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Reteach BookGrade 5PROVIDESTier 1 Intervention for Every Lesson
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Table of ContentsCRITICAL AREA 1: Fluency with Whole Numbers and DecimalsChapter 1: Place Value, Multiplication, and Expressions1.1Place Value and Patterns .R11.2Place Value of Whole Numbers .R21.3Algebra Properties .R31.4Algebra Powers of 10 and Exponents .R41.5Algebra Multiplication Patterns .R51.6Multiply by 1-Digit Numbers .R61.7Multiply by 2-Digit Numbers .R71.8Relate Multiplication to Division.R81.9Problem Solving Multiplication and Division .R91.10 Algebra Numerical Expressions .R101.11 Algebra Evaluate Numerical Expressions .R111.12 Algebra Grouping Symbols .R12Chapter 2: Divide Whole Numbers2.1Place the First Digit .R132.2Divide by 1-Digit Divisors .R142.3Division with 2-Digit Divisors .R152.4Partial Quotients.R162.5Estimate with 2-Digit Divisors .R172.6Divide by 2-Digit Divisors .R182.7Interpret the Remainder .R192.8Adjust Quotients .R202.9Problem Solving Division .R21Reteach Houghton Mifflin Harcourt Publishing CompanyiiiGrade 5
Chapter 3: Add and Subtract Decimals3.1Thousandths .R223.2Place Value of Decimals.R233.3Compare and Order Decimals .R243.4Round Decimals .R253.5Decimal Addition .R263.6Decimal Subtraction .R273.7Estimate Decimal Sums and Differences .R283.8Add Decimals .R293.9Subtract Decimals .R303.10 Algebra Patterns with Decimals .R313.11 Problem Solving Add and Subtract Money .R323.12 Choose a Method .R33Chapter 4: Multiply Decimals4.1Algebra Multiplication Patterns with Decimals .R344.2Multiply Decimals and Whole Numbers .R354.3Multiplication with Decimals and Whole Numbers .R364.4Multiply Using Expanded Form .R374.5Problem Solving Multiply Money .R384.6Decimal Multiplication .R394.7Multiply Decimals .R404.8Zeros in the Product .R41Chapter 5: Divide Decimals5.1Algebra Division Patterns with Decimals.R425.2Divide Decimals by Whole Numbers .R435.3Estimate Quotients .R445.4Division of Decimals by Whole Numbers.R455.5Decimal Division.R465.6Divide Decimals .R475.7Write Zeros in the Dividend .R485.8Problem Solving Decimal Operations .R49Reteach Houghton Mifflin Harcourt Publishing CompanyivGrade 5
CRITICAL AREA 2: Operations with FractionsChapter 6: Add and Subtract Fractions withUnlike Denominators6.1Addition with Unlike Denominators .R506.2Subtraction with Unlike Denominators .R516.3Estimate Fraction Sums and Differences .R526.4Factors .R536.5Common Denominators and Equivalent Fractions .R546.6Add and Subtract Fractions .R556.7Add and Subtract Mixed Numbers .R566.8Subtraction with Renaming .R576.9Algebra Patterns with Fractions .R586.10 Problem Solving Practice Addition and Subtraction .R596.11 Algebra Use Properties of Addition .R60Reteach Houghton Mifflin Harcourt Publishing CompanyvGrade 5
Chapter 7: Multiply Fractions7.1Find Part of a Group .R617.2Multiply Fractions and Whole Numbers .R627.3Fraction and Whole Number Multiplication .R637.4Multiply Fractions .R647.5Compare Fraction Factors and Products .R657.6Fraction Multiplication .R667.7Area and Mixed Numbers.R677.8Compare Mixed Number Factors and Products .R687.9Multiply Mixed Numbers .R697.10 Problem Solving Find Unknown Lengths .R70Chapter 8: Divide Fractions8.1Divide Fractions and Whole Numbers .R718.2Problem Solving Use Multiplication .R728.3Connect Fractions to Division .R738.4Fraction and Whole-Number Division .R748.5Interpret Division with Fractions .R75Reteach Houghton Mifflin Harcourt Publishing CompanyviGrade 5
