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GRADE 3 Mission 1 Multiply and Divide Friendly Numbers This mission introduces multiplication and division with friendly numbers 2 5 and 10 Students move gradually from skip counting and arrays to using the distributive property as a strategy for multiplying and dividing larger factors

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 062 9

Table of Contents MISSION OVERVIEW viii ASSESSMENTS xiii TOPIC A MULTIPLICATION AND THE MEANING OF FACTORS LESSON 1 3 LESSON 2 9 LESSON 3 15 TOPIC B DIVISION AS AN UNKNOWN FACTOR PROBLEM LESSON 4 21 LESSON 5 27 LESSON 6 33 TOPIC C MULTIPLICATION USING UNITS OF 2 AND 3 LESSON 7 39 LESSON 8 45 LESSON 9 51 LESSON 10 59 TOPIC D DIVISION USING UNITS OF 2 AND 3 LESSON 11 67 LESSON 12 75 LESSON 13 83 TOPIC E MULTIPLICATION AND DIVISION USING UNITS OF 4 LESSON 14 89 LESSON 15 95 LESSON 16 101 LESSON 17 109 TOPIC F D ISTRIBUTIVE PROPERTY AND PROBLEM SOLVING USING UNITS OF 2 5 AND 10 LESSON 18 115 LESSON 19 121 LESSON 20 127 LESSON 21 133 ZEARN MATH Teacher Edition iii

G3M1 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 G4 G5 Place Value with Decimal Fractions G7 G8 Key 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 Rates and Percentages M4 M3 Add Subtract Fractions M4 Dividing Fractions Proportional Measuring Relationships Circles and Percentages M2 Dilations Similarity and Introducing Slope M3 Linear Relationships Expanding Whole Numbers and Operations to Fractions and Decimals ZEARN MATH Teacher Edition M5 Rational Number Arithmetic M4 Linear Equations and Linear Systems M5 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 M6 Shapes Measurement Display Data M6 M4 Expressions Equations and Inequalities Shapes Time Fractions M7 M6 M5 Fractions as Numbers Multiply and Divide Fractions Decimals Arithmetic in Base Ten M8 M7 Equivalent Fractions M5 Add Subtract to 100 Length Money Data M5 Construct Lines Angles Shapes M3 M2 Base Ten Operations M6 Equal Groups M4 Find the Area M4 M3 Multiply Divide Big Numbers M1 M5 Multiply Divide Tricky Numbers M6 Work with Shapes Add Subtract Big Numbers M3 M2 Numbers to 20 Digital Activities 35 M5 Add Subtract Big Numbers Add Subtract Solve Measure It Numbers to 15 Digital Activities 35 M4 Measure Length M4 Counting Place Value Multiply Divide Friendly Numbers Add Subtract Round 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 G3M1 Topics and Lesson Objectives Lesson Objective Topic A Multiplication and the Meaning of Factors Lesson 1 Understand equal groups of as multiplication Lesson 2 Relate multiplication to the array model Lesson 3 Interpret the meaning of factors the size of the group or the number of groups Topic B Division as an Unknown Factor Problem Lesson 4 Understand the meaning of the unknown as the size of the group in division Lesson 5 Understand the meaning of the unknown as the number of groups in division Lesson 6 Interpret the unknown in division using the array model Topic C Multiplication Using Units of 2 and 3 Lessons 7 8 Demonstrate the commutativity of multiplication and practice related facts by skip counting objects in array models Lesson 9 Find related multiplication facts by adding and subtracting equal groups in array models Lesson 10 Model the distributive property with arrays to decompose units as a strategy to multiply Mid Mission Assessment Topics A C Topic D Division Using Units of 2 and 3 Lesson 11 Model division as the unknown factor in multiplication using arrays and tape diagrams Lesson 12 Interpret the quotient as the number of groups or the number of objects in each group using units of 2 Lesson 13 Interpret the quotient as the number of groups or the number of objects in each group using units of 3 Topic E Multiplication and Division Using Units of 4 Lesson 14 Skip count objects in models to build fluency with multiplication facts using units of 4 Lesson 15 Relate arrays to tape diagrams to model the commutative property of multiplication vi ZEARN MATH Teacher Edition

G3M1 Overview Lesson 16 Use the distributive property as a strategy to find related multiplication facts Lesson 17 Model the relationship between multiplication and division Topic F Distributive Property and Problem Solving Using Units of 2 5 and 10 Lessons 18 19 Apply the distributive property to decompose units Lesson 20 Solve two step word problems involving multiplication and division and assess the reasonableness of answers Lesson 21 Solve two step word problems involving all four operations and assess the reasonableness of answers End of Mission Assessment Topics D F ZEARN MATH Teacher Edition vii

