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GRADE 5 Mission 1 Place Value with Decimal Fractions This opening Mission is a culmination of 2nd 3rd and 4th grade Additionally students extend their understanding of decimal fractions to the thousandths place and more sophisticated patterns of our base ten system

2023 Zearn Portions of this work Zearn Math are derivative of Eureka Math and licensed by Great Minds 2019 Great Minds All rights reserved Zearn is a registered trademark Printed in the U S A ISBN 979 8 88868 991 2

Table of Contents MISSION OVERVIEW ASSESSMENTS viii xii TOPIC A MULTIPLICATIVE PATTERNS ON THE PLACE VALUE CHART LESSON 1 3 LESSON 2 13 LESSON 3 19 LESSON 4 29 TOPIC B DECIMAL FRACTIONS AND PLACE VALUE PATTERNS LESSON 5 41 LESSON 6 49 TOPIC C PLACE VALUE AND ROUNDING DECIMAL FRACTIONS LESSON 7 57 LESSON 8 65 TOPIC D ADDING AND SUBTRACTING DECIMALS LESSON 9 73 LESSON 10 79 TOPIC E MULTIPLYING DECIMALS LESSON 11 85 LESSON 12 93 TOPIC F DIVIDING DECIMALS LESSON 13 101 LESSON 14 107 LESSON 15 115 LESSON 16 121 ZEARN MATH Teacher Edition iii

G5M1 Overview CURRICULUM MAP 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 K M3 M2 M1 2D 3D Shapes Numbers to 10 Numbers to 5 Digital Activities 50 M1 G3 M2 Add Subtract Friendly Numbers M1 M2 Add Subtract Round G5 Place Value with Decimal Fractions G7 G8 Key Measure It Multiply Divide Big Numbers M1 M1 M2 Area and Surface Area Introducing Ratios M2 M1 Scale Drawings Introducing Proportional Relationships M1 Rigid Transformations and Congruence Whole Numbers and Operations M3 M2 Base Ten Operations M3 M3 Rates and Percentages M4 Measuring Circles M2 Dilations Similarity and Introducing Slope M4 Dividing Fractions Proportional Relationships and Percentages M3 Linear Relationships Expanding Whole Numbers and Operations to Fractions and Decimals ZEARN MATH Teacher Edition Add Subtract Fractions Fractions as Numbers M5 Rational Number Arithmetic M4 Linear Equations and Linear Systems M4 M5 M6 M5 M7 Functions and Volume Algebraic Thinking and Reasoning Leading to Functions M6 Associations in Data Geometry M6 M9 M8 Rational Numbers Angles Triangles and Prisms Multiply Measure The Coordinate Plane M7 Expressions and Equations M7 Decimal Fractions Volume Area Shapes M6 Expressions Equations and Inequalities Shapes Measurement Display Data M6 Multiply and Divide Fractions Decimals Arithmetic in Base Ten M7 M6 M5 Equivalent Fractions M5 M8 Shapes Time Fractions Length Money Data M5 Construct Lines Angles Shapes Add Subtract to 100 M7 Equal Groups M4 Find the Area M4 M3 M6 Add Subtract Big Numbers M3 M6 Work with Shapes M5 Multiply Divide Tricky Numbers Numbers to 20 Digital Activities 35 M5 Add Subtract Big Numbers Add Subtract Solve M2 Numbers to 15 Digital Activities 35 M4 Measure Length M4 Counting Place Value Multiply Divide Friendly Numbers G4 G6 M3 Explore Length M1 M3 Meet Place Value Measure Solve G2 M2 Add Subtract Small Numbers M6 Analyzing Comparing Composing Shapes Numbers 10 20 Count to 100 by Ones and Tens Number Pairs Addition Subtraction to 10 Numbers to 10 Digital Activities 50 M1 G1 M5 M4 Comparison of Length Weight Capacity Numbers to 10 Putting It ALL Together 1 Data Sets and Distributions M8 Probability and Sampling M7 Exponents and Scientific Notation M9 Putting It ALL Together M8 Pythagorean Theorem and Irrational Numbers M9 Putting It ALL Together WEEK Measurement Statistics and Probability v

Overview G5M1 Topics and Lesson Objectives Objective Topic A Multiplicative Patterns on the Place Value Chart Lesson 1 Reason concretely and pictorially using place value understanding to relate adjacent base ten units from millions to thousandths Lesson 2 Reason abstractly using place value understanding to relate adjacent base ten units from millions to thousandths Lesson 3 Use exponents to name place value units and explain patterns in the placement of the decimal point Lesson 4 Use exponents to denote powers of 10 with application to metric conversions Topic B Decimal Fractions and Place Value Patterns Lesson 5 Name decimal fractions in expanded unit and word forms by applying place value reasoning Lesson 6 Compare decimal fractions to the thousandths using like units and express comparisons with

G5M1 Overview Topic F Dividing Decimals Lesson 13 Divide decimals by single digit whole numbers involving easily identifiable multiples using place value understanding and relate to a written method Lesson 14 Divide decimals with a remainder using place value understanding and relate to a written method Lesson 15 Divide decimals using place value understanding including remainders in the smallest unit Lesson 16 Solve word problems using decimal operations End of Mission Assessment Topics D F ZEARN MATH Teacher Edition vii

Overview G5M1 MISSION 1 OVERVIEW In Mission 1 students understandings of the patterns in the base ten system are extended from Grade 4 s work with place value to include decimals to the thousandths place In Grade 5 students deepen their knowledge through a more generalized understanding of the relationships between and among adjacent places on the place value chart e g 1 tenth times any digit on the place value chart moves the digit one place value to the right Toward the mission s end students apply these new understandings as they reason about and perform decimal operations through the hundredths place Topic A opens the mission with a conceptual exploration of the multiplicative patterns of the base ten system using place value disks and a place value chart Students notice that multiplying by 1 000 is the same as multiplying by 10 10 10 Since each factor of 10 shifts the digits one place to the left multiplying by 10 10 10 which can be recorded in exponential form as 103 shifts the position of the digits to the left 3 places thus changing the digits relationships to the decimal point Application of these place value understandings to problem solving with metric conversions completes Topic A Topic B moves into the naming of decimal fraction numbers in expanded unit e g 4 23 4 ones 2 tenths 3 hundredths and word forms and concludes with using like units to compare decimal fractions Now in Grade 5 1 1 students use exponents and the unit fraction to represent expanded form e g 2 102 3 __ 10 4 ___ 100 200 34 Further students reason about differences in the values of like place value units and express those comparisons with symbols

G5M1 Overview Curriculum Study Teachers who have access to Curriculum Study Professional Development as part of their PD enabled Zearn Math School Accounts can log in to Zearn org for an interactive overview of this Mission including an in depth examination of the visual representations and strategies explored in this Mission connections to previously learned concepts and sample student work Digital Lessons Students also learn the concepts from this mission in their Independent Digital Lessons There are 16 Digital Lessons for Mission 1 It s important to connect teacher instruction and digital instruction at the mission level So when you start teaching Mission 1 set students to the first digital lesson of Mission 1 The intentional balance of learning with teachers and peers and learning independently in digital lessons ensures every student has multiple opportunities to represent engage with and express their math reasoning In the digital lessons students explore the concepts through interactive problem solving with embedded support that launches at the moment of misconception As students complete digital lessons they will automatically progress to the next lesson Go online to Zearn org to explore more of the digital lessons for this mission ZEARN MATH Teacher Edition ix

Overview G5M1 Terminology New or Recently Introduced Terms Exponent How many times a number is to be used in a multiplication sentence or expression Millimeter A metric unit of length equal to one thousandth of a meter Thousandths Related to place value Familiar Terms and Symbols1

G5M1 Overview Notes on Expression Equation and Number Sentence Please note the descriptions for the following terms which are frequently misused Expression A number or any combination of sums differences products or divisions of numbers that evaluates to a number e g 3 4 8 3 15 3 as distinct from an equation or number sentence Equation A statement that two expressions are equal e g 3 ____ 12 5 b 20 3 2 5 Number sentence also addition subtraction multiplication or division sentence An equation or inequality for which both expressions are numerical and can be evaluated to a single number e g 4 3 6 1 2 2 21 7 2 5 5 1 Number sentences are either true or false e g 4 4 6 2 and 21 7 4 and contain no unknowns Suggested Tools and Representations Number lines A variety of templates including a large one for the back wall of the classroom Personal white board Place value charts At least one per student for an insert in their personal board Place value disks Personal White Boards Materials Needed for Personal White Boards 1 heavy duty clear sheet protector 1 piece of stiff red tag board 11 8 1 4 1 piece of stiff white tag board 11 8 1 4 1 3 3 piece of dark synthetic cloth for an eraser e g felt 1 low odor blue dry erase marker fine point Directions for Creating Personal White Boards Cut your white and red tag to specifications Slide into the sheet protector Store your eraser on the red side Store markers in a separate container to avoid stretching the sheet protector Suggestions for Use The white side of the board is the paper Students generally write on it and if working individually turn the board over to signal to the teacher that they have completed their work Templates such as place value charts number bond mats and number lines can be stored between the two pieces of tag board for easy access and reuse The tag board can be removed if necessary to project the work ZEARN MATH Teacher Edition xi

PAGE 1 ZEARN MID MISSION ASSESSMENT Name G5 M1 Date 1 Compare using

G5M1 Mid Mission Assessment b Do all of the digits in 8 88 have the same value Explain using words numbers or the place value chart c Multiply 8 88 104 Explain the shift of the digits and the change in the value of each digit d Divide 8 88 102 Explain how you determine the placement of the decimal point in your quotient and how that changed the value of each digit 3 Rainfall collected in a rain gauge was found to be 2 3 cm Convert 2 3 cm to meters Write an equation to show your work PAGE 2

PAGE 3 G5M1 Mid Mission Assessment 4 Average annual rainfall totals for cities in New York are listed below City Rainfall Rochester 0 97 meter Ithaca 0 947 meter Saratoga Springs 1 5 meters New York City 1 268 meters a Put the rainfall measurements in order from least to greatest b Round each of the rainfall totals to the nearest tenth c Imagine New York City s rainfall is the same every year How much rain would fall in 100 years Show your work and or explain your reasoning d Write an equation using an exponent that would express the 100 year total rainfall Explain how the digits have shifted position and why

PAGE 1 ZEARN END OF MISSION ASSESSMENT Name G5 M1 Date 1 Solve each problem and write the answer in standard form a 7 hundredths 14 hundredths tenth s hundredth s hundredth s b 32 hundredths 18 hundredths tenth s c 4 7 0 3 d 5 0 2 hundredth s hundredth s tenth s tenth s tenth s tenth s tenth s tenth s 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use Portions of this work Zearn Math are derivative of Eureka Math and licensed by Great Minds 2019 Great Minds All rights reserved

PAGE 2 G5M1 End of Mission Assessment 2 Solve each by drawing a model of the place value chart with chips and using the vertical method a 9 40 2 8 b 7 1 42 c 24 07 6 93 d 63 54 54 47

PAGE 3 G5M1 End of Mission Assessment 3 Solve each by using a place value strategy such as an area model the place value chart or algorithm a 2 0 34 b 3 4 26 c 4 56 4 d 6 3 19

PAGE 4 G5M1 End of Mission Assessment 4 Complete the number sentence Express the quotient in unit form and then in standard form a 8 1 9 tenths 9 b 14 21 7 ones 7 ones tenths hundredths 7 hundredths

PAGE 5 G5M1 End of Mission Assessment 5 Solve each by drawing a model of the place value chart with chips and using the standard algorithm a 0 9 2 ones tenths hundredths tenths hundredths 2 0 9 b 7 6 5 ones 5 7 6

G5M1 Topic A TOPIC A Multiplicative Patterns on the Place Value Chart Topic A begins with a conceptual exploration of the multiplicative patterns of the base ten system This exploration extends the place value work done with multi digit whole numbers in Grade 4 to larger multi digit whole numbers and decimals Students use place value disks and a place value chart to build the place value chart from millions to thousandths They compose and decompose units crossing the decimal with a view toward 1 extending their knowledge of the 10 times as large and __ 10 as large relationships among whole number places to that of adjacent decimal places This concrete experience is linked to the effects on the product when multiplying any number by a power of ten For example students notice that multiplying 0 4 by 1 000 shifts the position of the digits to the left three places changing the digits relationships to the decimal point and producing a product with a value that is 10 10 10 as large 400 0 Students explain these changes in value and shifts in position in terms of place value Additionally students learn a new and more efficient way to represent place value units using exponents e g 1 thousand 1 000 103 Conversions among metric units such as kilometers meters and centimeters give students an opportunity to apply these extended place value relationships and exponents in a meaningful context by exploring word problems in the last lesson of Topic A Objective Topic A Multiplicative Patterns on the Place Value Chart Lesson 1 Reason concretely and pictorially using place value understanding to relate adjacent base ten units from millions to thousandths Lesson 2 Reason abstractly using place value understanding to relate adjacent base ten units from millions to thousandths Lesson 3 Use exponents to name place value units and explain patterns in the placement of the decimal point Lesson 4 Use exponents to denote powers of 10 with application to metric conversions ZEARN MATH Teacher Edition 1

G5M1 Topic A Lesson 1 Lesson 1 YOUR NOTES Reason concretely and pictorially using place value understanding to relate adjacent base ten units from millions to thousandths Warm Up FLUENCY PRACTICE Rename the Units Choral Response NOTE This fluency activity reviews foundations that lead into today s Concept Exploration T Write 10 ones ten Say the number sentence S 10 ones 1 ten T Write 20 ones tens Say the number sentence S 20 ones 2 tens T 30 ones S 3 tens Repeat the process for 80 ones 90 ones 100 ones 110 ones 120 ones 170 270 670 640 and 830 MULTIPLE MEANS OF ACTION AND EXPRESSION Throughout Zearn Math place value language is key In earlier grades teachers use units to refer to a number such as 245 as two hundred forty five Likewise in Grades 4 and 5 decimals should be read emphasizing their unit form For example 0 2 would be read 2 tenths rather than zero point two This emphasis on unit language not only strengthens student place value understanding but it also builds important parallels between whole number and decimal fraction understanding Decimal Place Value Materials S Personal white board unlabeled hundreds to hundredths place value chart Lesson 1 Fluency Template NOTE Reviewing this Grade 4 topic lays a foundation for students to better understand place value to bigger and smaller units T Project unlabeled hundreds to hundredths place value chart Draw 3 ten disks in the tens column How many tens do you see ZEARN MATH Teacher Edition 3

Topic A Lesson 1 YOUR NOTES G5M1 S 3 tens T Write 3 underneath the disks There are 3 tens and how many ones S Zero ones T Write 0 in the ones column Below it write 3 tens Fill in the blank S 3 tens 30 Repeat the process for 3 tenths 0 3 T Write 4 tenths Show the answer in your place value chart S Draw four 1 tenth disks Below it write 0 4 Repeat the process for 3 hundredths 43 hundredths 5 hundredths 35 hundredths 7 ones 35 hundredths 9 ones 24 hundredths and 6 tens 2 ones 4 hundredths NOTE Place value disks are used as models throughout the curriculum and can be represented in two different ways A disk with a value labeled inside of it as shown should be drawn or placed on a place value chart with no headings The value of the disk in its appropriate column indicates the column heading A place value disk drawn as a dot should be used on place value charts with headings The dot is a faster way to represent the place value disk and is used as students move further away from a concrete stage of learning WORD PROBLEM Farmer Jim keeps 12 hens in every coop If Farmer Jim has 20 coops how many hens does he have in all If every hen lays 9 eggs on Monday how many eggs will Farmer Jim collect on Monday Explain your reasoning using words numbers or pictures NOTE This problem is intended to activate prior knowledge from Grade 4 and offer a successful start to Grade 5 Some students may use area models to solve while others may choose to use the standard algorithm Still others may draw tape diagrams to show their thinking Allow students to share work and compare approaches Concept Exploration Materials S Millions through thousandths place value chart Concept Exploration Template personal white board The place value chart and its times 10 relationships are familiar territory for students New learning in Grade 5 focuses on understanding a new fractional unit of thousandths as well as 4 ZEARN MATH Teacher Edition

G5M1 Topic A Lesson 1 the decomposition of larger units to those that are 1 tenth as large Building the place value chart from right tenths to left millions before beginning the following problem sequence may be advisable Encourage students to multiply and then bundle to form the next largest place e g 10 1 hundred 10 hundreds which can be bundled to form 1 thousand YOUR NOTES PROBLEM 1 Divide single units by 10 to build the place value chart to introduce thousandths T Slide your millions through thousandths place value chart into your personal white board Show 1 million using disks on the place value chart S Work T How can we show 1 million using hundred thousands Work with your partner to show this on your chart S 1 million is the same as 10 hundred thousands T What is the result if I divide 10 hundred thousands by 10 Talk with your partner and use your chart to find the quotient T Circulate I saw that David put 10 disks in the hundred thousands place and then distributed them into 10 equal groups How many are in each group S When I divide 10 hundred thousands by 10 I get 1 hundred thousand in each group T Let me record what I hear you saying Record on class board 10 hundred thousands 10 1 hundred thousand 1 million 10 1 hundred thousand 1 hundred thousand is __ 10 as large as 1 million 1 Millions Hundred Ten Thousands Hundreds Thousands Thousands 1 10 1 Tens Ones Tenths Hundredths Thousandths T Draw 1 hundred thousands disk on your chart What is the result if we divide 1 hundred thousand by 10 Show this on your chart and write a division sentence Continue this sequence until the hundredths place is reached emphasizing the unbundling for 10 of the smaller unit and then the division Record the place values and equations using unit form on the board being careful to point out the 1 tenth as large relationship 1 million 10 1 hundred thousand 1 hundred thousand 10 1 ten thousand 1 ten thousand 10 1 thousand 1 thousand 10 1 hundred ZEARN MATH Teacher Edition 5