CRITICAL AREA 3: Geometry and MeasurementChapter 9: Algebra: Patterns and Graphing9.1Line Plots .R769.2Ordered Pairs .R779.3Graph Data .R789.4Line Graphs .R799.5Numerical Patterns .R809.6Problem Solving Find a Rule .R819.7Graph and Analyze Relationships .R82Chapter 10: Convert Units of Measure10.1 Customary Length .R8310.2 Customary Capacity .R8410.3 Weight .R8510.4 Multistep Measurement Problems .R8610.5 Metric Measures .R8710.6 Problem Solving Customary andMetric Conversions .R8810.7 Elapsed Time .R89Reteach Houghton Mifflin Harcourt Publishing CompanyviiGrade 5
Chapter 11: Geometry and Volume11.1 Polygons .R9011.2 Triangles .R9111.3 Quadrilaterals .R9211.4 Three-Dimensional Figures .R9311.5 Unit Cubes and Solid Figures .R9411.6 Understand Volume .R9511.7 Estimate Volume .R9611.8 Volume of Rectangular Prisms .R9711.9 Algebra Apply Volume Formulas .R9811.10 Problem Solving Compare Volumes .R9911.11 Find Volume of Composed Figures .R100Reteach Houghton Mifflin Harcourt Publishing CompanyviiiGrade 5
End-of-Year ResourcesGetting Ready for Grade 6Lesson 1 Compare Fractions and Decimals .GRR1Lesson 2 Order Fractions and Decimals .GRR2Lesson 3 Factor Trees .GRR3Lesson 4 Model Percent .GRR4Lesson 5 Relate Decimals and Percents .GRR5Lesson 6 Fractions, Decimals, and Percents .GRR6Lesson 7 Divide Fractions by a Whole Number .GRR7Lesson 8 Ratios .GRR8Lesson 9 Equivalent Ratios .GRR9Lesson 10 Rates .GRR10Lesson 11 Distance, Rate, and Time .GRR11Lesson 12 Understand Integers.GRR12Lesson 13 Algebra Write and Evaluate Expressions .GRR13Lesson 14 Algebra Understand Inequalities .GRR14Lesson 15 Polygons on a Coordinate Grid .GRR15Lesson 16 Area of a Parallelogram .GRR16Lesson 17 Median and Mode .GRR17Lesson 18 Finding the Average .GRR18Lesson 19 Histograms .GRR19Lesson 20 Analyze Histograms .GRR20Reteach Houghton Mifflin Harcourt Publishing CompanyixGrade 5
Lesson 1.1ReteachNamePlace Value and PatternsYou can use a place-value chart and patterns to write numbers1 of any given number.that are 10 times as much as or101 of the value of the place to its left.Each place to the right is101 of the1 of the1 of the1 of the10101010hundredten 1 of the10tens dredsTens10 times10 times the10 times the10 times the10 times thethe tenthousandshundredstens placeones placethousandsplaceplaceOnesplaceEach place to the left is 10 times the value of the place to its right.1 of 600.Find101 of 6 hundreds is 6 tens .101 of 600 is 60 .So,10Find 10 times as much as 600.10 times as much as 6 hundreds is 6 thousands.So, 10 times as much as 600 is 6,000 .Use place-value patterns to complete the table.Number10 times asmuch as1 ofNumber101. 2005. 9002. 106. 80,0003. 7007. 3,0004. 5,0008. 40Reteach Houghton Mifflin Harcourt Publishing CompanyR110 times asmuch as1 of10Grade 5
Lesson 1.2ReteachNamePlace Value of Whole NumbersYou can use a place-value chart to help you understand whole numbersand the value of each digit. A period is a group of three digits within anumber separated by a comma.Millions PeriodHundredsTensOnes2,Thousands PeriodHundreds3Tens6Ones PeriodOnes7,Hundreds0Tens8Ones9Standard form: 2,367,089Expanded Form: Multiply each digit by its place value, and then writean addition expression.(2 3 1,000,000) 1 (3 3 100,000) 1 (6 3 10,000) 1 (7 3 1,000) 1 (8 3 10) 1 (9 3 1)Word Form: Write the number in words. Notice that the millions and thethousands periods are followed by the period name and a comma.two million, three hundred sixty-seven thousand, eighty-nineTo find the value of an underlined digit, multiply the digit by its place value.In 2,367,089, the value of 2 is 2 3 1,000,000, or 2,000,000.Write the value of the underlined 1466.40,023,032Write the number in two other forms.5.701,245Reteach Houghton Mifflin Harcourt Publishing CompanyR2Grade 5