Overview G3M1 MISSION 1 OVERVIEW This mission begins the year by building on students fluency with addition and their knowledge of arrays In Topic A students initially use repeated addition to find the total from a number of equal groups As students notice patterns they let go of longer addition sentences in favor of more efficient multiplication facts Lessons in Topic A move students Grade 2 work with arrays and repeated addition a step further by developing skip counting rows as a strategy for multiplication Arrays become a cornerstone of the mission Students use the language of multiplication as they understand what factors are and differentiate between the size of groups and the number of groups within a given context In this mission the factors 2 3 4 5 and 10 provide an entry point for moving into more difficult factors in later missions The study of factors links Topics A and B Topic B extends the study to division Students understand division as an unknown factor problem and relate the meaning of unknown factors to either the number or the size of groups By the end of Topic B students are aware of a fundamental connection between multiplication and division that lays the foundation for the rest of the mission In Topic C students use the array model and familiar skip counting strategies to solidify their understanding of multiplication and practice related facts of 2 and 3 They become fluent enough with arithmetic patterns to add or subtract groups from known products to solve more complex multiplication problems They apply their skills to word problems using drawings and equations with a symbol to find the unknown factor This culminates in students using arrays to model the distributive property as they decompose units to multiply In Topic D students model write and solve partitive and measurement division problems with 2 and 3 Consistent skip counting strategies and the continued use of array models are pathways for students to naturally relate multiplication and division Modeling advances as students use tape diagrams to represent multiplication and division A final lesson in this topic solidifies a growing understanding of the relationship between operations Topic E shifts students from simple understanding to analyzing the relationship between multiplication and division Practice of both operations is combined this time using units of 4 and a lesson is explicitly dedicated to modeling the connection between them Skip counting the distributive property arrays number bonds and tape diagrams are tools for both operations A final lesson invites students to explore their work with arrays and related facts through the lens of the commutative property as it relates to multiplication Topic F introduces the factors 5 and 10 familiar from skip counting in Grade 2 Students apply the multiplication and division strategies they have used in mixed practice with all of the factors included in Mission 1 Students model relationships between factors analyzing the arithmetic patterns that emerge to compose and decompose numbers as they further explore the relationship between multiplication and division viii ZEARN MATH Teacher Edition

G3M1 Overview In the final lesson of the mission students apply the tools representations and concepts they have learned to problem solving with multi step word problems using all four operations They demonstrate the flexibility of their thinking as they assess the reasonableness of their answers for a variety of problem types The Mid Mission Assessment follows Topic C The End of Mission Assessment follows Topic F 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 21 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 G3M1 Terminology New or Recently Introduced Terms Array1 Arrangement of objects in rows and columns Commutative property commutative E g rotate a rectangular array 90 degrees to demonstrate that factors in a multiplication sentence can switch places Equal groups With reference to multiplication and division one factor is the number of objects in a group and the other is a multiplier that indicates the number of groups Distribute With reference to the distributive property e g in 12 3 10 3 2 3 the 3 is the multiplier for each part of the decomposition Divide division Partitioning a total into equal groups to show how many equal groups add up to a specific number e g 15 5 3 Factors Numbers that are multiplied to obtain a product Multiplication multiply An operation showing how many times a number is added to itself e g 5 3 15 Number of groups Factor in a multiplication problem that refers to the total equal groups Parentheses Symbols used around an expression or numbers within an equation Product The answer when one number is multiplied by another Quotient The answer when one number is divided by another Rotate Turn used with reference to turning arrays 90 degrees Row column2 In reference to rectangular arrays Size of groups Factor in a multiplication problem that refers to how many in a group Unit One segment of a partitioned tape diagram Unknown The missing factor or quantity in multiplication or division 1 2 Originally introduced in Grade 2 Mission 6 but treated as new vocabulary in this mission Originally introduced in Grade 2 Mission 6 but treated as new vocabulary in this mission x ZEARN MATH Teacher Edition

G3M1 Overview Familiar Terms and Symbols3 Add 1 unit subtract 1 unit Add or subtract a single unit of two ten etc Expression See expanded description in notes Number bond Illustrates part part whole relationship shown under Suggested Tools and Representations Ones twos threes etc Units of one two or three Repeated addition Adding equal groups together e g 2 2 2 2 Tape diagram A method for modeling problems Value How much 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 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 12 5 b 20 3 2 5 Suggested Tools and Representations 18 counters per student Tape diagram A method for modeling problems Number bond As shown Personal white boards Ones twos threes etc Arrangement of objects in rows and columns 3 These are terms and symbols students have used or seen previously ZEARN MATH Teacher Edition xi

Overview G3M1 Personal White Boards Materials Needed for Personal White Boards 1 heavy duty clear sheet protector 1 1 piece of stiff red tag board 11 8 __4 1 1 piece of stiff white tag board 11 8 __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 xii ZEARN MATH Teacher Edition

PAGE 1 ZEARN MID MISSION ASSESSMENT Name G3 M1 Date 1 Mrs Tran picks 15 tomatoes from her garden She divides them into 5 equal groups a Draw the number of tomatoes in each bag b Fill in the blanks to make a true multiplication sentence that describes your drawing in part a c Explain the meaning of each factor in the equation in part b 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 G3M1 Mid Mission Assessment 2 Mrs Tran plants 12 sunflowers in her garden She plants them in 3 rows a Draw an array to represent the problem b Fill in the blanks below to make a true division sentence that describes your drawing in part a c What does the quotient in part b represent d Mrs Tran adds 2 more identical rows of sunflowers to her 3 original rows She figured out how many total flowers she planted Her work is shown in the box below Would Mrs Tran get the same result if she multiplied 5 4 Explain why or why not 3 4 2 4 12 8 20

PAGE 1 ZEARN END OF MISSION ASSESSMENT Name G3 M1 Date 1 Ms Park buys a tray of apples for a class party There are 5 rows of 4 red apples There is 1 row of 4 green apples a The picture below shows Ms Park s apples Fill in the blanks to complete the expressions Red apples 4 Total apples 4 Green apples 4 b Fill in the unknowns in the equation below to match the picture of the apples in part a Use the break apart and distribute strategy to find the total number of apples Ms Park bought 4 4 4 Ms Park bought apples 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 G3M1 End of Mission Assessment 2 Mr Lewis arranges all the desks in his classroom into 6 equal groups of 4 a How many desks are in his classroom Show a picture and multiplication sentence in your work b What does the product in your multiplication sentence represent c Fill in the blanks below to complete a related division sentence 4 d What does the quotient in part c represent

