OverviewOverviewIn this unit the yearlong World Tour project is introduced. Besidesproviding links to social studies and language arts topics, the tour offersmany opportunities to apply the mathematical content of this unit. Unit 2 has three main areas of focus:

◆ To examine different uses and equivalent names of numbers andreview the base-ten place-value system,

◆ To review procedures for addition and subtraction of multidigit whole numbers, and

◆ To reintroduce and extend ideas about data collection, organization,display, and analysis.

66 Unit 2 Using Numbers and Organizing Data

Unit Organizer 67

Lesson Objective Page

Contents

2◆1 A Visit to Washington, D.C. 82To review examples of the various ways in which numbers are used; and to introduce the World Tour Project.

2◆2 Many Names for Numbers 89To review equivalent names for whole numbers and name-collection boxes.

2◆3 Place Value in Whole Numbers 94To provide practice identifying values of digits in numbers up to one billion; and to provide practice reading and writing numbers up to one billion.

2◆4 Place Value with a Calculator 100To provide practice with place-value skills using a calculator routine; and to review reading and writing large numbers.

2◆5 Organizing and Displaying Data 106To provide practice organizing and displaying data with a tally chart and determining the maximum, minimum, range, and mode of a set of data.

2◆6 The Median 112To review how to display a set of data with a line plot; and to review how to find the median of a set of data.

2◆7 Addition of Multidigit Numbers 119To review the partial-sums algorithm used to solve multidigit addition problems; and to introduce a column-addition method similar to the traditional addition algorithm.

2◆8 Displaying Data with a Bar Graph 126To provide practice measuring length to the nearest half-centimeter; and to guide the construction and use of bar graphs for a set of collected data.

2◆9 Subtraction of Multidigit Numbers 132To review the trade-first and counting-up methods, and to introduce the partial-differences method of solving multidigit subtraction problems; and to provide practice estimating differences for multidigit subtraction problems.

2◆10 Progress Check 2 138To assess students' progress on mathematical content through the end of Unit 2.

68 Unit 2 Using Numbers and Organizing Data

Learning In Perspective

2◆1

2◆2

2◆3

2◆4

2◆5

2◆6

2◆7

2◆8

2◆9

To review examples of the variousways in which numbers are used;and to introduce the World Tour Project.

To review equivalent names for wholenumbers and name-collection boxes.

To provide practice identifying values ofdigits in numbers up to one billion; andto provide practice reading and writingnumbers up to one billion.

To provide practice with place-valueskills using a calculator routine; and to review reading and writing large numbers.

To provide practice organizing anddisplaying data with a tally chart anddetermining the maximum, minimum,range, and mode of a set of data.

To review how to display a set of datawith a line plot; and to review how tofind the median of a set of data.

To review the partial-sums algorithmused to solve multidigit additionproblems; and to introduce a column-addition method similar to thetraditional addition algorithm.

To provide practice measuring length tothe nearest half-centimeter; and toguide the construction and use of bargraphs for a set of collected data.

To review the trade-first and counting-upmethods, and to introduce the partial-differences method of solving multidigitsubtraction problems; and to providepractice estimating differences formultidigit subtraction problems.

Grades 2 and 3: Discuss and sort different kinds ofnumbers by how they are used.

Grades 1–3: Use name-collection box routines toexpress numbers in many ways, including pictures,tallies, and words.

Grades 1–3: Practice place-value skills with base-10 blocks, place-value books, slate routines, and through games.

Grades 1–3: Introduce and practice calculatorroutines; practice place-value skills with base-10blocks, place-value books, slate routines, andthrough games.

Grades 1 and 2: Define and calculate minimum,maximum, median, and mode. Grade 3: Define and calculate mean (average) and range. Use lists,tally charts, line plots, and graphs to determine landmarks.

Grades 1 and 2: Use tally charts and bar graphs tosort, display, and describe data. Grade 3: Use lineplots to sort and display data; use tally charts, bargraphs, and line plots to find landmarks andinterpret data.

Grades 1–3: Use invented (student-generated)algorithms to solve multidigit addition problems;begin to practice the partial-sums focus algorithm for addition. Grades 2 and 3: Use ballpark estimates.

