unit 9: fractions, decimals, and percentsellis2020.org/itlg/itlg grade 4/u9.pdf · 708 unit 9...

OverviewOverviewUnit 9 focuses on the links among fraction, decimal, and percent namesfor numbers, with a special emphasis on percents. Unit 9 begins withpractice converting among fractions, decimals, and percents. Studentsthen use grid pictures, the multiplication rule for renaming fractions,memorization of simple conversions, and a calculator for more complexconversions. Finally, students begin to apply whole-numbermultiplication and division algorithms to multiplication and divisionwith decimals in the last two lessons of Unit 9. Unit 9 has three mainareas of focus:

◆ To reinforce naming equivalencies among fractions, decimals, and percents,

◆ To reinforce the use of a data table, guide the organization andtabulation of survey data, and rank and compare data reported as percents, and

◆ To introduce multiplication and division of decimals by whole numbers.

708 Unit 9 Fractions, Decimals, and Percents

Unit Organizer 709

Lesson Objective Page

Contents

9◆1 Fractions, Decimals, and Percents 722To guide the use of percents in describing real-life situations; and to reinforce naming equivalencies among fractions, decimals, and percents.

9◆2 Converting “Easy” Fractions to Decimals and Percents 728To reinforce renaming fourths, fifths, and tenths as decimals and percents; and to introduce solving percent problems by using equivalent fractions.

9◆3 Using a Calculator to Convert Fractions to Decimals 734To introduce renaming any fraction as a decimal by using a calculator; and to reinforce fraction/percent equivalencies for fourths, fifths, and tenths.

9◆4 Using a Calculator to Rename Fractions as Percents 739To reinforce renaming fractions as percents using a calculator; and to introduce solving number stories involving discounts expressed as percents.

9◆5 Conversions among Fractions, Decimals, and Percents 744To reinforce the use of a data table; and to reinforce renaming fractions as percents using a calculator and renaming decimals as percents.

9◆6 Comparing the Results of a Survey 750To guide the organization and tabulation of survey data; and to introduce the use of percents to compare quantities expressed as fractions with unlike denominators.

9◆7 Comparing Population Data 756To provide practice ranking and comparing data that are reported as percents and displaying ranked data by coloring maps.

9◆8 Multiplication of Decimals 762To introduce multiplication of decimals by whole numbers; and to reinforcethe partial-products and lattice methods for multiplication.

9◆9 Division of Decimals 768To introduce division of decimals by whole numbers; and to reinforce the partial-quotients division algorithm.

9◆10 Progress Check 9 774To assess students’ progress on mathematical content through the end of Unit 9.


To guide the use of percents indescribing real-life situations; and toreinforce naming equivalencies amongfractions, decimals, and percents.

To reinforce renaming fourths, fifths, andtenths as decimals and percents; and tointroduce solving percent problems byusing equivalent fractions.

To introduce renaming any fraction as adecimal by using a calculator; and toreinforce fraction/percent equivalenciesfor fourths, fifths, and tenths.

To reinforce renaming fractions aspercents using a calculator; and tointroduce solving number storiesinvolving discounts expressed as percents.

To reinforce the use of a data table; andto reinforce renaming fractions aspercents using a calculator andrenaming decimals as percents.

To guide the organization and tabulationof survey data; and to introduce the useof percents to compare quantitiesexpressed as fractions with unlikedenominators.

To provide practice ranking andcomparing data that are reported aspercents and displaying ranked data bycoloring maps.

To introduce multiplication of decimalsby whole numbers; and to reinforce thepartial-products and lattice methods formultiplication.

To introduce division of decimals bywhole numbers; and to reinforce thepartial-quotients division algorithm.

Lesson Objectives Links to the Past Links to the Future

Learning In Perspective

Grade 4: Find equivalent names for decimals (Units4 and 5).Grade 3: Find fraction/decimal equivalents.

Grade 3: Find equivalent fractions using FractionCards; identify fractions on a fraction number line.Find fraction/decimal equivalents.

Grade 3: Read and display numbers on a calculator.Perform operations on a calculator. Play Beat theCalculator.

