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MathematicsMathematicsMathematicsEnglish Language Artscom mon core3Did you know that a groupPerformanceCoachof goldfish is called a troubling? Youwill have less trouble with your teststhis year when you prepare withPerformance Coach!3common corePerformanceCoachcom mon core3PerformanceCoachStudent Editionwww.triumphlearning.comSample LessonPhone: (800) 338-6519 Fax: (866) 805-5723 E-mail: customerservice@triumphlearning.comTo order, call 800-338-6519 orvisit www.triumphlearning.com.ISBN-13: 978-1-62362-805-5900009 781623 628055310NASE G3 MATH SE cvr.indd 1310NASEPerformance Coach2/14/14 10:43 AM
CONTENTSStandardsLetter to the Student . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ivDOMAIN 1: OPERATIONS AND ALGEBRAIC THINKING . . . 5Introducing Multiplication . . . . . . . . . . . . . . . . . . . . . . 6Lesson 13.OA.1Lesson 2Introducing Division . . . . . . . . . . . . . . . . . . . . . . . . . . 153.OA.2Lesson 3Solving Multiplication Problems . . . . . . . . . . . . . . . 243.OA.3Lesson 4Solving Division Problems . . . . . . . . . . . . . . . . . . . . 333.OA.3Lesson 5Finding Unknown Values . . . . . . . . . . . . . . . . . . . . . . 413.OA.4, 3.OA.6Lesson 6Multiplication Properties . . . . . . . . . . . . . . . . . . . . . . 513.OA.5Lesson 7Multiplication and Division Facts . . . . . . . . . . . . . . . 593.OA.7Lesson 8Solving Two-Step Word Problems . . . . . . . . . . . . . 673.OA.8Lesson 9Patterns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 763.OA.9Domain 1 Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87DOMAIN 2: NUMBER AND OPERATIONS IN BASE TEN . . . 93Lesson 10 Whole Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . 943.NBT.1Lesson 11Rounding Whole Numbers . . . . . . . . . . . . . . . . . . 1023.NBT.1Lesson 12Addition Properties . . . . . . . . . . . . . . . . . . . . . . . . . 1103.NBT.2Lesson 13Adding 2- and 3-Digit Numbers to 1,000 . . . . . . . . 1193.NBT.2Lesson 14Subtracting 2- and 3-Digit NumbersWithin 1,000 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1293.NBT.2Multiplying by Multiples of 10 . . . . . . . . . . . . . . . . . 1413.NBT.3Lesson 15Domain 2 Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150Performance Task . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155DOMAIN 3: NUMBER AND OPERATIONS – FRACTIONS . . . . . 157Lesson 16 Understanding Fractions . . . . . . . . . . . . . . . . . . . . 1583.NF.1Lesson 17Fractions on a Number Line . . . . . . . . . . . . . . . . . . 1673.NF.2.a, 3.NF.2.bLesson 18Equivalent Fractions . . . . . . . . . . . . . . . . . . . . . . . . 1773.NF.3.a, 3.NF.3.bDuplicating any part of this book is prohibited by law. 2015 Triumph Learning, LLCPerformance Task . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92ii310NASE Mth G3 D1 PDF.indd 220/02/14 12:58 PM
StandardsLesson 19Whole Numbers as Fractions . . . . . . . . . . . . . . . . . 1873.NF.3.cLesson 20Comparing Fractions . . . . . . . . . . . . . . . . . . . . . . . 1963.NF.3.dDomain 3 Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205Performance Task . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 210DOMAIN 4: MEASUREMENT AND DATA . . . . . . . . . . . . . . . . 211Lesson 21 Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2123.MD.1Lesson 22Mass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2233.MD.2Lesson 23Liquid Volume . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2323.MD.2Lesson 24Picture Graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2413.MD.3Lesson 25Bar Graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2503.MD.3Lesson 26Line Plots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2613.MD.4Lesson 27Perimeter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2733.MD.8Lesson 28Understanding Area . . . . . . . . . . . . . . . . . . . . . . . . 2833.MD.5.a, 3.MD.5.b, 3.MD.6, 3.MD.7.aLesson 29Area of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2923.MD.7.a, 3.MD.7.b, 3.MD.7.c, 3.MD.7.dLesson 30Perimeter and Area of Rectangles . . . . . . . . . . . . . 3043.MD.7.b, 3.MD.8Domain 4 Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 314Duplicating any part of this book is prohibited by law. 2015 Triumph Learning, LLCDuplicating any part of this book is prohibited by law. 2015 Triumph Learning, LLCPerformance Task . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 320DOMAIN 5: GEOMETRY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 321Lesson 31 Two-Dimensional Shapes . . . . . . . . . . . . . . . . . . . . 3223.G.1Lesson 323.G.2Equal Areas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 332Domain 5 Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 342Performance Task . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 348Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 349Math Tools . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 357iii310NASE Mth G3 D1 PDF.indd 320/02/14 12:58 PM
