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Standards SuccessCommon Core State Standards Companion

for use with Saxon Math Intermediate 5

Intermediate 5

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Table of Contents

Instructions for Using This Book

Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i

Saxon Math Intermediate 5 Table of Contents with Common Core State Standards References . . . . . . . . . . . . . . . . . . . . . . . . . . . .1

Correlation to the Common Core State Standards . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .13

Lesson Extension ActivitiesLesson 68 Extension Activity 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .19 • Activity Master 1Lesson 76 Extension Activity 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .21 • Activity Master 2 Investigation 8 Extension Activity 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .23 • Activity Master 3Lesson 86 Extension Activity 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .25 • Activity Master 4Lesson 87 Extension Activity 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .27 • Activity Master 5Lesson 92 Extension Activity 6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .29 • Activity Master 6Lesson 103 Extension Activity 7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .31 • Activity Master 7Lesson 106 Extension Activity 8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .33 • Activity Master 8Lesson 119 Extension Activity 9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .35 • Activity Master 9Lesson 120 Extension Activity 10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .37 • Activity Master 10

Extension TestsExtension Test 1 – For use with Cumulative Test 13 Extension Test 2 – For use with Cumulative Test 15 Extension Test 3 – For use with Cumulative Test 15 Extension Test 4 – For use with Cumulative Test 17Extension Test 5 – For use with Cumulative Test 18 Extension Test 6 – For use with Cumulative Test 18 Extension Test 7 – For use with Cumulative Test 20 Extension Test 8 – For use with Cumulative Test 21 Extension Test 9 – For use with Cumulative Test 23 Extension Test 10 – For use with Cumulative Test 23

Lesson Extension Activity Answers and Activity Master Answers . . . . . . . . . . . . . . . . . . .49

Extension Test Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .50

© HMH Supplemental Publishers Inc.Saxon Math Intermediate 5



Instructions for Using This Book

Educators who use Saxon Math know that the programs help students become competent and confident learners. Because of the incremental nature of the program, some lessons provide foundational instruction necessary for developing more advanced skills used in later lessons. The Power Up, Problem Solving, and Written Practice sections of each lesson provide important review and practice needed for mastery. For those reasons, it is essential to teach all the lessons in the correct order and to include all parts of the lesson in the daily instruction.

The program Table of Contents included in this book shows references to the primary Common Core State Standards domain and cluster or Mathematical Practice addressed by each lesson and investigation. The Lesson Extension Activities provided in this book will help reinforce that knowledge. Each of these activities was developed to spring from the instruction of the designated lesson or investigation.

It is recommended that you review the Table of Contents to understand where the extension lessons are to be integrated into the program. Then place a reminder in the Teacher’s Manual, such as a colored flag or sticker, on the lesson or investigation with which the extension should be presented. Before the day the extension is to be taught, photocopy both the Lesson Extension Activity and Activity Master (one copy of each per student). The pages are perforated to make removal and copying easier. At this time, also check the extension activity for any materials that are required and be prepared for each student to have the necessary items. The problems on the Activity Masters may be solved directly following the Lesson Extension Activity, or may be used as additional practice at a later time. Continued practice of these activities (with appropriate modifications) throughout the remainder of the school year will provide reinforcement.

Extension Tests are provided to ensure that all Common Core objectives are evaluated. These multiple-choice assessments should be given with specified Cumulative Tests, as noted in the Table of Contents. Before test day, photocopy one copy of the Extension Test for each student’s use.

Best wishes for a successful school year!

© HMH Supplemental Publishers Inc. Saxon Math Intermediate 5



Saxon Math Intermediate 5 Standards Success Overview

Common Core State Standards and the Saxon Math PedagogyThe Saxon Math philosophy stresses that incremental and integrated instruction, with the opportunity to practice and internalize concepts, leads to successful mathematics understanding. This pedagogy aligns with the requirements of the Common Core State Standards, which emphasize that, in each grade, students will be instructed to mastery in specified math concepts that serve as a basis for future learning. For example, in Grade 5 students develop greater fluency in multiplication and division, including the manipulation of fractions, that can be carried forward to succeeding grades. Having established this solid foundation, the students will have the necessary tools (speed, accuracy, and confidence in their ability) to tackle increasingly complex problem solving.

The requisites featured in the Mathematical Practices are incorporated throughout the Saxon lessons and activities. For example, students are asked to share ideas and to think critically, to look for patterns, and to make connections in mathematical reasoning.

What Saxon Math Intermediate 5 Standards Success ProvidesSaxon Math Intermediate 5 Standards Success is a companion to Saxon Math Intermediate 5. The first section, the Table of Contents, lists the Common Core focus of each lesson. The second section, Correlation of Saxon Math Intermediate 5 to the Common Core State Standards for Mathematics Grade 5, demonstrates the depth of coverage provided by the Saxon Math Intermediate 5 program. The remaining sections, Lesson Extension Activities and Extension Tests, provide additional reinforcement for selected Common Core standards.

Saxon Math Intermediate 5 Table of Contents

The Intermediate 5 Table of Contents lists the primary Common Core domain and cluster addressed in the New Concept of each lesson and that section’s Investigation. Some lessons focus on a Mathematical Practice, such as a problem-solving technique. The primary Common Core State Standards focuses in the Power Up and Problem Solving activities of the ten lessons are listed on a chart at the bottom of each page of the Table of Contents.

Correlation of Saxon Math Intermediate 5 to the Common Core State Standards for Mathematics Grade 5

The correlation lists the specific Saxon Math Intermediate 5 components addressing each standard. This correlation is divided into three sections: Power Up (including Power Up and Problem Solving), Lessons (including New Concepts, Investigations, and Written Practices), and Other (including Calculator Activities, Performance Tasks, and Test Day Activities).

Lesson Extension Activities and Extension Tests

Lesson Extension Activities (with Activity Masters on the back) and Extension Tests are listed in the Table of Contents where they are intended to be used. These additional activities further address and reinforce the Common Core standards. Lesson Extension Activities, Activity Masters, and Extension Tests begin on page 19 of this book.

Saxon Math Intermediate 5 i© HMH Supplemental Publishers Inc.



Domains, Clusters, and Mathematical Practices for Grade 5The Common Core State Standards are separated into domains, which are divided into clusters.

Grade 5 Domains and ClustersLarge groups of connected standards are referred to as domains. In Grade 5 there are five domains. Groups of related standards within a domain are referred to as clusters.

5.OA–Operations and Algebraic Thinking1st cluster: Write and interpret numerical expressions.2nd cluster: Analyze patterns and relationships.

5.NBT–Number and Operations in Base Ten1st cluster: Understand the place value system.2nd cluster: Perform operations with multi-digit whole numbers and with decimals

to hundredths.

5.NF–Number and Operations—Fractions1st cluster: Use equivalent fractions as a strategy to add and subtract fractions.2nd cluster: Apply and extend previous understandings of multiplication and division

to multiply and divide fractions.

5.MD–Measurement and Data1st cluster: Convert like measurement units within a given measurement system.2nd cluster: Represent and interpret data.3rd cluster: Geometric measurement: understand concepts of volume and relate

volume to multiplication and to addition.

5.G–Geometry1st cluster: Graph points on the coordinate plane to solve real-world and

mathematical problems.2nd cluster: Classify two-dimensional figures into categories based on their properties.

Mathematical PracticesThe Standards for Mathematical Practice list the following essential competencies that students will develop throughout their mathematics education.

CC.K–12.MP.1 Make sense of problems and persevere in solving them.CC.K–12.MP.2 Reason abstractly and quantitatively.CC.K–12.MP.3 Construct viable arguments and critique the reasoning of others.CC.K–12.MP.4 Model with mathematics.CC.K–12.MP.5 Use appropriate tools strategically.CC.K–12.MP.6 Attend to precision.CC.K–12.MP.7 Look for and make use of structure.CC.K–12.MP.8 Look for and express regularity in repeated reasoning.

For the full text of the Common Core State Standards and a comprehensive correlation, including Mathematical Practices, see the Correlation of Saxon Math Intermediate 5 to the Common Core State Standards for Mathematics Grade 5 on pages 13–18.

ii Saxon Math Intermediate 5© HMH Supplemental Publishers Inc.


Ta b l e o f C o n T e n T sIntermediate 5


MP Mathematical Practices OA Operations and Algebraic Thinking NBT Number and Operations in Base TenNF Number and Operations—Fractions MD Measurement and Data G Geometry

Section 1 • Lessons 1–10, Investigation 1

Lesson

Common Core State Standards Focus of Lesson

Problem Solving Overview CC.K–12.MP.1

1• Sequences• Digits

CC.K–12.MP.7

2 • Even and Odd Numbers CC.K–12.MP.7

3 • Using Money to Illustrate Place Value CC.5.NBT (1st cluster)

4 • Comparing Whole Numbers CC.K–12.MP.2

5 • Naming Whole Numbers and Money CC.K–12.MP.2

6 • Adding Whole Numbers CC.K–12.MP.6

7• Writing and Comparing Numbers Through

Hundred Thousands• Ordinal Numbers

CC.5.NBT (1st cluster)

8 • Relationship Between Addition and Subtraction CC.K–12.MP.2

9 • Practicing the Subtraction Algorithm CC.K–12.MP.4

10 • Missing Addends CC.K–12.MP.2

Inv. 1 • Translating and Writing Word Problems CC.K–12.MP.1

Cumulative Assessment

The following table shows a CCSS (Common Core State Standards) focus of the Power Up (PU) and the Problem Solving (PS) activities, which appear at the beginning of each lesson.