G3M1 End of Mission Assessment PAGE 3 3 Mr Myer s class plays a game The class earns 5 points each time they answer a question correctly The class earns 50 points playing the game on Monday a How many questions did the class answer correctly Show a picture and division sentence in your work b Mr Myer uses the equation 5 50 to find how many questions the class answered correctly Is his method correct Why or why not c The class answered 7 questions correctly on Tuesday What is the total number of points the class earned on Monday and Tuesday Show your work and or explain your reasoning

PAGE 4 G3M1 End of Mission Assessment 4 Solve mentally a 2 3 b 10 5 c 4 2 d 2 2 e 15 5 f 10 3 h 3 3 i 5 g 4 12 j 16 4 k 2 8 l 10 4 m 2 4 n 12 4 o 4 p 5 5 q 50 10 r 15 3 s 24 4 t 5 v 3 21 w 4 7 30 15 u 35 5 x 27 3 20

G3M1 Topic A TOPIC A Multiplication and the Meaning of Factors Lesson 1 introduces students to multiplication starting with the concept of repeated addition which is familiar from Grade 2 Students use repeated addition to find totals for example they use counters to make 6 equal groups of 2 They learn to recognize equal groups of counters as units and count units using the language of groups and unit form 6 equal groups of 2 counters make 12 counters or 6 twos make 12 By the end of Lesson 1 students use the multiplication symbol to represent these descriptions as more efficient multiplication equations In Lesson 2 students relate the equal groups of objects in scattered configurations from Lesson 1 to the array model exploring the correspondence between 1 equal group and 1 row They begin to distinguish between the number of groups and the size of groups as they count rows and how many in 1 row to write multiplication facts Students recognize the efficiency of arrays as they skip count to find totals In Lesson 2 students use the following vocabulary row array number of groups and size of groups Lesson 3 solidifies students ability to differentiate the meaning of factors Students model dividing a whole into equal groups as well as analyze equal groups in scattered configurations and arrays to determine whether factors represent the number of groups or the size of groups They create pictures number bonds and multiplication equations to model their understanding In this topic students use a variety of factors since these lessons emphasize understanding the concept of multiplying rather than finding totals Later topics limit facts to those involving one or two specific factors allowing students to build fluency with simpler facts before moving on to more difficult ones Objective Topic A Multiplication and the Meaning of Factors Lesson 1 Understand equal groups of as multiplication Lesson 2 Relate multiplication to the array model Lesson 3 Interpret the meaning of factors the size of the group or the number of groups ZEARN MATH Teacher Edition 1

G3M1 Lesson 1 Topic A Lesson 1 YOUR NOTES Understand equal groups of as multiplication Warm Up FLUENCY PRACTICE Group Counting NOTE Basic skip counting skills from Grade 2 shift focus in this Grade 3 activity Group counting lays a foundation for interpreting multiplication as repeated addition When students count groups in this activity they add and subtract groups of 2 when counting up and down T Let s count to 20 forward and backward Watch my fingers to know whether to count up or down A closed hand means stop Show signals during the explanation T Rhythmically point up until a change is desired Show a closed hand then point down S 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0 T Let s count to 20 forward and backward again This time whisper every other number Say the other numbers in a regular voice S Whisper 1 speak 2 whisper 3 speak 4 whisper 5 speak 6 etc T Let s count to 20 forward and backward again This time hum every other number instead of whispering As you hum think of the number S Hum 2 hum 4 hum 6 etc T Let s count to 20 forward and backward again This time think every other number instead of humming S Think 2 think 4 think 6 etc T What did we just count by Turn and talk to your partner S Twos T Let s count by twos Direct students to count forward to and backward from 20 changing directions at times WORD PROBLEM There are 83 girls and 76 boys in the third grade How many total students are in the third grade ZEARN MATH Teacher Edition 3

Topic A Lesson 1 G3M1 YOUR NOTES NOTE Students may choose to use a tape diagram or a number bond to model the problem They are also likely to solve today s Word Problem in less than 10 minutes Ten minutes have been allotted to allow for review of the RDW Read Draw Write process for problem solving Directions on the Read Draw Write RDW process Read the problem draw and label write an equation and write a word sentence The more students participate in reasoning through problems with a systematic approach the more they internalize those behaviors and thought processes Concept Exploration Materials S 12 counters personal white board PROBLEM 1 Skip count to find the total number of objects T Select 10 students to come to the front At the signal say how many arms you each have Signal S 2 arms T Since we each represent a group of 2 arms let s skip count our volunteers by twos to find how many arms they have altogether To keep track of our count students will raise up their arms when we count them S Count 2 4 6 20 T How many raised arms do we have in all S 20 T Arms down How many twos did we count to find the total Turn and whisper to your partner S 10 twos T What did you count to find the number of twos S I counted the number of volunteers because each person has a group of two arms T Skip count to find the total number of arms 4 ZEARN MATH Teacher Edition