Grade 3: Read and display numbers on a calculator.Perform operations on a calculator. Play Beat theCalculator. Name fractional parts of regions andsets of objects. Fold rectangles to find fractions of fractions.

Grades 2 and 3: Collect, organize, interpret, anddisplay data.



Grade 4: Estimate the magnitude of a product ofmultidigit numbers (Unit 5).Grade 3: Model and solve multiplication numberstories using arrays, diagrams, and number models.Extend decimal notation to tenths and hundredths.

Grade 3: Model and solve division number storiesusing arrays, diagrams, and number models.Review division as equal sharing and equalgrouping. Extend decimal notation to tenths andhundredths using money and base-10 blocks.

Grades 5 and 6: Applications and extensions,including games to promote reflex recognition offraction/decimal/percent equivalents, and practicewith equivalent rates and ratios.

Grade 5: Develop reflex recognition of “easy”fraction-decimal equivalents. Grade 6: Applications and maintenance.

Grade 5: Use a calculator to find decimalequivalents. Grade 6: Use a calculator to renamefractions as decimals and percents.

Grade 5: Use a calculator to find decimalequivalents. Grades 5 and 6: Solve percent-ofproblems. Find the whole, given a percent of thewhole. Grade 6: Use a calculator to renamefractions as decimals and percents.

Grade 5: Applications and maintenance.

Grade 5: Use a percent circle to read a circle graph.

Grades 5 and 6: Solve percent-of problems. Find the whole, given a percent of the whole.

Grade 5: Make magnitude estimates to placedecimal points in products. Extend the partial-products algorithm and lattice method to decimals.Grade 6: Multiply decimals.

Grade 5: Make magnitude estimates for quotientsof whole numbers and decimals divided by wholenumbers. Grade 6: Extend the partial-quotientsalgorithm to decimal divisors.

9◆1

9◆2

9◆3

9◆4

9◆5

9◆6

9◆7

9◆8

9◆9

Name the “whole” or the ONE. Number and Numeration Goal 2Solve “percent-of” problems. Number and Numeration Goal 2Rename fractions with denominators of 100 as decimals. Number and Numeration Goal 5Find equivalent names for percents. Number and Numeration Goal 5

Find the fraction and percent of a collection and a region. Number and Numeration Goal 2Solve “percent-of” problems. Number and Numeration Goal 2Rename fractions with denominators of 100 as decimals. Number and Numeration Goal 5Find equivalent names for percents. Number and Numeration Goal 5

Explore terminating and repeating decimals. Number and Numeration Goal 5Use a calculator to rename fractions as decimals. Number and Numeration Goal 5Describe patterns in terminating and repeating decimals. Patterns, Functions, and Algebra Goal 1

Solve number stories involving discounts. Number and Numeration Goal 2Name the whole, or the ONE. Number and Numeration Goal 2Use a calculator to rename fractions as percents. Number and Numeration Goal 5Rename any decimal as a percent. Number and Numeration Goal 5

Read and use large numbers. Number and Numeration Goal 1Explore repeating and terminating decimals. Number and Numeration Goal 5Use a calculator to rename fractions as percents; rename decimals as percents by Number and Numeration Goal 5

multiplying by 100; round to the nearest whole-number percent. Compare two quantities with like units using division. Operations and Computation Goal 4Use a data table. Data and Chance Goal 2

Use a calculator to convert fractions to percents. Number and Numeration Goal 5Compare fractions with unlike denominators. Number and Numeration Goal 6Create a table and tally chart. Data and Chance Goal 1Analyze survey results and make predictions based on collected data. Data and Chance Goal 2

Interpret “percent-of” data. Number and Numeration Goal 2Order data reported as percents. Number and Numeration Goal 6Create a table, chart, and map to display data. Data and Chance Goal 1Interpret data displayed on a map. Data and Chance Goal 2

Identify place value in decimals through hundredths. Number and Numeration Goal 1Multiply decimals by whole numbers. Operations and Computation Goal 4Round decimals and estimate products. Operations and Computation Goal 6Use repeated addition to model multiplication. Operations and Computation Goal 7Use a formula to calculate the area of a rectangle. Measurement and Reference Frames Goal 2Use conventional notation to write number sentences. Patterns, Functions, and Algebra Goal 2