CCSS Reference 1 2 3 4 5 6 7 8 9 10

CC.K–12.MP.1 PS PS PS PS PS PS PS PS PS PS

CC.K–12.MP.3 PS

Correlation references are read as follows: CC indicates Common Core, the number following is the grade, the letters indicate the domain, and the cluster indicates the particular group of related standards. Mathematical Practices are described in the same way for all grades K–12.

Saxon Math Intermediate 5 1© HMH Supplemental Publishers Inc.

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Lesson CCSS Focus of Lesson

11 • Word Problems About Combining CC.K–12.MP.1

12• Lines• Number Lines• Tally Marks

CC.K–12.MP.1

13• Multiplication as Repeated Addition• Adding and Subtracting Dollars and Cents

CC.5.OA (1st cluster)

14 • Missing Numbers in Subtraction CC.K–12.MP.2

15 • Making a Multiplication Table CC.K–12.MP.7


16 • Word Problems About Separating CC.K–12.MP.1

17 • Multiplying by One-Digit Numbers CC.5.NBT (2nd cluster)

18 • Multiplying Three Factors and Missing Factors CC.K–12.MP.2

19 • Relationship Between Multiplication and Division CC.K–12.MP.2

20 • Three Ways to Show Division CC.K–12.MP.2

Inv. 2 • Fractions: Halves, Fourths, and Tenths CC.K–12.MP.8


The following table shows a CCSS focus of the Power Up (PU) and the Problem Solving (PS) activities, which appear at the beginning of each lesson.

CCSS Reference 11 12 13 14 15 16 17 18 19 20


CC.K–12.MP.2 PU PS

CC.K–12.MP.6 PU PU PU PU PU

CC.5.MD (1st cluster) PU PU PU

2 Saxon Math Intermediate 5© HMH Supplemental Publishers Inc.






21 • Word Problems About Equal Groups CC.K–12.MP.1

22 • Division With and Without Remainders CC.K–12.MP.7

23 • Recognizing Halves CC.5.NF (1st cluster)

24 • Parentheses and the Associative Property CC.5.OA (1st cluster)

25 • Listing the Factors of Whole Numbers CC.K–12.MP.8


26 • Division Algorithm CC.5.NBT (2nd cluster)

27 • Reading Scales CC.K–12.MP.5

28 • Measuring Time and Elapsed Time CC.K–12.MP.5

29 • Multiplying by Multiples of 10 and 100 CC.5.NBT (1st cluster)

30 • Interpreting Pictures of Fractions, Decimals, and Percents CC.K–12.MP.4

Inv. 3 • Fractions: Thirds, Fifths, and Eighths CC.K–12.MP.3



CCSS Reference 21 22 23 24 25 26 27 28 29 30


CC.K–12.MP.2 PU PU PU PU

CC.K–12.MP.6 PU


CC.5.NBT (2nd cluster) PU PU PU PU PU

CC.5.MD (1st cluster) PU PU PU PU PU






31• Pairs of Lines• Angles

CC.K–12.MP.3

32 • Polygons CC.5.G (2nd cluster)

33 • Rounding Numbers and Estimating CC.K–12.MP.5

34 • Division with Zeros in the Quotient CC.K–12.MP.1

35 • Word Problems About Comparing and Elapsed Time CC.K–12.MP.1


36 • Classifying Triangles CC.5.G (2nd cluster)

37 • Drawing Pictures of Fractions CC.K–12.MP.3

38 • Fractions and Mixed Numbers on a Number Line CC.K–12.MP.4

39 • Comparing Fractions by Drawing Pictures CC.5.NF (1st cluster)

40 • Writing Quotients with Mixed Numbers CC.5.NF (2nd cluster)

Inv. 4 • Pattern Recognition CC.5.OA (2nd cluster)



CCSS Reference 31 32 33 34 35 36 37 38 39 40


CC.K–12.MP.2 PU PU PU PU PU PU PU

CC.K–12.MP.4 PS

CC.K–12.MP.6 PU PU

CC.5.MD (1st cluster) PU PU PU PU







41• Adding and Subtracting Fractions with

Common DenominatorsCC.5.NF (1st cluster)

42• Short Division• Divisibility by 3, 6, and 9

CC.K–12.MP.3

43 • More Arithmetic with Mixed Numbers CC.5.NF (1st cluster)

44 • Measuring Lengths with a Ruler CC.5.MD (1st cluster)

45 • Classifying Quadrilaterals CC.5.G (2nd cluster)


46 • Word Problems About a Fraction of a Group CC.5.NF (2nd cluster)

47 • Simplifying Mixed Measures CC.5.OA (2nd cluster)

48• Reading and Writing Whole Numbers

in Expanded NotationCC.5.OA (1st cluster)

49 • Solving Multiple-Step Word Problems CC.5.OA (1st cluster)

50 • Finding an Average CC.K–12.MP.2

Inv. 5 • Organizing and Analyzing Data CC.K–12.MP.1



CCSS Reference 41 42 43 44 45 46 47 48 49 50


CC.K–12.MP.2 PU PU PU PU PU PU PU PU

CC.K–12.MP.3 PS

CC.K–12.MP.4 PS PS

CC.K–12.MP.5 PU PU PU


CC.5.NBT (2nd cluster) PU

CC.5.NF (2nd cluster) PU PU PU

CC.5.MD (1st cluster) PU PU PU PU

CC.5.G (2nd cluster) PU






51 • Multiplying by Two-Digit Numbers CC.5.OA (1st cluster)

52 • Naming Numbers Through Hundred Billions CC.5.NBT (1st cluster)

53• Perimeter• Measures of a Circle

CC.K–12.MP.1

54 • Dividing by Multiples of 10 CC.5.NBT (2nd cluster)

55 • Multiplying by Three-Digit Numbers CC.5.NBT (2nd cluster)


56 • Multiplying by Three-Digit Numbers that Include Zero CC.5.OA (2nd cluster)

57 • Probability CC.K–12.MP.1

58 • Writing Quotients with Mixed Numbers CC.5.NF (2nd cluster)

59 • Subtracting a Fraction from 1 CC.5.NF (1st cluster)

60 • Finding a Fraction to Complete a Whole CC.5.NF (1st cluster)

Inv. 6 • Line Graphs CC.5.OA (2nd cluster)



CCSS Reference 51 52 53 54 55 56 57 58 59 60



CC.K–12.MP.3 PS


CC.K–12.MP.6 PU

CC.5.NBT (2nd cluster) PU PU PU PU

CC.5.MD (1st cluster) PU PU PU PU PU PU








61 • Using Letters to Identify Geometric Figures CC.K–12.MP.6

62• Estimating Arithmetic Answers with Rounded

and Compatible NumbersCC.K–12.MP.5

63• Subtracting a Fraction from a Whole Number

Greater Than 1CC.5.NF (1st cluster)

64 • Using Money to Model Decimal Numbers CC.5.NBT (1st cluster)

65 • Decimal Parts of a Meter CC.5.MD (1st cluster)


66 • Reading a Centimeter Scale CC.5.MD (1st cluster)

67 • Writing Tenths and Hundredths as Decimal Numbers CC.5.NBT (1st cluster)

68

• Naming Decimal NumbersLesson Extension Activity 1 (p 19):• Writing Decimals to Thousandths Using

Expanded Form


69 • Comparing and Ordering Decimal Numbers CC.K–12.MP.2

70 • Writing Equivalent Decimal Numbers CC.K–12.MP.2

Inv. 7 • Displaying Data CC.K–12.MP.4

Cumulative AssessmentExtension Test 1


CCSS Reference 61 62 63 64 65 66 67 68 69 70


CC.K–12.MP.2 PU PU PU PS PU


CC.K–12.MP.4 PS

CC.K–12.MP.5 PU PS PU

CC.K–12.MP.6 PU

CC.5.NBT (2nd cluster) PU PU PU PU

CC.5.NF (1st cluster) PU PU PU PU PU PU

CC.5.NF (2nd cluster) PU PU PU PU PU

CC.5.MD (1st cluster) PU PU







71 • Fractions, Decimals, and Percents CC.5.NBT (1st cluster)

72 • Area, Part 1 CC.K–12.MP.2

73 • Adding and Subtracting Decimal Numbers CC.5.NBT (2nd cluster)

74 • Units of Length CC.5.MD (2nd cluster)

75 • Changing Improper Fractions to Whole or Mixed Numbers CC.5.NF (1st cluster)


76• Multiplying FractionsLesson Extension Activity 2 (p 21):• Finding Area of a Rectangle with Fractional Side Lengths

CC.5.NF (2nd cluster)

77 • Converting Units of Weight and Mass CC.5.MD (1st cluster)

78 • Exponents and Square Roots CC.5.OA (1st cluster)

79 • Finding Equivalent Fractions by Multiplying by 1 CC.K–12.MP.8

80 • Prime and Composite Numbers CC.K–12.MP.8

Inv. 8

• Graphing Points on a Coordinate Plane• TransformationsLesson Extension Activity 3 (p 23):• Graphing and Analyzing Relationships

CC.5.G (1st cluster)

CC.5.OA (2nd cluster)

Cumulative AssessmentExtension Test 2Extension Test 3


CCSS Reference 71 72 73 74 75 76 77 78 79 80



CC.K–12.MP.3 PS PS PS




CC.5.NF (1st cluster) PU


CC.5.MD (1st cluster) PU PU

CC.5.MD (3rd cluster) PS







81 • Reducing Fractions, Part 1 CC.K–12.MP.8

82 • Greatest Common Factor (GCF) CC.K–12.MP.8

83 • Properties of Geometric Solids CC.K–12.MP.3

84 • Mean, Median, Mode, and Range CC.K–12.MP.4

85 • Units of Capacity CC.5.MD (1st cluster)