Topic A Lesson 1 YOUR NOTES G5M1 Continue through 1 tenth 10 1 hundredth T What patterns do you notice in the way the units are named in our place value system S The ones place is the middle There are tens on the left and tenths on the right hundreds on the left and hundredths on the right T Point to the chart Using this pattern can you predict what the name of the unit that is to the right of the hundredths place 1 tenth as large as hundredths might be S Share Label the thousandths place T Think about the pattern that we ve seen with other adjacent places Talk with your partner and predict how we might show 1 hundredth using thousandths disks Show this on your chart S Just like all the other places it takes 10 of the smaller unit to make 1 of the larger so it will take 10 thousandths to make 1 hundredth T Use your chart to show the result if we divide 1 hundredth by 10 and write the division sentence S Share T Add this equation to the others on the board PROBLEM 2 Multiply copies of one unit by 10 100 and 1 000 0 4 10 0 4 100 0 4 1 000 T Use digits to represent 4 tenths at the top of your place value chart S Write T Work with your partner to find the value of 10 times 0 4 Show your result at the bottom of your place value chart S 4 tenths 10 40 tenths which is the same as 4 wholes 4 ones is 10 times as large as 4 tenths T On your place value chart use arrows to show how the value of the digits has changed On the place value chart draw an arrow to indicate the shift of the digit to the left and write 10 near the arrow T Why does the digit move one place to the left S Because it is 10 times as large it has to be bundled for the next larger unit Repeat with 0 4 100 and 0 4 1 000 Use unit form to state each problem and encourage students to articulate how the value of the digit changes and why it changes position in the chart 6 ZEARN MATH Teacher Edition

G5M1 PROBLEM 3 Divide copies of one unit by 10 100 and 1 000 6 10 6 100 6 1 000 Topic A Lesson 1 YOUR NOTES Follow a similar sequence to guide students in articulating changes in value and shifts in position while showing it on the place value chart Repeat with 0 7 10 0 7 100 and 0 05 10 PROBLEM 4 Multiply mixed units by 10 100 and 1 000 2 43 10 2 43 100 2 43 1 000 T Write the digits two and forty three hundredths on your place value chart and multiply by 10 then 100 and then 1 000 Compare these products with your partner Lead students to discuss how the digits shift as a result of their change in value by isolating one digit such as the 3 and comparing its value in each product PROBLEM 5 745 10 745 100 745 1 000 Engage in a similar discussion regarding the shift and change in value for a digit in these division problems See discussion above MULTIPLE MEANS OF ENGAGEMENT Look for students who may not yet be fluent with the place value chart and the relationships between adjacent place values understanding that a digit is 10 times what it is in the place to its right A lack of automaticity with the PVC will make it difficult for students to process the new concepts and place values presented early in this Mission Check your Tower Alerts Report frequently during the start of the Mission paying close attention to students for whom Zearn recommends bookmarking specific foundational content ZEARN MATH Teacher Edition 7

Topic A Lesson 1 YOUR NOTES G5M1 MULTIPLE MEANS OF ENGAGEMENT Proportional materials such as base ten blocks can help multilingual learners distinguish between place value labels like hundredth and thousandth more easily by offering clues to their relative sizes These students can be encouraged to name the units in their primary language and then compare them to the counterparts in the classroom s primary language Sometimes the roots of these number words are very similar These parallels enrich the experience and understanding of all students Independent Digital Lesson Lesson 1 Move the Digits Students also learn the concepts from this lesson in the Independent Digital Lesson The intentional balance of learning with teachers and peers and learning independently in digital lessons ensures every student has multiple opportunities to represent engage with and express their math reasoning See the digital lesson notes below for a glimpse of the paper to pencil transfer of these math ideas Go online to see the full digital lesson 8 ZEARN MATH Teacher Edition

G5M1 Wrap Up Topic A Lesson 1 YOUR NOTES LESSON SYNTHESIS Guide students in a conversation to process today s lesson and surface any misconceptions or misunderstandings The questions below may be used to lead the discussion What do you notice about the number of zeros in your products when multiplying by 10 100 and 1 000 relative to the number of places the digits shift on the place value chart What patterns do you notice EXIT TICKET After today s lesson instruct students to complete the Exit Ticket A review of their Exit Ticket as well as continuously monitoring your Digital Reports can help you assess your students understanding of the concepts explored in today s lesson and plan more effectively for future lessons The questions from the Exit Ticket may be read aloud to the students Task Use the place value chart and arrows to show how the value of each digit changes 1 6 671 100 ZEARN MATH Teacher Edition 9

Topic A Lesson 1 YOUR NOTES G5M1 2 684 1 000 Answers 1 667 1 2 0 684 10 ZEARN MATH Teacher Edition

G5M1 Topic A Lesson 1 Fluency Template UNLABELED HUNDREDS THROUGH HUNDREDTHS PLACE VALUE CHART FLUENCY TEMPLATE ZEARN MATH Teacher Edition 11

Topic A Lesson 1 Lesson Template G5M1 MILLIONS THROUGH THOUSANDTHS PLACE VALUE CHART CONCEPT EXPLORATION TEMPLATE 1 000 000 Millions 100 000 10 000 1 000 Hundred Ten Thousands Thousands Thousands 100 10 1 Hundreds Tens Ones 1 __ 10 Tenths 1 ___ 100 1 ____ 1000 Hundredths Thousandths 12 ZEARN MATH Teacher Edition

G5M1 Topic A Lesson 2 Lesson 2 YOUR NOTES Reason abstractly using place value understanding to relate adjacent base ten units from millions to thousandths Warm Up FLUENCY PRACTICE Skip Counting Direct students to count forward and backward by threes to 36 emphasizing the transitions of crossing the ten Direct students to count forward and backward by fours to 48 emphasizing the transitions of crossing the ten NOTE Practicing skip counting on the number line builds a foundation for accessing higher order concepts throughout the year NOTE Fluency tasks are included not only as warm ups for the Lesson but also as opportunities to retain past number understandings and to sharpen those understandings needed for coming work Skip counting in Grade 5 provides support for the common multiple work covered in Mission 3 Additionally returning to a familiar and well understood fluency can provide a student with a feeling of success before tackling a new body of work Consider including body movements to accompany skip counting exercises e g jumping jacks toe touches arm stretches or dance movements like the Macarena Take Out the Tens Materials S Personal white board NOTE Decomposing whole numbers into different units lays a foundation to do the same with decimal fractions T Write 83 ones tens ones Write the number sentence S Write 83 ones 8 tens 3 ones Repeat the process for 93 ones 103 ones 113 ones 163 ones 263 ones 463 ones and 875 ones Bundle Ten and Change Units NOTE Reviewing this fluency area helps students work toward full undersanding of changing place value units in the base ten system ZEARN MATH Teacher Edition 13

Topic A Lesson 2 YOUR NOTES G5M1 T Write 10 hundreds 1 Say the number sentence filling in the blank S 10 hundreds 1 thousand Repeat the process for 10 tens 1 10 ones 1 10 thousandths 1 and 10 hundredths 1 10 tenths 1 Multiply and Divide by 10 Materials T Millions through thousandths place value chart Lesson 1 Concept Exploration Template S Personal white board millions through thousandths place value chart Lesson 1 Concept Exploration Template NOTE Reviewing this skill from Lesson 1 helps students work toward full understanding T Project the place value chart from millions to thousandths Draw three ones disks and write the total value of the disks below it S Draw three disks in the ones column Below it write 3 T Multiply by 10 Cross out each disk and the number 3 to show that you re changing its value S Cross out each disk in the ones column and the 3 Draw arrows to the tens column and draw three disks in the tens column Below it write 3 in the tens column and 0 in the ones column Repeat the process for 2 hundredths 3 tenths 2 hundredths 3 tenths 2 hundredths 4 thousandths 2 tenths 4 hundredths 5 thousandths and 1 tenth 3 thousandths Repeat the process for dividing by 10 for this possible sequence 2 ones 3 tenths 2 ones 3 tenths 2 ones 3 tenths 5 hundredths 5 tenths 2 hundredths and 1 ten 5 thousandths WORD PROBLEM A school district ordered 247 boxes of pencils Each box contains 100 pencils If the pencils are to be shared evenly among 10 classrooms how many pencils will each class receive Draw a place value chart to show your thinking NOTE ON WORD PROBLEMS Word Problems are often designed to reach back to the learning in previous Lessons This problem requires students to show thinking using the concrete pictorial approach used in Lesson 1 to find the product and quotient This will act as an anticipatory set for today s Concept Exploration 14 ZEARN MATH Teacher Edition

G5M1 Concept Exploration Topic A Lesson 2 YOUR NOTES Materials S Millions through thousandths place value chart Lesson 1 Concept Exploration Template personal white board T Turn and share with your partner What do you remember from yesterday s lesson about how adjacent units on the place value chart are related S Share T Moving one position to the left on the place value chart makes units 10 times larger Conversely moving one position to the right makes units 1 tenth the size As students move through the sequence of problems encourage a move away from the concrete pictorial representations of the products and quotients and instead move toward reasoning about the patterns of the number of zeros in the products and quotients and the placement of the decimal PROBLEM 1 367 10 367 10 4 367 10 4 367 10 Write or project the first two expressions T Work with your partner to solve these problems Write two complete number sentences on your board S 367 10 3 670 367 10 36 7 T Explain how you got your answers What are the similarities and differences between the two answers S The digits are the same but their values have changed Their position in the number is different The 3 is 10 times larger in the product than in the factor It was 3 hundreds Now it is 3 thousands The six started out as 6 tens but once it was divided by 10 it is now 1 tenth as large because it is 6 ones T What patterns do you notice in the number of zeros in the product and the placement of the decimal in the quotient What do you notice about the number of zeros in your factors and the shift in places in your product What do you notice about the number of zeros in your divisor and the shift in places in your quotient S Share ZEARN MATH Teacher Edition 15

Topic A Lesson 2 YOUR NOTES G5M1 Repeat this sequence with the last pair of expressions 4 367 10 and 4 367 10 Encourage students to visualize the place value chart and attempt to find the product and quotient without drawing the chart Circulate Watch for misconceptions and students who are not ready to work on an abstract level As students share thinking encourage the use of the language 10 times as large and 1 tenth as large PROBLEM 2 215 6 100 215 6 100 3 7 100 3 7 100 T Now solve with your partner by visualizing your place value chart and recording only your products and quotients You may check your work using a place value chart Circulate Look for students who may still need the support of the place value chart S Solve T Compare your work with your partner s Do you agree How many times did the digits shift in each problem and why Share your thinking with your partner S The digits shifted two places to the left when we multiplied and two places to the right when we divided This time the digits each shifted two places because there are 2 zeros in 100 The values of the products are 100 times as large so the digits had to shift to larger units PROBLEM 3 0 482 1 000 482 1 000 Follow a similar sequence for these expressions MULTIPLE MEANS OF ACTION AND EXPRESSION Although students are being encouraged toward more abstract reasoning in the Concept Exploration it is important to keep concrete materials like place value charts and place value disks accessible to students while these place value relationships are being solidified Giving students the freedom to move between levels of abstraction on a task by task basis can decrease anxiety when working with more difficult applications 16 ZEARN MATH Teacher Edition

G5M1 Topic A Lesson 2 Independent Digital Lesson YOUR NOTES Lesson 2 Digit Dance Students also learn the concepts from this lesson in the Independent Digital Lesson The intentional balance of learning with teachers and peers and learning independently in digital lessons ensures every student has multiple opportunities to represent engage with and express their math reasoning There are no notes for this digital lesson Go online to see the full digital lesson Wrap Up LESSON SYNTHESIS Guide students in a conversation to process today s lesson and surface any misconceptions or misunderstandings The question below may be used to lead the discussion When asked to find the number 1 tenth as large as another number what operation would you use Explain how you know EXIT TICKET After today s lesson instruct students to complete the Exit Ticket A review of their Exit Ticket as well as continuously monitoring your Digital Reports can help you assess your students understanding of the concepts explored in today s lesson and plan more effectively for future lessons The questions from the Exit Ticket may be read aloud to the students Task 1 Solve a 32 1 10 b 3 632 1 10 b 455 1 000 2 Solve a 455 1 000 ZEARN MATH Teacher Edition 17

Topic A Lesson 2 YOUR NOTES G5M1 Answers 1 a 321 b 363 21 2 a 455 000 b 0 455 18 ZEARN MATH Teacher Edition

G5M1 Topic A Lesson 3 Lesson 3 YOUR NOTES Use exponents to name place value units and explain patterns in the placement of the decimal point Warm Up FLUENCY PRACTICE State the Unit as a Decimal Choral Response NOTE Reviewing these skills helps students work toward full understanding of decimal place value which assists them in applying their place value skills to more difficult concepts T Write 9 tenths as a decimal Complete the number sentence by saying the unknown value S 0 9 T Write 10 tenths S 1 0 T Write 11 tenths S 1 1 T Write 12 tenths S 1 2 T Write 18 tenths S 1 8 T Write 28 tenths S 2 8 T Write 58 tenths S 5 8 Repeat the process for 9 hundredths 10 hundredths 20 hundredths 60 hundredths 65 hundredths 87 hundredths and 118 tenths The last item is an extension Multiply and Divide by 10 100 and 1 000 Materials S Millions through thousandths place value chart Lesson 1 Concept Exploration Template NOTE This fluency drill reviews concepts taught in Lesson 2 ZEARN MATH Teacher Edition 19

Topic A Lesson 3 YOUR NOTES G5M1 T Project the place value chart from millions through thousandths Draw two disks in the thousandths place and write the value below it S Draw two disks in the thousandths column Below it write 0 002 in the appropriate place value columns T Multiply by 10 Cross out each disk and the number 2 to show that you re changing its value S Cross out each 1 thousandths disk and the 2 Draw arrows to the hundredths column and draw two disks there Below it they write 2 in the hundredths column and 0 in the ones and tenths column Repeat the process for the following possible sequence 0 004 100 0 004 1000 1 004 1000 1 024 100 1 324 100 1 324 10 and 1 324 1000 Repeat the process for dividing by 10 100 and 1000 for the following possible sequence 4 1 4 1 10 4 1 100 41 1000 and 123 1000 WORD PROBLEM Jack and Kevin are creating a mosaic for art class by using fragments of broken tiles They want the mosaic to have 100 sections If each section requires 31 5 tiles how many tiles will they need to complete the mosaic Explain your reasoning with a place value chart NOTE This Word Problem provides an opportunity for students to reason about the value of digits after being multiplied by 100 Concept Exploration Materials S Powers of 10 chart Concept Exploration Template personal white board PROBLEM 1 T Draw or project the powers of 10 chart adding numerals as the discussion unfolds 100 10 x 10 10 10 x 1 T Write 10 10 on the board On your personal board fill in the unknown factor to complete this number sentence 20 ZEARN MATH Teacher Edition

G5M1 Topic A Lesson 3 YOUR NOTES S 10 1 10 T Write 10 number sentence 100 on the board Fill in the unknown factor to complete this S 10 10 100 T This time using only 10 as a factor how could you multiply to get a product of 1 000 Write the multiplication sentence on your personal board S 10 10 10 1 000 T Work with your partner What would the multiplication sentence be for 10 000 using only 10 as a factor Write it on your personal board S Write T How many factors of 10 did we have to multiply to get to 1 000 S 3 T How many factors of 10 do we have to multiply to get 10 000 S 4 T Say the number sentence S 10 10 10 10 10 000 T How many zeros are in our product of 10 000 S 4 zeros T What patterns do you notice Turn and share with your partner S The number of zeros is the same on both sides of the equation The number of zeros in the product is the same as the total number of zeros in the factors I see three zeros on the left side and there are three zeros on the right side for 10 10 10 1 000 The 1 moves one place to the left every time we multiply by 10 It s like a place value chart Each number is 10 times as much as the last one T Using this pattern how many factors of 10 do we have to multiply to get 1 million Work with your partner to write the multiplication sentence S Write T How many factors of 10 did you use S 6 T Why did we need 6 factors of 10 S 1 million has 6 zeros T Write the term exponent on the board We can use an exponent to represent how many times we use 10 as a factor We can write 10 10 as 102 Add to the chart We say Ten to the second power The 2 point to exponent is the exponent and it tells us how many times to use 10 as a factor T How do you express 1 000 using exponents Turn and share with your partner S We multiply 10 10 10 which is three times so the answer is 103 There are three zeros in 1 000 so it s ten to the third power T Working with your partner complete the chart using the exponents to represent each value on the place value chart ZEARN MATH Teacher Edition 21

Topic A Lesson 3 G5M1 YOUR NOTES 1 000 000 100 000 10 000 1 000 100 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 1 106 105 104 103 102 101 After reviewing the chart with the students challenge them to multiply 10 one hundred times As some start to write it out others may write 10100 a googol with exponents T Now look at the place value chart Let s read our powers of 10 and the equivalent values S Ten to the second power equals 100 Ten to the third power equals 1 000 Continue to read chorally up to 1 million T A googol has 100 zeros Write it using an exponent on your personal board S Write 10100 PROBLEM 2 105 T Write ten to the fifth power as a product of tens S 105 10 10 10 10 10 T Find the product S 105 100 000 Repeat with more examples as needed PROBLEM 3 10 100 T Work with your partner to write this expression using an exponent on your personal board Explain your reasoning S I multiply 10 100 to get 1 000 so the answer is ten to the third power There are 3 factors of 10 There are three tens I can see one 10 in the first factor and two more tens in the second factor Repeat with 100 1 000 and other examples as needed PROBLEM 4 3 102 3 4 103 T Compare these expressions to the ones we ve already talked about S These have factors other than 10 22 ZEARN MATH Teacher Edition

G5M1 Topic A Lesson 3 T Write 3 102 without using an exponent Write it on your personal board YOUR NOTES S 3 100 T What s the product S 300 T If you know that 3 100 equals 300 then what is 3 102 Turn and explain to your partner S The product is also 300 102 and 100 are the same amount so the product will be the same T Use what you learned about multiplying decimals by 10 100 and 1 000 and your new knowledge about exponents to solve 3 4 103 with your partner S 3 4 103 3 400 Repeat with 4 021 102 and other examples as needed Have students share their solutions and reasoning about multiplying decimal factors by powers of 10 In particular students should articulate the relationship between the exponent how the values of the digits change and the placement of the decimal in the product PROBLEM 5 700 102 7 1 102 T Write 700 102 without using an exponent and find the quotient Write it on your personal board S 700 100 7 T If you know that 700 100 equals 7 then what is 700 102 Turn and explain to your partner S The quotient is 7 because 102 100 7 hundreds divided by 1 hundred equals 7 T Use what you know about dividing decimals by multiples of 10 and your new knowledge about exponents to solve 7 1 102 with your partner S Work T Tell your partner what you notice about the relationship between the exponents and how the values of the digits change Discuss how you decided where to place the decimal Repeat with more examples as needed PROBLEM 6 Complete this pattern 0 043 4 3 430 T Write the pattern on the board Turn and talk with your partner about the pattern on the board How is the value of the 4 changing as we move to the next term in the sequence Draw a place value chart to explain your ideas as you complete the pattern and use an exponent to express the relationships ZEARN MATH Teacher Edition 23