Grades 1–3: Choose and use appropriatemeasuring tools; refer to tables of equivalent unitsof metric measure. Grades 1 and 2: Use tally chartsand bar graphs to sort, display, and describe data.

Grades 1–3: Use invented (student-generated)algorithms to solve multidigit subtraction problems; begin to practice the trade-first andcounting up focus algorithms. Grades 2 and 3: Use ballpark estimates.

Grade 4: Find lines of latitude and longitude(Unit 6). Grade 5: Applications and maintenance;conduct American Tour Project.

Grade 4: Find equivalent names for decimals;rename numbers using exponential notationand powers of 10; start a table of equivalentfractions and decimals. Grades 5 and 6:Applications and extensions.

Grade 4: Read, write, and compare numbersup to billions; introduce exponential notation forpowers of 10 (Unit 5). Grades 5 and 6: Extendplace-value facility beyond billions; use exponential and scientific notation.

Grade 4: Read, write, and compare numbersup to billions; introduce exponential notationfor powers of 10 (Unit 5). Grade 5: Extend place-value facility beyond billions; use exponential andscientific rotation.

Grade 4: Use side-by-side graphs and color-coded maps to compare data (Unit 9).Grade 5: Use stem-and-leaf plots to list and sortdata and to calculate landmarks. Grade 6:Application and maintenance.

Grade 4: Compare the mean and median of datasets; convert average rates to more easilyunderstood rates (Units 3 and 4). Grade 5: Usestem-and-leaf plots. Grade 6: Applications andmaintenance.

Grade 4: Develop strategies for addition ofdecimals (Unit 4). Grades 4–6: Applications and maintenance to develop proficiency with the focus algorithms, including adding multidigit numbers with mental strategies.

Grade 4–6: Repeated opportunities to measure in metric units. Grade 5: Use stem-and-leaf plots,broken-line graphs, and circle graphs. Grade 6: Use step graphs.

Grade 4: Develop strategies for subtraction of decimals (Unit 4). Grades 4–6: Developproficiency with the focus algorithms, includingsubtracting with mental strategies.

Lesson Objectives Links to the Past Links to the Future

Key Concepts and Skills Grade 4 Goals*

*See the Appendix for a complete list of Grade 4 Goals.

Unit Organizer 69

2◆1

2◆2

2◆3

2◆4

2◆5

2◆6

2◆7

2◆8

2◆9

Use numbers written in number-word notation. Number and Numeration Goal 1Compare uses of estimates and exact counts. Operations and Computation Goal 6Locate points on a letter-number coordinate map. Measurement and Reference Frames Goal 4Extend numerical patterns. Patterns, Functions, and Algebra Goal 1

Give equivalent mathematical expressions for whole numbers. Number and Numeration Goal 4Use conventional notation to write expressions using the four basic arithmetic operations. Patterns, Functions, and Algebra Goal 2Insert grouping symbols to make number sentences true. Patterns, Functions, and Algebra Goal 3

Read and write numbers up to 1,000,000,000; identify the values of digits. Number and Numeration Goal 1Write numbers in expanded notation. Number and Numeration Goal 4Find the sum of numbers written in expanded notation. Operations and Computation Goal 2Use and describe patterns to find sums. Patterns, Functions, and Algebra Goal 1

Read and write large numbers. Number and Numeration Goal 1Identify places in whole numbers and the values of the digits in those places. Number and Numeration Goal 1Add and subtract multidigit whole numbers. Operations and Computation Goal 2Solve open sentences. Patterns, Functions, and Algebra Goal 2

Create a tally chart. Data and Chance Goal 1Find the maximum, minimum, range, mode, median, and mean for a set of data. Data and Chance Goal 2Use data landmarks to make a prediction. Data and Chance Goal 2Use and describe a strategy for estimating volume; describe the difference between an Measurement and Reference Frames Goal 2

estimate and a guess.

Create a line plot. Data and Chance Goal 1Find the maximum, minimum, range, mode, median, and mean for a set of data. Data and Chance Goal 2Use data landmarks and representations to answer questions and draw conclusions. Data and Chance Goal 2

Identify places in whole numbers and the values of the digits in those places. Number and Numeration Goal 1Apply extended addition facts. Operations and Computation Goal 1

Use the partial-sums and column-addition algorithms to solve multidigit addition problems; Operations and Computation Goal 2choose an appropriate paper and-pencil algorithm to solve multidigit addition problems.