86• Multiplying Fractions and Whole NumbersLesson Extension Activity 4 (p 25):• Using Fraction Operations with Line Plots


CC.5.MD (2nd cluster)

87

• Using Manipulatives and Sketches to Divide FractionsLesson Extension Activity 5 (p 27):• Dividing a Fraction by a Whole Number and

Dividing a Whole Number by a Fraction


88 • Transformations CC.K–12.MP.6

89 • Analyzing Prisms CC.K–12.MP.3

90 • Reducing Fractions, Part 2 CC.K–12.MP.8

Inv. 9 • Performing Probability Experiments CC.K–12.MP.1



CCSS Reference 81 82 83 84 85 86 87 88 89 90


CC.K–12.MP.2 PS


CC.5.OA (1st cluster) PU PU PU PU PU PU PU PU PU

CC.5.NF (2nd cluster) PU PU

CC.5.MD (1st cluster) PU







91 • Simplifying Improper Fractions CC.5.NF (1st cluster)

92• Dividing by Two-Digit NumbersLesson Extension Activity 6 (p 29):• Dividing by Two-Digit Numbers Using Models

CC.5.NBT (2nd cluster)

93 • Comparative Graphs CC.K–12.MP.4

94 • Using Estimation When Dividing by Two-Digit Numbers CC.5.NBT (2nd cluster)

95 • Reciprocals CC.5.NF (2nd cluster)


96 • Using Reciprocals to Divide Fractions CC.5.NF (2nd cluster)

97 • Ratios CC.K–12.MP.4

98 • Temperature CC.K–12.MP.5

99• Adding and Subtracting Whole Numbers

and Decimal NumbersCC.5.NBT (2nd cluster)

100 • Simplifying Decimal Numbers CC.5.NBT (1st cluster)

Inv. 10 • Measuring Angles CC.K–12.MP.5



CCSS Reference 91 92 93 94 95 96 97 98 99 100


CC.K–12.MP.3 PS

CC.K–12.MP.4 PS

CC.K–12.MP.5 PS


CC.5.NF (2nd cluster) PU PU PU PU PU PU PU









101 • Rounding Mixed Numbers CC.K–12.MP.8

102 • Subtracting Decimal Numbers Using Zeros CC.5.NBT (2nd cluster)

103

• VolumeLesson Extension Activity 7 (p 31):• Using Formulas to Find Volume of Prisms

and Composed Figures

CC.5.MD (3rd cluster)

104• Rounding Decimal Numbers to the Nearest

Whole NumberCC.5.NBT (1st cluster)

105 • Symmetry and Transformations CC.K–12.MP.3


106

• Reading and Ordering Decimal Numbers Through Ten-Thousandths

Lesson Extension Activity 8 (p 33):• Rounding Decimal Numbers


107 • Using Percent to Name Part of a Group CC.K–12.MP.4

108 • Schedules CC.K–12.MP.4

109 • Multiplying Decimal Numbers CC.5.NBT (2nd cluster)

110• Multiplying Decimal Numbers: Using Zeros

as PlaceholdersCC.5.NBT (2nd cluster)

Inv. 11 • Scale Drawings CC.K–12.MP.4



CCSS Reference 101 102 103 104 105 106 107 108 109 110



CC.K–12.MP.5 PS


CC.5.NBT (1st cluster) PU



CC.5.MD (3rd cluster) PS PS PS






111• Multiplying Decimal Numbers by 10, by 100,

and by 1000CC.5.NBT (2nd cluster)

112 • Finding the Least Common Multiple of Two Numbers CC.K–12.MP.8

113 • Writing Mixed Numbers as Improper Fractions CC.K–12.MP.8

114 • Using Formulas CC.5.MD (3rd cluster)

115 • Area, Part 2 CC.K–12.MP.2


116• Finding Common Denominators to Add, Subtract,

and Compare FractionsCC.5.NF (1st cluster)

117 • Dividing a Decimal Number by a Whole Number CC.5.NBT (2nd cluster)

118 • More on Dividing Decimal Numbers CC.5.NBT (2nd cluster)

119

• Dividing by a Decimal NumberLesson Extension Activity 9 (p 35):• Comparing Fraction Factors and Products

and Mixed Number Factors and Products

CC.5.NBT (2nd cluster)


120• Multiplying Mixed NumbersLesson Extension Activity 10 (p 37):• Multiplying Mixed Numbers


Inv. 12 • Tessellations CC.K–12.MP.3



CCSS Reference 111 112 113 114 115 116 117 118 119 120


CC.K–12.MP.2 PU PU PU PU PU PU PU

CC.K–12.MP.3 PS


CC.K–12.MP.5 PS


CC.5.NF (1st cluster) PU

CC.5.MD (1st cluster) PU PU PU PU PU






Key: BT: Benchmark Test ET: Extension Test LXA: Lesson Extension Activity PU: Power UpCA: Calculator Activity Inv: Investigation PS: Problem Solving TDA: Test-Day ActivityCT: Cumulative Test L: Lesson PT: Performance Task WP: Written PracticeECE: End-of-Course Exam LS: Learning Station

Correlation of Saxon Math Intermediate 5 to the Common Core State Standards for Mathematics Grade 5

Mathematical Practices – These standards are covered throughout the program; the following are examples.

Make sense of problems and persevere in solving 1. them.

Power Up: PS17, PS25, PS28, PS32, PS33, PS35, PS39, PS45, PS46, PS51, PS53, PS55, PS57, PS58, PS60, PS65, PS74, PS79, PS83, PS99, PS100, PS106, PS109, PS113Lessons: Problem Solving Overview (pages 1–6), Inv1, L11, L16, L21, L35, L46, Inv5, L60

Reason abstractly and quantitatively.2. Power Up: PU13, PS16, PU21, PU22, PU23, PU29, PU31, PU32, PU33, PU34, PU35, PU39, PU40, PU42, PU43, PU44, PU45, PU46, PU47, PU48, PU50, PU53, PU54, PU55, PU56, PU59, PU62, PU63, PU64, PS65, PU68, PU73, PU75, PU77, PU79, PS90, PU103, PU104, PU105, PU108, PU110, PU112, PU113, PU115, PU116, PU117, PU119, PU120Lessons: Inv1, L11, L14, L16, L21, L24, Inv4, L72, L103, L114, L115Other: PT5

Construct viable arguments and critique the 3. reasoning of others.

Power Up: PS7, PS43, PS51, PS63, PS66, PS73, PS74, PS76, PS83, PS90, PS100, PS113Lessons: WP22, L24, WP27, L29, Inv3, WP34, L36, L37, L42, WP42, WP43, L89, Inv9Other: PT1, PT5, PT9

Model with mathematics.4. Power Up: PS40, PS45, PS49, PS52, PS55, PS67, PS91, PS114, PS115Lessons: Inv2, L30, Inv3, L35, L38, L39, L40, Inv4, L41, Inv5, L60, Inv6, L64, L68, Inv7, L84, L97, L107, L108, Inv11

Use appropriate tools strategically.5. Power Up: PU41, PU43, PU49, PU61, PS65, PU70, PU71, PU76, PU78, PU80, PS95, PS104, PS111Lessons: L27, WP27, L28, Inv3, L43, L44, WP49, L55, L72, L98, Inv10Other: CA11, CA13, CA22, CA24, CA49, CA51, CA72, CA76, CA81, CA89, CA96

Attend to precision.6. Power Up: PU15, PU16, PU17, PU18, PU19, PU26, PU38, PU40, PU44, PU48, PU55, PU66, PU72, PU77, PU96, PU98, PU101, PU102, PU106, PU107, PU109Lessons: L27, L44, WP45, WP46, L47, WP47, Inv5, L53, L56, Inv6, L61, L65, L66, Inv7, L73, L74, L77, Inv8, L85, L88, L109, L110

Look for and make use of structure.7. Lessons: L15, L22, L24, WP24, L26, L34, Inv4, L48, L51, L54, L55, L56, L59, L75, L78, L86, L92, L94, L102, L106, L116, L117, L118, L119, L120

Look for and express regularity in repeated 8. reasoning.

Power Up: PU25, PU26, PU27, PU28Lessons: L13, Inv2, L22, L25, L29, L35, L42, WP43, L59, L70, L71, L76, L79, L80, L81, L82, L90, L91, L95, L100, L101, L104, L111, L112, L113

© HMH Supplemental Publishers Inc.Saxon Math Intermediate 5 13

I5_MNLAEAN628165_CORR.indd 13 3/17/11 10:09:29 AM


Common Core State Standards Saxon Math Intermediate 5 Italic references indicate foundational.

Operations and Algebraic Thinking 5.OA

Write and interpret numerical expressions.

Use parentheses, brackets, or braces in numerical 1. expressions, and evaluate expressions with these symbols.

Power Up: PU82, PU83, PU84, PU85, PU86, PU87, PU88, PU89, PU90Lessons: L24, WP24, WP25, WP27, WP28, WP29, WP31, WP33, WP35, WP37, WP38, WP40, WP41, WP42, WP44, WP47, L48, WP48, L49, WP49, WP50, L51, WP51, L52, WP52, WP53, WP55, WP57, WP62, WP63, WP65, WP66, WP67, WP68, WP69, WP70, WP71, WP72, WP77, L78, WP79, WP81, WP85, WP86, WP90, WP91, WP93, WP94, WP95, WP96, WP97, WP99, WP102, WP103, WP104, WP108, WP109, WP112, WP113, WP114, WP119Other: LS24, CT5, CT6, CT7, BT2, CT8, LS48, CT9, BT3, CT12, CT13, CT14, CT15, CT17, CT20, CT21, CT22, CT23, ECE

Write simple expressions that record calculations with 2. numbers, and interpret numerical expressions without evaluating them.