Topic A Lesson 3 YOUR NOTES G5M1 S The 4 shifted two places to the left Each number is being multiplied by 100 to get the next one Each number is multiplied by 10 twice Each number is multiplied by 102 Repeat with 6 300 000 630 6 3 and other patterns as needed MULTIPLE MEANS OF REPRESENTATION Providing non examples is a powerful way to clear up mathematical misconceptions and generate conversation around the work Highlight those examples such as 105 pointing out its equality to 10 10 10 10 10 but not to 10 5 or even 510 MULTIPLE MEANS OF ACTION AND EXPRESSION Very large numbers like one million and beyond can capture the imagination of students The following benchmarks may help students appreciate just how large a googol is There are approximately 1024 stars in the observable universe There are approximately 1080 atoms in the observable universe A stack of 70 numbered cards can be ordered in approximately 1 googol different ways That means that the number of ways a stack of only 70 cards can be shuffled is more than the number of atoms in the observable universe Independent Digital Lesson Lesson 3 Excellence with Exponents Students also learn the concepts from this lesson in the Independent Digital Lesson The intentional balance of learning with teachers and peers and learning independently in digital lessons ensures every student has multiple opportunities to represent engage with and express their math reasoning See the digital lesson notes below for a glimpse of the paper to pencil transfer of these math ideas Go online to see the full digital lesson 24 ZEARN MATH Teacher Edition

G5M1 Topic A Lesson 3 YOUR NOTES Wrap Up LESSON SYNTHESIS Guide students in a conversation to process today s lesson and surface any misconceptions or misunderstandings The questions below may be used to lead the discussion What is an exponent and how can exponents be useful in representing numbers This question could also serve as a prompt for math journals Journaling about new vocabulary throughout the year can be a powerful way for students to solidify their understanding of new terms How would you write 1 000 using exponents How would you write it as a multiplication sentence using only 10 as a factor Explain to your partner the relationship we saw between the exponents and the number of places the digits shift when you multiplied or divided by a power of 10 ZEARN MATH Teacher Edition 25

Topic A Lesson 3 YOUR NOTES G5M1 EXIT TICKET After today s lesson instruct students to complete the Exit Ticket A review of their Exit Ticket as well as continuously monitoring your Digital Reports can help you assess your students understanding of the concepts explored in today s lesson and plan more effectively for future lessons The questions from the Exit Ticket may be read aloud to the students Task 1 Write the following in exponential form and as a multiplication sentence using only 10 as a factor e g 100 10 10 10 a 1 000 b 100 100 2 Write the following in standard form e g 4 10 400 a 3 10 b 2 16 10 c 800 10 d 754 2 10 Answers 1 a 10 3 10 10 10 b 10 4 10 10 10 10 2 a 300 b 21 600 c 0 8 d 7 542 26 ZEARN MATH Teacher Edition

G5M1 Topic A Lesson 3 Lesson Template 10 x 10 POWERS OF 10 CHART CONCEPT EXPLORATION TEMPLATE ZEARN MATH Teacher Edition 27

G5M1 Lesson 4 Topic A Lesson 4 YOUR NOTES Use exponents to denote powers of 10 with application to metric conversions Warm Up FLUENCY PRACTICE Multiply and Divide Decimals by 10 100 and 1 000 Materials S Millions through thousandths place value chart Lesson 1 Concept Exploration Template personal white board NOTE This fluency activity reviews concepts taught in earlier lessons and helps students work toward full understanding of multiplying and dividing decimals by 10 100 and 1000 T Project the place value chart from millions to thousandths Draw 3 disks in the tens place 2 disks in the ones place and 4 disks in the tenths place Say the value as a decimal S 32 4 thirty two and four tenths T Write the number on your personal boards and multiply it by 10 S Write 32 4 on their place value charts cross out each digit and shift the number one place value to the left to show 324 T Show 32 4 divided by 10 S Write 32 4 on their place value charts cross out each digit and shift the number one place value to the right to show 3 24 Repeat the process and sequence for 32 4 100 32 4 100 837 1000 and 0 418 1000 Write the Unit as a Decimal Materials S Personal white board NOTE Reviewing these skills helps students work toward full understanding of decimal place value This in turn helps them apply their place value skills to more difficult concepts T Write 9 tenths on the board Show this unit form as a decimal S 0 9 T Write 10 tenths on the board S 1 0 ZEARN MATH Teacher Edition 29

Topic A Lesson 4 YOUR NOTES G5M1 Repeat the process for 20 tenths 30 tenths 70 tenths 9 hundredths 10 hundredths 11 hundredths 17 hundredths 57 hundredths 42 hundredths 9 thousandths 10 thousandths 20 thousandths 60 thousandths 64 thousandths and 83 thousandths Write in Exponential Form Materials S Personal white board NOTE Reviewing this skill in isolation lays a foundation for students to apply it when multiplying during today s Concept Exploration T Write 100 10 Write 100 in exponential form S Write 100 102 Repeat the process for 1 000 10 000 and 1 000 000 Convert Units Materials S Personal white board NOTE Reviewing conversions in isolation lays a foundation for students to apply it when multiplying and dividing during today s Concept Exploration Use this quick fluency drill to activate prior knowledge of these familiar equivalents T Write 1 km m Fill in the unknown number S Write 1 km 1 000 m Repeat the process and procedure for 1 kg g 1 liter mL 1 m cm WORD PROBLEM Materials S Meter strip Word Problem Template 1 Thousands to thousandths metric length place value chart Word Problem Template 2 T Here is a place value chart Show the Thousands to thousandths metric length place value chart Have students turn to the Thousands to thousandths metric length place value chart in their workbooks thousands hundreds tens ones tenths hundredths thousandths 1000 meters 100 meters 10 meters 1 meter 1 _ 10 meter 1 _ 100 meter 1 _ 1000 meter 30 ZEARN MATH Teacher Edition

G5M1 Topic A Lesson 4 T Here is a set of column headings based on metric length related to our place value chart designating one meter as the base unit or the ones place YOUR NOTES T Use your meter strip to show and explain to your partner the lengths that relate to the tenths hundredths and thousandths places Move through the tenths hundredths and 1 thousandths until identifying and naming _ 1000 meter as 1 millimeter Have students then explain to their partner lengths that relate to the tens hundreds and thousands places For example 10 meters would be about the length of the classroom 100 meters about the length of a football field and 1 000 meters is a kilometer which may be conceived in relation to the distance to their home from school NOTE Be sure to establish the following which is essential to today s Concept Exploration 1 1 millimeter mm _ 1000 meter m 0 001 meter 1 1 centimeter cm _ 100 meter m 0 01 meter The relationship of metric lengths to the place value chart will also help students to realize when they are moving from smaller to larger or larger to smaller units Consider reviewing the multiplicative relationships between the units MULTIPLE MEANS OF ACTION AND ENGAGEMENT The place value chart can be used throughout today s lesson to help students think through whether they are renaming from small to large units or large to small units Throughout the school day take the opportunity to extend thinking by asking students to make a conversion to the unit that is 1 tenth as large as a meter decimeter and the unit 10 times as large decameter Students can do research about these and other metric units that are less commonly used or investigate industry applications for the less familiar units For example decameters are often used to measure altitude in meteorology and decimeters are commonly used in physical chemistry Concept Exploration Materials S Meter strip Word Problem Template 1 personal white board Each problem below includes conversions from both large units to smaller units and small to larger units Allow students the time to reason about how the change in the size of the unit will affect the quantity and size of the units needed to express an equivalent measure NOTE We recommend that you draw the measurements in each problem below as size can be distorted on a computer ZEARN MATH Teacher Edition 31

Topic A Lesson 4 YOUR NOTES G5M1 PROBLEM 1 Rename or convert large units as smaller units using multiplication equations with exponents T Draw and label a line 2 meters long on the board T How many centimeters equal 2 meters S 200 centimeters Label the same 2 meter point as 200 centimeters Fill in the first row of the t chart T Tell me a multiplication equation multiplying by 2 to get 200 S 2 100 200 T Restate the equation renaming 100 with an exponent S 2 102 200 T With your partner determine how many centimeters are equal to 1 37 meters Use your meter strip if it helps you S It s 1 meter and 37 centimeters It s more than 1 meter and less than 2 meters 37 hundredths of a meter is 37 centimeters 100 cm 37 cm 137 cm T What is the equivalent measure in centimeters S 137 centimeters On the board label the same 1 37 meter point as 137 centimeters Fill in the second row of the chart T On your boards show this conversion using a multiplication equation with an exponent meters centimeters millimeters 2 200 2 000 1 37 137 1 370 2 6 260 2 600 S 1 37 100 137 1 37 102 137 To rename meters as centimeters multiply by 102 T What must we do to the number of meters to rename them as centimeters To rename meters as millimeters multiply by 103 S Multiply the number of meters by 100 or 102 Record the rule on the chart Repeat with 2 6 meters T How can we use multiplication to rename a meter as millimeters Discuss with your partner S Multiply the number of meters by 1 000 or by 103 T Take a moment to write multiplication equations with exponents to find the number of millimeters to complete the third column of our chart T Show me your boards S Show 2 103 2 000 1 37 103 1 370 and 2 6 103 2 600 T S Fill in the equivalent millimeter measures together T Explain the difference between A and B to your partner Problem A Problem B 32 2 meters 103 2 000 meters 2 103 2 000 2 meters 2 000 millimeters ZEARN MATH Teacher Edition

G5M1 Topic A Lesson 4 S Problem A is not renaming or converting but multiplying 2 meters by 103 so the answer is 2 000 meters Problem B is renaming by multiplying 1 000 by 2 because each meter has a thousand millimeters in it After we multiply then we can name the unit That is the exact same measurement as 2 meters YOUR NOTES T Yes we are multiplying the number of meters by 103 Explain why we multiply to rename large units as small units Point to the 2 meter line drawn on the board S 1 meter 1 000 millimeters 2 meters 2 000 millimeters It s the number of meters that is being multiplied not the meters Multiplying didn t make 2 meters into more meters but renamed the 2 meters as 2 000 millimeters One meter got chopped up into 1 000 millimeters so we multiply the number of meters by 1 000 The length stays the same because we re making more units by decomposing a meter not by making more copies of a meter PROBLEM 2 Rename millimeters and centimeters as meters using division equations with exponents Again using the 2 meter line and chart reverse Problem 1 s sequence and convert from smaller to larger units dividing by 102 to rename or convert centimeters as meters dividing by 103 to rename or convert millimeters as meters millimeters centimeters meters 2 000 200 2 1 370 137 1 37 2 600 260 2 6 To rename centimeters to meters divide by 102 To rename millimeters to meters divide by 103 Culminate with the same reflection T We are dividing the number of meters by 102 or by 103 That is a method for renaming centimeters as meters and millimeters as meters Explain the difference between C and D with your partner Problem C Problem D 2 000 mm 103 2 mm 2 000 103 2 2 000 mm 2 m S 1 000 millimeters 1 meter 2 000 millimeters 2 meters It s the number of millimeters that is being divided not the millimeters Division renamed the 2 000 mm as 2 meters How many groups of 1 000 are in 2 thousands 1 000 millimeters got grouped together as 1 meter so we divide or make groups of 1 000 PROBLEM 3 A ribbon measures 4 5 meters Convert its length to centimeters A wire measures 67 millimeters Convert its length to meters ZEARN MATH Teacher Edition 33

Topic A Lesson 4 YOUR NOTES G5M1 NOTE The most important concept is the equivalence of the two measurements that is the length did not change which becomes very apparent when conversions are contextualized The ribbon and wire are not getting longer or shorter Clarify this understanding before moving on to finding the conversion equation by asking How can 4 5 and 4 500 represent the same length While the numeric values differ the unit size is also different 4 5 is meters 4 500 is millimeters Meters are 1 000 times as large as millimeters Therefore it takes fewer meters to represent the same amount as something measured in millimeters Lead students to articulate that when converting the number of large units to a number of smaller units they multiplied and when converting from small units to larger units they divided MULTIPLE MEANS OF REPRESENTATION The drawing of the 2 meter 200 centimeter and 2 000 millimeter lines supports student understanding especially when plotting 1 37 meters Butcher paper can be used if there is insufficient space on the class board or other surface normally used This also promotes student success with plotting decimal fractions on the number line Independent Digital Lesson Lesson 4 Millimeters Centimeters Meters Students also learn the concepts from this lesson in the Independent Digital Lesson The intentional balance of learning with teachers and peers and learning independently in digital lessons ensures every student has multiple opportunities to represent engage with and express their math reasoning See the digital lesson notes below for a glimpse of the paper to pencil transfer of these math ideas Go online to see the full digital lesson 34 ZEARN MATH Teacher Edition

G5M1 Topic A Lesson 4 YOUR NOTES Wrap Up LESSON SYNTHESIS Guide students in a conversation to process today s lesson and surface any misconceptions or misunderstandings The questions below may be used to lead the discussion Which of the following statements is false Explain your thinking to your partner 2 m 103 2 000 m 2 m 103 2 000 mm 2 103 2 000 2 m 2 000 mm Is it easier for you to think about converting from large units to smaller units or small units to larger units Why What is the difference in both the thinking and the operation required ZEARN MATH Teacher Edition 35

Topic A Lesson 4 YOUR NOTES G5M1 Let s look at the place value chart Explain to your partner the way the equivalence of 2 meters 20 tenth meters 200 centimeters and 2 000 millimeters is shown thousands 1 103 hundreds 1 102 tens 1 101 ones 1 tenths 1 101 hundredths 1 102 thousandths 1 103 1000 meters kilometer 100 meters hectometer 10 meters decameter 1 meter 1 _ 10 meter 1 _ 100 meter 1 _ 1000 meter decimeter centimeter millimeter 2 2 0 2 0 0 2 0 0 0 How can we use what we know about renaming meters to millimeters to rename kilograms to grams and liters to milliliters EXIT TICKET After today s lesson instruct students to complete the Exit Ticket A review of their Exit Ticket as well as continuously monitoring your Digital Reports can help you assess your students understanding of the concepts explored in today s lesson and plan more effectively for future lessons The questions from the Exit Ticket may be read aloud to the students Task 1 Convert using an equation with an exponent a 2 meters to centimeters 2 m b 40 millimeters to meters 40 mm cm m 2 Read each aloud as you write the equivalent measures a A piece of fabric measures 3 9 meters Express this length in centimeters b Ms Ramos s thumb measures 4 centimeters Express this length in meters Answers 1 a 200 2 10 2 200 b 0 04 40 10 3 0 04 2 a 390 cm b 0 04 m 36 ZEARN MATH Teacher Edition

ZEARN MATH Teacher Edition 37 METER STRIP WORD PROBLEM TEMPLATE 1

Topic A Lesson 4 Lesson Template G5M1 THOUSANDS TO THOUSANDTHS METRIC LENGTH PLACE VALUE CHART WORD PROBLEM TEMPLATE 2 thousands hundreds tens ones tenths hundredths thousandths 1000 meters 100 meters 10 meters 1 meter 1 _ 10 meter 1 _ 100 meter 1 _ 1000 meter 38 ZEARN MATH Teacher Edition

G5M1 Topic B TOPIC B Decimal Fractions and Place Value Patterns Naming decimal fractions in expanded unit and word forms in order to compare decimal fractions is the focus of Topic B Familiar methods of expressing expanded form are used but students are also encouraged to apply 1 their knowledge of exponents to expanded forms e g 4 300 01 4 103 3 102 1 ___ 100 Place value charts and disks offer a beginning for comparing decimal fractions to the thousandths but are quickly supplanted by reasoning about the meaning of the digits in each place noticing differences in the values of like units and expressing those comparisons with symbols

G5M1 Topic B Lesson 5 Lesson 5 YOUR NOTES Name decimal fractions in expanded unit and word forms by applying place value reasoning Warm Up FLUENCY PRACTICE Multiply and Divide by Exponents Materials S Millions to thousandths place value chart Lesson 1 Concept Exploration Template personal white board NOTE This fluency activity helps students work toward full understanding of the concept introduced in Lesson 4 Depending on students depth of knowledge this activity may be done with support from a personal place value chart or done simply by responding on the personal white board with the product or quotient T Project the place value chart from millions to thousandths Write 54 tenths as a decimal S Write 5 in the ones column and 4 in the tenths column T Say the decimal S 5 4 five and four tenths T Multiply it by 102 S Indicate change in value by using arrows from each original place value to the product on their personal white boards Or instead simply write the product T Say the product S 540 Repeat the process and sequence for 0 6 102 0 6 102 2 784 103 and 6 583 103 Multiplying Metric Units Materials S Millions to thousandths place value chart Lesson 1 Concept Exploration Template personal white board NOTE This fluency activity helps students work toward full understanding of the concept introduced in Lesson 4 T Write 3 m cm Show 3 on your place value chart ZEARN MATH Teacher Edition 41

Topic B Lesson 5 YOUR NOTES G5M1 S Write 3 in the ones column T How many centimeters are in 1 meter S 100 centimeters T Show how many centimeters are in 3 meters on your place value chart S Cross out the 3 and shift it two place values to the left to show 300 T How many centimeters are in 3 meters S 300 centimeters Repeat the process and procedure for 7 kg 7 500 m km m and 8 350 g g 7 000 mL kg L g WORD PROBLEM Jordan measures a desk at 200 cm James measures the same desk in millimeters and Amy measures the same desk in meters What is James s measurement in millimeters What is Amy s measurement in meters Show your thinking using a place value chart or an equation with exponents NOTE Today s Word Problem offers students a quick review of Lesson 4 s concepts before moving forward to naming decimals Concept Exploration Materials S Personal white board thousands through thousandths place value chart Concept Exploration Template OPENER T Write three thousand forty seven on the board On your personal board write this number in standard form expanded form and unit form T Explain to your partner the purpose of writing this number in these different forms S Standard form shows us the digits that we are using to represent that amount Expanded form shows how much each digit is worth and that the number is a total of those values added together Unit form helps us see how many of each size unit are in the number 42 ZEARN MATH Teacher Edition