Make ballpark estimates for multidigit addition problems. Operations and Computation Goal 6

Create a bar graph. Data and Chance Goal 1Determine the maximum, minimum, range, mode, and median of a data set. Data and Chance Goal 2Ask and answer questions and draw conclusions based on data landmarks and a bar graph. Data and Chance Goal 2Measure to the nearest half-centimeter. Measurement and Reference Frames Goal 1

Identify places in whole numbers and the values of the digits in those places. Number and Numeration Goal 1Apply extended subtraction facts. Operations and Computation Goal 1Use the trade-first and partial-differences algorithms to solve multidigit subtraction problems; Operations and Computation Goal 2

choose an appropriate paper-and-pencil algorithm to solve multidigit subtraction problems.Make ballpark estimates for multidigit subtraction problems. Operations and Computation Goal 6

Key Concepts and Skills

Ongoing Learning and Practice

Math BoxesMath Boxes are paired across lessons as shown in the brackets below.This makes them useful as assessment tools. Math Boxes also preview content of the next unit.

Practice through Games Games are an essential component of practice in the Everyday Mathematicsprogram. Games offer skills practice and promote strategic thinking.

132

4

Ongoing Learning and Practice

2 ◆1 Polygon Pair-Up Identifying properties of polygonsGeometry Goal 2

2◆2 Name That Number Representing numbers in different waysNumber and Numeration Goal 4

2◆4 Fishing for Digits Identifying digits and expressing values of digits in whole numbersNumber and Numeration Goal 1

2◆5 Addition Top-It Developing automaticity with addition factsOperations and Computation Goal 1

2◆6 Subtraction Top-It Developing automaticity with subtraction factsOperations and Computation Goal 1

2◆7 High-Number Toss Comparing numbersNumber and Numeration Goal 6

2◆9 Subtraction Target Practice Developing place-value and subtraction skillsNumber and Numeration Goal 1Operations and Computation Goal 2

Lesson Game Skill Practiced

See the Differentiation Handbook for ways to adapt games to meet students’ needs.

70 Unit 2 Using Numbers and Organizing Data

Mixed practice [2◆1, 2◆3], [2◆2, 2◆4], [2◆5, 2◆7, 2◆9], [2◆6, 2◆8]

Mixed practice with multiple-choice 2◆1, 2◆4, 2◆6, 2◆9

Mixed practice with writing/reasoning opportunity 2◆2, 2◆3, 2◆5, 2◆7, 2◆8

▲

Home Communication Study Links provide homework and home communication.

Home Connection Handbook provides more ideas to communicateeffectively with parents.

Unit 2 Family Letter provides families with an overview, Do-AnytimeActivities, Building Skills Through Games, and a list of vocabulary.

Encourage students to use a variety of strategies to solve problems and toexplain those strategies. Strategies that students might use in this unit:

◆ Using information from a reference book

◆ Writing a number sentence◆ Using computation

Lesson Activity

See Chapter 18 in the Teacher’s Reference Manual for more information about problem solving.

2◆1 Examine numerical information about Washington, D.C.

2◆2 Name a target number using numbers 1 through 20 and the four operations.

2◆4 Practice place-value using a calculator.

2◆5 Determine about how many raisins are in a typical �12� ounce box of raisins.

2◆6 Find landmarks in family-size data for the class.

2◆8 Determine the median head size for the class.

Unit Organizer 71

Problem SolvingProblem Solving

Unit 2Lessons

NCTMStandards

2 ◆1 2 ◆2 2 ◆3 2 ◆4 2 ◆5 2 ◆6 2 ◆7 2 ◆8 2 ◆9 2 ◆10

1, 4, 6–10 1, 6–8 1, 6,

8, 101, 6, 8, 10

4, 5, 7–10 5–10 1,

6–84, 5, 7–10

1, 6–8 6–10

Content Standards: 1 Number and Operations, 2 Algebra, 3 Geometry, 4 Measurement, 5 Data Analysis and ProbabilityProcess Standards: 6 Problem Solving, 7 Reasoning and Proof, 8 Communication, 9 Connections, 10 Representation

Planning Tips

Lessons thatteach throughproblem solving,not just aboutproblem solving

PacingPacing depends on a number of factors, such as students’ individual needsand how long your school has been using Everyday Mathematics. At thebeginning of Unit 2, review your Content by Strand Poster to help you seta monthly pace.