Lessons: L13, WP13, WP14, WP15, WP16, WP17, WP18, L24, WP24, WP25, L49, L51, WP51, WP52, WP53, WP54, WP56, WP59Other: CT3, BT1

Analyze patterns and relationships.

Generate two numerical patterns using two given rules. 3. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane.

Lessons: Inv4, WP45, WP47, WP48, WP49, WP56, Inv6, WP76, Inv8Other: LXA3, ET3

Number and Operations in Base Ten 5.NBT

Understand the place value system.

Recognize that in a multi-digit number, a digit in one place 1. represents 10 times as much as it represents in the place to its right and 1 __ 10 of what it represents in the place to its left.

Lessons: L3, WP3, L7, WP7, WP8, WP24, WP29, L52, WP52, WP56, L64, WP66, WP69, WP80, L106Other: LS3, LS52, LS64

Explain patterns in the number of zeros of the product when 2. multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10.

Lessons: L29, WP30, WP34, WP35, WP46, L64, WP64, L68, L78, WP78, WP79, WP80, L111, WP111, WP112, WP113, WP114, WP115, WP116, WP117, L118, WP118, WP119, WP120Other: LS29, LS64, LS111, CT23

Read, write, and compare decimals to thousandths.3.

Read and write decimals to thousandths using base-ten a. numerals, number names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × ( 1 __ 10 ) + 9 × ( 1

___ 100 ) + 2 × ( 1

____ 1000 ).

Lessons: L64, WP64, L66, L67, L68, WP68, WP74, WP81, WP82, WP85, WP102, WP105, L106, WP109, WP110, WP111, WP112Other: LXA1, LS68, ET1, CT14, BT4

Compare two decimals to thousandths based on b. meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.

Lessons: L69, L70, WP70, L71, WP71, WP73, WP74, WP75, WP76, WP77, WP79, WP83, L100, WP102, L106, WP117Other: LS69, CT14, CT15, LS106, CT22

4. Use place value understanding to round decimals to any place.

Power Up: PU105Lessons: L62, L64, L88, L104, WP104, WP105, L106, WP106, WP107, L108, WP110Other: LXA8, CT21, ET8, CT22, CT23






Perform operations with multi-digit whole numbers and with decimals to hundredths.

5. Fluently multiply multi-digit whole numbers using the standard algorithm.

Power Up: PU23, PU25, PU26, PU27, PU28, PU45, PU59, PU68, PU118Lessons: L17, WP17, WP18, WP19, WP20, WP21, WP22, WP23, WP24, WP25, WP26, WP27, L29, WP29, WP30, WP31, WP32, WP33, WP37, WP40, WP45, WP46, WP47, WP48, WP49, L51, WP51, L55, L56, WP56, WP57, WP58, WP59, WP65, WP70, WP71, WP74, WP75, WP79, WP86, WP91, WP103, WP116Other: LS29, CT6, CT7, CT8, CT9, LS51, LS55, CT10, LS56, CT11, BT3, CT12, CT13, CT14, BT4, CT17, CT18, CT19, CT21, ECE

6. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

Power Up: PU56, PU58, PU60, PU61, PU62, PU64, PU72Lessons: L54, WP54, WP55, WP57, WP58, WP59, WP60, WP61, WP62, WP63, WP64, WP65, WP66, WP67, WP68, WP69, WP70, WP72, WP75, WP79, WP81, WP82, WP84, WP86, WP87, WP89, WP91, L92, L94, WP94, WP96, WP98, WP99, WP101, WP103, WP114, WP116, WP119, WP120Other: LS54, CT11, CT12, CT13, CT17, LXA6, LS92, ET6, CT19, CT20, CT21, CT23

7. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.

Lessons: L13, L17, L26, L29, L51, L54, L56, L73, WP73, WP75, WP78, WP80, WP85, L99, WP99, WP100, WP101, L102, WP102, WP103, WP105, WP106, WP107, WP108, L109, WP109, L110, WP110, L111, WP111, WP112, WP113, WP114, WP115, WP116, L117, WP117, L118, WP118, L119, WP119, WP120Other: CT15, BT4, CT16, CT17, LS99, CT19, LS102, CT20, LS109, LS110, CT21, LS111, CT22, LS117, LS118, LS119, CT23, ECE

Number and Operations—Fractions 5.NF

Use equivalent fractions as a strategy to add and subtract fractions.

Add and subtract fractions with unlike denominators 1. (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators.

Power Up: PU61, PU62, PU64, PU65, PU66, PU73, PU116Lessons: L116, WP116, WP117, WP118, WP119, WP120Other: LS116

Solve word problems involving addition and subtraction of 2. fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers.

Power Up: PU63Lessons: L23, WP26, WP28, WP31, WP32, L41, L43, L59, L60, L63, WP66, WP67, WP72, L75, WP86, WP87, L91, WP94, WP99, WP101, WP107, WP110, WP112, WP113, WP114, L116, WP116, WP118Other: LS41, LS59, LS60, LS63, CT13, LS75, LS91, BT5





Apply and extend previous understandings of multiplication and division to multiply and divide fractions.

Interpret a fraction as division of the numerator by the 3. denominator ( a __ b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem.

Power Up: PU95, PU96, PU98, PU99, PU100, PU101, PU103, PU104Lessons: L20, L40, WP41, WP42, L43, WP44, WP46, WP47, WP49, WP53, WP57, L58, WP58, WP59, WP61, WP62, WP66, WP67, WP68, L91, WP91, L95Other: LS40, LS43, CT13, CT14, CT15, BT4

Apply and extend previous understandings of multiplication 4. to multiply a fraction or whole number by a fraction.

Interpret the product (a. a __ b ) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b.

Power Up: PU48, PU49, PU50, PU63, PU64, PU66, PU68, PU69, PU71, PU73, PU75, PU77, PU79, PU81, PU90, PU92, PU94, PU95, PU96, PU104, PU106, PU108 Lessons: L46, WP48, WP49, WP50, WP53, WP54, WP55, WP56, WP57, WP58, WP65, L76, WP76, L86, WP88, WP89, WP96, WP104, WP111, WP115, WP117, WP118Other: PT4, TDA4, BT3, CT12, LS76, CT17, CT18, CT19, BT5, CT20, CT21, CT22, CT23, ECE

Find the area of a rectangle with fractional side lengths b. by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas.

Lessons: L76, WP77, WP115Other: LXA2, LS76, ET2

5. Interpret multiplication as scaling (resizing), by:

Comparing the size of a product to the size of one a. factor on the basis of the size of the other factor, without performing the indicated multiplication.

Lesson: L86Other: LXA9, ET9

Explaining why multiplying a given number by a fraction b. greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a __ b = (n × a)

_____ (n × b) to the effect of multiplying a __ b by 1.

Lessons: L86, L120Other: LS86, LXA9, ET9

6. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem.

Lessons: L76, WP78, L86, WP96, WP111, WP115, WP117, L120Other: PT4, LXA10, LS120, ET10

7. Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions.1

Interpret division of a unit fraction by a non-zero whole a. number, and compute such quotients.

Lessons: L87, WP87, WP92, WP93, L95, WP95, WP96, WP97Other: LXA5, LS87, LS95, ET5

Interpret division of a whole number by a unit fraction, b. and compute such quotients.

Lessons: L87, WP90, WP93, L96, WP96 Other: TDA2, LXA5, ET5

Solve real world problems involving division of unit c. fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem.

Lessons: L87, L92, L93, L94, L95Other: LXA5, ET5

1 Students able to multiply fractions in general can develop strategies to divide fractions in general, by reasoning about the relationship between multiplication and division. But division of a fraction by a fraction is not a requirement at this grade.





Measurement and Data 5.MDConvert like measurement units within a given measurement system.

Convert among different-sized standard measurement 1. units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems.

Power Up: PU14, PU18, PU20, PU21, PU23, PU24, PU27, PU28, PU32, PU38, PU39, PU40, PU41, PU44, PU48, PU50, PU52, PU53, PU55, PU56, PU57, PU58, PU65, PU66, PU76, PU78, PU82, PU91, PU99, PU100, PU106, PU107, PU110, PU111, PU112, PU114, PU117, PU118Lessons: L44, WP44, WP45, L46, WP46, L47, WP47, WP50, L65, WP65, L66, WP67, L74, WP74, WP75, L77, WP77, L85, WP85, WP86, WP89, WP90, WP97Other: LS47, BT3, LS65, LS66, LS74, LS77, CT15, BT4, LS85, CT16, CT19, BT5, CT20, CT22, ECE

Represent and interpret data.Make a line plot to display a data set of measurements 2. in fractions of a unit ( 1 __ 2 , 1 __ 4 , 1 __ 8 ). Use operations on fractions for this grade to solve problems involving information presented in line plots.

Lessons: Inv5, WP52, L74Other: LXA4, ET4

Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition.

Recognize volume as an attribute of solid figures and 3. understand concepts of volume measurement.

A cube with side length 1 unit, called a “unit cube,” is a. said to have “one cubic unit” of volume, and can be used to measure volume.

Lessons: L103, WP103, WP104, WP105, WP106, WP107, WP108, WP109, WP113, WP117, WP119, WP120Other: LS103, TDA10

A solid figure which can be packed without gaps or b. overlaps using n unit cubes is said to have a volume of n cubic units.

Lessons: L103, WP103, WP104, WP105, WP106, WP107, WP108, WP109, WP113, WP117, WP119, WP120Other: LS103, PT11

4. Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units.