Lesson 1.3ReteachNameAlgebra PropertiesProperties of operations are characteristics of the operations that are always true.PropertyExamplesCommutative Property ofAddition or MultiplicationAddition: 3 1 4 5 4 1 3Multiplication: 8 3 2 5 2 3 8Associative Property ofAddition or MultiplicationAddition: (1 1 2) 1 3 5 1 1 (2 1 3)Multiplication: 6 3 (7 3 2) 5 (6 3 7) 3 2Distributive Property8 3 (2 1 3) 5 (8 3 2) 1 (8 3 3)Identity Property of Addition9105901353Identity Property of Multiplication 54 3 1 5 541 3 16 5 16Use properties to find 37 1 24 1 43.37 1 24 1 43 5 24 1 37 1 435 24 1 (37 1 43)5 24 1 80Use the Commutative Property of Additionto reorder the addends.Use the Associative Property of Additionto group the addends.Use mental math to add.5 104Grouping 37 and 43 makes the problem easier to solvebecause their sum, 80 , is a multiple of 10.Use properties to find the sum or product.1.31 1 27 1 292.41 3 0 3 33.4 1 (6 1 21)Complete the equation, and tell which property you used.4.(2 3) 1 (2 3 2) 5 2 3 (5 1 2)Reteach Houghton Mifflin Harcourt Publishing Company5.R33 1 5 15Grade 5
Lesson 1.4ReteachNameAlgebra Powers of 10 and ExponentsYou can represent repeated factors with a base and an exponent.Write 10 3 10 3 10 3 10 3 10 3 10 in exponent form.10 is the repeated factor, so 10 is the base.The base is repeated 6 times, so 6 is the exponent.10 3 10 3 10 3 10 3 10 3 10 5 106A base with an exponent can be written in words.106exponentbaseWrite 106 in words.The exponent 6 means “the sixth power.”106 in words is “the sixth power of ten.”You can read 102 in two ways: “ten squared” or “the second power of ten.”You can also read 103 in two ways: “ten cubed” or “the third power of ten.”Write in exponent form and in word form.1.10 3 10 3 10 3 10 3 10 3 10 3 10exponent form:2.10 3 10 3 10exponent form:3.word form:word form:10 3 10 3 10 3 10 3 10exponent form:word form:Find the value.4.104Reteach Houghton Mifflin Harcourt Publishing Company5.2 3 1036.R46 3 102Grade 5
Lesson 1.5ReteachNameAlgebra Multiplication PatternsYou can use basic facts, patterns, and powers of 10 to helpyou multiply whole numbers by multiples of 10, 100, and 1,000.Use mental math and a pattern to find 90 3 6,000. 9 3 6 is a basic fact.9 3 6 5 54 Use basic facts, patterns, and powers of 10 to find 90 3 6,000.9 3 60 5 (9 3 6) 3 1015 54 3 1015 54 3 105 5409 3 600 5 (9 3 6) 3 1025 54 3 1025 54 3 1005 5,4009 3 6,000 5 (9 3 6) 3 1035 54 3 1035 54 3 1,0005 54,00090 3 6,000 5 (9 3 6) 3 (10 3 1,000)5 54 3 1045 54 3 10,0005 540,000So, 90 3 6,000 5 540,000.Use mental math to complete the pattern.1.3.331532.8 3 2 5 163 3 101 5(8 3 2) 3 101 53 3 102 5(8 3 2) 3 102 53 3 103 5(8 3 2) 3 103 54 3 5 5 204.7365(4 3 5) 35 200(7 3 6) 35 420(4 3 5) 35 2,000(7 3 6) 35 4,200(4 3 5) 35 20,000(7 3 6) 35 42,000Reteach Houghton Mifflin Harcourt Publishing CompanyR5Grade 5
Lesson 1.6ReteachNameMultiply by 1-Digit NumbersYou can use place value to help you multiply by 1-digit numbers.Estimate. Then find the product. 378 3 6Estimate: 400 3 6 5 2,400Step 1 Multiply Step 3 Multiply HundredsThousands3Step 2 Multiply thetens.22,68So, 378 3 6 5 2,268.Complete to find the product.1.7 3 472Estimate: 7 3Multiply the ones.Multiply the tens.Multiply the hundreds.1514723 74723 754723 7Estimate. Then find the product.2.Estimate:8633 8Reteach Houghton Mifflin Harcourt Publishing Company3.Estimate:4.8093 8Estimate:9323 7R65.Estimate:2,76737Grade 5