Identify place value in decimals through hundredths. Number and Numeration Goal 1Divide decimals by whole numbers. Operations and Computation Goal 4Round decimals and estimate quotients. Operations and Computation Goal 6Use conventional notation to write number sentences. Patterns, Functions, and Algebra Goal 2

Key Concepts and Skills Grade 4 Goals*

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

Unit Organizer 711

Key Concepts and Skills

9◆1

9◆2

9◆3

9◆4

9◆5

9◆6

9◆7

9◆8

9◆9

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 previewcontent of the next unit.

Ongoing Learning and Practice

9◆1 Fraction Match Naming equivalent fractionsNumber and Numeration Goal 5

9◆2 Rugs and Fences Finding the area and perimeter of a polygonMeasurement and Reference Frames Goal 2

9◆3 Fraction/Percent Developing automaticity with “easy” Concentration fraction/percent equivalencies

Number and Numeration Goal 5

9◆8 Over and Up Squares Locating and plotting points on acoordinate gridMeasurement and Reference Frames Goal 4

9◆9 Polygon Pair-Up Identifying properties of polygonsGeometry Goal 2

Lesson Game Skill Practiced

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


▲

Home Communication Study Links provide homework and home communication.

Home Connection Handbook provides more ideas to communicateeffectively with parents.

Unit 9 Family Letter provides families with an overview, Do-AnytimeActivities, Building Skills Through Games, and a list of vocabulary.

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

132

4

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

Mixed practice with multiple choice 9◆1, 9◆2, 9◆4, 9◆6, 9◆8

Mixed practice with writing/reasoning opportunity 9◆2, 9◆3, 9◆7, 9◆8, 9◆9

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

◆ Using number sense ◆ Making a table◆ Using computation ◆ Drawing a picture◆ Finding a pattern ◆ Using estimation◆ Using data in a table ◆ Writing a problem

Lesson Activity

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

9◆1 Write equivalent names for percents.

9◆4 Solve number stories involving percents.

9◆5 Rename fractions as percents.

9◆6 Tabulate survey results for the whole class.

9◆7 Tally predictions.

9◆8 Estimate products of decimals.

9◆9 Estimate quotients of decimals.

MOST CLASSROOMS

F E B R U A R Y M A R C H A P R I L

Unit Organizer 713

Problem SolvingProblem Solving

Unit 9Lessons

NCTMStandards

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

1, 5–10

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

1, 6–10

1, 6–10

1, 5–10

1, 5–10

1, 5–10

1, 5–10

1, 6–10

1, 6–10 6–10

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 9, review your Content by Strand Poster to help you seta monthly pace.

NCTM Standards

http://standards.nctm.org


Balanced Assessment

9◆1 Find equivalent fractions.[Number and Numeration Goal 5]

9◆2 Rename fourths, fifths, tenths, and hundredths as decimals and percents.[Number and Numeration Goal 5]

9◆3 Rename fourths, fifths, tenths, and hundredths as decimals and percents. [Number and Numeration Goal 5]

9◆4 Solve “fraction-of” problems. [Number and Numeration Goal 2]

9◆5 Divide a multidigit whole number by a 1-digit divisor.[Operations and Computation Goal 4]

9◆6 Interpret a map scale.[Operations and Computation Goal 7]

9◆7 Draw conclusions from a data representation. [Data and Chance Goal 2]

9◆8 Estimate the product of a whole number and a decimal.[Operations and Computation Goal 6]

9◆9 Estimate the quotient of a decimal divided by a whole number.[Operations and Computation Goal 6]

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 9◆1 Understand percents as “per 100”

Lesson 9◆4 Explain why decimals move when multiplying by 100

Lesson 9◆5 Use a different division strategy for large numbers

Lesson 9◆7 Understand fractional parts of a spinner

Unit Organizer 715

Find a fraction or a percent of a number.[Number and Numeration Goal 2]

Rename fractions as decimals and percents. [Number and Numeration Goal 5]