G5M1 Topic B Lesson 5 PROBLEM 1 YOUR NOTES This problem is optional Represent 1 thousandth and 3 thousandths in standard expanded and unit form T Model and read each number How is this comparison different from our first comparison T Write 1 thousandth using digits on your place value chart T How many ones tenths hundredths thousandths S Zero Zero Zero One T This is the standard form of the decimal for 1 thousandth T We write 1 thousandth as a fraction like this 1 1 _ 1000 Write _ 1000 on the board T 1 thousandth is a single copy of a thousandth We write the expanded form using a fraction 1 1 like this 1 _ 1000 Write 1 _ 1000 on the board and say 1 copy of 1 thousandth And we write the expanded form using a decimal like this 1 0 001 Write 1 0 001 on the board 1 One thousandth 0 001 _ 1000 1 1 _ 1000 1 _ 1000 0 001 1 0 001 1 thousandth T We write the unit form of 1 thousandth like this 1 thousandth Write on the board We write a numeral point to 1 and the unit name point to thousandth as a word T Imagine 3 copies of 1 thousandth How many thousandths is that 3 Three thousandths 0 003 _ 1000 S 3 thousandths T Write in standard form and as a fraction T 3 thousandths is 3 copies of 1 thousandth Turn and talk to your partner about how this would be written in expanded form using a fraction and using a decimal 3 1 _ 1000 3 _ 1000 0 003 3 0 001 3 thousandths PROBLEM 2 Represent 13 thousandths in standard expanded and unit form T Write 13 thousandths in standard form and expanded form using fractions and then using decimals Turn and share with your partner S Zero point zero one three is standard form Expanded forms are 1 _ 100 3 _ 1000 and 1 0 01 3 0 001 1 1 T Now write this decimal in unit form S 1 hundredth 3 thousandths 13 thousandths ZEARN MATH Teacher Edition 43

Topic B Lesson 5 YOUR NOTES G5M1 T Circulate and write responses on the board I notice that there seems to be more than one way to write this decimal in unit form Why 13 Thirteen thousandths 0 013 _ 1000 13 1 _ 1000 13 _ 1000 S This is 13 copies of 1 thousandth You can write the units separately or write the 1 hundredth as 10 thousandths You add 10 thousandths and 3 thousandths to get 13 thousandths 0 013 1 0 01 3 0 001 1 hundredth 3 thousandths 13 thousandths Repeat with 0 273 and 1 608 allowing students to combine units in their unit forms e g 2 tenths 73 thousandths 273 thousandths 27 hundredths 3 thousandths Use more or fewer examples as needed reminding students who need it that and indicates the decimal in word form PROBLEM 3 This problem is optional Represent 25 413 in word expanded and unit form T Write 25 413 on the board Write 25 413 in word form on your personal board S Write twenty five and four hundred thirteen thousandths T Now write this decimal in unit form on your personal board S Write 2 tens 5 ones 4 tenths 1 hundredth 3 thousandths T What are other unit forms of this number S 25 ones 413 thousandths 254 tenths 13 thousandths 25 413 thousandths T Write 25 413 as a mixed number and then in expanded form Compare your work with your partner s 413 Twenty five and four hundred thirteen thousandths 25 _ 1000 25 413 3 _ 1000 25 _ _ 10 1 _ 100 1000 2 10 5 1 4 413 1 1 1 25 413 2 10 5 1 4 0 1 1 0 01 3 0 001 2 tens 5 ones 4 tenths 1 hundredth 3 thousandths 25 ones 413 thousandths Repeat the sequence with 12 04 and 9 495 Use more or fewer examples as needed 44 ZEARN MATH Teacher Edition

G5M1 Topic B Lesson 5 PROBLEM 4 YOUR NOTES Write the standard expanded and unit forms of four hundred four thousandths and four hundred and four thousandths T Work with your partner to write these decimals in standard form Circulate Look for misconceptions about the use of the word and T Tell the digits you used to write four hundred four thousandths T How did you know where to write the decimal in the standard form 404 Four hundred four thousandths _ 1000 0 404 404 1 1 _ 1000 4 _ 10 4 _ 1000 S The word and tells us where the fraction part of the number starts T Now work with your partner to write the expanded and unit forms for these numbers 0 404 4 0 1 4 0 001 4 tenths 4 thousandths 4 Four hundred and four thousandths 400 _ 400 004 1000 Repeat this sequence with two hundred two thousandths and nine hundred and nine tenths 400 _ 4 100 4 _ 1000 1000 4 1 400 004 4 100 4 0 001 4 hundreds 4 thousandths MULTIPLE MEANS OF REPRESENTATION Students struggling with naming decimals using different unit forms may benefit from a return to concrete materials Try using place value disks to make trades for smaller units Also place value understandings from Lessons 1 and 2 help make the connection between 1 hundredth 3 thousandths and 13 thousandths It may also be fruitful to invite students to extend their Grade 4 experiences with finding equivalent fractions for tenths and hundredths to finding equivalent fraction representations in thousandths MULTIPLE MEANS OF REPRESENTATION Guide students to draw on their experiences with whole numbers and make parallels to decimals Whole number units are named by smallest base ten unit e g 365 000 365 thousand and 365 365 ones Likewise we can name decimals by the smallest unit e g 0 63 63 hundredths ZEARN MATH Teacher Edition 45

Topic B Lesson 5 YOUR NOTES G5M1 Independent Digital Lesson Lesson 5 Name That Decimal Students also learn the concepts from this lesson in the Independent Digital Lesson The intentional balance of learning with teachers and peers and learning independently in digital lessons ensures every student has multiple opportunities to represent engage with and express their math reasoning See the digital lesson notes below for a glimpse of the paper to pencil transfer of these math ideas Go online to see the full digital lesson Wrap Up LESSON SYNTHESIS Guide students in a conversation to process today s lesson and surface any misconceptions or misunderstandings The questions below may be used to lead the discussion 46 What is the purpose of writing a decimal number in expanded form using fractions ZEARN MATH Teacher Edition

G5M1 When might expanded form be useful as a calculation tool It helps us see the like units and could help to add and subtract mentally How is expanded form related to the standard form of a number Topic B Lesson 5 YOUR NOTES EXIT TICKET After today s lesson instruct students to complete the Exit Ticket A review of their Exit Ticket as well as continuously monitoring your Digital Reports can help you assess your students understanding of the concepts explored in today s lesson and plan more effectively for future lessons The questions from the Exit Ticket may be read aloud to the students Task 1 Express nine thousandths as a decimal 2 Express twenty nine thousandths as a fraction 3 Express 24 357 in words a Write the expanded form using fractions or decimals b Express in unit form Answers 1 0 009 29 2 _ 1000 3 Twenty four and three hundred fifty seven thousandths a 2 10 4 1 3 0 1 5 0 01 7 0 001 or expanded fraction form b 2 tens 4 ones 3 tenths 5 hundredths 7 thousandths ZEARN MATH Teacher Edition 47

Topic B Lesson 5 Lesson Template G5M1 Thousands Hundreds Tens Ones Tenths Hundredths Thousandths THOUSANDS THROUGH THOUSANDTHS PLACE VALUE CHART CONCEPT EXPLORATION TEMPLATE 48 ZEARN MATH Teacher Edition

G5M1 Topic B Lesson 6 Lesson 6 YOUR NOTES Compare decimal fractions to the thousandths using like units and express comparisons with

Topic B Lesson 6 YOUR NOTES G5M1 T Write 750 cm m cm Rename the units S 7 meters 50 centimeters Repeat the process for 450 cm 630 cm and 925 cm Multiply by Decimal Fractions Materials S Personal white board millions to thousandths place value chart Lesson 1 Concept Exploration Template NOTE Reviewing helps students work toward full understanding of this skill which was introduced in previous lessons T Project a place value chart from tens to thousandths Beneath the chart write 3 10 Say the multiplication sentence S 3 10 30 T Write 3 in the tens column Below the multiplication sentence write 30 To the right of 3 10 write 4 1 Say the multiplication sentence S 4 1 4 T Write 4 in the ones column and fill in the addition sentence so that it reads 30 4 Repeat the process with each of the expressions below so that in the end the number 34 652 will be written in the place value chart and 30 4 0 6 0 05 0 002 is written underneath it 1 1 1 6 _ 10 5 _ _ 100 2 1000 T Say the addition sentence S 30 4 0 6 0 05 0 002 34 652 T Write 75 614 on the place value chart Write the number in expanded form Repeat with the following possible sequence 75 604 20 197 and 40 803 WORD PROBLEM Ms Meyer measured the edge of her dining table to the hundredth of a meter The edge of the table measured 32 15 meters Write her measurement in word form unit form and expanded form using fractions and decimals NOTE Encourage students to name the decimal by decomposing it into various units e g 3 215 hundredths 321 tenths 5 hundredths 32 ones 15 hundredths 50 ZEARN MATH Teacher Edition

G5M1 Concept Exploration Topic B Lesson 6 YOUR NOTES Materials S Millions to thousandths place value chart Lesson 1 Concept Exploration Template personal white board PROBLEM 1 This problem is optional for extra support Compare 13 196 and 13 296 T Point to 13 196 Read the number S 13 thousand 1 hundred ninety six T Point to 13 296 Read the number S 13 thousand 2 hundred ninety six T Which number is greater How can you tell S 13 296 is greater than 13 196 because the digit in the hundreds place is one greater 13 296 is 100 more than 13 196 13 196 has 131 hundreds and 13 296 has 132 hundreds so 13 296 is greater T Use a symbol to show which number is greater S 13 196 13 296 PROBLEM 2 Compare 0 012 and 0 002 T Write 2 thousandths in standard form on your place value chart Write 2 thousandths on the board S Write T Say the digits that you wrote on your chart S Zero point zero zero two T Write 12 thousandths in standard form underneath 0 002 on your chart Write 12 thousandths on the board S Write T Say the digits that you wrote on your chart S Zero point zero one two T Say this number in unit form S 1 hundredth 2 thousandths T Which number is greater Turn and talk to your partner about how you can tell ZEARN MATH Teacher Edition 51

Topic B Lesson 6 YOUR NOTES G5M1 S 0 012 is bigger than 0 002 In 0 012 there is a one in the hundredths place but 0 002 has a zero in the hundredths so that means 0 012 is greater than 0 002 12 of something is greater than 2 of the same thing Just like 12 apples are more than 2 apples T Write an expression comparing these two values S 0 002 0 012 PROBLEM 3 299 3 Compare _ 1000 and _ 10 T Write 3 tenths in standard form on your place value chart S Write T Write 299 thousandths in standard form on your place value chart under 3 tenths S Write T Which decimal has more tenths S 0 3 T If we traded 3 tenths for thousandths how many thousandths would we need Turn and talk to your partner S 300 thousandths T Name these decimals using unit form and compare Tell your partner which is greater S 299 thousandths 300 thousandths is more T Show this relationship with a symbol S 0 299 0 3 705 7 Repeat the sequence with _ 1000 and _ 10 and 15 203 and 15 21 Encourage students to name the fractions and decimals using like units as above e g 15 ones 20 hundredths 3 thousandths and 15 ones 21 hundredths 0 thousandths or 15 203 thousandths and 15 210 thousandths Be sure to have students express the relationships using and PROBLEM 4 Order from least to greatest 0 413 0 056 0 164 and 0 531 Have students order the decimals and then explain their strategy e g renaming in unit form using a place value chart to compare largest to smallest units looking for differences in value Repeat with the following in ascending and descending order 27 005 29 04 27 019 and 29 5 119 177 119 173 119 078 and 119 18 52 ZEARN MATH Teacher Edition

G5M1 Topic B Lesson 6 MULTIPLE MEANS OF ENGAGEMENT YOUR NOTES Help students deepen their understanding of comparing decimals by returning to concrete materials Some students may not see that 0 4 0 399 because they are focusing on the number of digits to the right of the decimal rather than their value Comparison of like units becomes a concrete experience when students attention is directed to comparisons of largest to smallest place value on the chart and when they are encouraged to make trades to the smaller unit using disks MULTIPLE MEANS OF ENGAGEMENT Provide an extension by including fractions along with decimals to be ordered 5 Order from least to greatest 29 5 27 019 and 27 _ 1000 Independent Digital Lesson Lesson 6 Classy Comparisons Students also learn the concepts from this lesson in the Independent Digital Lesson The intentional balance of learning with teachers and peers and learning independently in digital lessons ensures every student has multiple opportunities to represent engage with and express their math reasoning There are no notes for this digital lesson Go online to see the full digital lesson Wrap Up LESSON SYNTHESIS Guide students in a conversation to process today s lesson and surface any misconceptions or misunderstandings The questions below may be used to lead the discussion How is comparing whole numbers like comparing decimal fractions How is it different You learned two strategies to help you compare numbers finding a common unit and looking at the place value chart Which strategy do you like best Explain Compare 7 tens and 7 tenths How are they alike How are they different Encourage students to notice that both quantities are 7 but the units have different values Also encourage students to notice that they are placed symmetrically in relation to the ones place on a place value chart Tens are 10 times greater than ones while tenths are 1 tenth as much Repeat with other values e g 2 000 0 002 or ask students to generate values that are symmetrically placed on the chart ZEARN MATH Teacher Edition 53

Topic B Lesson 6 YOUR NOTES G5M1 EXIT TICKET After today s lesson instruct students to complete the Exit Ticket A review of their Exit Ticket as well as continuously monitoring your Digital Reports can help you assess your students understanding of the concepts explored in today s lesson and plan more effectively for future lessons The questions from the Exit Ticket may be read aloud to the students Task 1 Show the numbers on the place value chart using digits Use

G5M1 Topic C TOPIC C Place Value and Rounding Decimal Fractions In Topic C students generalize their knowledge of rounding whole numbers to round decimal numbers to any place In Grades 3 and 4 vertical number lines provided a platform for students to round whole numbers to any place In Grade 5 vertical number lines again provide support for students to make use of patterns in the base ten system allowing knowledge of whole number rounding to be easily applied to rounding decimal values The vertical number line is used initially to find more than or less than halfway between multiples of decimal units In these lessons students are encouraged to reason more abstractly as they use place value understanding to approximate by using nearest multiples Naming those nearest multiples is an application of flexibly naming decimals using like place value units To round 3 85 to the nearest tenth students find the nearest multiples 3 80 38 tenths 0 hundredths and 3 9 39 tenths 0 hundredths and then decide that 3 85 38 tenths 5 hundredths is exactly halfway between and therefore must be rounded up to 3 9 Objective Topic C Place Value and Rounding Decimal Fractions Lessons 7 8 Round a given decimal to any place using place value understanding and the vertical number line ZEARN MATH Teacher Edition 55

G5M1 Topic C Lesson 7 Lesson 7 YOUR NOTES Round a given decimal to any place using place value understanding and the vertical number line Warm Up FLUENCY PRACTICE Compare Decimal Fractions Materials S Personal white board NOTE This review fluency activity helps students work toward full understanding of comparing decimal numbers a topic introduced in Lesson 6 T Write 12 57 12 75 On your personal boards compare the numbers using the greater than less than or equal sign S Write 12 57 12 75 on boards Repeat the process and procedure 0 67 67 83 _ _ 100 100 4 07 forty seven tenths twenty four and 9 thousandths 0 084 328 2 328 099 3 tens MULTIPLE MEANS OF ENGAGEMENT Fluency activities like Compare Decimal Fractions may be made more active by allowing students to stand and use their arms to make the

Topic C Lesson 7 YOUR NOTES G5M1 Repeat the process for 17 5 27 5 24 5 24 3 and 42 3 WORD PROBLEM Craig Randy Charlie and Sam ran in a 5K race on Saturday They were the top 4 finishers Here are their race times Craig 25 9 minutes Randy 32 2 minutes Charlie 32 28 minutes Sam 25 85 minutes Who won first place Who won second place Third Fourth NOTE This Word Problem offers students a quick review of Lesson 6 before moving toward the rounding of decimals Students may need reminding that in a race the lowest number indicates the fastest time Concept Exploration Materials S Personal white board hundreds to thousandths place value chart Concept Exploration Template PROBLEM 1 Strategically decompose 155 using multiple units to round to the nearest ten and nearest hundred T Work with your partner to name 155 in unit form Next rename 155 using the greatest number of tens possible Finally rename 155 using only ones Record your ideas on your place value chart 58 Hundreds Tens Ones 1 5 5 15 5 Tenths 155 ZEARN MATH Teacher Edition

G5M1 Topic C Lesson 7 YOUR NOTES T Which decomposition of 155 helps you round this number to the nearest ten Turn and talk S 15 tens and 5 ones The one that shows 15 tens This helps me see that 155 is between 15 tens and 16 tens on the number line It is exactly halfway so 155 would round to the next greater ten which is 16 tens or 160 T Let s record that on the number line Record both of the nearest multiples of ten the halfway point and the number being rounded Circle the correct rounded figure T Using your chart which of these representations helps you round 155 to the nearest 100 Turn and talk to your partner about how you will round S The one that shows 1 hundred I can see that 155 is between 1 hundred and 2 hundred The midpoint between 1 hundred and 2 hundred is 150 155 is past the midpoint so 155 is closer to 2 hundreds It rounds up to 200 T Label your number line with the nearest multiples of one hundred the halfway point and the number we re rounding Then circle the one to which 155 would round PROBLEM 2 Strategically decompose 1 57 to round to the nearest tenth T Work with your partner to name 1 57 in unit form Next rename 1 57 using the greatest number of tenths possible Finally rename 1 57 using only hundredths Record your ideas on your place value chart Ones Tenths Hundredths 1 5 7 15 7 157 S Work and share T Which decomposition of 1 57 best helps you to round this number to the nearest tenth Turn and talk Label your number line and circle your rounded number S Share Bring to students attention that this problem parallels conversions between meters and centimeters since different units are being used to name the same quantity 1 57 meters 157 centimeters ZEARN MATH Teacher Edition 59

Topic C Lesson 7 YOUR NOTES G5M1 PROBLEM 3 This problem is optional for Enrichment Strategically decompose to round 4 381 to the nearest ten one tenth and hundredth T Work with your partner to decompose 4 381 using as many tens ones tenths and hundredths as possible Record your work on your place value chart S Share T We want to round this number to the nearest ten first How many tens did you need to name this number Tens Ones 0 4 Tenths Hundredths Thousandths 3 8 1 43 8 1 438 1 4381 S Zero tens T Between what two multiples of 10 will we place this number on the number line Turn and talk Draw your number line and circle your rounded number S Share T Work with your partner to round 4 381 to the nearest one tenth and hundredth Explain your thinking with a number line Follow the sequence from above to guide students in realizing that the number 4 381 rounds down to 4 ones up to 44 tenths 4 4 and down to 438 hundredths 4 38 PROBLEM 4 This problem is optional for Enrichment Strategically decompose to round 9 975 to the nearest one ten tenth and hundredth Tens Ones 9 Tenths 9 99 Hundredths 7 7 997 Thousandths 5 5 5 9975 Follow a sequence similar to the previous problem to lead students in rounding to the given places This problem can prove to be a problematic rounding case Naming the number with different units however allows students to choose easily between nearest multiples of the given place value 60 ZEARN MATH Teacher Edition