Lesson 1.7ReteachNameMultiply by 2-Digit NumbersYou can use place value and regrouping to multiply.Find 29 3 63.Step 1 Write the problem vertically.Multiply by the ones.2633 2956763 3 9 5 ( 60 3 9) 1 ( 3 3 9)5 540 1 27 , or 567Step 2 Multiply by the tens.2633 295671,26063 3 20 5 ( 60 3 20) 1 ( 3 3 20)5 1,200 1 60 , or 1,260Step 3 Add the partial products.633 2956711,2601,827So, 63 3 29 5 1,827.Complete to find the product.1.573142.763453.57 314.139 376 357 376 31Find 26 3 69. Estimate first.1393121139 3693 26Estimate:Reteach Houghton Mifflin Harcourt Publishing CompanyR7Grade 5
Lesson 1.8ReteachNameRelate Multiplication to DivisionUse the Distributive Property to find the quotient of 56 4 4.Step 1Write a related multiplication sentencefor the division problem.56 4 4 543Step 2Use the Distributive Property to break apartthe product into lesser numbers that aremultiples of the divisor in the division problem.Use a multiple of 10 for one of the multiples.5 56(40 1 16) 5 56(4 3 10) 1 (4 3 4) 5 564 3 (10 1 4) 5 56Step 3To find the unknown factor, find the sum of the numbersinside the parentheses.10 1 4 5 144 3 14 5 56Step 4Write the multiplication sentence with the unknownfactor you found. Then, use the multiplication sentenceto complete the division sentence.56 4 4 5 14Use multiplication and the Distributive Property to find the quotient.1.68 4 4 52.75 4 3 53.96 4 6 54.80 4 5 55.54 4 3 56.105 4 7 5Reteach Houghton Mifflin Harcourt Publishing CompanyR8Grade 5
Lesson 1.9ReteachNameProblem Solving Multiplicationand DivisionIn Brett’s town, there are 128 baseball players on 8 different teams.Each team has an equal number of players. How many playersare on each team?Read the ProblemSolve the ProblemWhat do I need to find?how manyplayers are on eachteam in Brett’s town First, I use the total number of players.128 playersI need to find To find the number of players on eachteam, I will need to solve this problem.?128 4 8 5. To find the quotient, I break 128 intotwo simpler numbers that are easier todivide.What information do I need to use?8 teamstotal of 128 players.There arewith aHow will I use the information?I candividethe total number ofplayers by the number of teams. I can use asimpler problem to1.divide.Susan makes clay pots. She sells125 pots per month to 5 stores. Eachstore buys the same number of pots.How many pots does each store buy?5 (100 4 5) 1 (52.)45125 4 5 5 (100 114 5)5(5 Houghton Mifflin Harcourt Publishing Company)4Lou grows 112 rosemary plants. He shipsan equal number of plants to customers in8 states. How many rosemary plants doeshe ship to each customer?112 4 8 5 (80 155Reteach4885 ( 80 4 8) 1 ( 48 4 8)10 1565 16So, there are 16 players on each team.128 4 8 5 (80 1)484 8) 1 (14 8)45R9Grade 5
Lesson 1.10ReteachNameAlgebra Numerical ExpressionsWrite words to match the expression.6 3 (12 2 4)Think: Many word problems involve finding the cost of a store purchase.Step 1 Examine the expression. What operations are in the expression?multiplication and subtractionStep 2 Describe what each part of the expression can represent whenfinding the cost of a store purchase. What can multiplying by 6 represent?buying 6 of the same itemStep 3 Write the words. Joe buys 6 DVDs. Each DVD costs 12. If Joe receives a 4 discounton each DVD, what is the total amount of money Joe spends?1.What is multiplied and what is subtracted?2.What part of the expression is the price of the item?3.What can subtracting 4 from 12 represent?Write words to match the expression.4.4 3 (10 2 2)Reteach Houghton Mifflin Harcourt Publishing Company5.R103 3 (6 2 1)Grade 5