Use an estimation strategy to divide decimals by wholenumbers. [Operations and Computation Goal 6]

Use an estimation strategy to multiply decimals bywhole numbers. [Operations and Computation Goal 6]

Find the area and perimeter of polygons.[Measurement and Reference Frames Goal 2]

Insert grouping symbols to make number sentencestrue. [Patterns, Functions, and Algebra Goal 3]

CONTENT ASSESSED Self Oral/Slate Written Open Response

ASSESSMENT ITEMS

✔ ✔✔✔

✔✔

✔✔

✔ ✔✔

✔ ✔✔

✔ ✔✔✔

Periodic Assessment9◆10 Progress Check 9

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

◆ Writing, illustrating, and solving “percent-of ” number stories, Lesson 9 ◆2◆ Estimating measures of angles, Lesson 9 ◆3◆ Comparing the discounts of two items to solve number stories, Lesson 9 ◆4◆ Creating a side-by-side (double) bar graph to display results of a class survey, Lesson 9 ◆6◆ Explaining how to solve “percent-of ” problems, Lesson 9 ◆7◆ Ranking countries and coloring a map to show literacy data, Lesson 9 ◆7◆ Exploring area and perimeter of parallelograms, Lesson 9 ◆9◆ Writing and solving number stories involving the division of a decimal by a whole number,

Lesson 9 ◆9◆ Solving a multistep problem involving percents, Lesson 9 ◆10

Assessment HandbookUnit 9 Assessment Support

◆ Grade 4 Goals, pp. 37–50 ◆ Unit 9 Open Response◆ Unit 9 Assessment Overview, pp. 118–125 • Detailed rubric, p. 122

• Sample student responses, pp. 123–125

Unit 9 Assessment Masters◆ Unit 9 Self Assessment, p. 195◆ Unit 9 Written Assessment, pp. 196–198◆ Unit 9 Open Response, p. 199◆ Unit 9 Class Checklist, pp. 280, 281, and 303◆ Quarterly Checklist: Quarter 3, pp. 298

and 299

◆ Unit 9 Individual Profile of Progress, pp. 278,279, and 302

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

305, 309, and 310

Daily Lesson Support

Differentiated Instruction

ENGLISH LANGUAGE LEARNERS

READINESS ENRICHMENT

EXTRA PRACTICE9◆1 Creating a Percents All Around Museum9◆4 Discussing vocabulary used in

discount number stories9◆7 Creating a poster to illustrate the terms

rural and urban

9◆1 Shading 50% of a square different ways9◆2 Solving percent problems9◆4 Solving “percent-of” problems9◆5 Rounding percents9◆6 Comparing estimates9◆8 Multiplying whole numbers and

estimating products9◆8 Solving multiplication number stories9◆9 Dividing whole numbers by whole

numbers and estimating quotients9◆9 Solving division number stories

9◆2 Writing and solving “percent-of”number stories

9◆3 Finding “easy” fractions close to given decimals

9◆4 Comparing discounts9◆6 Making a double bar graph9◆7 Displaying literacy data9◆8 Comparing products9◆9 Writing and solving number stories

involving division of decimals

9◆2 Finding equivalent names for fractions9◆3 Memorizing equivalent fraction names

5-Minute Math 9◆4 Practicing percents9◆5 Practicing fraction conversions

Adjusting the Activity9◆1 Writing fractions with denominators of

100 and in simplest form9◆2 Playing variations of Rugs and Fences9◆3 Using game variations of

Fraction/Percent Concentration9◆4 Rephrasing discount number stories9◆5 Renaming percents without a

calculator ELL

9◆6 Combining data and discussing whycombined data is more reliable

9◆7 Highlighting a specific row of data9◆7 Shading a hundreds grid ELL9◆8 Using lattice multiplication for

decimals9◆9 Renaming quotients involving amounts

in dollars and cents as cents

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 LinksLanguage Arts

Lesson 9◆1 Students think of words that begin with cent-.

Consumer

Lesson 9◆4 Students use their calculators and mental arithmetic to solve discount number stories.