Power Up: PS77, PS87, PS98, PS103, PS108, PS118Lessons: L103, WP103, WP104, WP105, WP106, WP107, WP108, WP109, WP113, WP117, WP119, WP120Other: PT11

5. Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume.

Find the volume of a right rectangular prism with whole-a. number side lengths by packing it with unit cubes, and show that the volume is the same as would be found by multiplying the edge lengths, equivalently by multiplying the height by the area of the base. Represent threefold whole-number products as volumes, e.g., to represent the associative property of multiplication.

Power Up: PS77, PS87, PS98, PS103, PS108, PS118Lessons: L103, L104Other: LS103, PT11

Apply the formulas b. V = l × w × h and V = b × h for rectangular prisms to find volumes of right rectangular prisms with whole-number edge lengths in the context of solving real world and mathematical problems.

Power Up: PS105, PS108Lessons: L103, WP103, L104, WP104, WP105, WP106, WP107, WP108, WP109, WP113, L114, WP117, WP119, WP120Other: LXA7, LS104, ET7, CT21, PT11, CT22

Recognize volume as additive. Find volumes of solid figures c. composed of two non-overlapping right rectangular prisms by adding the volumes of the non-overlapping parts, applying this technique to solve real world problems.

Power Up: PS118Lessons: L103, L104, L114Other: LXA7, ET7






Geometry 5.G

Graph points on the coordinate plane to solve real-world and mathematical problems.

Use a pair of perpendicular number lines, called axes, 1. to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate).

Lessons: Inv8, WP101, WP103, WP104, WP105, WP107, WP112Other: CT20, CT23, ECE

Represent real world and mathematical problems by 2. graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation.

Lessons: Inv6, Inv8, WP84, WP101, WP103, WP104, WP105, WP107, WP112

Classify two-dimensional figures into categories based on their properties.

Understand that attributes belonging to a category of 3. two-dimensional figures also belong to all subcategories of that category.

Lessons: L32, L36, WP44, L45, WP45, WP46Other: LS32

Classify two-dimensional figures in a hierarchy based on 4. properties.

Power Up: PU47, PU57, PU67Lessons: L32, WP32, L36, WP36, WP37, WP38, WP41, WP42, L45, WP54Other: LS32, LS36, CT7, BT2, LS45, CT8, CT9, CT11, BT3, ECE





L E S S O N

• Writing Decimals to Thousandths Using Expanded Form (CC.5.NBT.3a)

At the end of Lesson 68 complete the following activity.

ActivityMaterials needed:

• Activity Master 1

In Lesson 68 we learned to read and write decimals to thousandths using base-ten numerals and number names. In this activity we will write decimals to thousandths using expanded form. Recall from Lesson 3 that expanded form is a way of writing a number that shows the value of each digit.

Write 256.483 in expanded form using fractions.

Step 1: Complete the chart below to show how the number can be represented using your money manipulatives.

Step 2: Write the value of each digit in 256.483. Show the value of each digit to the right of the decimal using a decimal number.

Step 3: Then write the value of each digit to the right of the decimal using a fraction.

Model$100 bills

2$10 bills

5$1 bills

6dimes

4pennies

8mills

3

Decimalhundreds

200tens50

ones6

tenths0.4

hundredths0.08

thousandths0.003

Fraction 10 100 1000

Step 4: Write 256.483 in expanded form using decimals.

256.483 = 200 + 50 + 6 + 0.4 + 0.08 + 0.003

Step 5: Write 256.483 in expanded form using fractions, showing each number as a multiple of its place value.

256.483 = × 100 + × 10 + × 1 + × ( 1 ___ 10

) + × ( 1 ____ 100

) + × ( 1 _____ 1000

)

Write 542.709 in expanded form using fractions.

Complete Activity Master 1.

Saxon Math Intermediate 5 Extension Activity 1

68


I5_MNLAEAN628165_EA.indd 19 3/22/11 4:41:49 PM


Activity MasterName 1

• Writing Decimals to Thousandths Using Expanded Form

1. Write 325.169 in expanded form using fractions.

First, write 325.169 in the place-value chart.

Write 325.169 in expanded form using decimals.

300 + 20 + 5 + + +

Next, write each digit to the right of the decimal point as a fraction.

The value of the digit 1 is tenth, or .

The value of the digit 6 is hundredths, or .

The value of the digit 9 is thousandths, or .

325.169 = 3 × 100 + 2 × 10 + 5 × 1 + × ( 1 ___ 10

) + × ( 1 ____ 100

) + × ( 1 _____ 1000

)

2. Write 708.614 in expanded form using fractions.

For use with Lesson 68 Extension Activity

tenths place

hundredths place

thousandthsplace

hundreds place

tens place

ones place




L E S S O N

76Saxon Math Intermediate 5

Extension Activity 2

• Finding Area of a Rectangle with Fractional Side Lengths (CC.5.NF.4b)


ActivityMaterials needed: • Activity Master 2

We can use square unit tiles with fractional side lengths to find the area of a rectangle.

Lydia wants to cover the top of a rectangular table with tiles. The table measures 4 1 __ 2 feet by 2 1 __ 2 feet. She wants to use the fewest tiles possible and she does not want to cut any tiles. The tiles come in the three sizes shown in the diagram. Choose a tile and find the area of the table.

Step 1: Choose the largest tile Lydia can use to tile the tabletop without having gaps or overlaps.

Discuss why the unit square you chose is the best choice.

Step 2: Draw a diagram of the tabletop on the grid. Each square

represents the dimensions of the tile.

Step 3: Find how many squares cover the diagram.

× , or squares Describe how to find the area of the tile you chose.

Since one square on your diagram represents an area of square foot,

the area represented by squares is × or square feet.

So, the area of the table top, written as a mixed number, is square feet.

• Use the grid to find the area of a rug that measures 1 2 __ 3 yards by 2 1 __ 3 yards. Let each unit square represent 1 __ 3 yard by 1 __ 3 yard.


1 ft

1 ft ft1

4

ft14

ft12

ft12





• Finding Area of a Rectangle with Fractional Side Lengths

We can use an area model to solve this problem. A rectangle measures 2 1 __ 4 feet by 1 1 __ 2 feet. Find the area of the rectangle.

Step 1: Draw an area model to show the rectangle.

Step 2: Rewrite each mixed number as the sum of a whole number and a fraction.

2 1 __ 4 = and 1 1 __ 2 =

Step 3: Draw dashed lines and label each section to show how we can break apart the mixed numbers in Step 2.

Step 4: Find the area of each section.

Step 5: Add the areas of each section to find the total area of the rectangle.

Rename 1 __ 4 as 2 __ 8 before adding. + + + =

So, the area of a rectangle that measures 2 1 __ 4 feet by 1 1 __ 2 feet is square feet.

Use an area model to solve this problem.

A garden measures 1 1 __ 2 yards by 3 1 __ 2 yards. What is the area of the garden?


112

124

1

12

142 1

2 315

122

14 1 53

14

12 53

1

3 5






• Graphing and Analyzing Relationships (CC.5.OA.3)

At the end of Investigation 8 complete the following activity.


Vocabulary:

• coordinate plane: A grid on which any point can be identified by its distance from the x- and y-axes.

• ordered pair: A pair of numbers, such as (4, 3), that can be used to locate a point on the coordinate plane. The first number is the x-coordinate and the second number is the y-coordinate. Also called coordinates.

Use the rules given in the chart to complete the number patterns.

Axis Rule First Number

x Add 2 0 2y Add 1 0 1

Look at the x and y numbers that correspond in each sequence. Describe the relationship between the corresponding terms.

Use the corresponding terms in the two patterns to form ordered pairs. Let each term in the Add 2 pattern represent the x-coordinate and each term in the Add 1 pattern represent the y-coordinate. Write the four new ordered pairs.

( 0 , 0 ) ( , ) ( , )

( , ) ( , )

Compare your ordered pairs with your class. Then graph all five ordered pairs on the coordinate plane at the right.


2

1

0

6

7

8

9

10

10

5

4

3

2

1 x3 4 5 6 7 8 9

y

INvEStIgatION





• Graphing and Analyzing Relationships

1. Use the rules given in the chart below to complete the number patterns.

Axis Rule First Number

x Add 1 0y Add 2 0

2. Look at the x and y numbers that correspond in each sequence. Describe the relationship between the corresponding terms.

3. Use the corresponding terms in the two patterns to form ordered pairs. Let each term in the Add 1 pattern represent the x-coordinate and each term in the Add 2 pattern represent the y-coordinate. Write the four new ordered pairs.

( 0 , 0 ) ( , ) ( , ) ( , ) ( , )

4. Graph the ordered pairs on the coordinate plane.

For use with Investigation 8 Extension Activity

2

1

0

6

7

8

9

10

10

5

4

3

2

1 x3 4 5 6 7 8 9

y



L E S S O N


• Using Fraction Operations with Line Plots (CC.5.MD.2)



[If] We can display a data set of measurements in fractions of a unit on a line plot. Then we can use what we know about fractions to solve problems involving the information presented in the line plot.

Sidney measured different amounts of water, which she poured into glasses. The amount of water in each of the glasses is listed below.

1 __ 2 c, 3 __

4 c, 1 __

2 c, 1 __

4 c, 3 __

4 c, 1 __

2 c, 1 __

4 c, 1 __

2 c

Complete the line plot showing the data. Then find how much water would be in each glass if the total amount of water stayed the same and each glass held an equal amount.

Step 1: Find the total amount of water in all the glasses containing 1 __ 4 cup of water.

Find the total amount of water in all the glasses containing 1 __ 2 cup of water.

Find the total amount of water in all the glasses containing 3 __ 4 cup of water.

Step 2: Find the total amount of water in all the glasses together.