Lesson 1.11ReteachNameAlgebra Evaluate Numerical ExpressionsA numerical expression is a mathematical phrase thatincludes only numbers and operation symbols.You evaluate the expression when you perform allthe computations to find its value.Order of Operations1. Parentheses2. Multiply and Divide3. Add and SubtractTo evaluate an expression, use the order of operations.Evaluate the expression (10 1 6 3 6) 2 4 3 10.Step 1 Start with computations inside theparentheses.10 1 6 3 6Step 2 Perform the order of operations insidethe parentheses.Multiply and divide from left to right.3610 1 6 3 6 5 10 1Add and subtract from left to right.10 1 36 546Step 3 Rewrite the expression with theparentheses evaluated.46 2 4 3 10Step 4 Multiply and divide from left to right.46 2 4 3 10 5 46 2Step 5 Add and subtract from left to right.46 2 40 5640So, (10 1 6 3 6) 2 4 3 10 5 6.Evaluate the numerical expression.1.8 2 (7 3 1)2.5 2 2 1 12 4 43.8 3 (16 4 2)4.4 3 (28 2 20 4 2)5.(30 2 9 4 3) 4 96.(6 3 6 2 9) 2 9 4 37.11 4 (8 1 9 4 3)8.13 3 4 2 65 4 139.9 1 4 3 6 2 65 4 13Reteach Houghton Mifflin Harcourt Publishing CompanyR11Grade 5
Lesson 1.12ReteachNameAlgebra Grouping SymbolsParentheses ( ), brackets [ ], and braces { }, are different groupingsymbols used in expressions. To evaluate an expression with differentgrouping symbols, perform the operation in the innermost set ofgrouping symbols first. Then evaluate the expression from the inside out.Evaluate the expression 2 3 [(9 3 4) 2 (17 2 6)].Step 1 Perform the operations in the parentheses first.2 3 [(9 3 4) 2 (17 2 6)]23[36211]Step 2 Next perform the operations in the brackets.2 3 [ 36 2 11 ]2325Step 3 Then multiply.2 3 25 5 50So, 2 3 [(9 3 4) 2 (17 2 6)] 5 50Evaluate the numerical expression.1.4.4 3 [(15 2 6) 3 (7 2 3)]4 3 [9 3]43[]5 1 [(10 2 2) 1 (4 2 1)]Reteach Houghton Mifflin Harcourt Publishing Company2.40 2 [(8 3 7) 2 (5 3 6)]3.60 4 [(20 2 6) 1 (14 2 8)]5.3 3 [(9 1 4) 2 (2 3 6)]6.32 4 [(7 3 2) 2 (2 3 5)]R12Grade 5
Lesson 2.1ReteachNamePlace the First DigitWhen you divide, you can use estimation or place valueto place the first digit of the quotient.Divide.6qw1,266 Estimate. 1,200 4 6 5 200, so the first digit of the quotient isin the hundreds place. Divide the hundreds. Divide the tens. Divide the ones.2116qw1,266212062606So, 1,266 4 6 5 211.260Since 211 is close to the estimate, 200, the answer is reasonable.Divide.8,895 4 81,111 r78qw8,895280828092815287 Use place value to place the first digit. Look at the first digit.If the first digit is less than the divisor, then the first digit ofthe quotient will be in the hundreds place.If the first digit is greater than or equal to the divisor, thenthe first digit of the quotient will be in the thousands place. Since 8 thousands can be shared among 8 groups, the first digitof the quotient will be in the thousands place. Now divide.So, 8,895 4 8 is 1,111 8qw2,8696.6qw1,2997.4qw8938.7qw4,418Reteach Houghton Mifflin Harcourt Publishing CompanyR13Grade 5