LESSON10Whole NumbersStudent Edition pages 94–101LESSON OVERVIEWStandardObjectives3.NBT.1Students will: Use place value to identify the value of digits in four-digit andKey Terms Write numbers in standard form, word form, and expanded formexpanded formplace valuefive-digit numbersDiscussion QuestionsMP4 How does place value help you determine and understand anumber in different forms?MP5 How is it helpful to use place-value models and place-valuecharts to write numbers?MP6 How does the position of a digit in a number affect its value?standard formword formMaterials Math Tool: Place-Value Models,p. C9 (Student Edition, p. 367) Math Tool: Place-Value Chart, p. C10(Student Edition, p. 379)DifferentiationLesson Support Encourage students to use Math Tool: Place-ValueModels and Math Tool: Place-Value Charts as theywork through the lesson. It may be helpful for somestudents to build the number first using models andthen filling in the chart. Point out that the place-value chart shows placevalues for 6-digit numbers. Students are workingwith 4- and 5-digit numbers, so they will not usethe far-left column. If needed, have them cross outcolumn(s) they do not need before recording anumber.Lesson Extension Have students write a 5-digitnumber with a different numeral in each place. Thenhave them create a new number by switching theplaces of two of the digits. Ask students to comparethe two numbers they have made. Ask them tocontinue switching digits and comparing the numbersuntil they have created five different numbers.Challenge students to use what they have learnedabout the numbers to write true/false statements inwhich at least two of the five statements are true.1 GETTING THE IDEALesson OpenerReview the relationship between thousands,hundreds, tens, and ones in a 4-digit number. UseMath Tool: Place-Value Models to show students aunit cube and a tens rod. Ask: How many ones arethere in one ten? (10) Then show students a tens rod22Domain 2: Number And Operations In Base Tenand a hundreds flat. Ask: How many tens are therein one hundred? (10) Next, show a thousands cube.Ask: How many hundreds are there in one thousand?(10) Have students describe the relationship betweendigits in each place of the number 1,348.Duplicating this page is prohibited by law. 2015 Triumph Learning, LLC
ELL Support The cognate for the word digit inSpanish is el dígito.Have students add expanded form, place value,standard form, and word form to their studentdictionaries. As you progress through the lesson, havestudents record examples of expanded form, standardform, and word form.Emphasize the connection between the place-valuemodels and the place-value chart. Ask: How does theplace-value model help you understand the value ofthe digits? Discuss how the value of a digit is relatedto its place in the number.u Example 2Help students recognize that, for numbers greaterthan 999, they write the word name for the number intwo parts. They first write the word name for the digitbefore the comma. Then they write the word name forthe digits that come after the comma. Point out thatthe word names are based on the values of each digit.u Example 3Point out that the number has 5 digits and that thegreatest place value is ten thousands. Have studentscompare the digits in the place-value chart to theexpanded form of the number. Ask: Why do youthink that the value of the tens digit is not shown inexpanded form? (The value of the tens digit is zero.It does not affect the sum of the digits, so you do notneed to show it.) Common Error When a number has a zero as one ofits digits, students may not account for the zero when theywrite the number in expanded form. For example, theymay write 47,903 as 40,000 1 7,000 1 900 1 30.Encourage students to compare each number in theexpanded form to the digits in the number, and the digitsin the place-value chart, to make sure they have recordedthe correct value.2 COACHED EXAMPLEMonitor students as they work through the CoachedExample. Point out that 85,012 has a zero in thehundreds place. Ask: How does the zero affect theword form of the number? Help students correctlycomplete the sentence frames as needed.For answers, see page A15.3 LESSON PRACTICEEncourage students to use the Math Tools to helpthem solve the problems. Problem 4 would be agood problem to use as a quick check for students’understanding of the concepts taught in this lesson.Duplicating this page is prohibited by law. 2015 Triumph Learning, LLCFor problem 6, remind students that the digit 0 is notshown in expanded form. Point out that each numberhas one or two digits with a 0.For answers, see page A15.Lesson 10: Whole Numbers23DOMAIN 2u Example 1 Journal Prompt MP2 How does the comma in thenumber 3,423 help you write the number in word form?
LESSON103.NBT.1Whole Numbers1 GETTING THE IDEAYou can write whole numbers in different ways.Standard form: 1,348Word Form: one thousand, three hundred forty-eightExpanded Form: 1,000 1 300 1 40 1 894ThousandsHundredsTensOnes1,348Domain 2: Number and Operations in Base TenDuplicating any part of this book is prohibited by law. 2015 Triumph Learning, LLCPlace value can help you determine how to write numbers correctly.Place value is the value of a digit based on its position in that number.A place-value chart breaks a number down into individual digits to show their value.This is 1,348 in a place value chart.