NCTM Standards

◆ Using estimation◆ Making and using a table (tally chart)◆ Making and using a graph

MOST CLASSROOMS

S E P T E M B E R O C T O B E R N O V E M B E R

72 Unit 2 Using Numbers and Organizing Data

Balanced Assessment

2◆1 Compute extended addition facts. [Operations and Computation Goal 1]

2◆2 Give equivalent names for whole numbers.[Number and Numeration Goal 4]

2◆3 Identify the values of digits in whole numbers.[Number and Numeration Goal 1]

2◆4 Identify places in whole numbers and the values of the digits in those places.[Number and Numeration Goal 1]

2◆5 Compute basic addition facts.[Operations and Computation Goal 1]

2◆6 Identify the maximum, minimum, range, and mode of a data set.[Data and Chance Goal 2]

2◆7 Solve multidigit addition problems.[Operations and Computation Goal 2]

2◆8 Use data landmarks and bar graphs to drawconclusions about a data set.[Data and Chance Goal 2]

2◆9 Solve multidigit subtraction problems.[Operations and Computation Goal 2]

Lesson Content Assessed

Use the Assessment

Management System

to collect and analyze dataabout students’ progressthroughout the year.

Ongoing Assessment

Recognizing Student AchievementOpportunities to assess students’ progress toward Grade 4 Goals:

Informing InstructionTo anticipate common student errors and to highlight problem-solving strategies:

Lesson 2◆1 Distinguish between measurements and counts

Lesson 2 ◆3 Use the word and correctly when reading numbers

Lesson 2◆5 Correctly place the fifth tally mark

Lesson 2◆6 Order numbers to find the median of a data set

Lesson 2◆8 Measure length to the nearest half-centimeter

Unit Organizer 73

Read and write whole numbers up to 1,000,000,000;identify places in such numbers and the values of thedigits in those places. [Number and Numeration Goal 1]

Use numerical expressions to give equivalent names forwhole numbers. [Number and Numeration Goal 4]

Solve problems involving the addition and subtraction ofwhole numbers. [Operations and Computation Goal 2]

Make reasonable estimates for whole-number additionand subtraction problems.[Operations and Computation Goal 6]

Use a tally chart; create a bar graph.[Data and Chance Goal 1]

Find the maximum, minimum, range, median, and modeof a data set. [Data and Chance Goal 2]

Measure length to the nearest �12� centimeter.

[Measurement and Reference Frames Goal 1]

Describe and classify plane figures.[Geometry Goal 2]

CONTENT ASSESSED Self Oral/Slate Written Open Response

ASSESSMENT ITEMS

✔✔

✔

✔ ✔✔✔

✔✔✔

✔✔

✔✔

✔✔

✔ ✔

Periodic Assessment2◆10 Progress Check 2

Portfolio OpportunitiesOpportunities to gather samples of students’ mathematical writings, drawings, and creations to add balance to the assessment process:

◆ Representing numbers in different ways,Lesson 2◆2

◆ Identifying places and expressing the values of the digits, Lesson 2◆4

◆ Deciphering a place-value code, Lesson 2◆4 ◆ Describing parallel sides, Lesson 2◆5◆ Making and explaining predictions based on

a sample, Lesson 2◆5◆ Comparing similar data collected from

different sources, Lesson 2◆6

Assessment HandbookUnit 2 Assessment Support

◆ Grade 4 Goals, pp. 37–50 ◆ Unit 2 Open Response◆ Unit 2 Assessment Overview, pp. 60–67 • Detailed rubric, p. 64

• Sample student responses, pp. 65–67

Unit 2 Assessment Masters◆ Unit 2 Self Assessment, p. 159◆ Unit 2 Written Assessment, pp. 160–162◆ Unit 2 Open Response, p. 163◆ Unit 2 Class Checklist, pp. 252, 253, and 303

◆ Unit 2 Individual Profile of Progress, pp. 250,251, and 302

◆ Exit Slip, p. 311◆ Math Logs, pp. 306–308◆ Other Student Assessment Forms, pp. 304,