G3M1 S Say 2 4 6 Topic A Lesson 1 Sample Teacher Board YOUR NOTES T As they count write 2 2 2 T Look at our addition sentence Show thumbs up if you see the correct number of twos S Show thumbs up T Under the addition sentence write 10 twos Clap 3 times if you agree that 10 groups of two is 20 S Clap 3 times T Write 10 groups of two is 20 under the other number sentences PROBLEM 2 Understand the relationship between repeated addition counting groups in unit form and multiplication sentences Seat students at tables with personal white boards and 12 counters each T You have 12 counters Use your counters to make equal groups of two How many counters will you put in each group Show with your fingers S Hold up 2 fingers and make groups of two T How many equal groups of two did you make Tell at the signal Signal S 6 groups T 6 equal groups of how many counters S 6 equal groups of 2 counters T 6 equal groups of 2 counters equal how many counters altogether S 12 counters T Write an addition sentence to show your groups on your personal white board S Write 2 2 2 2 2 2 12 T Record the addition sentence on the board In unit form how many twos did we add to make 12 S 6 twos T Record 6 twos 12 under the addition sentence 6 2 is another way to write 2 2 2 2 2 2 or 6 twos Record 6 2 12 under 6 twos 12 on the board These number sentences are all saying the same thing T Turn and talk to your partner How do you think 6 2 12 relates to the other number sentences Sample Teacher Board S They all have twos in them and the answer is 12 I think the 6 shows how many twos there are You have to count two 6 times because there are 6 groups of them That s how you get 6 times 2 6 2 might be an easier way to write a long addition sentence ZEARN MATH Teacher Edition 5

Topic A Lesson 1 YOUR NOTES G3M1 T Ways that are easier and faster are efficient When we have equal groups multiplication is a more efficient way to find the total than repeated addition Repeat the process with 4 threes 3 fours and 2 sixes to get students comfortable with the relationship between repeated addition counting groups in unit form and multiplication sentences PROBLEM 3 Write multiplication sentences from equal groups Draw or project the picture shown T These are equal groups Turn and tell your partner why they are equal S There is the same number of grey circles in each group All of the grey circles are the same size and shape and there are 4 in each group T Work with your partner to write a repeated addition and a multiplication sentence for this picture S Write 4 4 8 and either 2 4 8 or 4 2 8 T Project or draw the following Look at my new drawing and the multiplication sentence I wrote to represent it Check my work by writing an addition sentence and counting to find the total number of objects S Write 4 4 3 11 T Use your addition sentence as you talk to your partner about why you agree or disagree with my work S I disagree because my addition sentence equals 11 not 12 It s because that last group doesn t have 4 circles You can do multiplication when the groups are equal Here the groups aren t equal so the drawing doesn t show 3 4 T I hear most students disagreeing because my groups are not equal True to multiply you must have equal groups MULTIPLE MEANS OF REPRESENTATION It may be necessary to explicitly connect times and the symbol Have students analyze the model How many times do you see a group of two Have them count the groups write the number sentence and say the words together 6 6 groups of two equals 12 6 times 2 equals 12 ZEARN MATH Teacher Edition

G3M1 Topic A Lesson 1 MULTIPLE MEANS OF REPRESENTATION YOUR NOTES Some students may need more scaffolding to realize that multiplication cannot be used to find totals with groups that are not equal Use the following questions to scaffold Does the drawing show equal groups What expression represents this drawing For Problem 3 does 3 times 4 accurately represent this drawing How might we redraw the picture to make it show 3 4 Independent Digital Lesson Lesson 1 Need for Speed 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 7

Topic A Lesson 1 YOUR NOTES G3M1 Wrap Up LESSON SYNTHESIS Guide students in a conversation to process today s lesson and surface any misconceptions or misunderstandings The prompts below may be used to lead the discussion Discuss the relationship between repeated addition and the unit form 2 groups of three or 3 groups of two depending on the drawing Discuss the relationship between repeated addition unit form and the multiplication sentence 3 2 6 Review the new vocabulary presented in the lesson equal groups multiplication and multiply 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 The picture below shows 4 groups of 2 slices of watermelon Fill in the blanks to make true repeated addition and multiplication sentences that represent the picture 2 4 2 Draw a picture to show 3 3 3 9 Then write a multiplication sentence to represent the picture Answers 1 2 2 2 8 2 8 2 Picture showing 3 3 3 9 drawn 3 3 9 8 ZEARN MATH Teacher Edition

G3M1 Lesson 2 Topic A Lesson 2 YOUR NOTES Relate multiplication to the array model Warm Up FLUENCY PRACTICE Group Counting NOTE Basic skip counting skills from Grade 2 shift focus in this Grade 3 activity Group counting lays a foundation for interpreting multiplication as repeated addition When students count groups in this activity they add and subtract groups of three when counting up and down T Let s count to 18 forward and backward I want you to whisper whisper and then speak numbers T Watch my fingers to know whether to count up or down A closed hand means stop Show signals while explaining T Rhythmically point up until a change is desired Show a closed hand then point down S Whisper 1 whisper 2 speak 3 etc T Let s count to 18 forward and backward again This time think every number instead of whispering S Think think 3 think think 6 think think 9 etc T What did we just count by Turn and talk to your partner S Threes T Let s count by threes Direct students to count forward and backward to 18 periodically changing directions Emphasize the 9 to 12 transition Add Equal Groups Materials S Personal white board NOTE This activity reviews Lesson 1 Students directly relate repeated addition to multiplication They interpret products as the number of equal groups times the number of objects in each group T Project a picture array with 3 groups of 2 circled How many groups are circled S 3 T How many are in each group S 2 T Write this as an addition sentence ZEARN MATH Teacher Edition 9