Example 1What is the value of each digit in 3,256?StrategyStep 1Use place-value models and a place-value chart.Model 3,256.Show thousands, hundreds, tens, and ones.There are 3 thousands, 2 hundreds, 5 tens, and 6 ones.Step 2Write 3,256 in a place-value chart.Use the place-value models in Step 1 to help.Duplicating any part of this book is prohibited by law. 2015 Triumph Learning, LLCWrite a comma after the number in the thousands place.Step 3ThousandsHundredsTensOnes3,256Find the value of each digit.The digit 3 has a value of 3,000.The digit 2 has the value of 200.The digit 5 has a value of 50.The digit 6 has a value of 6.SolutionThe value of each digit is shown in Step 3.Lesson 10: Whole Numbers 95
Example 2Pia took a plane trip. It was 2,594 miles. Write 2,594 in word form.StrategyStep 1Step 2Use a place-value chart.Write 2,594 in a place-value chart.ThousandsHundredsTensOnes2,594Write the value and the word name of the digit before the comma.The digit before the comma is the 2 in the thousands place.2 thousands 2,000Write a comma after the word thousand.two thousand,Step 3Write the value and the word name for the digits after the comma.The digits after the comma are 594.5 hundreds 5009 tens 904 ones 4five hundred ninety-fourStep 4Write the word name for the whole number.SolutionThe word form of 2,594 is two thousand, five hundred ninety-four.Example 3A stadium holds 47,903 people. What is 47,903 in expanded form?StrategyStep 1Use a place-value chart to find the value of each digit.Write 47,903 in a place-value chart.Write each digit in the chart. Write a comma after the thousands place.96Ten ThousandsThousandsHundredsTensOnes47,903Domain 2: Number and Operations in Base TenDuplicating any part of this book is prohibited by law. 2015 Triumph Learning, LLCtwo thousand, five hundred ninety-four
Step 2Write the value of each digit.40,000Step 37,0009003Write the number in expanded form.Write a 1 sign between the values of each digit.Since the tens digit has a 0, you do not have to list the value.40,000 1 7,000 1 900 1 3SolutionThe expanded form of 47,903 is 40,000 1 7,000 1 900 1 3.2 COACHED EXAMPLEA park had 85,012 visitors. Write 85,012 in word form.Write the number in a place-value chart.Ten ThousandsThousandsHundredsTensOnesWrite the word name for the value of the digits before the comma.Duplicating any part of this book is prohibited by law. 2015 Triumph Learning, LLCWrite a comma after the word thousand.Next, write the word name for the value of the digits after the comma.Write the word name for the whole number.The word form of 85,012 is.Lesson 10: Whole Numbers 97
3 LESSON PRACTICE298A movie theater sold 31,809 tickets. Read each statement about thenumber of tickets. Select True or False.A. The word form is thirty-one thousand, eighty-nine. True FalseB. The value of the digit 3 is 30,000. True FalseC. The expanded form is 30,000 1 1,000 1 800 1 9. True FalseD. The value of the digit 8 is 80. True FalseE. The tens place has a value of 0. True FalseF. The value of the digit 9 is 90. True FalseDraw a line from each place-value model to the number it represents.A. 1,032B. 1,230C. 1,302D. 1,320Domain 2: Number and Operations in Base TenDuplicating any part of this book is prohibited by law. 2015 Triumph Learning, LLC1
3An elephant has a mass of 6,145 kilograms. Write the number ofkilograms in word form. Explain how you wrote the number.4For each number, write an “X” to show the value of the digit 7.Number of licating any part of this book is prohibited by law. 2015 Triumph Learning, LLC91,7405A pet shelter received bags of dog food. It received four thousand,eighty-eight bags. Select True or False for each statement.A. The shelter received 4,088 bags. True FalseB. The number of bags can be written as4,000 1 800 1 8. True FalseC. The value of both 8s in the number ofbags is the same. True FalseD. The expanded form for the number ofbags has no hundreds. True FalseLesson 10: Whole Numbers 99
6Complete the expanded form for each number.Standard FormExpanded Form1 400 140,40440,44440,000 1144,00440,000 1144,0407141 401Felipe and Ava wrote the word form for the number 9,000 100 1.FelipeAvanine thousand, one hundred onenine thousand, one hundred tenPart AWho wrote the number in correct word form?Part BPart CWhat error did the other student make?100Domain 2: Number and Operations in Base TenDuplicating any part of this book is prohibited by law. 2015 Triumph Learning, LLCHow do you know who wrote the correct word form?
89A ballpark has 50,287 seats. Is the word form or expanded form correct?Select Yes or No.A. fifty thousand, two hundred eighty-seven Yes NoB. 50,000 1 2,000 1 80 1 7 Yes NoC. fifty thousand, twenty-eight hundred seven Yes NoD. 50,000 1 200 1 80 1 7 Yes NoCody used models to represent the length of the Missouri River.Write the length of the Missouri River in standard form.Duplicating any part of this book is prohibited by law. 2015 Triumph Learning, LLCmiles10Mr. Diaz drove his car a certain number of miles. Read the clues to findhow many miles he drove. There is a 2 in the hundreds place. The value of the digit in the ten thousands place is 20,000. The digit in the tens place has a value of 60. The digit 8 is used twice in the number.It has a value of 8,000 and a value of 8.Mr. Diaz drovemiles.Lesson 10: Whole Numbers 101
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