G5M1 Topic C Lesson 7 YOUR NOTES Repeat this sequence with 99 799 Round to the nearest ten one tenth and hundredth MULTIPLE MEANS OF REPRESENTATION Vertical number lines may be a novel representation for any students who did not engage with them in earlier grades Their use offers an important scaffold for students understanding of rounding in that numbers are quite literally rounded up and down to the nearest multiple rather than left or right as in a horizontal number line Consider showing both a horizontal and vertical line and comparing their features so that students can see the parallels and gain comfort in the use of the vertical line Independent Digital Lesson Lesson 7 Decimal Round Students also learn the concepts from this lesson in the Independent Digital Lesson The intentional balance of learning with teachers and peers and learning independently in digital lessons ensures every student has multiple opportunities to represent engage with and express their math reasoning See the digital lesson notes below for a glimpse of the paper to pencil transfer of these math ideas Go online to see the full digital lesson ZEARN MATH Teacher Edition 61

Topic C Lesson 7 G5M1 YOUR NOTES Wrap Up LESSON SYNTHESIS Guide students in a conversation to process today s lesson and surface any misconceptions or misunderstandings The questions below may be used to lead the discussion When a number rounds up when rounded to the tenths place does it follow that it will always round up when rounded to the hundredth Thousandth Why or why not How does the unit we are rounding to affect the result EXIT TICKET After today s lesson instruct students to complete the Exit Ticket A review of their Exit Ticket as well as continuously monitoring your Digital Reports can help you assess your students understanding of the concepts explored in today s lesson and plan more effectively for future lessons The questions from the Exit Ticket may be read aloud to the students 62 ZEARN MATH Teacher Edition

G5M1 Topic C Lesson 7 Task YOUR NOTES Use the table to round the number to the given places Label the number lines and circle the rounded value Answers a 855 hundredths 8 55 b 1 ten 10 ZEARN MATH Teacher Edition 63

Topic C Lesson 7 Lesson Template G5M1 Hundreds Tens Ones Tenths Hundredths Thousandths HUNDREDS TO THOUSANDTHS PLACE VALUE CHART CONCEPT EXPLORATION TEMPLATE 64 ZEARN MATH Teacher Edition

G5M1 Topic C Lesson 8 Lesson 8 YOUR NOTES Round a given decimal to any place using place value understanding and the vertical number line Warm Up FLUENCY PRACTICE Rename the Units NOTE Decomposing common units as decimals strengthens student understanding of place value T Write 13 tenths Say the decimal S One and 3 tenths Repeat the process for 14 tenths 24 tenths 124 tenths and 524 tenths T Name the number of tenths Write 2 5 S 25 tenths Repeat the process for 17 5 27 5 24 5 24 3 and 42 3 Then repeat the entire process with hundredths T Write 37 hundredths Say the decimal S 0 37 T Write 37 hundredths 0 37 Below it write 137 hundredths Say the decimal S 1 37 Repeat the process for 537 hundredths and 296 hundredths T Write 0 548 thousandths Say the number sentence S 0 548 548 thousandths T Write 0 548 548 thousandths Below it write 1 548 number sentence thousandths Say the S 1 548 1 548 thousandths Repeat the process for 2 548 and 7 352 Round to Different Place Values Materials S Personal white board NOTE Reviewing this skill introduced in Lesson 7 helps students work toward full understanding of rounding decimal numbers to different place values ZEARN MATH Teacher Edition 65

Topic C Lesson 8 YOUR NOTES G5M1 Although the approximation sign is used in Grade 4 a quick review of its meaning may be in order T Project 8 735 Say the number S 8 and 735 thousandths T Draw a vertical number line on your boards with two endpoints and a midpoint T Between what two ones is 8 735 S 8 ones and 9 ones T What s the midpoint for 8 and 9 S 8 5 T Fill in your endpoints and midpoint T 8 5 is the same as how many tenths S 85 tenths T How many tenths are in 8 735 S 87 tenths T Is 87 tenths more than or less than 85 tenths S More than T Write 8 735 Show 8 735 on your number line Write the number sentence when rounded to the nearest one S Write 8 735 between 8 5 and 9 on the number line and write 8 735 9 Repeat the process for the tenths place and hundredths place Follow the same process and procedure for 7 458 WORD PROBLEM Organic whole wheat flour sells in bags weighing 2 915 kilograms a How much flour is this when rounded to the nearest tenth Use a place value chart and number line to explain your thinking b How much flour is this when rounded to the nearest one Extension What is the difference of the two answers NOTE This problem is a review of Lesson 7 which focused on rounding The extension serves as an opportunity for students to recall the work they did in Grade 4 when subtracting fractions 66 ZEARN MATH Teacher Edition

G5M1 Topic C Lesson 8 YOUR NOTES Concept Exploration Materials S Personal white board hundreds to thousandths place value chart Lesson 7 Concept Exploration Template PROBLEM 1 This problem is optional Round 49 67 to the nearest ten T Turn and talk to your partner about the different ways 49 67 could be decomposed On your place value chart show the decomposition that you think will be most helpful in rounding to the nearest ten T Which one of these decompositions did you decide was the most helpful S The decomposition with more tens is most helpful because it helps me identify the two rounding choices 4 tens or 5 tens Tens 4 Ones 9 49 Tenths 6 6 496 Hundredths 7 7 7 T Draw and label a number line and circle the rounded value Explain your reasoning to your neighbor Repeat this sequence with rounding 49 67 to the nearest one and then to the nearest tenth PROBLEM 2 Decompose 9 949 and round to the nearest tenth and hundredth Show your work on a number line Ones 9 Tenths 9 99 Hundredths Thousandths 4 9 4 9 994 9 T What decomposition of 9 949 best helps to round this number to the nearest tenth S The one using the most tenths to name the decimal fraction I knew I would round to either 99 tenths or 100 tenths I looked at the hundredths Four hundredths is not past the midpoint so I rounded to 99 tenths Ninety nine tenths is the same as 9 9 ZEARN MATH Teacher Edition 67

Topic C Lesson 8 YOUR NOTES G5M1 T Which digit made no difference when you rounded to the nearest tenth Explain your thinking S The thousandths because the hundredths decided which direction to round Since there are not 5 hundredths I rounded to the lesser number Repeat the process rounding to the nearest hundredth PROBLEM 3 A decimal number has 1 digit to the right of the decimal point If we round this number to the nearest whole number the result is 27 What are the maximum and minimum possible values of these two numbers Use a number line to show your reasoning Include the midpoint on the number line T Draw a vertical number line with 3 points T What do we know about the unknown number S It has a digit in the tenths place but nothing else beyond the tenths place We know that it has been rounded to 27 T Write 27 at the bottom point on the number line and circle it Why did I place 27 as the lesser rounded value S We are looking for the largest number that will round down to 27 That number will be greater than 27 but less than the midpoint between 27 and 28 T What is the midpoint between 27 and 28 S 27 5 T Place 27 5 on the number line T If we look at numbers that have exactly 1 digit to the right of the decimal point what is the greatest one that will round down to 27 S 27 4 If we go to 27 5 that would round up to 28 Repeat the same process to find the minimum value MULTIPLE MEANS OF ENGAGEMENT Turn and talk is a strategy intended to broaden active student participation by offering opportunity for all to speak during a lesson Spend time in the beginning of the school year helping students understand what turn and talk looks like and sounds like by demonstrating with a student for the whole class This strategy allows students to formulate test and refine their developing understanding of math 68 ZEARN MATH Teacher Edition

G5M1 Topic C Lesson 8 Independent Digital Lesson YOUR NOTES Lesson 8 More Rounding Students also learn the concepts from this lesson in the Independent Digital Lesson The intentional balance of learning with teachers and peers and learning independently in digital lessons ensures every student has multiple opportunities to represent engage with and express their math reasoning There are no notes for this digital lesson Go online to see the full digital lesson Wrap Up LESSON SYNTHESIS Guide students in a conversation to process today s lesson and surface any misconceptions or misunderstandings The questions below may be used to lead the discussion Compare our approach to rounding in today s lesson and in Lesson 7 How are they alike How are they different Once a number rounds up at one place value does it follow then that every place value will round up Why or why not How does the place value chart help organize your thinking when rounding Finding the maximum and minimum values poses a significant increase in cognitive load and an opportunity to build excitement Make time to deeply discuss ways of reasoning about these tasks as they are sure to be many and varied EXIT TICKET After today s lesson instruct students to complete the Exit Ticket A review of their Exit Ticket as well as continuously monitoring your Digital Reports can help you assess your students understanding of the concepts explored in today s lesson and plan more effectively for future lessons The questions from the Exit Ticket may be read aloud to the students ZEARN MATH Teacher Edition 69

Topic C Lesson 8 YOUR NOTES G5M1 Task 1 Round the quantity to the given place value Draw number lines to explain your thinking Circle the rounded value on the number line a 13 989 to the nearest tenth b 382 993 to the nearest hundredth Answers 1 a 14 0 b 382 99 70 ZEARN MATH Teacher Edition

G5M1 Topic D TOPIC D Adding and Subtracting Decimals Topics D through F mark a shift from the opening topics of Mission 1 From this point to the conclusion of the mission students begin to use base ten understanding of adjacent units and whole number algorithms to reason about and perform decimal fraction operations addition and subtraction in Topic D multiplication in Topic E and division in Topic F In Topic D unit form provides the connection that allows students to use what they know about general methods for addition and subtraction with whole numbers to reason about decimal addition and subtraction e g 7 tens 8 tens 15 tens 150 is analogous to 7 tenths 8 tenths 15 tenths 1 5 Place value charts and disks both concrete and pictorial representations and the relationship between addition and subtraction are used to provide a bridge for relating such understandings to a written method Real world contexts provide opportunities for students to apply their knowledge of decimal addition and subtraction as well in Topic D Objective Topic D Adding and Subtracting Decimals Lesson 9 Add decimals using place value strategies and relate those strategies to a written method Lesson 10 Subtract decimals using place value strategies and relate those strategies to a written method ZEARN MATH Teacher Edition 71

G5M1 Topic D Lesson 9 Lesson 9 YOUR NOTES Add decimals using place value strategies and relate those strategies to a written method Warm Up FLUENCY PRACTICE Decompose the Unit Materials S Personal white board NOTE Decomposing common units as decimals strengthens student understanding of place value T Project 6 358 Say the number S 6 and 358 thousandths T How many tenths are in 6 358 S 63 tenths T Write 6 358 63 tenths separating the tenths thousandths On your boards write the number S Write 6 358 63 tenths 58 thousandths Repeat the process for hundredths Follow the same process for 7 354 Round to Different Place Values Materials S Personal white board NOTE Reviewing this skill introduced in Lesson 8 helps students work toward full understanding of rounding decimal numbers to different place values T Project 2 475 Say the number S 2 and 475 thousandths T On your board round the number to the nearest tenth S Write 2 475 2 5 Repeat the process rounding 2 457 to the nearest hundredth Follow the same process for 2 987 but vary the sequence ZEARN MATH Teacher Edition 73

Topic D Lesson 9 YOUR NOTES G5M1 One Unit More Materials S Personal white board NOTE This anticipatory fluency drill lays a foundation for the concept taught in today s Concept Exploration T Write 5 tenths Say the decimal that s one tenth more than the given value S Six tenths Repeat the process for 5 hundredths 5 thousandths 8 hundredths 3 tenths and 2 thousandths Specify the unit to increase by T Write 0 052 On your board write one more thousandth S Write 0 053 Repeat the process for 1 tenth more than 35 hundredths 1 thousandth more than 35 hundredths and 1 hundredth more than 438 thousandths WORD PROBLEM Ten baseballs weigh 1 417 4 grams About how much does 1 baseball weigh Round your answer to the nearest tenth of a gram Round your answer to the nearest gram Which answer would you give if someone asked About how much does a baseball weigh Explain your choice NOTE The Word Problem requires students to divide by powers of ten and round These are skills learned in the first part of this mission Concept Exploration Materials S Hundreds to thousandths place value chart Lesson 7 Concept Exploration Template personal white board PROBLEMS 1 3 74 2 tenths 6 tenths 2 ones 3 thousandths 6 ones 1 thousandth 2 tenths 5 thousandths 6 hundredths ZEARN MATH Teacher Edition

G5M1 T Write 2 tenths 6 tenths on the board Solve 2 tenths plus 6 tenths using disks on your place value chart Topic D Lesson 9 YOUR NOTES S Solve T Say the sentence using unit form S 2 tenths 6 tenths 8 tenths T How is this addition problem the same as a whole number addition problem Turn and share with your partner S In order to find the sum I added like units tenths with tenths 2 tenths plus 6 tenths equals 8 tenths just like 2 apples plus 6 apples equals 8 apples Since the sum is 8 tenths we don t need to bundle or regroup T On the board write Problems 2 and 3 Work with your partner and solve the next two problems with place value disks on your place value chart S Solve T Let s record our last problem vertically Write 0 205 and the plus sign underneath on the board What do I need to think about when I write my second addend Lead students to see that the vertical written method mirrors the placement of disks on the chart Like units should be aligned with like units Avoid procedural language like line up the decimals Students should justify alignment of digits based on place value units PROBLEMS 4 6 1 8 13 tenths 1 hundred 8 hundredths 2 ones 4 hundredths 148 thousandths 7 ones 13 thousandths T Write 1 8 13 tenths on the board Use your place value chart and draw disks to show the addends of our next problem S Show T Tell how you represented these addends Some students may represent 13 tenths by drawing 13 disks in the tenths column or as 1 disk in the ones column and 3 disks in the tenths column Others may represent 1 8 using mixed units or only tenths S Share T Which way of composing these addends requires the fewest number of disks Why S Using ones and tenths because each ones disk is worth 10 tenths disks T Will your choice of units on your place value chart affect your answer sum ZEARN MATH Teacher Edition 75

Topic D Lesson 9 YOUR NOTES G5M1 S No Either is OK It will still give the same answer T Add Share your thinking with your partner S 1 8 13 tenths 1 one and 21 tenths There are 10 tenths in one whole I can compose 2 wholes and 1 tenth from 21 tenths so the answer is 3 and 1 tenth 13 tenths is the same as 1 one 3 tenths 1 one 3 tenths 1 one 8 tenths 2 ones 11 tenths which is the same as 3 ones 1 tenth T Let s record what we did on our charts Lead students to articulate the need to align like units in the vertical algorithm T What do you notice that was different about this problem What was the same Turn and talk S We needed to rename in this problem because 8 tenths and 3 tenths is 11 tenths We added ones with ones and tenths with tenths like units just like before T On the board write Problems 5 and 6 Work with your partner to solve the next two problems on your place value chart and record your thinking vertically T As students work 148 thousandths 7 ones 13 thousandths discuss which composition of 148 thousandths is the most efficient PROBLEMS 7 9 0 74 0 59 7 048 5 196 7 44 0 774 T Write 0 74 0 59 horizontally on the board Using disks and the place value chart find the sum of 0 74 and 0 59 Record your work S Solve T How was this problem like others we ve solved How was it different S We still add by combining like units ones with ones tenths with tenths hundredths with hundredths but this time we had to bundle in two place value units We still record our thinking the same way we do with whole numbers aligning like units T Solve the next two problems using the written method You may also use your disks to help you Write 7 048 5 196 and 7 44 0 774 on the board horizontally S Solve T How is 7 44 0 774 different from the other problems we ve solved Turn and talk S One addend had hundredths and the other had thousandths We still had to add like units We could think of 44 hundredths as 440 thousandths 76 ZEARN MATH Teacher Edition

G5M1 Topic D Lesson 9 MULTIPLE MEANS OF REPRESENTATION YOUR NOTES Understanding the meaning of tenths hundredths and thousandths is essential Proportional manipulatives such as base ten blocks can be used to ensure understanding of the vocabulary Students may eventually move to concrete place value disks or drawing which are more efficient MULTIPLE MEANS OF ACTION AND EXPRESSION Allow students the option of communicating their thinking in writing through a combination of graphics symbols and words and or through the use of physical manipulatives Independent Digital Lesson Lesson 9 Add by Place Students also learn the concepts from this lesson in the Independent Digital Lesson The intentional balance of learning with teachers and peers and learning independently in digital lessons ensures every student has multiple opportunities to represent engage with and express their math reasoning There are no notes for this digital lesson Go online to see the full digital lesson Wrap Up LESSON SYNTHESIS Guide students in a conversation to process today s lesson and surface any misconceptions or misunderstandings The questions below may be used to lead the discussion How is adding decimal fractions the same as adding whole numbers How is it different What are some different words you have used through the grades for changing 10 smaller units for 1 of the next larger units or changing 1 unit for 10 of the next smaller units For enrichment ask students to generate addition problems that have 2 decimal place values but add up to specific sums like 1 or 2 e g 0 74 0 26 ZEARN MATH Teacher Edition 77

Topic D Lesson 9 YOUR NOTES G5M1 EXIT TICKET After today s lesson instruct students to complete the Exit Ticket A review of their Exit Ticket as well as continuously monitoring your Digital Reports can help you assess your students understanding of the concepts explored in today s lesson and plan more effectively for future lessons The questions from the Exit Ticket may be read aloud to the students Task 1 Solve a 4 hundredths 8 hundredths hundredths tenth s hundredths tenth s hundredths b 64 hundredths 8 hundredths hundredths 2 Solve using the standard algorithm a 2 40 1 8 b 36 25 8 67 Answers 1 a 12 1 2 b 72 7 2 2 a 4 20 b 44 92 78 ZEARN MATH Teacher Edition

G5M1 Topic D Lesson 10 Lesson 10 YOUR NOTES Subtract decimals using place value strategies and relate those strategies to a written method Warm Up FLUENCY PRACTICE Take Out the Unit Materials S Personal white board NOTE Decomposing common units as decimals strengthens student understanding of place value T Project 76 358 Say the number S 76 and 358 thousandths T Write 76 358 7 tens blank thousandths On your personal white board fill in the S Write 76 358 7 tens 6358 thousandths Repeat the process for tenths and hundredths 76 358 763 tenths 76 358 hundredths 8 thousandths thousandths Add Decimals Materials S Personal white board NOTE Reviewing this skill introduced in Lesson 9 helps students work toward full understanding of adding common decimal units T Write 3 tenths 2 tenths Write the addition sentence in standard form S 0 3 0 2 0 5 Repeat the process for 5 hundredths 4 hundredths and 35 hundredths 4 hundredths One Unit Less Materials S Personal white board NOTE This fluency is a review of skills taught in Lesson 9 and lays the foundation for the concept taught in today s Concept Exploration ZEARN MATH Teacher Edition 79