Topic A Lesson 2 YOUR NOTES G3M1 S Write 2 2 2 6 T Write a multiplication sentence for 3 twos equals 6 S Write 3 2 6 Continue with this possible sequence 3 groups of 5 5 groups of 10 and 3 groups of 4 WORD PROBLEM Jordan uses 3 lemons to make 1 pitcher of lemonade He makes 4 pitchers How many lemons does he use altogether Use the RDW process to show your solution NOTE Present the image of 4 groups of 3 lemons with the word problem as a scaffold This problem reviews multiplying equal groups from Lesson 1 It also leads into today s Concept Exploration in which students relate multiplication to the array model Concept Exploration Materials S threes array Concept Exploration Template pictured in Problem 1 1 sheet of blank paper PROBLEM 1 Relate equal groups to arrays NOTE Students templates should be vertical rather than horizontal as shown T Look at Jordan s lemons Compare the way his lemons are organized with the groups of 3 circles on your template in your workbook S The lemons are touching each other but the circles have space between them Each line on the template shows three like each group of lemons The template is organized with everything in straight lines T Many students are noticing straight lines on the template Let s call a straight line going across a row Use your blank paper to cover all but the top row S Cover all but the top row T Uncover 1 row at a time in the picture As you uncover each row write the new total number of circles to the right of it 10 ZEARN MATH Teacher Edition

G3M1 Topic A Lesson 2 S Skip count by three using the threes array template T At the signal say the total number of circles you counted Signal Threes array template with student work YOUR NOTES S 30 circles T Take 10 seconds to find how many rows of 3 you counted At the signal say how many Signal S 10 rows T True or false 10 rows of 3 circles equals 30 circles S True T Write 10 3 30 on the board Use the picture on your template to talk with your partner about why this equation is true S Yesterday we learned that we can multiply equal groups We skip counted 10 rows of 3 circles each and the total is 30 It means 10 groups of 3 When you add 10 threes you get 30 Yeah but writing 10 3 is a lot easier than writing out 3 3 3 3 T We call this type of organized picture an array T Project or draw the image of the rectangles shown Take a look at this array At the signal tell how many rectangles are in the top row Signal S 4 rectangles T The size of 1 row is 4 rectangles Each row of 4 can also be called a group of 4 At the signal tell how many groups of four are in the array Signal S 3 groups of four T To write this as an equation we first write the number of groups How many groups S 3 groups T Write 3 are in each group Next we write the size of the group How many rectangles S 4 rectangles T Fill in the equation to read 3 4 rectangles in the array Skip count to find the total number of S 4 8 12 T Fill in the equation to read 3 4 12 We just found the answer to the multiplication equation that represents the array In multiplication the answer or total is called the product Show an array of 2 rows of 6 and repeat the process ZEARN MATH Teacher Edition 11

Topic A Lesson 2 YOUR NOTES G3M1 PROBLEM 2 Redraw equal groups as arrays T Project or draw the image of the triangles shown The drawing shows 3 equal groups of 5 On your personal white board re draw the picture as an array with 3 rows of 5 S Draw 3 rows of 5 T Write a multiplication expression to describe your array Remember an expression is different from an equation because it doesn t have an equal sign S Write 3 5 T Skip count to find the product S 5 10 15 T With your partner compare my drawing with your array Which is easier to count Why S Discuss Show 6 groups of 2 and repeat the process MULTIPLE MEANS OF REPRESENTATION The words array and row were introduced in Grade 2 Mission 6 but are treated as new vocabulary in this lesson When reviewing the concept have students trace a row on the array with a finger while saying the word row Provide a real world example by having students count the rows on various cupcake pans miniature and regular size before using the template MULTIPLE MEANS OF ENGAGEMENT Provide a challenge in this part of the lesson by giving an equation e g 5 4 and no picture Have students draw both the equal groups and the array to represent the equation Then they skipcount to find the total MULTIPLE MEANS OF REPRESENTATION When presenting the concept of an array it may be beneficial for students to model an array using concrete materials Then ask students to turn and talk to describe or define an array for their partner Independent Digital Lesson Lesson 2 Can You Dig It 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 12 ZEARN MATH Teacher Edition

G3M1 Topic A Lesson 2 Wrap Up YOUR NOTES LESSON SYNTHESIS Guide students in a conversation to process today s lesson and surface any misconceptions or misunderstandings The prompts below may be used to lead the discussion Compare equal groups in scattered configurations and arrays Review new vocabulary row array number of groups size of groups and product Prompt students to notice arrays around the room and possibly think of arrays in realworld situations 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 a There are 4 rows of stars How many stars are in each row b Write a multiplication equation to describe the array 2 Judy collects seashells She arranges them in 3 rows of 6 Draw Judy s array to show how many seashells she has altogether Then write a multiplication equation to describe the array Answers 1 a 3 b 4 3 12 2 3 rows of 6 drawn 3 6 18 ZEARN MATH Teacher Edition 13

Topic A Lesson 2 Lesson Template G3M1 THREES ARRAY CONCEPT EXPLORATION TEMPLATE 14 ZEARN MATH Teacher Edition

G3M1 Lesson 3 Topic A Lesson 3 YOUR NOTES Interpret the meaning of factors the size of the group or the number of groups Warm Up FLUENCY PRACTICE Group Counting NOTE Basic skip counting skills from Grade 2 shift focus in this Grade 3 activity Group counting reviews interpreting multiplication as repeated addition Counting by twos and threes in this activity anticipates work with those factors in Topic B T Let s count by twos Direct students to count forward and backward to 20 periodically changing directions T Let s count by threes Direct students to count forward and backward to 21 periodically changing directions Emphasize the 9 to 12 and 18 to 21 transitions Add to Multiply Materials S Personal white board NOTE This activity reviews Lesson 2 Students directly relate repeated addition to multiplication They interpret products using the array T Project a picture with 3 groups of 5 circled How many groups are circled S 3 T How many are in each group S 5 T Write it as an addition sentence S Write 5 5 5 15 T Write a multiplication sentence representing 3 fives equals 15 S 3 5 15 Continue with this possible sequence 3 groups of 10 3 groups of 4 and 7 groups of 2 ZEARN MATH Teacher Edition 15