Lesson 2.2ReteachNameDivide by 1-Digit DivisorsYou can use compatible numbers to help you place the first digitin the quotient. Then you can divide and check your answer.Divide. 4qw757Step 2 Divide.Step 1 Estimate withcompatible numbers todecide where to place thefirst digit.757 4 4Step 3 Check your answer.1893 47561 1757189 r14qw7572435232372 361800 4 4 5 200The first digit of the quotientis in the hundreds place.quotientdivisorremainderdividendSince 189 is close to the estimate of 200, the answer is reasonable.So, 757 4 4 is 189 r1.Divide. Check your 16.7qw456Reteach Houghton Mifflin Harcourt Publishing CompanyR14Grade 5
Lesson 2.3ReteachNameDivision with 2-Digit DivisorsYou can use base-ten blocks to model division with 2-digit divisors.Divide. 154 4 11Step 1 Model 154 with base-ten blocks.Step 2 Make equal groups of 11. Each groupshould contain1ten and1one.You can make 4 groups of 11 withoutregrouping.10 tens .Regroup 1 ten as 10 ones .Step 3 Regroup 1 hundred asStep 4 Use the regrouped blocks to make asmany groups of 11 as possible. Then count thetotal number of groups.There are14groups. So, 154 4 11 514.Divide. Use base-ten blocks.1.192 4 12Reteach Houghton Mifflin Harcourt Publishing Company2.R15182 4 14Grade 5
Lesson 2.4ReteachNamePartial QuotientsDivide. Use partial quotients.858 4 57QuotientStep 1 Estimate the number of groups of57 that are in 858. You know 57 3 10 5 570.Since 570 , 858, at least 10 groups of 57are in 858. Write 10 in the quotient column,because 10 groups of the divisor, 57, are inthe dividend, 858.858102882228604288Step 2 Now estimate the number of groupsof 57 that are in 288. You know 60 3 4 5 240.So at least 4 groups of 57 are in 288. Subtract228 from 288, because 57 3 4 5 228. Write4 in the quotient column, because 4 groups ofthe divisor, 57, are in 288.Step 3 Identify the number of groups of57 that are in 60. 57 3 1 5 57, so there is1 group of 57 in 60. Write 1 in the quotientcolumn.257060remainder257Step 4 Find the total number of groups of thedivisor, 57, that are in the dividend, 858, byadding the numbers in the quotient column.Include the remainder in your answer.31115Answer: 15 r3Divide. Use partial quotients.1.17qw4762.14qw3653.25qw7534.462 4 115.1,913 4 476.1,085 4 32Reteach Houghton Mifflin Harcourt Publishing CompanyR16Grade 5
Lesson 2.5ReteachNameEstimate with 2-Digit DivisorsYou can use compatible numbers to estimate quotients. Compatiblenumbers are numbers that are easy to compute mentally.To find two estimates with compatible numbers, first round thedivisor. Then list multiples of the rounded divisor until you find thetwo multiples that are closest to the dividend. Use the one less thanand the one greater than the dividend.Use compatible numbers to find two estimates. 4,125 4 49Step 1 Round the divisor to the nearest ten.49 rounds to 50 .Step 2 List multiples of 50 until you get the two closest to the dividend, 4,125.Some multiples of 50 are:5001,0001,5002,0002,5003,0003,5004,0004,000 and 4,500 are closest to the dividend.4,500Step 3 Divide the compatible numbers to estimate the quotient.4,000 4 50 5 804,500 4 50 5 90The more reasonable estimate is 4,000 4 50 5 80,because 4,000 is closer to 4,125 than 4,500 is.Use compatible numbers to find two estimates.1.42qw1,5782.4.4,093 4 635.73qw4,8584,785 4 793.54qw3436.7,459 4 949.218 4 29Use compatible numbers to estimate the quotient.7.847 4 37Reteach Houghton Mifflin Harcourt Publishing Company8.6,577 4 89R17Grade 5
Lesson 2.6ReteachNameDivide by 2-Digit DivisorsWhen you divide by
1.3 Algebra Properties .R3 1.4 Algebra Powers of 10 and Exponents . Use mental math to add. Grouping 37 and 43 makes the problem easier to solve because their sum, 80, is a multiple of 10. 37 1 24 1 43 5 24 1371 43 5 24 1 (37 1 43) 5 24 180