Step 3: Divide the total amount of water by the number of glasses. Write the division using a fraction bar.

So, each glass would have cup of water.




2 __ 1 × 1 __

4 = or c

4 __ 1 × 1 __

2 = or c

2 __ 1 × 3 __

4 = or c

1 __ 2 + 2 + 1 1 __

2 = or c

4 ÷ 8 = 4 __ 8 , or c

Water Used (in cups)

14

12

34



Activity MasterName

LaurelTech/HMH Design Pass First Pages Confirming Pages Digital Pages

4

• Using Fraction Operations with Line Plots

Use the data below for problems 1–6. The data represents the length of each insect in Mark’s collection.

1 __ 2 in., 3 __

8 in., 3 __

8 in., 1 __

4 in., 1 __

2 in., 3 __

8 in., 1 __

4 in., 3 __

8 in.

1. Complete the line plot.

2. What is the combined length of all the insects that measure 1 __ 4 inch?



5. What is the total length of all the insects in the collection?

6. Suppose the total length of all the insects in the collection stayed the same, but all insects measure an equal length. What would be the length of each insect?


Lengths of Mark’s Insects(in inches)

14

38

34



L E S S O N




• Dividing a Fraction by a Whole Number and Dividing a Whole Number by a Fraction (CC.5.NF.7a, CC.5.NF.7b, CC.5.NF.7c)


ActivityMaterials needed: • fraction circles • Activity Master 5

When dividing whole numbers, we can use the inverse relationship between multiplication and division to explain and check our quotients. For example, 10 ÷ 2 = 5 because 5 × 2 = 10. The same relationship can be used with fractions.

• Divide a whole number by a fraction. Stacy has 2 liters of juice to serve her friends. If each

serving is 1 __ 6 of a liter, how many servings can she make?Step 1: Draw a number line from 0 to 2.

Divide the number line into sixths. Label each sixth on your number line.

Step 2: Skip count by sixths from 0 to 2 to find 2 ÷ 1 __ 6 .

Step 3: Record and check the quotient. 2 ÷ 1 __ 6 = because × 1 __ 6 = 2

So, Stacy can make servings of juice.

Describe how the quotient compares to the dividend when we divide a whole number by a fraction.

• Divide a fraction by a whole number. Dot cut a pizza in half. She then divided one half into 4 equal

parts. What fraction of the whole pizza is each of the 4 parts?Step 1: Place a 1 __ 2 -circle piece over 1 whole circle.

Step 2: Find 4 circle fraction pieces, all with the same denominator, which fit exactly over the 1 __ 2 circle piece.

Each part is of the whole.

Step 3: Record and check the quotient. 1 __ 2 ÷ 4 = because × 4 = 1 __ 2

So, each of the 4 parts is of the whole pizza.

Describe how the quotient compares to the dividend when we divide a fraction by a whole number.


0 1

1 2 3 4 5 6 7 8 9 10 11 12

216

16

26

26

36

36

46

46

56

56





• Dividing a Fraction by a Whole Number and Dividing a Whole Number by a Fraction

Divide. Use a model and write a related multiplication expression to help solve each problem.

1. 5 ÷ 1 __ 3

=

2. Kendall has 3 yards of ribbon to use for making bows. She cuts the ribbon into pieces that are 1 __ 4 yard long. How many pieces of ribbon does Kendall have?

3. 1 __ 4 ÷ 3 =

4. Carson cuts a piece of rectangular-shaped poster board in half. He then divides one half into 3 equal parts. What fraction of the whole piece of poster board is each of the 3 parts?




L E S S O N




• Dividing by Two-Digit Numbers Using Models (CC.5.NBT.6)



• base-ten blocks • Activity Master 6

We can use base-ten blocks to model and understand how to divide whole numbers.

The Loma Vista School had 168 students sign up for soccer. If an equal number of students are placed on 12 teams, how many students will be on each team?

Step 1: Use base-ten blocks to model the dividend 168.

Step 2: Use 1 hundred and 2 tens to form a rectangle. The rectangle shows groups of 12.

How much of the dividend is not shown in the rectangle?

Step 3: Combine the rest of the tens and ones into as many groups of 12 as possible.

There are groups of 12.

Step 4: Place these groups of 12 on the right side of the rectangle to make a larger rectangle.

The two sets of groups of 12 we found are partial quotients. First we found groups of 12 and then we found groups of 12.

Step 5: The final rectangle shows groups of 12.

So, there will be students on each of the 12 teams.

Describe how you can use base-ten blocks to find the quotient 165 ÷ 15.







• Dividing by Two-Digit Numbers Using Models

Use base-ten blocks.

Divide: 192 ∏ 16

Sometimes we may need to regroup before we can show a partial product.

Step 1: Model the dividend, 192, using 1 hundred 9 tens 2 ones.

Step 2: Model the first partial quotient by making a rectangle with 1 hundred and 6 tens.

The rectangle shows groups of 16.

Step 3: Regroup 1 ten as 10 ones.

There are now tens and ones.

Step 4: Decide how many additional groups of 16 can be made with the remaining tens and ones. The number of groups is the second partial quotient.

Step 5: Make the rectangle larger by including these groups of 16. There are now groups of 16.

So, the quotient for 192 ÷ 16 is .

Divide using base-ten blocks.

1. 154 ÷ 14

2. 176 ÷ 11



L E S S O N


Saxon Math Intermediate 5 Extension Activity 7

103

• Using Formulas to Find Volume of Prisms and Composed Figures (CC.5.MD.5b, CC.5.MD.5c)



In Lesson 103 we found the volume of a rectangular prism using its length, width, and height.

Volume = length × width × height or V = l × w × h

These were the steps we used:

• First, identify the length, width, and height. V = l × w × h• Next, use the Associative Property to group the part of the V = (l × w) × h

formula that represents area and multiply the length by the width.

• Then multiply the product of the length and width by the height. V = area × h

From this, we can use another formula to find the volume of a rectangular prism.

Volume = Base × height or V = B × h

Base = area of the base

h = height of the rectangular prism

Solve this problem using the area of the base times the height formula.

Mr. Lopez bought a case to display an autographed football. The case is a rectangular prism like the one shown at the right. What is the volume of the case?

Step 1: Write the area of the base times the height formula. V = B × h

Step 2: Replace B with an expression for the area V = ( × ) × of the base. Replace h with the height of the rectangular prism.

Step 3: Multiply. V = × =

So, the volume of the case is cubic inches.


10 in.

8 in.12 in.





• Using Formulas to Find Volume of Prisms and Composed Figures

We can use a formula to find the volume of composed figures.

The shape at the right is a composed figure. It is made of two rectangular prisms that are combined. How can you find the volume of the figure?

Step 1: Break apart the solid figure Step 2: Identify the length, width, into two rectangular prisms. and height of each prism.

Discuss how we can find the height of the top prism.

Step 3: Find the volume of each prism. Step 4: Add the volumes of the two prisms. + =

So, the volume of the composed figure is cu. cm.

• Use a formula to solve the problem.

Mr. Wynn built a two-story birdhouse. The diagram shows its dimensions. How many cubic inches of space does the birdhouse have?


12 in.

6 in.

6 in.

6 in.

8 in.

3 cm

4 cm

7 cm

3 cm

2 cm

4 cm

7 cm

3 cm

2 cm

width 3 cm

length 4 cm

height cm

length 7 cm

width 3 cm

height 2 cm



L E S S O N




• Rounding Decimal Numbers (CC.5.NBT.4)




In Lesson 106 we rounded decimal numbers to the nearest whole number. In this activity we will round decimal numbers to the nearest tenth or hundredth.

• Round 10.381 to the nearest tenth.

Step 1: Underline the places that will be included in the answer. The tenths place is one place to the right of the decimal point. 10.381

Step 2: Consider the possible answers. The number we are rounding is more than 10.3 but less than 10.4.

Step 3: Look at the digit in the next place to the right, which is the hundredths place. If the digit is 5 or more, we round up. 10.381

So, 10.381 rounded to the nearest tenth is .

Use a number line to explain how you know you rounded correctly.

• Round 10.381 to the nearest hundredth.

Step 1: Underline the places that will be included in the answer. 10.381

Step 2: Consider the possible answers. The number we are rounding is more than 10.38 but less than 10.39.

Step 3: Look at the digit in the next place to the right, which is the thousandths place. Since the digit is less than 5, we know 10.381 our number rounds down.

So, 10.381 rounded to the nearest hundredth is .

Use a number line to explain how you know you rounded correctly.

Complete Activity Master 8.10.385

Nearer to 10.38 Nearer to 10.39

10.3810.380

10.3910.390

10.35

Nearer to 10.3 Nearer to 10.4

10.310.3010.300

10.410.4010.400





• Rounding Decimal Numbers

Use place value to round each decimal number to the nearest tenth.


1. 45.267

2. 8.539

3. 18.345

Use place value to round each decimal number to the nearest hundredth.

4. 19.064

5. 3.266

6. 39.708



L E S S O N




• Comparing Fraction Factors and Products and Mixed Number Factors and Products (CC.5.NF.5a, CC.5.NF.5b)



We can think of multiplication as resizing one number using another number. For example, 3 × 4 or 3 multiplied by 4, will result in a product that is 3 times as great as 4.

We can use a model to see what happens to the size of a product when a number is multiplied by a fraction.

During one week, the Lewis family used 2 __ 3 of a carton of milk.

Shade a model to show 2 __ 3 of a carton of milk.

Write an expression for 2 __ 3 of a carton of milk.

Describe the size of the product of any number multiplied by 1.

The Adams family has 3 cartons of milk.

They used 2 __ 3 of 3 cartons during the week.

