandsarein875,380? q TEKS 3.2.B

A 8 C 87

B 875 D 8,753

15. Therewere4,619studentsenrolledinamilitaryserviceacademyinColorado.Whichisthenumberofstudentswritteninexpandedform? q TEKS 3.2.A

A 4,000+600+10+9

B 9,000+100+60+4

C 400+600+10+9

D 4,000+600+9

16. OnekillerwhaleattheSeaCenterweighed9,485pounds.Whichisawaytomodel9,485withbase-tenblocks? q TEKS 3.2.A

A 9thousands48hundreds5ones

B 94thousands85ones

C 9,485tens

D 9thousands48tens5ones

17. Alexisrounded73tothenearestten.Whatis73roundedtothenearestten? q TEKS 3.2.C

Recordyouranswerandfillinthebubblesonthegrid.Besuretousethecorrectplacevalue.

.0 0 0

1 1 1

2 2 2

3 3 3

4 4 4

5 5 5

6 6 6

7 7 7

8 8 8

9 9 9

07

36

© H

ough

ton

Miff

lin H

arco

urt P

ublis

hing

Com

pany

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

3_MTXESE061873_M01A.indd 36 1/28/15 3:11 PM

1

2

3

Data-Driven Decision Making

*TEKS—Texas Essential Knowledge and Skills; RtI—Response to Intervention

Depth of Knowledge

DOK Level Items

1 3–4, 5–7, 8–10, 11–13, 17

2 14, 15–16

Item Lesson TEKS* Common Error Intervene With RtI* Tier 1 Lessons

Soar to Success Math

14 1.3 3.2.B May incorrectly rename ten thousands 3 2.26

15 1.2 3.2.A May confuse the different forms of writing numbers 2 2.25

16 1.1 3.2.A May incorrectly decompose numbers 1 2.24

17 1.4 3.2.C May not identify correct multiples of 10 4 35.17

36  Module 1 Assessment

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