305, 309, and 310

◆ Identifying properties of parallelograms,Lesson 2◆7

◆ Writing and solving number stories,Lesson 2◆7

◆ Describing patterns in number sentences,Lesson 2◆8

◆ Applying computation and estimation skills,Lesson 2◆9

◆ Using landmarks of data to solve a jellybeanproblem, Lesson 2◆10

74 Unit 2 Using Numbers and Organizing Data

Differentiated Instruction

Daily Lesson Support

ENGLISH LANGUAGE LEARNERS

READINESS ENRICHMENT

EXTRA PRACTICE2◆1 Exploring a world map2◆3 Building a Math Word Bank2◆6 Building a Math Word Bank2◆7 Building a Math Word Bank

2◆1 Solving Frames-and-Arrows problems2◆2 Sorting dominoes by sums2◆4 Using a place-value tool2◆5 Recording data with tally marks2◆6 Finding the middle value2◆7 Solving parts-and-total number stories 2◆8 Constructing a pattern block graph2◆9 Subtracting by counting up

2◆1 Finding missing numbers2◆2 Solving pan-balance problems2◆3 Solving number-grid puzzles2◆4 Deciphering a place-value code2◆5 Making a prediction based on a sample2◆6 Comparing family-size data2◆7 Writing addition number stories2◆8 Analyzing data2◆9 Solving number-tile problems

2◆1 Solving Frames-and-Arrows problems2◆2 Completing name-collection boxes

5-Minute Math2◆2 Exploring Roman numerals2◆3 Practicing place value skills2◆5 Identifying data landmarks

Adjusting the Activity2◆1 Estimating distance using a map scale2◆1 Locating additional reference points2◆2 Using a calculator to complete

name-collection boxes2◆2 Using cards with operation symbols to

play Name That Number2◆3 Writing decimal numbers less than one2◆3 Reading large numbers ELL2◆4 Exploring place value ELL2◆4 Selecting the appropriate operation key 2◆5 Discussing data landmarks2◆6 Labeling data landmarks ELL2◆6 Modeling the median ELL2◆6 Comparing mean and median

2◆7 Solving addition problems using base-10 blocks ELL

2◆7 Modeling trading using base-10 blocks ELL

2◆7 Playing a variation of High-NumberToss

2◆8 Discussing the word record ELL2◆8 Discussing whether the mean is a

useful landmark for a data set2◆8 Analyzing bar graph data2◆9 Solving subtraction problems using

base-10 blocks ELL2◆9 Modeling subtraction using a

number line ELL

A U D I T O R Y � K I N E S T H E T I C � T A C T I L E � V I S U A L

Cross-Curricular LinksSocial Studies ConsumerLesson 2◆1 Students begin the Lesson 2 ◆8 Students verify an advertising

year-long World Tour Project. claim.

Differentiation HandbookSee the Differentiation Handbook for materials on Unit 2.

▲

Language SupportEveryday Mathematics provides lesson-specific suggestions to help allstudents, including non-native English speakers, to acquire, process, and express mathematical ideas.

Connecting Math and Literacy12 Ways to Get to 11, by Eve Merriam, Aladdin, 1996If You Made a Million, by David M. Schwartz, HarperTrophy, 1994How Tall, How Short, How Far Away? by David A. Adler, Holiday House, 2000The History of Counting, by Denise Schmandt-Besserat, HarperCollins, 1999

Student Reference Bookpp. 2, 10–12, 14, 15, 71, 242, 252, 254, 258, 262–264, and

267–270

Multi-age Classroom ◆ Companion LessonsCompanion Lessons from Grades 3 and 5 can help you meet instructionalneeds of a multi-age classroom. The full Scope and Sequence can be foundin the Appendix.