Topic A Lesson 3 YOUR NOTES G3M1 WORD PROBLEM Robbie sees that a carton of eggs shows an array with 2 rows of 6 eggs What is the total number of eggs in the carton Use the RDW process to show your solution NOTE This problem reviews writing multiplication sentences from arrays learned in Lesson 2 The egg carton provides a natural array for students to see 2 rows of 6 Concept Exploration Materials S Personal white board NOTE Adjust the directions for the opening activity depending on the total number of students in the class Avoid having students make 4 groups of four Do this either by having students form groups near objects in the classroom rather than in corners to adjust the number of groups or by having an adult teddy bear etc stand in to adjust the size of the groups T Here are the rules for our opening activity 1 Divide yourselves into 4 equal groups 2 Each group will stand in a corner of the room 3 Divide silently You can use body movements to gesture but no words T Show thumbs up when your group is ready Be sure to look around the room to double check that all 4 groups are equal before showing you re ready S Move around the room silently until there are 4 equal groups 1 in each corner T At the signal tell how many equal groups we ve made Signal S 4 equal groups T Write 4 At the signal tell the size of each group Signal S Respond depending on class numbers T Fill in the equation on the board These numbers the number of groups and the number in each group are called factors Students transition back to their seats T Use the multiplication equation on the board to draw an array Make sure that your board is vertical S Draw a 4 array T Let s draw a number bond for our equation Draw a circle with our class total S Draw 16 ZEARN MATH Teacher Edition

G3M1 T Draw parts coming from the total Make 1 part to represent each row in our array Topic A Lesson 3 YOUR NOTES S Draw 4 circles coming from the total T Show the size of 1 row with your fingers S Show fingers T Write the factor representing the size of the group inside the circles S Write 6 inside each circle T Look back at the equation How is the factor 4 represented in the number bond S It s in the number of parts Groups are like parts In the number bond the part circles actually represent equal groups so there are 4 The number inside is the size of the group T Here is an analysis of our equation This problem is optional As time allows continue with the following possible suggestions 2 groups of 8 3 rows of 5 Number bond showing 6 groups of 3 The equation 5 4 20 MULTIPLE MEANS OF REPRESENTATION The number bond is a pictorial representation of part part whole relationships and shows that within a part whole relationship smaller numbers the parts make up larger numbers the whole MULTIPLE MEANS OF ACTION AND EXPRESSION The number bond is another way for students to explore the relationship between factors in multiplication Suggested explorations and questions Let s count the groups to make sure the number bond matches our number sentence 1 six 2 sixes etc What is the number of groups ZEARN MATH Teacher Edition 17

Topic A Lesson 3 YOUR NOTES G3M1 What is the size of each group What multiplication sentence represents the number bond Another option is to have students compare how the number bond can represent multiplication and addition to distinguish the importance of equal groups in multiplication Independent Digital Lesson Lesson 3 Factor Factor 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 18 ZEARN MATH Teacher Edition

G3M1 Wrap Up Topic A Lesson 3 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 Why do you think I started the lesson by asking you to divide yourselves into equal groups in the corners of the room Relate factors to their meaning the size of the group or the number of groups Have students share the definition in pairs 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 an array that shows 5 rows of 3 squares Then show a number bond where each part represents the amount in one row Answers 1 Array showing 5 rows of 3 squares drawn number bond showing 5 units of 3 equals 15 drawn ZEARN MATH Teacher Edition 19

Topic B G3M1 TOPIC B Division as an Unknown Factor Problem The study of factors links Topics A and B Topic B extends the study to division Students continue to use a variety of factors in this topic as the emphasis in these lessons rests on conceptually understanding division and learning to interpret problems by writing division equations Students understand division as an unknown factor problem and in Lessons 4 and 5 they relate the meaning of the unknown in division to the size of groups and the number of groups respectively They work through word problems that help give meaning through context and then analyze more abstract drawings In Lesson 6 students explore division in the context of the array model interpreting arrays by writing division equations Through the array students relate the unknown factor in multiplication to the quotient in division They use arrays to write multiplication equations and find unknown factors then write division equations where the quotient represents the same as the unknown factor By the end of this topic students use the vocabulary terms quotient and unknown factor and discussion moves toward solidifying understanding of the relationship between multiplication and division Objective Topic B Division as an Unknown Factor Problem Lesson 4 Understand the meaning of the unknown as the size of the group in division Lesson 5 Understand the meaning of the unknown as the number of groups in division Lesson 6 Interpret the unknown in division using the array model 20 ZEARN MATH Teacher Edition

G3M1 Topic B Lesson 4 Lesson 4 YOUR NOTES Understand the meaning of the unknown as the size of the group in division Warm Up FLUENCY PRACTICE Group Counting NOTE Group counting reviews interpreting multiplication as repeated addition Counting by twos and threes in this activity anticipates work with those factors in today s Concept Exploration T Let s count by twos Direct students to count forward and backward to 20 periodically changing directions e g 2 4 6 8 10 8 10 12 10 12 14 16 18 20 18 20 18 16 14 12 10 12 10 8 10 8 6 4 2 0 T Let s count by threes Direct students to count forward and backward to 24 periodically changing directions Emphasize the 9 to 12 and 18 to 21 transitions e g 3 6 9 12 9 12 9 12 15 18 21 18 21 18 21 24 21 18 21 18 15 12 15 12 9 12 9 6 3 0 Array Multiplication Materials S Personal white board NOTE This activity reviews Topic A s objectives Students directly relate repeated addition to multiplication interpreting products using the array T Project a picture with 3 groups of 2 circled Say the repeated addition equation S 2 2 2 6 T Write 3 equation On your personal white board complete the multiplication S Write 3 2 6 Continue with the following possible sequence 4 groups of 10 3 groups of 4 7 groups of 3 and 8 groups of 2 ZEARN MATH Teacher Edition 21