Differentiation HandbookSee the Differentiation Handbook for materials on Unit 9.▲

Social Studies

Lesson 9◆5 Students investigate populationand land-area, data, and use their calculatorsto convert these to percents of the worldpopulation and land area.

Lesson 9◆5 Students follow the establishedWorld Tour routine.

Lesson 9◆7 Students discuss populationand life expectancy data.


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

Connecting Math and LiteracyLesson 9◆5 Count Your Way through China, by Jim Haskins, CarolrhodaBooks, 1988 Piece = Part = Portion: Fractions = Decimals = Percents, by Scott Gifford,Tricycle Press, 2003

Student Reference Bookpp. 243, 246, 257, 258, 260, 261, 271, 281, and 299–302

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

Unit 9 Vocabulary100% boxdiscountdiscounted pricefraction of discountlife expectancylist pricepercentpercent of discount rankregular pricerepeating decimalruralsale priceterminating decimalurban

Grade 3

Grade 4

Grade 5

8◆5,8◆6

8◆5,8◆6

8◆5,8◆6

11◆5

9◆1 9◆2 9◆3 9◆4 9◆5 9◆6 9◆7 9◆8 9◆9

6◆8 6◆8,8◆8

5◆8 5◆8,6◆8

3◆2 2◆8 4◆5

Professional Development

Unit Organizer 717

Teacher’s Reference Manual LinksSection

9.3.1

9.3.5

11.4.3

3.1.1

11.4.1

11.4.3

3.1.1

11.4.1

11.4.3

9.3.5

Topic

Fraction and Decimal Notation

Percents

Fraction/Decimal/PercentConversions

Calculators

Entering Fractions and MixedNumbers


Calculators

Entering Fractions and MixedNumbers


Percents

Lesson

9◆1

9◆2

9◆3

9◆4

11.4.3

12.2.2

12.2.3

12.2.4

11.2.3

11.2.4

Section


Collecting and Recording Data

Organizing and Displaying Data

Data Analysis

See 9◆6.

Multiplication Algorithms

Division Algorithms

Topic

9◆5

9◆6

9◆7

9◆8

9◆9

Lesson


Materials

Lesson Masters Manipulative Kit Items Other Items

* Denotes optional materials

Technology Assessment Management System, Unit 9iTLG, Unit 9

Study Link 8◆6 slate Fraction Match CardsStudy Link Masters, pp. 279 and 280Teaching Masters, pp. 278 and 281

Study Link 9◆1 slate Rugs and Fences CardsStudy Link Master, p. 282Game Master, p. 502Teaching Master, p. 283Teaching Aid Master, p. 445

Study Link 9◆2 calculator scissorsTeaching Aid Masters, pp. 388 or 389 slate

and 446Study Link Master, p. 284Game Masters, pp. 481 and 482

Study Link 9◆3 calculator overheard calculator*; store Study Link Master, p. 285 slate catalogs or advertisementsTeaching Masters, pp. 286 and 287 counters

Study Link 9◆4 calculator classroom world mapStudy Link Master, p. 288 slateTeaching Aid Masters, pp. 419* and 420*Teaching Master, p. 289

Study Link 9◆1 and 9◆5 calculator pen or colored pencil; large, clear transparency of Math Masters, p. 290* slate containerStudy Link Master, p. 291 pattern blocksTeaching Aid Masters, pp. 403,

410, 414, and 416Teaching Master, p. 292

Study Link 9◆6 slate red, green, and blue pencils, crayons, or Teaching Masters, pp. 293 and 295 markers; index card*; old magazines; Teaching Aid Master, p. 426* chart paper; scissorsStudy Link Master, p. 294

Study Link 9◆7 slate colored pencil; coinsTeaching Aid Masters, pp. 388 or per group: 2 six-sided dice

389, 404, 428, and 434Study Link Master, p. 296Game Master, p. 494Teaching Masters, pp. 114 and 297

Study Link 9◆8 slate Polygon Pair-Up Polygon Deck and Teaching Aid Masters, pp. 404* Property Deck; coins

and 428Study Link Master, p. 298Teaching Masters, pp. 114 and 299

Study Link 9◆9 calculator markers or crayonsAssessment Masters, pp. 195–199Study Link Masters, pp. 300–303

9◆1

9◆2

9◆3

9◆5

9◆6

9◆7

9◆8

9◆9

9◆10

9◆4

Unit Organizer 719

Mathematical Background

Note

Terminating andrepeating decimals willbe covered formally inSixth Grade EverydayMathematics.