Unit 2 Vocabularyballpark estimatebar graphcolumn-addition methodcounting numberdigitequivalent nameestimateguesslandmarkline plotmaximummedianminimummodename-collection boxpartial-differences methodpartial-sums methodplacerangetally charttrade-first methodwhole number

Grade 3

Grade 4

Grade 5

1◆1,1◆6

5◆1,5◆3

1◆9 1◆5,10◆7

1◆5,10◆6, 10◆7

2◆1,2◆7

1◆5 2◆1,2◆8

2◆1 2◆2 2◆3 2◆4 2◆5 2◆6 2◆7 2◆8 2◆9

3◆1 2◆4 2◆2,2◆3

2◆2,2◆3

6◆1, 6◆3,12◆7

10◆4,10◆7

2◆2,2◆3

5◆9 2◆3

Professional Development

Teacher’s Reference Manual LinksSection

9.1

1.2.6

1.3.3

9.9.3

9.2

16.1.2

3.1.1

12.2.3

12.2.4

Topic

Number Uses

Museums

Name-Collection Boxes

Name-Collection Boxes

Whole Numbers

Extreme Numbers

Calculators

Organizing and Displaying Data

Data Analysis

Lesson

2◆1

2◆2

2◆3

2◆4

2◆5

Topic

2◆6

2◆7

2◆8

2◆9

Lesson Section

Unit Organizer 75

See 2◆5

Addition Algorithms

Why Estimate?

Estimates in Calculations

Metric System

Length

Organizing and Displaying Data

Subtraction Algorithms

Estimates in Calculations

12.2.2

11.2.1

16.1.1

16.1.3

14.2.2

14.3

12.2.3

11.2.2

16.1.3

76 Unit 2 Using Numbers and Organizing Data

Materials

Lesson Masters Manipulative Kit Items Other Items

* Denotes optional materials

Technology Assessment Management System, Unit 2iTLG, Unit 2

Teaching Masters, pp. 38, 40 and 41 slate straightedgeStudy Link Master, p. 39Game Masters, pp. 496 and 497Teaching Aid Master, p. 393

Study Link 2◆1 calculator* index cards*Teaching Aid Masters, pp. 389 and slate

394–397 deck of number cardsStudy Link Master, p. 42 number cards 0–18Game Master, p. 489Teaching Masters, pp. 43 and 44

Study Link 2◆2 calculator transparency of Math Masters, slate

p. 398*Study Link Master, p. 44Teaching Master, p. 46

Study Link 2◆3 calculator overhead calculator*Teaching Aid Masters, pp. 388 or slate scissors; stapler

389* and 399–402transparency of Math Masters, p. 47*Study Link Master, p. 48Game Master, p. 472Teaching Masters, pp. 49 and 50

Study Link 2◆4 slate per student: small box of raisins Study Link Master, p. 51 per group: deck of number cards (or 3-ounce cup of raisin substitute); Game Master, p. 506 regular or polyhedral dice* 1 large box of raisins (12 or 15 ounces)Teaching Masters, pp. 52 and 53 two 6-sided dice

Study Link 2◆5 slate; per group: (4 of each) number 3-inch-square stick-on notes; tape*Study Link Master, p. 54 cards 1–10; regular and polyhedral Game Master, p. 506 dice*; deck of number cards Teaching Masters, pp. 55 and 56

Study Link 2◆6 base-10 blocks quarter-sheet of paper; 3-section paper Teaching Aid Masters, pp. 403* or per group: one 6-sided die dinner plates*

404* and 405Study Link Masters, pp. 57 and 58Game Master, p. 487Teaching Master, p. 59

Study Link 2◆7 per group: tape measure ruler; stick-on notes; computer Teaching Masters, pp. 60, 62, and 63 slate with Internet access*; straightedge; Study Link Master, p. 61 compass tape; adjustable baseball capsTeaching Aid Master, p. 406 pattern blocks

Study Link 2◆8 slate quarter-sheet of paper; scissorsTeaching Aid Master, p. 403* or 404* base-10 blocksStudy Link Masters, pp. 64 and 65 calculatorGame Master, p. 504* number cards 0–9 Teaching Masters, pp. 66 and 67

Study Link 2◆9 Geometry TemplateAssessment Masters, pp. 159–163 slateStudy Link Masters, pp. 68–71

2◆1

2◆2

2◆3

2◆5

2◆6

2◆7

2◆8

2◆9

2◆10

2◆4

Unit Organizer 77

The discussion below highlights the major content ideas presented in Unit 2 and helps establish instructional priorities.