Topic D Lesson 10 YOUR NOTES G5M1 T Write 5 tenths Say the decimal that is 1 tenth less than the given unit S 0 4 Repeat the process for 5 hundredths 5 thousandths 7 hundredths and 9 tenths Specify the unit to decrease by T Write 0 029 On your board write the decimal that is one less thousandth S Write 0 028 Repeat the process for 1 tenth less than 0 61 1 thousandth less than 0 061 and 1 hundredth less than 0 549 WORD PROBLEM At the 2012 London Olympics Michael Phelps won the gold medal in the men s 100 meter butterfly He swam the first 50 meters in 26 96 seconds The second 50 meters took him 25 39 seconds What was his total time NOTE Adding decimal numbers is a skill learned in Lesson 9 Concept Exploration Materials S Hundreds to thousandths place value chart Lesson 7 Concept Exploration Template personal white board PROBLEM 1 5 tenths 3 tenths 7 ones 5 thousandths 2 ones 3 thousandths 9 hundreds 5 hundredths 3 hundredths T Write 5 tenths 3 tenths on the board Let s read this expression aloud together Turn and tell your partner how you ll solve this problem and then find the difference using your place value chart and disks T Explain your reasoning when solving this subtraction expression S Since the units are alike we can just subtract 5 3 2 This problem is very similar to 5 ones minus 3 ones or 5 people minus 3 people The units may change but the basic fact 5 3 2 is the same 80 ZEARN MATH Teacher Edition

G5M1 T Write 7 ones 5 thousandths 2 ones 3 thousandths on the board Find the difference Solve this problem with the place value chart and disks Record your thinking vertically using the algorithm Topic D Lesson 10 YOUR NOTES S Solve T What did you have to think about as you wrote the problem vertically S Like units are being subtracted so my work should also show that Ones with ones and thousandths with thousandths T Write 9 hundreds 5 hundredths 3 hundredths on board Solve 9 hundreds 5 hundredths 3 hundredths Read carefully and then tell your neighbor how you ll solve this problem S In word form these units look similar but they re not I ll just subtract 3 hundredths from 5 hundredths T Use your place value chart to help you solve and record your thinking vertically PROBLEM 2 83 tenths 6 4 9 2 6 ones 4 tenths T Write 83 tenths 6 4 on the board How is this problem different from the problems we ve seen previously S This problem involves regrouping S Solve using disks recording their work in the standard algorithm T Share how you solved S We had to regroup before we could subtract tenths from tenths Then we subtracted ones from ones using the same process as with whole numbers Repeat the sequence with 9 2 6 ones 4 tenths Students may use various strategies to solve Comparison of strategies makes for interesting discussion PROBLEM 3 0 831 0 292 4 083 1 29 6 0 48 T Write 0 831 0 292 on the board Use your disks to solve Record your work vertically using the standard algorithm S Write and share ZEARN MATH Teacher Edition 81

Topic D Lesson 10 YOUR NOTES G5M1 T Write 4 083 1 29 on the board What do you notice about the thousandths place Turn and talk S There is no digit in the thousandths place in 1 29 We can think of 29 hundredths as 290 thousandths In this case I don t have to change units because there are no thousandths that must be subtracted T Solve with your disks and record Repeat the sequence with 6 0 48 While some students may use a mental strategy to find the difference others will use disks to regroup in order to subtract Continue to stress the alignment based on like units when recording vertically When the ones place is aligned students will recognize that there are not as many digits in the minuend of 6 wholes as in the subtrahend of 48 hundredths Ask How can we think about 6 wholes in the same units as 48 hundredths Then lead students to articulate the need to record 6 ones as 600 hundredths or 6 00 in order to subtract vertically Ask By decomposing 6 wholes into 600 hundredths have we changed its value No we just converted it to smaller units similar to exchanging six dollars for 600 pennies MULTIPLE MEANS OF REPRESENTATION Support oral or written responses with sentence frames such as is hundredths Allow the use of place value charts and the sentence frames to scaffold the process of converting units in subtraction Some students need concrete materials to support their learning as renaming in various units may not yet be an abstract construct for them MULTIPLE MEANS OF REPRESENTATION Give students struggling to model the problem with a pictorial representation the option of using concrete materials like place value disks This may require a larger place value chart Independent Digital Lesson Lesson 10 Place to Subtract Students also learn the concepts from this lesson in the Independent Digital Lesson The intentional balance of learning with teachers and peers and learning independently in digital lessons ensures every student has multiple opportunities to represent engage with and express their math reasoning There are no notes for this digital lesson Go online to see the full digital lesson 82 ZEARN MATH Teacher Edition

G5M1 Topic D Lesson 10 YOUR NOTES Wrap Up LESSON SYNTHESIS Guide students in a conversation to process today s lesson and surface any misconceptions or misunderstandings The questions below may be used to lead the discussion How is subtracting decimal fractions the same as subtracting whole numbers How is it different EXIT TICKET After today s lesson instruct students to complete the Exit Ticket A review of their Exit Ticket as well as continuously monitoring your Digital Reports can help you assess your students understanding of the concepts explored in today s lesson and plan more effectively for future lessons The questions from the Exit Ticket may be read aloud to the students Task 1 Subtract 1 7 0 8 tenths tenths tenths 2 Subtract vertically showing all work a 84 637 28 56 b 7 0 35 Answers 1 17 8 9 0 9 2 a 56 077 b 6 65 ZEARN MATH Teacher Edition 83

Topic E G5M1 TOPIC E Multiplying Decimals A focus on reasoning about the multiplication of a decimal fraction by a one digit whole number in Topic E provides the link that connects Grade 4 multiplication work and Grade 5 fluency with multi digit multiplication Place value understanding of whole number multiplication coupled with an area model of the distributive property is used to help students build direct parallels between whole number products and the products of one digit multipliers and decimals Once the decimal has been placed students use an estimation based strategy to confirm the reasonableness of the product through place value reasoning Word problems provide a context within which students can reason about products Objective Topic E Multiplying Decimals Lesson 11 Multiply a decimal fraction by single digit whole numbers relate to a written method through application of the area model and place value understanding and explain the reasoning used Lesson 12 Multiply a decimal fraction by single digit whole numbers including using estimation to confirm the placement of the decimal point 84 ZEARN MATH Teacher Edition

G5M1 Topic E Lesson 11 Lesson 11 YOUR NOTES Multiply a decimal fraction by single digit whole numbers relate to a written method through application of the area model and place value understanding and explain the reasoning used Warm Up FLUENCY PRACTICE Take Out the Unit Materials S Personal white board NOTE Decomposing common units as decimals strengthens student understanding of place value T Project 1 234 thousandths Say the number Think about how many thousandths are in 1 234 T Project 1 234 1 234 thousandths How much is one thousand thousandths S One thousand thousandths is the same as 1 T Project 65 247 Say the number in unit form S 65 ones 247 thousandths T Write 76 358 7 tens thousandths On your personal white board fill in the blank S Write 76 358 7 tens 6358 thousandths Repeat the process for 76 358 763 tenths hundredths 8 thousandths thousandths and 76 358 Add and Subtract Decimals Materials S Personal white board NOTE Reviewing these skills introduced in Lessons 9 and 10 helps students work toward full understanding of adding and subtracting common decimal units T Write 7 258 thousandths 1 thousandth standard form Write the addition sentence in S 7 258 0 001 7 259 Repeat the process for 7 ones 258 thousandths 3 hundredths 7 ones 258 thousandths 4 tenths 6 ones 453 thousandths 4 hundredths 2 ones 37 thousandths 5 tenths and 6 ones 35 hundredths 7 thousandths ZEARN MATH Teacher Edition 85

Topic E Lesson 11 YOUR NOTES G5M1 T Write 4 ones 8 hundredths 2 ones subtraction sentence in standard form ones hundredths Write the S Write 4 08 2 2 08 Repeat the process for 9 tenths 7 thousandths 4 thousandths 4 ones 582 thousandths 3 hundredths 9 ones 708 thousandths 4 tenths and 4 ones 73 thousandths 4 hundredths WORD PROBLEM After school Marcus ran 3 2 km and Cindy ran 1 95 km Who ran farther How much farther NOTE This Word Problem requires students to subtract decimal numbers as studied in Lesson 10 Concept Exploration Materials S Hundreds to thousandths place value chart Lesson 7 Concept Exploration Template personal white board PROBLEMS 1 3 Problems 1 3 are optional 3 0 2 0 6 3 0 3 0 9 4 0 3 1 2 T Draw 2 tenths on your place value chart S Draw T Make 3 copies of 2 tenths How many tenths do you have in all S 6 tenths T With your partner write the algorithm showing 6 tenths S I wrote 0 2 0 2 0 2 0 6 because I added 2 tenths three times to get 6 tenths I multiplied 2 tenths by 3 and got 6 tenths So I wrote 3 0 2 0 6 T On the board write 3 copies of 2 tenths is equation in unit form 86 Complete the sentence Say the ZEARN MATH Teacher Edition

G5M1 Topic E Lesson 11 YOUR NOTES S 6 tenths 3 2 tenths 6 tenths T Work with your partner to find the values of 3 0 3 and 4 0 3 S Work to solve T How was 4 3 tenths different from 3 3 tenths S I had to bundle the 10 tenths I made 1 one and I had 2 tenths left I didn t do this before We made a number greater than 1 whole T 4 copies of 3 tenths is 12 tenths Show on the place value chart 12 tenths is the same as S 1 one and 2 tenths PROBLEMS 4 6 2 0 43 0 86 2 0 423 0 846 4 0 423 1 692 T On the board write 2 0 43 How can we use our knowledge from the previous problems to solve this problem S We can make copies of hundredths like we made copies of tenths A hundredth is a different unit but we can multiply it just like a tenth T Use your place value chart to find the product of 2 0 43 Complete the sentence 2 copies of 43 hundredths is S Work T Read what your place value chart shows S I have 2 groups of 4 tenths and 2 groups of 3 hundredths I need to combine tenths with tenths and hundredths with hundredths T Draw an area model Let me record what I hear you saying Discuss with your partner the difference between these two models S Share observations T On the board write 2 0 423 What is different about this problem 4 tenths 3 hundredths 2 8 tenths 6 hundredths 0 8 0 06 0 86 S There is a digit in the thousandths place We are multiplying thousandths T Use your place value chart to solve this problem Allow students time to work ZEARN MATH Teacher Edition 87

Topic E Lesson 11 YOUR NOTES G5M1 T Read what your place value chart shows S 846 thousandths T Now draw an area model and write an equation with the partial products to show how you found the product Allow students time to draw 4 tenths 2 8 tenths T Write 4 0 423 on the board Solve by drawing on your place value chart 2 hundredths 3 thousandths 4 hundredths 0 8 0 04 6 thousandths 0 006 0 846 S Solve T Read the number that is shown on your chart S 1 and 692 thousandths T How was this problem different from the last S 4 times 3 thousandths is 12 thousandths so we had to bundle 10 thousandths to make 1 hundredth T Did any other units have to be regrouped S The units in the tenths place Four times 4 tenths is 16 tenths so we had to regroup 10 tenths to make 1 whole T Let s record what happened using an area model and an equation showing the partial products 4 tenths 4 16 tenths 2 hundredths 3 thousandths 8 hundredths 1 6 0 08 12 thousandths 0 012 1 692 PROBLEMS 7 9 Use the area model to represent the distributive property 6 1 21 7 2 41 8 2 34 T On the board write 6 1 21 Let s imagine our disks but use an area model to represent our thinking as we find the product of 6 times 1 and 21 hundredths T On the board draw a rectangle for the area model On our area model how many sections do we have S 3 We have one for each place T Divide the rectangle into three sections and label the area model I have a section for 1 whole 2 tenths and 1 hundredth I am multiplying each by what number S 6 88 ZEARN MATH Teacher Edition

G5M1 Topic E Lesson 11 T With a partner solve the equation using an area model and an equation that shows the partial products YOUR NOTES S Work with partners to solve Have students solve the last two expressions using area models and recording equations Circulate Look for any misconceptions MULTIPLE MEANS OF ACTION AND EXPRESSION The area model can be considered a graphic organizer It organizes the partial products Some students may need support in order to remember which product goes in each cell of the area model especially as the model becomes more complex The organizer can be modified by writing the expressions in each cell This might eliminate the need for some students to visually track the product into the appropriate cell Independent Digital Lesson Lesson 11 Copying Decimals Students also learn the concepts from this lesson in the Independent Digital Lesson The intentional balance of learning with teachers and peers and learning independently in digital lessons ensures every student has multiple opportunities to represent engage with and express their math reasoning See the digital lesson notes below for a glimpse of the paper to pencil transfer of these math ideas Go online to see the full digital lesson ZEARN MATH Teacher Edition 89

Topic E Lesson 11 G5M1 YOUR NOTES Wrap Up LESSON SYNTHESIS Guide students in a conversation to process today s lesson and surface any misconceptions or misunderstandings The questions below may be used to lead the discussion Propose questions with a common error such as 7 x 2 6 14 42 Ask students to use a place value chart or an area model to show the error Discuss the similarities and differences between the place value chart and the area model EXIT TICKET After today s lesson instruct students to complete the Exit Ticket A review of their Exit Ticket as well as continuously monitoring your Digital Reports can help you assess your students understanding of the concepts explored in today s lesson and plan more effectively for future lessons The questions from the Exit Ticket may be read aloud to the students 90 ZEARN MATH Teacher Edition

G5M1 Topic E Lesson 11 Task YOUR NOTES 1 Solve by drawing disks on a place value chart Write an equation and express the product in standard form 4 copies of 3 tenths 2 Complete the area model and then find the product 3 9 63 3 ones tenths 3 3 hundredths Answers 1 4 0 3 1 2 2 9 ones 6 tenths 3 hundredths 3 9 6 3 27 ones 18 tenths 9 hundredths 28 89 ZEARN MATH Teacher Edition 91

G5M1 Topic E Lesson 12 Lesson 12 YOUR NOTES Multiply a decimal fraction by single digit whole numbers including using estimation to confirm the placement of the decimal point Warm Up FLUENCY PRACTICE Find the Product Materials S Personal white board NOTE Reviewing this skill introduced in Lesson 11 helps students work toward full understanding of multiplying single digit numbers times decimals T Write 4 2 ones Write the multiplication sentence S 4 2 8 T Say the multiplication sentence in unit form S 4 2 ones 8 ones Repeat the process for 4 0 2 4 0 02 5 3 5 0 3 5 0 03 3 0 2 3 0 03 3 0 23 and 2 0 14 WORD PROBLEM Patty buys 7 juice boxes a month for lunch If one juice box costs 2 79 how much money does Patty spend on juice each month Use an area model to solve Extension How much will Patty spend on juice in 10 months In 12 months NOTE The first part of this Word Problem asks students to multiply a number with two decimal digits by a single digit whole number This skill taught in Lesson 11 provides a bridge to today s ZEARN MATH Teacher Edition 93

Topic E Lesson 12 G5M1 YOUR NOTES Concept Exploration topic which involves reasoning about such problems on a more abstract level The extension problem looks back to Topic A and requires multiplication by powers of 10 Although students have not multiplied a decimal number by a two digit number they can solve 12 2 79 by using the distributive property 10 2 79 2 2 79 Concept Exploration Materials S Personal white board PROBLEMS 1 3 Problems 1 3 are optional 31 4 124 3 1 4 12 4 0 31 4 1 24 T Write all three problems on the board How are these three problems alike S They are alike because they all have 3 1 and 4 as part of the problem T Use an area model to find the products S Draw 3 tens 4 12 tens 120 1 one 4 ones 124 4 3 ones 4 12 ones 12 1 tenth 4 tenths 12 4 0 4 3 tenths 1 hundreth 4 12 tenths 4 hundreths 1 2 0 04 1 24 T How are the products of all three problems alike S Every product has the digits 1 2 and 4 and they are always in the same order T If the products have the same digits and those digits are in the same order do the products have the same value Why or why not Turn and talk S The decimal is not in the same place in every product No The values are different because the units that we multiplied are different The digits that we multiplied are the same but you have to think about the units to make sure the answer is right T So let me repeat what I hear you saying I can multiply the numerals first and then think about the units to help place the decimal 94 ZEARN MATH Teacher Edition

G5M1 Topic E Lesson 12 PROBLEMS 4 6 YOUR NOTES The first problem 5 1 x 6 30 6 is optional 5 1 6 30 6 11 4 4 45 6 7 8 3 23 4 T Write 5 1 6 on the board What is the smallest unit in 5 1 S Tenths T Multiply 5 1 by 10 to convert it to tenths How many tenths is the same as 5 1 S 51 tenths T Suppose our multiplication sentence was 51 6 Multiply and record your multiplication vertically What is the product 5 1 tenths 6 S 306 30 6 tenths T We know that our product will contain these digits but is 306 a reasonable product for our actual problem of 5 1 6 Turn and talk S We have to think about the units 306 ones is not reasonable but 306 tenths is 5 1 is close to 5 and 5 6 30 so the answer should be around 30 306 tenths is the same as 30 ones and 6 tenths T Using this reasoning where does it make sense to place the decimal in 306 What is the product of 5 1 6 S Between the zero and the six The product is 30 6 T Write 11 4 4 on the board What is the smallest unit in 11 4 S Tenths T What power of 10 must I use to convert 11 4 to tenths How many tenths are the same as 11 ones 4 tenths Turn and talk S 101 We have to multiply by 10 11 4 is the same as 114 tenths T Multiply vertically to find the product of 114 tenths 4 S 456 tenths 1 1 4 tenths 4 4 5 6 tenths T We know that our product will contain these digits How will we determine where to place our decimal S We can estimate 11 4 is close to 11 and 11 4 is 44 The only place that makes sense for the decimal is between the five and six The actual product is 45 6 456 tenths is the same as 45 ones and 6 tenths Repeat the sequence with 7 8 3 Elicit from students the similarities and differences between this problem and others Must compose tenths into ones ZEARN MATH Teacher Edition 95

Topic E Lesson 12 YOUR NOTES G5M1 PROBLEMS 7 9 3 12 4 12 48 3 22 5 16 10 3 42 6 20 52 T Write 3 12 4 on the board Use hundredths to name 3 12 and multiply vertically by 4 What is the product S 1 248 hundredths T I will write four possible products for 3 12 4 on my board Turn and talk to your partner about which of these products is reasonable Then confirm the actual product using an area model Be prepared to share your thinking Write 1 248 1 248 12 48 and 124 8 on the board S Work and share Repeat this sequence for the other problems in this set Write possible products and allow students to reason about decimal placement both from an estimation based strategy and from a composition of smaller units into larger units e g 2 052 hundredths is the same as 20 ones and 52 hundredths Students should also find the products using an area model and then compare the two methods for finding products PROBLEMS 10 12 0 733 4 2 932 10 733 4 42 932 5 733 4 22 932 T Write 0 733 4 on the board Rename 0 733 using its smallest units and multiply vertically by 4 What is the product S 2 932 thousandths T Write 2 932 29 32 293 2 and 2 932 on the board Which of these is the most reasonable product for 0 733 4 Why Turn and talk S 2 932 0 733 is close to one whole and 1 4 4 None of the other choices make sense I know that 2 000 thousandths make 2 wholes so 2 932 thousandths is the same as 2 ones 932 thousandths T Solve 0 733 4 using an area model Compare your products using these two different strategies Repeat this sequence for 10 733 4 and allow independent work for 5 733 4 Require students to decompose to smallest units to reason about decimal placement and solve using the area model so that products and strategies may be compared 96 ZEARN MATH Teacher Edition