Shade the model to show 2 __ 3 of 3 cartons of milk.

Write an expression for 2 __ 3 of 3 cartons of milk.

Describe the size of the product when 2 __ 3 is multiplied by a number greater than 1.

The Wong family has only 1 __ 2 of a carton of milk at the beginning of the week. They used 2 __ 3 of the 1 __ 2 carton of milk.

Shade the model to show 2 __ 3 of 1 __ 2 carton of milk.

Write an expression to show 2 __ 3 of 1 __ 2 carton of milk.

Describe the size of the product when 2 __ 3 is multiplied by a number less than 1.

Complete each statement with equal to, greater than, or less than.

2 __ 3 ×

2 __ 3 ×

2 __ 3 ×

1. 3 __ 4 × 1 __ 2 will be 3 __ 4 2. 5 __ 6 × 5 will be 5 __ 6






• Comparing Fraction Factors and Products and Mixed Number Factors and Products

We can use models to make generalizations about the relative size of a product when one factor is less than 1, is equal to 1, or is greater than 1.

Kelsey has a recipe for making play dough that calls for 1 1 __ 3 cups of flour. She wants to know how much flour she would need if she made 1 recipe of the play dough, if she made 1 __ 2 the recipe, and if she made 1 1 __ 2 times the recipe.

We can shade models to show the size of the product when 1 1 __ 3 is multiplied by 1, by 1 __ 2 , and by 1 1 __ 2 .

• 1 × 1 1 __ 3

What can we say about the size of the product when 1 1 __ 3 is multiplied by 1? Explain why.

• 1 __ 2 × 1 1 __ 3

What can we say about the size of the product when 1 1 __ 3 is multiplied by a fraction less than 1?

• 1 1 __ 2 × 1 1 __ 3 = (1 × 1 1 __ 3 ) + ( 1 __ 2 × 1 1 __ 3 )

What can we say about the size of the product when 1 1 __ 3 is multiplied by a fraction greater than 1?

Complete each statement with equal to, greater than, or less than.


1. 4 __ 4 × 1 1 __ 4 will be 1 1 __ 4 2. 3 × 2 2 __ 3 will be 2 2 __ 3



L E S S O N


• Multiplying Mixed Numbers (CC.5.NF.6)




We can use a model to multiply mixed numbers.

One-fourth of a 1 2 __ 3 -acre nursery has been set aside as a wildflower garden. Find the number of acres that are used as a wildflower garden.

Multiply: 1 __ 4 × 1 2 __ 3

Step 1: Shade a model to represent the size of the whole nursery.

The whole nursery is ____________ acres. 1 = 3 __ 3 1 2 __ 3 = 3 __ 3 + 2 __ 3 = 5 __ 3

Step 2: Draw horizontal lines across each rectangle to show ________________.

Step 3: Double-shade the model to represent the part of the nursery that is used as a wildflower garden.

How many parts does each rectangle show? _______________

What fraction of the rectangles is shaded twice? ____________

So, ________________ acre has been set aside.

We can also multiply mixed numbers using equations. Use the steps we learned in Lesson 120.

Multiply: 1 __ 4 × 1 2 __ 3

Step 1: Write the mixed number as an improper fraction. 1 __ 4 × 1 2 __ 3 = 1 __ 4 × 5 __ 3

Step 2: Multiply the fractions. 1 __ 4 × 5 __ 3 = 5 __ 12

So, 1 __ 4 × 1 2 __ 3 = .

Since we are finding part of ___________, the answer should be less than ___________ and greater than ___________.

Since 5 __ 12 is between both factors, we know our answer is reasonable.








• Multiplying Mixed Numbers

Use a model and an equation to solve each problem.

1. A soup recipe calls for 1 1 __ 2 teaspoons of salt. Darin wants to use 1 __ 2 that amount. How much salt will Darin use?

2. Jenni used 2 3 __ 4 yards of ribbon to make a bow. She wants to make another bow 1 1 __ 2 times the size of that bow. How many yards of ribbon will she need?




Extension TestName

Score


1. Which shows 6.375 written in expanded form using fractions?

𝖠 6 × 1 + 3 × ( 1 __ 10 ) + 7 × ( 1 ___ 100 ) + 5 × ( 1 ____ 1000 )

𝖡 6 × 1 + 3 × ( 1 __ 10 ) + 5 × ( 1 ___ 100 ) + 7 × ( 1 ____ 1000 )

𝖢 6 × 10 + 3 × ( 1 __ 10 ) + 7 × ( 1 ___ 100 ) + 5 × ( 1 ____ 1000 )

𝖣 6 × 1 + 7 × ( 1 __ 10 ) + 3 × ( 1 ___ 100 ) + 5 × ( 1 ____ 1000 )


𝖠 2 × 1 + 8 × ( 1 __ 10 ) + 3 × ( 1 ___ 100 )

𝖡 2 × 10 + 8 × 1 + 3 × ( 1 __ 10 )

𝖢 2 × 10 + 8 × ( 1 __ 10 ) + 3 × ( 1 ____ 1000 )

𝖣 2 × 1 + 8 × ( 1 __ 10 ) + 3 × ( 1 ____ 1000 )


𝖠 4 × 100 + 9 × 10 + 6 × ( 1 __ 10 )

𝖡 4 × 100 + 9 × 10 + 6 × ( 1 ___ 100 )

𝖢 4 × 100 + 9 × ( 1 __ 10 ) + 6 × ( 1 ____ 1000 )

𝖣 4 × 100 + 9 × 1 + 6 × ( 1 ____ 1000 )


𝖠 8 × 100 + 7 × 10 + 4 × ( 1 __ 10 ) + 9 × ( 1 ___ 100 )

𝖡 8 × 10 + 7 × 1 + 4 × ( 1 __ 10 ) + 9 × ( 1 ___ 100 )

𝖢 8 × 10 + 7 × 1 + 4 × ( 1 ___ 100 ) + 9 × ( 1 ____ 1000 )

𝖣 8 × 1 + 7 × ( 1 __ 10 ) + 4 × ( 1 ___ 100 ) + 9 × ( 1 ____ 1000 )

• Writing Decimals to Thousandths Using Expanded Form

Fill in the circle with the correct answer.

For use with Cumulative Test 13

1


I5_MNLAEAN628165_ET.indd 39 3/21/11 6:54:55 PM

Extension TestName

Score


• Finding Area of a Rectangle with Fractional Side Lengths


2

Find the area of a rectangle with sides that measure 1 1 __ 2 in. by 1 1 __ 4 in.Use the grid to draw a diagram to represent the dimensions of the rectangle.

1. What should each unit square represent?

𝖠 1 __ 4 inch by 1 __

4 inch

𝖡 1 __ 2 inch by 1 __

2 inch

𝖢 1 __ 3 inch by 1 __

3 inch

𝖣 1 __ 8 inch by 1 __

8 inch

2. How many squares cover the diagram?

𝖠 25

𝖡 30

𝖢 40

𝖣 45

3. What is the area of each unit square?

𝖠 1 __ 4 square inch

𝖡 1 __ 2 square inch

𝖢 1 __ 8 square inch

𝖣 1 ___ 16

square inch

4. What is the area of the rectangle?

𝖠 2 3 __ 4 square inches

𝖡 2 square inches

𝖢 1 14 ___ 16

square inches

𝖣 1 3 __ 4 square inches




Extension TestName

Score



3

Use the coordinate plane to solve problems 1–4.

• Graphing and Analyzing Relationships

1. Which ordered pair names a point on the coordinate plane?

𝖠 (2, 4)

𝖡 (4, 6)

𝖢 (6, 8)

𝖣 (8, 10)

2. What pattern represents the x-coordinate?

𝖠 add 1

𝖡 add 2

𝖢 add 3

𝖣 add 4

3. What pattern represents the y-coordinate?

𝖠 add 1

𝖡 add 2

𝖢 add 3

𝖣 add 4

4. If the patterns used to form the ordered pairs were extended, which would be the next ordered pair?

𝖠 (9, 14)

𝖡 (10, 14)

𝖢 (10, 15)

𝖣 (11, 15)

2

1

0

6

7

8

9

10

11

12

13

14

15

5

4

3

2

1 x3 4 5 6 7 8 9 10 11 12 13 14 15

y




1. What is the combined mass of all the beads that weigh 1 __ 4 gram?

𝖠 3 __ 4 gram

𝖡 1 gram

𝖢 1 1 __ 4 grams

𝖣 1 1 __ 2 grams

2. What is the combined mass of all the beads that weigh 1 __ 2 gram?

𝖠 1 __ 2 gram

𝖡 1 gram

𝖢 1 1 __ 2 grams

𝖣 2 grams

3. What is the total mass of all the beads on the necklace?

𝖠 1 1 __ 2 grams

𝖡 2 grams

𝖢 2 1 __ 2 grams

𝖣 3 grams

4. Suppose the total mass of the beads stays the same, but all the beads have an equal mass. What would be the mass of each bead?

𝖠 1 __ 4 gram

𝖡 3 __ 8 gram

𝖢 1 __ 2 gram

𝖣 3 __ 4 gram


Extension TestName

Score


14

12

34

Mass of Mia’s Beads(in grams)

• Using Fraction Operations with Line Plots

The line plot below shows the masses of different beads on Mia’s bracelet. Use the data shown in the line plot for problems 1–4.


4



Extension TestName

Score



5

• Dividing a Fraction by a Whole Number and Dividing a Whole Number by a Fraction

Use a model and write a related multiplication expression to help solve each problem. Fill in the circle with the correct answer.