Introduction to the World Tour;Number Uses (Lesson 2◆1)This lesson introduces the yearlong World Tour Project that focuses on the studyof number uses. Students begin the tour by traveling from their hometowns toWashington, D.C. (They will not travel to foreign countriesuntil Unit 3.) They use the tourist information aboutWashington, D.C., which appears in the Student ReferenceBook, and consider different uses of numbers.

Most of these numbers fall into one of five major categories.

◆ counts (5 people; 10,200,000 cars)◆ measures (2.6 kilograms; 35 mph; 7�

38� inches)

◆ locations in reference frames (36°F; A.D. 1266; 5:41 P.M.)

◆ ratios, percents, and scale numbers (95%; �

23� as many)

◆ identification numbers and codes (1-312-555-9816; ZIP code 08648)

Although it is not important that students know thisclassification scheme, they should be exposed to everydayuses of numbers in each of these categories. As the exampleslisted above suggest, it is difficult to know how a number isbeing used without looking at its label. “Miles per hour” is a measurement unitlabel, and “degrees Fahrenheit” identifies a temperature scale. On the bar graphshown below, “days” is a counting unit label.

For additional information about number uses, see Section 9.1 of the Teacher's Reference Manual.

Mathematical Background

Note

Encourage students toinclude examples fromall the major usecategories by making aclassroom display ofsome of the moreinteresting number-useexamples that students collect.30

40

50

20

10

0Italy Canada United

States

Num

ber

of D

ays

Average Number of Vacation Days Per Year

Source: World Tourism Organization

Countries

Many Names for Numbers (Lesson 2◆2)The name-collection box, which is used to record equivalent names fornumbers, is reviewed in this lesson. The idea that a number can berepresented in many (equivalent) ways is so important that it is taughtand practiced throughout the Everyday Mathematics program. By now,students should be very familiar with the idea of equivalent names fornumbers, for they have been filling in name-collection boxes since themiddle of first grade.

See the Teacher's Reference Manual, Chapter 9, for additional information about number names.

Playing Games (Lessons 2◆1–2◆2, 2◆4–2◆7, and 2◆9)Practice through games is an integral part of the Everyday Mathematicscurriculum. The authors believe that games are an efficient means of building number skills. Games allow the frequent practice that isnecessary to attain mastery of many skills, and games do not tend tobecome tedious, as drills so often do.

Additional information about games may be found in Section 1.2.1 of the Teacher's Reference Manual.

NoteGames are featured inall of the units. Theyshould be played notonly when they areintroduced, but at othertimes and on a regularbasis as well.

489

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Name

Date

Time

Name That Number Record Sheet

132

4

Round 1

Target Number:My Cards:

My best solution (number sentence):

Number of cards used:

Round 2

Target Number:My Cards:

My best solution (number sentence):

Number of cards used:

254

Name

Date

Time

Name That Number Record Sheet

132

4

Round 1

Target Number:My Cards:

My best solution (number sentence):

Number of cards used:

Round 2

Target Number:My Cards:

My best solution (number sentence):

Number of cards used:

254

16

26 � 10

4 � 4 � 4 � 4

42

116 � 100

8 � (4 � 2)

32 � 2

78 Unit 2 Using Numbers and Organizing Data

16-box

The Base-Ten Place-Value System(Lessons 2◆3 and 2◆4)

The earliest human societies devised systems for counting objects. Thesesystems evolved into a variety of methods for recording the number ofobjects counted. They ranged from simple tallies to the more sophisticatedEgyptian, Babylonian, and Roman notational systems. More recently, thebase-ten place-value system, which is in widespread use today, wasinvented. This system is based on three principles:

◆ Using the digits 0 through 9, one can write any whole number, no matter how large.

◆ The value of each digit in a numeral depends on its position, or place,in the numeral.

◆ Place values increase tenfold from each place to the next higher place.

In Lesson 2-3, students review and practice these underlying concepts,with a special focus on reading and writing whole numbers to one billion.In Lesson 2-4, they practice place-value skills by using a calculator tochange one or more digits in a number. They also play Fishing for Digits,a game that involves identifying digits in whole numbers and expressingtheir value.

For additional information about place value and the base-ten numeration system, see Section 9.9.1 of the Teacher's ReferenceManual.