The discussion below highlights the major content ideas presented in Unit 9and helps establish instructional priorities.

Conversions among Fractions,Decimals, and Percents (Lessons 9◆1–9◆5)Students begin their work with fraction/decimal/percent names for numbersby exploring pictorial representations of such numbers on a 10-by-10 grid.They use these representations to restate percent situations as fractions anddecimals. In particular, they find and memorize equivalencies for “easy”fractions (halves, fourths, fifths, and tenths).

One way to convert a fraction to a percent is to first rename it as a fractionwith a denominator of 100. This can be done for “easy” fractions by using themultiplication rule for equivalent fractions.

Example �35� � �

35

��

22

00� � �1

6000�

�16000� � 0.60 � 60%

More complicated fractions, which do not lend themselves to conversions bythe multiplication rule, can be renamed as decimals by dividing thenumerator by the denominator with the help of a calculator.

Example �37� � 3 � 7 = 0.428571 ...

To convert the decimal to a percent, multiply it by 100 and attach thepercent symbol to the result.

0.428571 � (0.428571 � 100)% � 42.8571%, or 43%, rounded to thenearest percent

The percent key on a calculator is really not needed, since the percent equivalent of any ratio or fraction can be calculated by using the division key and multiplying by 100. The authors include a discussion of the percent key mainly to take one more “mystery” off the keypad.

For further information on conversions among fractions, decimals, and percents, refer to Section 9.3 of the Teacher’s Reference Manual.

Solving Problems InvolvingPercents (Lessons 9◆4–9◆7)As was mentioned in the Overview, solving percent problems ofteninvolves conversions among fractions, decimals, and percents. In Lessons9-4 through 9-7, students use their conversion skills to solve a variety of problems.

In Lesson 9-4, students solve problems that involve percents of discounts.These problems are simple enough so that students can do the conversionswithout the use of a calculator.

In Lesson 9-5, students use World Tour data to answer questions, such asthe following:

◆ What percent of the world’s population lives in China?◆ What percent of the world’s land area belongs to Russia?

For Study Link 9-1, students conduct a survey. They analyze the results of the survey in Lesson 9-6. In order to compare the results, they need toconvert various ratios to percents.

In Lesson 9-7, students create color-coded maps to organize and representcertain population data.

Section 9.3.5 of the Teacher’s Reference Manual contains moreinformation about solving problems involving percents.


�

�

�

�

Unit Organizer 721

Multiplication and Division withDecimals (Lessons 9◆8 and 9◆9)

The approach to multiplication and division of decimals used in EverydayMathematics is based on two assumptions:

◆ The same multiplication and division algorithms may be used forwhole numbers and decimals.

◆ The placement of the decimal point in the answer can be determinedby making a rough estimate of the answer.

Example 42 � 23.8 � ?

Step 1: Estimate the product: 40 � 20 � 800, or 50 � 20 � 1,000; so 42 � 23.8 will be about 800 or 1,000.

Step 2: Multiply the numbers, leaving out the decimal point.

238� 42

9996

Step 3: Insert the decimal point in the answer. Since theestimated product is close to 1,000, the exact productmust be 999.6.

Example 259.2 � 8 � ?

Step 1: Estimate the quotient: 259.2 is close to 260, and 260 � 8 is between 30 and 40.

Step 2: Divide the numbers, leaving out the decimal point.

2592 � 8 � 324

Step 3: Insert the decimal point in the answer. Since theestimated quotient is between 30 and 40, the exactquotient must be 32.4.

Consult Section 9.3.4 of the Teacher’s Reference Manual for moreinformation about multiplication and division with decimals.

unit 9: fractions, decimals, and percentsellis2020.org/itlg/itlg grade 4/u9.pdf · 708 unit 9...

Documents