G5M1 Topic E Lesson 12 MULTIPLE MEANS OF ENGAGEMENT YOUR NOTES Once students are able to determine the reasonable placement of decimals through estimation by composition of smaller units to larger units and by using the area model teachers should have students articulate which strategy they might choose first Students who have choices develop self determination and feel more connected to their learning Independent Digital Lesson Lesson 12 What s Reasonable Students also learn the concepts from this lesson in the Independent Digital Lesson The intentional balance of learning with teachers and peers and learning independently in digital lessons ensures every student has multiple opportunities to represent engage with and express their math reasoning See the digital lesson notes below for a glimpse of the paper to pencil transfer of these math ideas Go online to see the full digital lesson ZEARN MATH Teacher Edition 97

Topic E Lesson 12 YOUR NOTES G5M1 Wrap Up LESSON SYNTHESIS Guide students in a conversation to process today s lesson and surface any misconceptions or misunderstandings The question below may be used to lead the discussion How can whole number multiplication help you with decimal multiplication Elicit from students that the digits in a product can be found through whole number multiplication The actual product can be deduced through estimation based logic or composing smaller units into larger units EXIT TICKET After today s lesson instruct students to complete the Exit Ticket A review of their Exit Ticket as well as continuously monitoring your Digital Reports can help you assess your students understanding of the concepts explored in today s lesson and plan more effectively for future lessons The questions from the Exit Ticket may be read aloud to the students Task 1 Use estimation to choose the correct value for each expression a 5 1 2 0 102 1 02 10 2 102 b 4 8 93 3 572 35 72 357 2 3 572 2 Estimate the answer for 7 13 6 Explain your reasoning using words pictures or numbers Answers 1 a Circle 10 2 b Circle 35 72 2 About 42 answers will vary 98 ZEARN MATH Teacher Edition

G5M1 Topic F TOPIC F Dividing Decimals Topic F concludes Mission 1 with an exploration of division of decimal numbers by one digit whole number divisors using place value charts and disks Lessons begin with easily identifiable multiples such as 4 2 6 and move to quotients that have a remainder in the smallest unit through the thousandths Written methods for decimal cases are related to place value strategies properties of operations and familiar written methods for whole numbers Students solidify their skills with an understanding of the algorithm before moving on to division involving two digit divisors in Mission 2 Students apply their accumulated knowledge of decimal operations to solve word problems at the close of the mission Objective Topic F Dividing Decimals Lesson 13 Divide decimals by single digit whole numbers involving easily identifiable multiples using place value understanding and relate to a written method Lesson 14 Divide decimals with a remainder using place value understanding and relate to a written method Lesson 15 Divide decimals using place value understanding including remainders in the smallest unit Lesson 16 Solve word problems using decimal operations ZEARN MATH Teacher Edition 99

G5M1 Topic F Lesson 13 Lesson 13 YOUR NOTES Divide decimals by single digit whole numbers involving easily identifiable multiples using place value understanding and relate to a written method Warm Up FLUENCY PRACTICE Find the Product Materials S Personal white board NOTE Reviewing this skill introduced in Lessons 11 and 12 helps students work toward full understanding of multiplying single digit numbers times decimals T Write 4 3 Say the multiplication sentence in unit form S 4 3 ones 12 ones T Write 4 0 2 Say the multiplication sentence in unit form S 4 2 tenths 8 tenths T Write 4 x 3 2 Say the multiplication sentence in unit form S 4 3 ones 2 tenths 12 and 8 tenths T Write the multiplication sentence S Write 4 3 2 12 8 Repeat the process for 4 3 21 9 2 9 0 1 9 0 03 9 2 13 4 012 4 and 5 3 237 Compare Decimal Fractions Materials S Personal white board NOTE This review fluency helps solidify student understanding of place value in the decimal system T Write 13 78 13 86 On your personal white boards compare the numbers using the greater than less than or equal sign S Write 13 78 13 86 78 _ Repeat the process and procedure for 0 78 100 439 3 fifty eight tenths and thirty five and 9 thousandths ZEARN MATH Teacher Edition 4 39 5 08 4 tens 101

Topic F Lesson 13 YOUR NOTES G5M1 WORD PROBLEM Louis buys 4 chocolates Each chocolate costs 2 35 Louis multiplies 4 235 and gets 940 Place the decimal to show the cost of the chocolates and explain your reasoning using words numbers and pictures NOTE This Word Problem requires students to estimate 4 2 35 in order to place the decimal point in the product This skill was taught in Lesson 12 Concept Exploration Materials S Hundreds to thousandths place value chart Lesson 7 Concept Exploration Template personal white board PROBLEMS 1 3 The first problem 0 9 3 0 3 is optional 0 9 3 0 3 0 24 4 0 06 0 032 8 0 004 T Draw disks to show 9 tenths on your hundreds to thousandths place value chart S Show T Divide 9 tenths into 3 equal groups S Make 3 groups of 3 tenths T How many tenths are in each group S There are 3 tenths in each group T Write 0 9 3 0 3 on the board Read the number sentence using unit form S 9 tenths divided by 3 equals 3 tenths T How does unit form help us divide S When we identify the units then it s just like dividing 9 apples into 3 groups If you know what unit you are sharing then it s just like whole number division You can just think about the basic fact T Write 3 groups of sentence 0 9 on the board What is the unknown in our number S 3 tenths 0 3 102 ZEARN MATH Teacher Edition

G5M1 Repeat this sequence with 0 24 4 0 06 24 hundredths divided by 4 equals 6 hundredths and 0 032 8 0 004 32 thousandths divided by 8 equals 4 thousandths Topic F Lesson 13 YOUR NOTES PROBLEMS 4 6 1 5 5 0 3 1 05 5 0 21 3 015 5 0 603 T Write on the board 1 5 5 Read the equation stating the whole in unit form S Fifteen tenths divided by 5 T What is useful about reading the decimal as 15 tenths S When you say the units it s like a basic fact T What is 15 tenths divided by 5 S 3 tenths T On the board complete the equation 1 5 5 0 3 T On the board write 1 05 5 Read the expression using unit form for the dividend S 105 hundredths divided by 5 T Is there another way to decompose name or group this quantity S 1 one and 5 hundredths 10 tenths and 5 hundredths T Which way of naming 1 05 is most useful when dividing by 5 Why Turn and talk and then solve S 10 tenths and 5 hundredths because they are both multiples of 5 This makes it easy to use basic facts to divide mentally The answer is 2 tenths and 1 hundredth 105 hundredths is easier for me because I know 100 is 20 fives so 105 is 1 more 21 21 hundredths I just used the algorithm from Grade 4 and got 21 I knew it was hundredths Repeat this sequence with 3 015 5 Have students decompose the decimal several ways and then reason about which is the most useful for division It is also important to draw parallels among the next three problems Lead students by asking questions such as How does the answer to the second set of problems help you find the answer to the third if necessary PROBLEMS 7 9 Problems 7 9 are optional for Enrichment Compare the relationships between 4 8 6 0 8 and 48 6 8 4 08 8 0 51 and 408 8 51 63 021 7 9 003 and 63 021 7 9 003 ZEARN MATH Teacher Edition 103

Topic F Lesson 13 YOUR NOTES G5M1 T Write 4 8 6 0 8 and 48 6 8 on the board What relationships do you notice between these two equations How are they alike S 8 is 10 times greater than 0 8 48 is 10 times greater than 4 8 The digits are the same in both equations but the decimal points are in different places T How can 48 6 help you with 4 8 6 Turn and talk S If you think of the basic fact first then you can get a quick answer Then you just have to remember what units were really in the problem This one was really 48 tenths The division is the same the units are the only difference Repeat the process for 4 08 8 0 51 and 408 8 51 and 63 021 7 9 003 and 63 021 7 9 003 MULTIPLE MEANS OF ENGAGEMENT Students can also be challenged to use a compensation strategy to make another connection to wholenumber division The dividend is multiplied by a power of ten which converts it to its smallest units Once the dividend is shared among the groups it must be converted back to the original units by dividing it by the same power of ten For example 1 5 5 1 5 10 5 15 5 3 3 10 0 3 MULTIPLE MEANS OF REPRESENTATION Unfamiliar vocabulary can slow down the learning process or even confuse students Reviewing key vocabulary such as dividend divisor or quotient may benefit all students Displaying the words in a familiar mathematical sentence may serve as a useful reference for students For example display Dividend Divisor Quotient Independent Digital Lesson Lesson 13 Mindful Division Students also learn the concepts from this lesson in the Independent Digital Lesson The intentional balance of learning with teachers and peers and learning independently in digital lessons ensures every student has multiple opportunities to represent engage with and express their math reasoning There are no notes for this digital lesson Go online to see the full digital lesson 104 ZEARN MATH Teacher Edition

G5M1 Topic F Lesson 13 YOUR NOTES Wrap Up LESSON SYNTHESIS Guide students in a conversation to process today s lesson and surface any misconceptions or misunderstandings The questions below may be used to lead the discussion When decomposing decimals in different ways how can you tell which is the most useful We are looking for easily identifiable multiples of the divisor 4 221 7 Explain how you would decompose 4 221 so that you only need knowledge of basic facts to find the quotient EXIT TICKET After today s lesson instruct students to complete the Exit Ticket A review of their Exit Ticket as well as continuously monitoring your Digital Reports can help you assess your students understanding of the concepts explored in today s lesson and plan more effectively for future lessons The questions from the Exit Ticket may be read aloud to the students Task 1 Complete the sentences with the correct number of units and then complete the equation a 2 groups of tenths is 1 8 1 8 2 b 4 groups of hundredths is 0 32 0 32 4 c 7 groups of thousandths is 0 021 0 021 7 2 Complete the number sentence Express the quotient in unit form and then in standard form a 4 5 5 tenths 5 b 6 12 6 ones 6 ones ZEARN MATH Teacher Edition tenths hundredths 6 hundredths 105

Topic F Lesson 13 YOUR NOTES G5M1 Answers 1 a 9 0 9 b 8 0 08 c 3 0 003 2 a 45 9 0 9 b 6 12 1 2 1 02 106 ZEARN MATH Teacher Edition

G5M1 Lesson 14 Topic F Lesson 14 YOUR NOTES Divide decimals with a remainder using place value understanding and relate to a written method Warm Up FLUENCY PRACTICE Multiply and Divide by Exponents Materials T Millions to thousandths place value chart Lesson 1 Concept Exploration Template S Millions to thousandths place value chart Lesson 1 Concept Exploration Template personal white board NOTE This review fluency helps solidify student understanding of multiplying by 10 100 and 1 000 in the decimal system T Project the place value chart from millions to thousandths Using the place value chart write 65 tenths as a decimal S Write 6 in the ones column and 5 in the tenths column T Say the decimal S 6 5 T Multiply it by 102 S Cross out 6 5 and write 650 Repeat the process and sequence for 0 7 102 0 8 102 3 895 103 and 5 472 103 Round to Different Place Values Materials S Personal white board NOTE This review fluency helps solidify student understanding of rounding decimals to different place values T Project 6 385 Say the number S 6 and 385 thousandths T On your personal white boards round the number to the nearest tenth S Write 6 385 6 4 Repeat the process rounding 6 385 and 37 645 to the nearest hundredth ZEARN MATH Teacher Edition 107

Topic F Lesson 14 YOUR NOTES G5M1 Find the Quotient Materials S Personal white board NOTE Reviewing these skills introduced in Lesson 13 helps students work toward full understanding of dividing decimals by single digit whole numbers T Write 14 2 Write the division sentence S 14 2 7 T Say the division sentence in unit form S 14 ones 2 7 ones Repeat the process for 1 4 2 0 14 2 24 3 2 4 3 0 24 3 30 3 3 3 and 0 3 3 WORD PROBLEM A bag of potato chips contains 0 96 grams of sodium If the bag is split into 8 equal servings how many grams of sodium will each serving contain Extension What other ways can the bag be divided into equal servings so that the amount of sodium in each serving has two digits to the right of the decimal and the digits are greater than zero in the tenths and hundredths place NOTE This Word Problem reviews dividing decimal numbers by a single digit whole number Concept Exploration Materials S Hundreds to thousandths place value chart Lesson 7 Concept Exploration Template place value disks personal white board 108 ZEARN MATH Teacher Edition

G5M1 PROBLEM 1 Topic F Lesson 14 YOUR NOTES This problem is optional 6 72 3 5 16 4 T Write 6 72 3 on the board and draw a place value chart with 3 groups at the bottom Show 6 72 on your place value chart using your place value disks I ll draw on my chart S Represent work with the place value disks For the first problem students show their work with the place value disks The teacher will represent the work in a drawing and in the algorithm In Problems 2 and 3 students may draw instead of using the disks T Let s begin with our largest units We will share 6 ones equally with 3 groups How many ones are in each group S 2 ones Move the place value disks to show the distribution T Draw 2 place value disks in each group and cross off in the dividend as they are shared We gave each group 2 ones In the algorithm record 2 in the ones place in the quotient How many ones did we share in all S 6 ones T Show the subtraction in the algorithm How many ones are left to share S 0 ones T Let s share our tenths 7 tenths divided by 3 How many tenths can we share with each group S 2 tenths T Using your place value disks share your tenths I ll show what we did on my place value chart and in my written work Draw to share and cross off in the dividend Record in the algorithm S Move the place value disks T Record 2 in the tenths place in the quotient How many tenths did we share in all S 6 tenths T Record subtraction Let s stop here a moment Why are we subtracting the 6 tenths S We have to take away the tenths we have already shared We distributed the 6 tenths into 3 groups so we have to subtract them T Since we shared 6 tenths in all how many tenths are left to share S 1 tenth T Can we share 1 tenth with 3 groups S No T What can we do to keep sharing S We can change 1 tenth for 10 hundredths ZEARN MATH Teacher Edition 109

Topic F Lesson 14 YOUR NOTES G5M1 T Make that exchange on your place value chart I ll record T How many hundredths do we have now S 12 hundredths T Can we share 12 hundredths with 3 groups If so how many hundredths can we share with each group S Yes We can give 4 hundredths to each group T Share your hundredths and I ll record T Record 4 hundredths in the quotient Each group received 4 hundredths How many hundredths did we share in all S 12 hundredths T Record subtraction Remind me why we subtract these 12 hundredths How many hundredths are left S We subtract because those 12 hundredths have been shared They are now divided into the groups so we have to subtract 12 hundredths minus 12 hundredths is equal to 0 hundredths T Look at the 3 groups you made How many are in each group S 2 and 24 hundredths T Do we have any other units to share S No T How is the division we did with decimal units like whole number division Turn and talk S It s the same as dividing whole numbers except we are sharing units smaller than ones Our quotient has a decimal point because we are sharing fractional units The decimal shows where the ones place is Sometimes we have to change the decimal units just like we change the whole number units in order to continue dividing T Write 5 16 4 on the board Let s switch jobs for this problem I will use place value disks You record using the algorithm Follow the questioning sequence from above Students record the steps of the algorithm as the teacher models using the place value disks PROBLEM 2 6 72 4 20 08 8 T Write 6 72 4 on the board Using the place value chart solve this problem with your partner Partner A will draw the place value disks and Partner B will record all steps using the standard algorithm S Work to solve 110 ZEARN MATH Teacher Edition

G5M1 Topic F Lesson 14 T Compare the drawing to the algorithm Match each number to its counterpart in the drawing YOUR NOTES Circulate to ensure that students are using their whole number experiences with division to share decimal units Check for misconceptions in recording For the second problem in the set partners should switch roles PROBLEM 3 6 372 6 T Write 6 372 6 algorithm to solve on the board Work independently using the standard S Work to solve T Compare your quotient with your partner s MULTIPLE MEANS OF REPRESENTATION In order to activate prior knowledge have students solve one or two whole number division problems using the place value disks Help them record their work step by step in the standard algorithm This may help students understand that division of whole numbers and the division of decimal fractions are the same concept and process MULTIPLE MEANS OF ACTION AND EXPRESSION Students should have the opportunity to use tools that will enhance their understanding In math class this often means using manipulatives Communicate to students that the journey from concrete understanding to representational understanding drawings to abstraction is rarely a linear one Create a learning environment in which students feel comfortable returning to concrete manipulatives when problems are challenging Throughout this mission the place value disks should be readily available to all learners Independent Digital Lesson Lesson 14 Decimal Division Students also learn the concepts from this lesson in the Independent Digital Lesson The intentional balance of learning with teachers and peers and learning independently in digital lessons ensures every student has multiple opportunities to represent engage with and express their math reasoning See the digital lesson notes below for a glimpse of the paper to pencil transfer of these math ideas Go online to see the full digital lesson ZEARN MATH Teacher Edition 111

Topic F Lesson 14 G5M1 YOUR NOTES Wrap Up LESSON SYNTHESIS Guide students in a conversation to process today s lesson and surface any misconceptions or misunderstandings The questions below may be used to lead the discussion How are dividing decimals and dividing whole numbers similar How are they different EXIT TICKET After today s lesson instruct students to complete the Exit Ticket A review of their Exit Ticket as well as continuously monitoring your Digital Reports can help you assess your students understanding of the concepts explored in today s lesson and plan more effectively for future lessons The questions from the Exit Ticket may be read aloud to the students 112 ZEARN MATH Teacher Edition

G5M1 Topic F Lesson 14 Task YOUR NOTES 1 Draw place value disks on the place value chart to solve Show each step using the standard algorithm 5 372 2 2 Solve using the standard algorithm 0 576 4 Answers 1 2 686 2 0 144 ZEARN MATH Teacher Edition 113