Algorithms for Adding andSubtracting Numbers (Lessons 2◆7 and 2◆9)Numbers make the most sense when they are in a real-world context.However, students need to practice computation, and to do this, theyfrequently operate with numbers that have no context and no label or unit of measure.

The focus of Lessons 2-7 and 2-9 is on methods for adding and subtractingmultidigit numbers. The review of place value in Lessons 2-3 and 2-4prepares students for the addition and subtraction methods that theprogram presents.

one ten one hundred one thousand

ten thousand one hundredthousand

one million ten million

Unit Organizer 79

80 Unit 2 Using Numbers and Organizing Data

Computational algorithms are systematic procedures that are importantin mathematics. In programming computers, for example, systematicprocedures are developed for working out complex calculations. However,in this calculator and computer age, the authors believe that the usualattention given to drill and reinforcement of particular algorithmsinvolving complex paper-and-pencil calculations is not worth the time thatit takes. The plain truth is that if a person has many calculations to do,the sensible choice is to reach for a calculator, to program the calculationsinto a computer, or to use a computer spreadsheet or other software tomake the calculations. This is not to say that students should not learn to perform paper-and-pencil calculations. But it is not our goal to enablestudents to do all the things that a $5 calculator can do for them.

The authors also believe that it is harmful to suggest to students thatthere is only one proper way to do each operation. Hence, EverydayMathematics exposes students to several methods for adding, subtracting,multiplying, and dividing whole numbers and decimals. For each of theseoperations, all students are expected to know a particular algorithm. (Foraddition, it is the partial-sums algorithm; for subtraction, the trade-firstalgorithm.) But students are encouraged to use whatever algorithm theylike to solve problems, or even to invent one of their own.

For students who have already learned reliable addition and subtractionalgorithms, these lessons remind them that there is more than one way to solve a problem. For students who are still struggling, these lessonsprovide an opportunity to learn reliable methods that will work for them.

See Sections 11.2.1 and 11.2.2 in the Teacher's Reference Manual foradditional information about addition and subtraction algorithms.

NoteStudents should not usetheir calculators whileexploring and practicingthe algorithms foradding and subtractingmultidigit numbers. Thejournal pages, StudyLinks, and Masters used for assessmentwith these lessons aremarked with the no-calculator icon toremind students of this.However, calculatorusage is encouraged in other parts of theprogram. For example,students use a calculator to practiceplace-value skills in Lesson 2-4.

Partial-Sums Method Using Base-10 Blocks

The total is 300 � 120 � 15 � 435.

248 � 187 � 435

248

187

300 120 15

100s 10s 1s

�

Collecting, Organizing, andDescribing Data (Lessons 2◆5, 2◆6, and 2◆8)These first data lessons review and introduce several devices that enablestudents to organize their data. Such organization makes it easier tounderstand the data.

The simple tally chart and bar graph should be familiar to students whohave used Everyday Mathematics in earlier grades. Line plots (also calledsketch graphs) are introduced and are used extensively to organize anddisplay data.

One of the simplest devices for displaying data is to arrange the data inorder from largest to smallest data value. Such an arrangement often canbe done without using a tally table or line plot. For example, on a tangiblelevel, students can line up by either age or height.

Once the data are organized in some way, encourage students at everyopportunity to discuss things they notice about their data. Their discussionsgenerally should include the following “landmarks” in the data: themaximum, minimum, median, mode, and range. Students can use theselandmarks as reference points when they discuss other features of thedata, just as cartographers use landmarks when they discuss map facts.

For additional information about data and landmarks of data, seeSection 12.2 of the Teacher's Reference Manual.

Note

During the school year,many sources of dataare used, and studentsgather their data indifferent ways. Thelessons in this unit rely on counting andmeasuring in theclassroom. In futurelessons, studentscollect data in otherways, such as byobserving andmeasuring at home, bytaking surveys, and byrecording informationfrom reference books.

Number of Head SizeChildren (cm)

49

49.5

50

50.5

51

51.5

52

52.5

53

53.5

54

Tally Chart

12

Head Sizes in 4th Grade Class

0

5

Num

ber

of S

tude

nts

4

3

2

1

Head Sizes to the Nearest cm

49 49.5 50 50.5 51 51.5 52 52.5 53 53.5 54

Unit Organizer 81