Topic B Lesson 4 YOUR NOTES G3M1 WORD PROBLEM The student council holds a meeting in Mr Chang s classroom They arrange the chairs in 3 rows of 5 How many chairs are used in all Use the RDW process NOTE This problem reviews relating multiplication to the array model from Lesson 2 Students might choose to solve by drawing an array Lesson 2 or a number bond Lesson 3 where each part represents the amount of chairs in each row Concept Exploration Materials S Personal white board 18 counters CONCRETE TO ABSTRACT Division as fair share relate the answer to the unknown factor T Yesterday Mr Ziegler bought a new pack of 18 markers He shared them with me by dividing them into 2 equal groups Now I have a bunch of new markers for making our charts Do you want to know how many he gave me S Yes T What are we trying to find the number of groups or the size of the group S The size of the group T Your 18 counters represent the markers Divide your 18 counters into 2 equal groups by giving one to Mr Z one to me one to Mr Z one to me Model partitioning S Divide using the fair share strategy T Using a complete sentence tell how many counters are in each group S There are 9 counters in each group T Then how many markers did Mr Ziegler give me S 9 markers T Let s write a number sentence to show our work starting from the beginning What is our total number of counters S 18 counters T Write 18 on the board We divided our 18 counters into how many equal groups S We divided into 2 equal groups T Write 2 22 on the board next to the 18 ZEARN MATH Teacher Edition

G3M1 T If 18 is our total and 2 represents our equal groups then remind me what does our unknown factor represent Point to where the answer will go Topic B Lesson 4 YOUR NOTES S The size of the groups T That is S 9 T 18 divided by 2 equals 9 Finish writing as you read 18 2 9 T How many markers did Mr Ziegler give me S 9 markers Repeat the process with 15 3 Suppose Mr Ziegler had 15 markers and shared fairly with 3 teachers This time also review that means to divide T In what ways does dividing remind you of our work with multiplication S It s also about the size of groups and the number of groups but we used a different symbol It still uses factors and a total This time the total is not the answer It s the beginning So the answer has to do with groups not the total T Right We multiply when we want to find the total Here we divided when we knew the total and wanted to find the size of the groups PICTORIAL TO ABSTRACT Analyze a picture to write a division sentence in which the solution tells the size of the group T Project or draw the following image This is how Diana arranges her star stickers T What does 12 represent in the picture S The total number of Diana s star stickers T What does 3 represent S The number of equal groups T What does 4 represent S The size of each group T Write a number sentence to represent Diana s stickers where the answer represents the size of the group S Write 12 3 4 T Write 12 3 4 and 12 4 3 on the board even if students have written the correct number sentence What is the difference between these division sentences S In the first one the answer represents the size of each group In the second one the answer represents the number of groups T If we re writing a division sentence where the answer represents the size of the group then which number sentence should we use S 12 3 4 ZEARN MATH Teacher Edition 23

Topic B Lesson 4 YOUR NOTES G3M1 ABSTRACT TO PICTORIAL Analyze equations for the meaning of the solution and represent the equation with a drawing Write 8 4 T If 8 is the total and 4 is the number of groups then what does the unknown factor represent S The size of the groups T Draw a picture on your personal white board to go with my division equation Use your picture to help you find the unknown factor then write the complete equation S Draw various pictures that show 8 4 then write 8 4 2 This problem is optional Repeat the process with 10 2 While designing examples keep in mind that Lesson 5 introduces students to division where the unknown factor represents the number of groups MULTIPLE MEANS OF ACTION AND EXPRESSION This may be students first time independently dividing in a formal context Life experience has likely taught them the fair share strategy of going back and forth to give 1 and 1 2 and 2 3 and 3 etc until there are no more to distribute Encourage those who are unsure what to do or who are using a less efficient strategy toward fair share MULTIPLE MEANS OF REPRESENTATION Preview this lesson for cognates words that sound similar and have the same meaning between two languages Encourage students to listen for cognates and share them with the class This may help students learning the primary language of the classroom actively listen and also boost auditory comprehension as they make links between prior knowledge and new learning In addition use concrete materials such as markers when appropriate to further understanding for students learning the primary language of the classrrom Independent Digital Lesson Lesson 4 Cookie Cluster 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 24 ZEARN MATH Teacher Edition

G3M1 Topic B 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 prompts below may be used to lead the discussion Guide students to articulate the similarities and differences between multiplication and division so that they are clear that division is used to find the total number of groups or objects in a group Students can think of division problems as having a known factor and an unknown factor Review phrases that include new vocabulary such as unknown factor and divided by 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 There are 16 glue sticks for the class The teacher divides them into 4 equal groups Draw the number of glue sticks in each group There are glue sticks in each group 16 2 Draw a picture to show 15 3 Then fill in the blank to make a true division sentence 15 3 Answers 1 Four glue sticks drawn in each group 4 4 4 2 Picture showing 15 3 drawn 5 ZEARN MATH Teacher Edition 25