1. 4 ÷ 1 __ 5 = _______

𝖠 4 __ 5

𝖡 1 ___ 20

𝖢 20

𝖣 24

2. Kelli cut a pie in half. She cut one half of the pie into 3 equal parts. What fraction of the whole pie is each of the 3 parts?

𝖠 1 __ 6

𝖡 1 __ 4

𝖢 1 __ 3

𝖣 1 __ 2

3. 1 __ 3 ÷ 4 = _________

𝖠 12

𝖡 1 1 __ 3

𝖢 3 __ 4

𝖣 1 ___ 12

4. Jolie used 4 containers of glitter to make posters. If she used 1 __ 4 container of glitter for each poster she made, how many posters did Jolie make?

𝖠 20

𝖡 16

𝖢 12

𝖣 8



Extension TestName

Score


• Dividing by Two-Digit Numbers Using Models

Divide. Use base-ten blocks to model. Fill in the circle with the correct answer.

1. 221 ÷ 17

𝖠 15

𝖡 14

𝖢 13

𝖣 12

2. 198 ÷ 11

𝖠 18

𝖡 17

𝖢 16

𝖣 15

3. 266 ÷ 19

𝖠 13

𝖡 14

𝖢 15

𝖣 16

4. A florist used 143 roses in 13 arrangements. An equal number of roses were placed in each arrangement. How many roses were placed in each arrangement?

𝖠 14

𝖡 13

𝖢 12

𝖣 11


6



Extension TestName

Score


• Using Formulas to Find Volume of Prisms and Composed Figures

Use a formula to find the volume. Fill in the circle with the correct answer.

1. Lynn stores quilts in a cedar chest. The base of the chest is 4 feet by 2 feet. The height of the chest is 3 feet. How many cubic feet of storage space does the cedar chest have?

𝖠 8 cubic feet

𝖡 9 cubic feet

𝖢 12 cubic feet

𝖣 24 cubic feet

2. The volume of this composed figure is ________ cubic meters.

𝖠 27 cubic meters

𝖡 72 cubic meters

𝖢 152 cubic meters

𝖣 200 cubic meters


7

8 m

5 m

5 m 3 m

3 m

3 m



Extension TestName

Score



• Rounding Decimal Numbers


1. Which shows 23.75 rounded to the nearest tenth.

𝖠 23

𝖡 23.7

𝖢 23.8

𝖣 24

2. Which shows 60.846 rounded to the nearest tenth.

𝖠 60

𝖡 60.8

𝖢 60.85

𝖣 60.9

3. Which shows 86.134 rounded to the nearest hundredth.

𝖠 86.1

𝖡 86.13

𝖢 86.14

𝖣 86.2

4. Which shows 7.048 rounded to the nearest hundredth.

𝖠 7.0

𝖡 7.04

𝖢 7.05

𝖣 7.1

8



Extension TestName

Score


• Comparing Fraction Factors and Products and Mixed Number Factors and Products


1. 7 __ 8 × 1 will be _______ 7 __ 8 .

𝖠 equal to

𝖡 greater than

𝖢 less than

2. 6 × 4 __ 5 will be _______ 6.

𝖠 equal to

𝖡 greater than

𝖢 less than

3. 2 × 1 3 __ 4 will be _________ 1 3 __ 4 .

𝖠 equal to

𝖡 greater than

𝖢 less than

4. Ethan’s kitten weighs 1 1 __ 2 times what it weighed when it was born. The kitten weighed 1 3 __ 4 pounds at birth. Which statement below is true?

𝖠 The kitten weighs the same as it did at birth.

𝖡 The kitten weighs less than it did at birth.

𝖢 The kitten weighs more than it did at birth.


9



Extension TestName

Score



10

• Multiplying Mixed Numbers

Use a model and an equation to solve each problem. Fill in the circle with the correct answer.

1. Paige is training for a marathon. The first week of training she plans to run 4 __ 5 mile each day. The second week of training she plans to run 2 1 __ 2 times that distance each day. How many miles will Paige run each day of the second week of training?

𝖠 2 __ 5 mile

𝖡 1 3 __ 5 miles

𝖢 2 miles

𝖣 2 1 __ 2 miles

2. A recipe calls for 1 2 __ 3 cups of vegetable oil. Emerson plans to replace 3 __ 4 of the amount of oil with applesauce. How much applesauce will she use?

𝖠 1 1 __ 4 cups

𝖡 1 cup

𝖢 2 __ 3 cup

𝖣 1 __ 2 cup



Lesson Extension Activity Answers

Lesson Extension Activity 1

256.483 = 2 × 100 + 5 × 10 + 6 × 1 + 4 × ( 1 __ 10 ) + 8 × ( 1 ___ 100 ) + 3 × ( 1 ____ 1000 ); 542.709 = 5 × 100 + 4 × 10 + 2 × 1 + 7 × ( 1 __ 10 ) + 9 × ( 1 ____ 1000 )


1 __ 2 ft by 1 __ 2 ft; Multiply 1 __ 2 × 1 __ 2 ; 11 1 __ 4 ; 3 8 __ 9 sq. yd


x-axis: 4, 6, 8; y-axis: 2, 3, 4; Each term for the x-coordinate is twice the corresponding term for the y-coordinate. Ordered pairs: (2,1), (4,2), (6,3), (8,4); See student work.


See student work. 1 __ 2


12; The quotient is greater than the dividend. 1 __ 8 ; The quotient is less than the dividend.


14; Find the partial products by showing 10 groups of 15 and then 1 group of 15 for a total of 11 groups of 15.


960


10.4; 10.38


The product will be equal to the other factor. The product will be greater than 2 __ 3 . The product will be less than 2 __ 3 .

1. less than 2. greater than


5 __ 12 ; 5 __ 12 ; 1 2 __ 3 ; 1 2 __ 3 ; 1 __ 4

Activity Master 1

See student work.

1. 325.169 = 3 × 100 + 2 × 10 + 5 × 1 + 1 × ( 1 __ 10 ) + 6 × ( 1 ___ 100 ) + 9 × ( 1 ____ 1000 )

2. 708.614 = 7 × 100 + 8 × 1 + 6 × ( 1 __ 10 ) + 1 × ( 1 ___ 100 ) + 4 × ( 1 ____ 1000 )

Activity Master 2

3 3 __ 8 ; 5 1 __ 4 square yards

Activity Master 3

1. x-axis 1, 2, 3, 4; y-axis 2, 4, 6, 8

2. Each term for the x-coordinate is half the corresponding term for the y-coordinate.

3. (1,2), (2,4), (3,6), (4,8)

4. See student work.

Activity Master 4

1. See student work.

2. 1 __ 2 in. 3. 1 1 __ 2 in. 4. 1 in.

5. 3 in. 6. 3 __ 8 in.

Activity Master 5

1. 15; See student work. 15 × 1 __ 3 = 5

2. 12; See student work. 12 × 1 __ 4 = 3

3. 1 __ 12 ; See student work. 1 __ 12 × 3 = 3 __ 12 , or 1 __ 4

4. 1 __ 6 ; See student work. 1 __ 6 × 3 = 3 __ 6 , or 1 __ 2

Activity Master 6

See student work. 12

1. See student work. 11 2. See student work. 16

Activity Master 7

66 cu. cm; 864 cu. in.

Activity Master 8

1. 45.3 2. 8.5 3. 18.3 4. 19.06 5. 3.27 6. 39.71

Activity Master 9

1. equal to 2. greater than

Activity Master 10

1. 3 __ 4 teaspoon; See student work. 2. 4 1 __ 8 yards; See student work.

Activity Master Answers



I5_MNLAEAN628165_ANS.indd 49 3/17/11 10:16:41 AM

Extension Test Answers

Extension Test 1

1. 𝖠 6 × 1 + 3 × ( 1 __ 10 ) + 7 × ( 1 ___ 100 ) + 5 × ( 1 ____ 1000 )

2. 𝖢 2 × 10 + 8 × ( 1 __ 10 ) + 3 × ( 1 ____ 1000 )

3. 𝖣 4 × 100 + 9 × 1 + 6 × ( 1 ____ 1000 )

4. 𝖢 8 × 10 + 7 × 1 + 4 × ( 1 ___ 100 ) + 9 × ( 1 ____ 1000 )

Extension Test 2

1. 𝖠 1 __ 4 inch by 1 __ 4 inch

2. 𝖡 30

3. 𝖣 1 __ 16 square inch

4. 𝖢 1 14 __ 16 square inches

Extension Test 3

1. 𝖡 (4, 6)

2. 𝖡 add 2

3. 𝖢 add 3

4. 𝖢 (10, 15)

Extension Test 4

1. 𝖢 1 1 __ 4 grams

2. 𝖡 1 gram

3. 𝖣 3 grams

4. 𝖡 3 __ 8 gram

Extension Test 5

1. 𝖢 20

2. 𝖠 1 __ 6

3. 𝖣 1 __ 12

4. 𝖡 16

Extension Test 6

1. 𝖢 13

2. 𝖠 18

3. 𝖡 14

4. 𝖣 11

Extension Test 7

1. 𝖣 24 cubic feet

2. 𝖢 152 cubic meters

Extension Test 8

1. 𝖢 23.8

2. 𝖡 60.8

3. 𝖡 86.13

4. 𝖢 7.05

Extension Test 9

1. 𝖠 equal to

2. 𝖢 less than

3. 𝖡 greater than

4. 𝖢 The kitten weighs more than it did a birth.

Extension Test 10

1. 𝖢 2 miles; See student work.

2. 𝖠 1 1 __ 4 cups; See student work.


© HMH Supplemental Publishers Inc.50 Saxon Math Intermediate 5

I5_MNLAEAN628165_ANS.indd 50 3/17/11 10:16:41 AM

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