G5M1 Topic F Lesson 15 Lesson 15 YOUR NOTES Divide decimals using place value understanding including remainders in the smallest unit Warm Up FLUENCY PRACTICE Find the Quotient Materials S Millions to thousandths place value chart Lesson 1 Concept Exploration Template personal white board NOTE This review fluency drill helps students work toward full understanding of dividing decimals using concepts introduced in Lesson 14 T Project the place value chart showing ones tenths and hundredths Write 0 48 2 On your place value chart draw 48 hundredths using place value disks Allow students time to draw T Write 48 hundredths 2 division problem hundredths tenths hundredths Solve the S Write 48 hundredths 2 24 hundredths 2 tenths 4 hundredths T Solve using the standard algorithm Repeat the process for 0 42 3 3 52 2 and 96 tenths 8 WORD PROBLEM Jose bought a bag of 6 oranges for 2 82 He also bought 5 pineapples He gave the cashier 20 and received 1 43 change How much did each pineapple cost NOTE This multi step problem requires several skills taught in this mission such as multiplying decimal numbers by single digit whole numbers subtraction of decimal numbers and division of decimal numbers Working with these three operations helps activate prior knowledge and helps scaffold today s Concept Exploration which focuses on decimal division Labeling the tape diagram as a class may be a beneficial scaffold for some learners ZEARN MATH Teacher Edition 115

Topic F Lesson 15 YOUR NOTES G5M1 MULTIPLE MEANS OF REPRESENTATION Tape diagrams are a form of modeling that offers students a way to organize prioritize and contextualize information in story problems Students create pictures represented in bars from the words in the story problems Once bars are drawn and the unknown identified students can find viable solutions Concept Exploration Materials S Hundreds to thousandths place value chart Lesson 7 Concept Exploration Template personal white board PROBLEMS 1 2 The first problem 1 7 2 is optional 1 7 2 2 6 4 T Write 1 7 2 on the board and draw a place value chart Show 1 7 on your place value chart by drawing place value disks For this problem students are only using the place value chart and drawing the place value disks However the teacher should record the standard algorithm and draw the place value disks as each unit is decomposed and shared T Let s begin with our largest unit Can 1 one be divided into 2 groups S No T Each group gets how many ones S 0 ones T Record 0 in the ones place of the quotient in the algorithm We need to keep sharing How can we share this single ones disk S Unbundle it or exchange it for 10 tenths T Draw that unbundling and tell me how many tenths we have now S 17 tenths T 17 tenths divided by 2 How many tenths can we put in each group S 8 tenths T Cross them off as you divide them into 2 equal groups S Cross out tenths and share them in 2 groups 116 ZEARN MATH Teacher Edition

G5M1 T Record 8 tenths in the quotient in the algorithm How many tenths did we share in all Topic F Lesson 15 YOUR NOTES S 16 tenths T Record 16 tenths in the algorithm Explain to your partner why we are subtracting the 16 tenths S Discuss T How many tenths are left S 1 tenth T Record the subtraction in the algorithm Is there a way for us to keep sharing Turn and talk S We can make 10 hundredths with 1 tenth Yes 1 tenth is still equal to 10 hundredths even though there is no digit in the hundredths place in 1 7 We can think about 1 and 7 tenths as 1 and 70 hundredths They are equal T Unbundle the 1 tenth to make 10 hundredths S Unbundle and draw T Have you changed the value of what we needed to share Explain S No It s the same amount to share but we are using smaller units The value is the same 1 tenth is the same as 10 hundredths T I can show this by placing a zero in the hundredths place Record the 0 in the hundredths place of the algorithm 1 tenth becomes 10 hundredths T Now that we have 10 hundredths can we divide this between our 2 groups How many hundredths are in each group S Yes 5 hundredths are in each group T Let s cross them off as you divide them into 2 equal groups S Work T Record 5 hundredths in the quotient in the algorithm How many hundredths did we share in all S 10 hundredths T Record 10 hundredths in the algorithm How many hundredths are left S 0 hundredths T Record the subtraction in the algorithm Do we have any other units that we need to share S No T Tell me the quotient in unit form and then in standard form S 0 ones 8 tenths 5 hundredths 85 hundredths 0 85 T Show 6 72 3 2 24 recorded in the standard algorithm from Lesson 14 and 1 7 2 0 85 recorded in the standard algorithm side by side Compare these two problems How do they differ Turn and share with your partner S One equation has a divisor of 3 and the other equation has a divisor of 2 Both quotients have 2 decimal places 6 72 has digits in the tenths and hundredths and 1 7 only has a digit ZEARN MATH Teacher Edition 117

Topic F Lesson 15 G5M1 YOUR NOTES in the tenths In order to divide 1 7 we have to think about our dividend as 1 and 70 hundredths to keep sharing T That s right In today s problem we had to record a zero in the hundredths place to show how we unbundled Did recording that zero change the amount that we had to share 1 and 7 tenths Why or why not S No because 1 and 70 hundredths is the same amount as 1 and 7 tenths For the next problem 2 6 4 repeat this sequence Model the process on the place value chart while students record the steps of the algorithm Stop along the way to make connections between the concrete materials and the written method PROBLEMS 3 4 The first problem 17 4 is optional 17 4 22 8 T Write 17 4 on the board Look at this expression What do you notice Turn and share with your partner S When we divide 17 into 4 groups we have a remainder T In fourth grade we recorded this remainder as R1 What have we done today that lets us keep sharing this remainder S We can unbundle the ones into tenths or hundredths and continue to divide T With your partner use the place value chart to solve this problem Partner A will draw the place value disks and Partner B will solve using the standard algorithm S Solve T Compare your work Match each number in the algorithm with its counterpart in the drawing Circulate to ensure that students are using their whole number experiences with division to share decimal units Check for misconceptions in recording For the second problem in the set partners should switch roles PROBLEM 5 7 7 4 T Write 7 7 4 algorithm on the board Solve independently using the standard S Solve T Compare your answer with your partner s 118 ZEARN MATH Teacher Edition

G5M1 Topic F Lesson 15 PROBLEM 6 YOUR NOTES 0 84 4 T Write 0 84 4 algorithm on the board Solve independently using the standard S Solve T Compare your answer with your neighbor s MULTIPLE MEANS OF REPRESENTATION In this lesson students will need to know that a number can be written in multiple ways In order to activate prior knowledge and heighten interest the teacher may display a dollar bill while writing 1 on the board The class could discuss that in order for the dollar to be divided between two people it must be thought of as tenths 1 0 Additionally if the dollar were to be divided by more than 10 people it would be thought of as hundredths 1 00 If students need additional support this could be demonstrated using concrete materials Independent Digital Lesson Lesson 15 Dynamo Division Students also learn the concepts from this lesson in the Independent Digital Lesson The intentional balance of learning with teachers and peers and learning independently in digital lessons ensures every student has multiple opportunities to represent engage with and express their math reasoning There are no notes for this digital lesson Go online to see the full digital lesson Wrap Up LESSON SYNTHESIS Guide students in a conversation to process today s lesson and surface any misconceptions or misunderstandings The question below may be used to lead the discussion Will a whole number divided by a whole number always result in a whole number ZEARN MATH Teacher Edition 119

Topic F Lesson 15 YOUR NOTES G5M1 EXIT TICKET After today s lesson instruct students to complete the Exit Ticket A review of their Exit Ticket as well as continuously monitoring your Digital Reports can help you assess your students understanding of the concepts explored in today s lesson and plan more effectively for future lessons The questions from the Exit Ticket may be read aloud to the students Task 1 Draw place value disks on the place value chart to solve Show each step using the standard algorithm 0 9 4 2 Solve using the standard algorithm 9 8 5 Answers 1 0 225 2 1 96 120 ZEARN MATH Teacher Edition

G5M1 Topic F Lesson 16 Lesson 16 YOUR NOTES Solve word problems using decimal operations Warm Up FLUENCY PRACTICE Find the Quotient Materials S Hundreds to thousandths place value chart Lesson 7 Concept Exploration Template personal white board NOTE This review fluency drill helps students work toward full understanding of dividing decimals using concepts introduced in Lesson 15 T Project the place value chart showing ones tenths and hundredths Write 0 3 2 Use place value disks to draw 3 tenths on your place value chart Allow students time to draw T Write 3 tenths 2 hundredths 2 on the board Solve the division problem tenths hundredths S Write 3 tenths 2 30 hundredths 2 1 tenth 5 hundredths T Write the algorithm below 3 tenths 2 30 hundredths 2 1 tenth 5 hundredths Solve using the standard algorithm Allow students time to solve Repeat the process for 0 9 5 6 7 5 0 58 4 and 93 tenths 6 WORD PROBLEM Jesse and three friends buy snacks for a hike They buy trail mix for 5 42 apples for 2 55 and granola bars for 3 39 If the four friends split the cost of the snacks equally how much should each friend pay ZEARN MATH Teacher Edition 121

Topic F Lesson 16 YOUR NOTES G5M1 NOTE Adding and dividing decimals are taught in this mission Teachers may choose to help students draw the tape diagram before students do the calculations independently Concept Exploration NOTE Today s lesson uses the Problem Set Solutions for each problem are included below Materials T S Problem Set pencil Instruct students to turn to the Problem Set in their student workbooks PROBLEM 1 This problem is optional Mr Frye distributed 126 equally among his 4 children for their weekly allowance How much money did each child receive As the teacher creates each component of the tape diagram students should re create the tape diagram on their Problem Sets T We will solve Problem 1 on the Problem Set together Project the problem on the board Read the word problem together S Read chorally T Who and what is this problem about Let s identify our variables S Mr Frye s money Mr Frye s Money T Draw a bar to represent Mr Frye s money Draw a rectangle on the board T Let s read the problem sentence by sentence and adjust our diagram to match the information in the problem Read the first sentence together S Read T What is the important information in the first sentence Turn and talk S 126 and 4 children received an equal amount T Underline the stated information How can I represent this information in my diagram S 126 dollars is the total so put a bracket on top of the bar and label it T Draw a bracket over the diagram and label as 126 Have students label their diagrams 122 ZEARN MATH Teacher Edition

G5M1 Topic F Lesson 16 126 YOUR NOTES Mr Frye s Money T How many children share the 126 dollars S 4 children T How can we represent this information S Divide the bar into 4 equal parts T Partition the diagram into 4 equal sections and have students do the same 126 Mr Frye s Money T What is the question S How much did each child receive T What is unknown in this problem How will we represent it in our diagram S The amount of money one of Mr Frye s children received for allowance is what we are trying to find We should put a question mark inside one of the parts T Write a question mark inside one section of the tape diagram 126 Mr Frye s Money T Make a unit statement about your diagram How many unit bars are equal to 126 S Four units is the same as 126 T How can we find the value of one unit S Divide 126 by 4 Use division because we have a whole that we are sharing equally T What is the expression that will give us the amount that each child received S 126 4 T Solve and express your answer in a complete sentence 126 Mr Frye s Money 4 units 126 1 unit 1 unit 126 4 ZEARN MATH Teacher Edition 31 50 123

Topic F Lesson 16 YOUR NOTES G5M1 S Each child received 31 50 for their weekly allowance T Read Part b of Problem 1 and solve using a tape diagram S Work time As students are working circulate and be attentive to accuracy and labeling of information in the students tape diagrams Refer to the example student work on the Problem Set for one example of an accurate tape diagram PROBLEM 2 Ava is 23 cm taller than Olivia and Olivia is half the height of Lucas If Lucas is 1 78 m tall how tall are Ava and Olivia Express their heights in centimeters T Complete Problem 2 on the Problem Set using a tape diagram and calculations to solve Circulate as students work Listen for sound mathematical reasoning PROBLEM 3 This problem is optional Mr Hower can buy a computer with a down payment of 510 and 8 monthly payments of 35 75 If he pays cash for the computer the cost is 699 99 How much money will he save if he pays cash for the computer instead of paying for it in monthly payments T Complete Problem 3 on the Problem Set using a tape diagram and calculations to solve Circulate as students work Listen for sound mathematical reasoning 124 ZEARN MATH Teacher Edition

G5M1 Topic F Lesson 16 PROBLEM 4 YOUR NOTES Brandon mixed 6 83 lb of pretzels with 3 57 lb of popcorn After filling up 6 bags that were the same size with the mixture he had 0 35 lb left What was the weight of each bag T Project Problem 4 Read the problem Identify the variables who and what and draw a bar S Read and draw Draw a bar on the board Brandon s Pretzels and Popcorn T Read the first sentence S Read T What is the important information in this sentence Tell a partner S 6 83 lb of pretzels and 3 57 lb of popcorn T Underline the stated information How can I represent this information in the tape diagram S Show two parts inside the bar T Should the parts be equal in size S No The pretzels part should be about twice the size of the popcorn part T Draw and label Let s read the next sentence How will we represent this part of the problem S We could draw another bar to represent both kinds of snacks together Then split the bar into parts to show the bags and the part that was left over We could erase the bar separating the snacks put the total on the bar we already drew and split it into the equal parts We would have to remember he had some snacks left over T Both are good ideas Choose one for your model I am going to use the bar that I ve already drawn I ll label my bags with the letter b and I ll label the part that wasn t put into a bag T Erase the bar between the types of snacks Draw a bracket over the bar and write the total Show the leftover snacks and the 6 bags T What is the question S How much did each bag weigh T Where should we put our question mark S Inside one of the units that is labeled with the letter b T How will we find the value of 1 unit in our diagram Turn and talk S Part of the weight is being placed into 6 bags so we need to divide that part by 6 There ZEARN MATH Teacher Edition 125

Topic F Lesson 16 YOUR NOTES G5M1 was a part that didn t get put in a bag We have to take the leftover part away from the total so we can find the part that was divided into the bags Then we can divide T Perform your calculations and state your answer in a complete sentence See the solution below 6 units 0 35 10 4 1 unit 10 4 0 35 6 1 unit 1 675 lb Each bag contained 1 675 lb PROBLEM 5 This problem is optional for Enrichment The bakery bought 4 bags of flour containing 3 5 kg each 0 475 kg of flour is needed to make a batch of muffins and 0 65 kg is needed to make a loaf of bread a If 4 batches of muffins and 5 loaves of bread are baked how much flour will be left Give your answer in kilograms 126 ZEARN MATH Teacher Edition

G5M1 b The remaining flour is stored in bins that hold 3 kg each How many bins will be needed to store the flour Explain your answer Topic F Lesson 16 YOUR NOTES T Complete Problem 5 on the Problem Set using a tape diagram and calculations to solve Circulate as students work Listen for sound mathematical reasoning MULTIPLE MEANS OF REPRESENTATION Students may use various approaches for calculating the quotient In Problem 1 some may use place value units such as 12 tens 60 tenths Others may use the division algorithm Comparing computation strategies may help students develop their mathematical thinking MULTIPLE MEANS OF ENGAGEMENT If students struggle to draw a model of word problems involving division with decimal values scaffold their understanding by modeling an analogous problem substituting simpler whole number values Then using the same tape diagram erase the whole number values and replace them with the parallel values from the decimal problem MULTIPLE MEANS OF REPRESENTATION Complex relationships within a tape diagram can be made clearer to students with the use of color The bags of pretzels and popcorn in Problem 4 could be made more visible by outlining the bagged snacks in red This creates a classic part part whole problem Students can readily see the portion that must be subtracted in order to produce the portion divided into 6 bags If using color to highlight relationships is still too abstract for students colored paper can be cut marked and manipulated ZEARN MATH Teacher Edition 127

Topic F Lesson 16 YOUR NOTES G5M1 Independent Digital Lesson Lesson 16 Decimal Problem Solving Students also learn the concepts from this lesson in the Independent Digital Lesson The intentional balance of learning with teachers and peers and learning independently in digital lessons ensures every student has multiple opportunities to represent engage with and express their math reasoning See the digital lesson notes below for a glimpse of the paper to pencil transfer of these math ideas Go online to see the full digital lesson Wrap Up LESSON SYNTHESIS Guide students in a conversation to process today s lesson and surface any misconceptions or misunderstandings The questions below may be used to lead the discussion 128 How did the tape diagram in Problem 1 a help you solve Problem 1 b ZEARN MATH Teacher Edition

G5M1 Topic F Lesson 16 In Problem 3 how did you represent the information using the tape diagram Look at Problem 1 b and Problem 5 b How are the questions different Problem 1 b is partitive division number of groups are known size of group is unknown Problem 5 b is measurement division size of group is known number of groups is unknown Does the difference in the questions affect the calculation of the answers For enrichment have students generate word problems based on labeled tape diagrams or have them create one of each type of division problem group size unknown and number of groups unknown YOUR NOTES EXIT TICKET After today s lesson instruct students to complete the Exit Ticket A review of their Exit Ticket as well as continuously monitoring your Digital Reports can help you assess your students understanding of the concepts explored in today s lesson and plan more effectively for future lessons The questions from the Exit Ticket may be read aloud to the students Task Write a word problem with two questions that match the tape diagram below and then solve Answers 2 Word problems will vary Jim s dog weighs 5 41 lb _ 3 of John s dog s weight is 10 82 lb ZEARN MATH Teacher Edition 129

Topic F Lesson 16 Problem Set G5M1 PROBLEM SET Name Date Solve Problem 1 Mr Frye distributed 126 allowance equally among his 4 children for their weekly allowance a How much money did each child receive b John the oldest child paid his siblings to do his chores If John pays his allowance equally to his brother and two sisters how much money will each of his siblings have received in all Problem 2 Ava is 23 cm taller than Olivia and Olivia is half the height of Lucas If Lucas is 1 78 m tall how tall are Ava and Olivia Express their heights in centimeters 130 ZEARN MATH Teacher Edition

G5M1 Topic F Lesson 16 Problem Set Problem 3 Mr Hower can buy a computer with a down payment of 510 and 8 monthly payments of 35 75 If he pays cash for the computer the cost is 699 99 How much money will he save if he pays cash for the computer instead of paying for it in monthly payments Problem 4 Brandon mixed 6 83 lb of pretzels with 3 57 lb of popcorn After filling up 6 bags that were the same size with the mixture he had 0 35 lb left What was the weight of each bag Use a tape diagram and show your calculations Problem 5 The bakery bought 4 bags of flour containing 3 5 kg each 0 475 kg of flour is needed to make a batch of muffins and 0 65 kg is needed to make a loaf of bread a If 4 batches of muffins and 5 loaves of bread are baked how much flour will be left Give your answer in kilograms b The remaining flour is stored in bins that hold 3 kg each How many bins will be needed to store the flour Explain your answer ZEARN MATH Teacher Edition 131

Math Math TEACHER EDITION GRADE 5 TEACHER EDITION Mission 1 1 Mission 1 Place Value with Decimal Fractions Mission 2 Base Ten Operations Mission 3 Add and Subtract Fractions Mission 4 Multiply and Divide Fractions and Decimals Mission 5 Volume Area and Shapes 4 5 6 5 GRADE Mission 6 The Coordinate Plane Grade 5 Mission 1 Zearnmath_TE_Grade5_M1 indd 1 3 TEACHER EDITION GRADE 5 2 12 10 22 10 12 AM