G3M1 Lesson 5 Topic B Lesson 5 YOUR NOTES Understand the meaning of the unknown as the number of groups in division Warm Up FLUENCY PRACTICE Group Counting NOTE Group counting reviews interpreting multiplication as repeated addition Counting by twos and threes in this activity supports work with those factors in Topic B T Let s count by twos Direct students to count forward and backward to 20 emphasizing the 8 to 10 10 to 12 and 18 to 20 transitions T Let s count by threes Direct students to count forward and backward to 27 changing directions Emphasize the 9 to 12 and 18 to 21 transitions Divide Equal Groups Materials S Personal white board NOTE Students directly relate repeated addition to division They interpret the number of groups as the unknown in division This activity anticipates the lesson objective T Project an array with 2 groups of 5 How many groups are there S 2 T How many are in each group S 5 T Say the total as a repeated addition sentence S 5 5 10 T Write a division sentence for 10 divided into 2 equal groups S Write 10 2 5 Continue with the following possible sequence 4 groups of 2 3 groups of 4 and 2 groups of 6 ZEARN MATH Teacher Edition 27

Topic B Lesson 5 YOUR NOTES G3M1 WORD PROBLEM Stacey has 18 bracelets After she organizes the bracelets by color she has 3 equal groups How many bracelets are in each group NOTE This problem reviews the meaning of the unknown as the size of the group in division from Lesson 4 It also provides a comparison to Problem 1 of today s Concept Exploration where the unknown represents the number of groups in division Concept Exploration Materials S Personal white board 18 counters PROBLEM 1 Division as fair share with the unknown as the number of groups T Next weekend my friend Cynthia is having a party Eighteen people are coming I told her I d help her set up tables We know that 6 people can sit at each table but we re not sure how many tables we ll need Turn and talk with your partner What information do Cynthia and I already have S You know the total number of people It s 18 Yeah and you know how many people are sitting together 6 That s the size of the group T What information don t we know S You don t know how many tables Tables are like groups You don t know the number of groups T Let s use counters to show the problem and check our thinking Each of you has 18 counters 1 for each person coming to the party Put them into groups of 6 S Make groups of 6 T Do you still agree we know the total and the size of each group S Yes T Looking at our models what else do we now know S We know there are 3 groups So that means Cynthia needs 3 tables to fit everyone T Write 18 6 3 on the board How does this number sentence relate to the problem we just solved S It shows that we divided We knew the total 18 people We divided them into groups with 6 people Then we figured out that meant 3 groups of people We divided the total by the size of the group and found the number of groups 28 ZEARN MATH Teacher Edition

G3M1 Topic B Lesson 5 T Look back at your work from today s Word Problem With your partner compare the steps you took to solve both the bracelet problem and the party problem Notice the number sentences too YOUR NOTES S For the bracelets I drew circles to show 3 groups first Then I shared the bracelets between the groups In the party problem we put the people in groups of 6 first Then we found how many groups The 6 and 3 switched places That s because in the bracelet problem we had to find the size of the groups but in the party problem we had to find the number of groups T I m hearing you notice that the unknown was different in each problem We divide when we want to find the size of the groups or the number of groups Repeat the process using 14 7 without a story context Focus on 7 being the size of the groups Match the problem to a number bond like the one shown PROBLEM 2 Relate finding the number of groups to counting by the divisor This problem is optional T Cynthia plans to buy 15 burgers Three burgers come in each pack How many packs should she buy Whisper to your partner what the numbers 15 and 3 represent in this problem S Fifteen is the total number of burgers Three is the number of burgers in a pack T Is the unknown the number of groups or the size of the group S The number of groups T On your personal white board write the equation you would use to find how many packs to buy S Write 15 3 T Let s draw to find out how many packs Cynthia needs S Draw T How many packs does Cynthia need S 5 packs T 15 3 is S 5 T Let s write the total number of burgers under each pack How many total burgers does Cynthia have in 1 pack S 3 burgers T In 2 packs S 6 burgers repeat the process up to 15 T Let s read our numbers ZEARN MATH Teacher Edition 29

Topic B Lesson 5 YOUR NOTES G3M1 S 3 6 9 12 15 T Why did we stop at 15 S Because Cynthia only needs 15 burgers T What connection can you make between this problem and our fluency indicate the countby threes series from earlier S It s like counting by threes T Yes Each time we add a group we add a three T Count by threes with me and track the number of threes on your fingers S 3 6 9 12 15 Track count using fingers T How many threes did we count S 5 threes T Skip counting also shows us that Cynthia needs 5 packs Repeat the process with 21 3 and 14 2 without a story context T A count by can be a quick way to solve division problems when we need to find the number of equal groups especially if we have a big total like 21 MULTIPLE MEANS OF REPRESENTATION Drawing a picture in the second problem is essential to highlight an important pattern students need to understand to solve correctly There are not 6 burgers in the second pack rather there are 6 burgers in 2 packs The visual helps make clear why the count by works and also makes the connection to addition evident MULTIPLE MEANS OF ACTION AND EXPRESSION Since Kindergarten students have tracked counts on their fingers the Math Way that is by starting with the left pinky and moving across their fingers to the right This mimics the number line and also facilitates easily recognizing groups of 5 Depending on the class students may need to be reminded to utilize this familiar strategy as they track the count Independent Digital Lesson Lesson 5 Divide and Conquer 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 30 ZEARN MATH Teacher Edition

G3M1 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 Topic B Lesson 5 YOUR NOTES Wrap Up LESSON SYNTHESIS Guide students in a conversation to process today s lesson and surface any misconceptions or misunderstandings The prompt below may be used to lead the discussion Review the relationship between multiplication and division Guide students to observe that division is used to find either factor the unknown can be the size of groups or the number of groups 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 31

Topic B Lesson 5 YOUR NOTES G3M1 Task 1 Divide the 12 triangles into groups of 6 12 6 2 Spencer buys 20 strawberries to make smoothies Each smoothie needs 5 strawberries Skip count to find the number of smoothies Spencer can make Make a drawing to match your counting Answers 1 Two groups of 6 shown 2 2 Skip count by ves from 5 to 20 written and drawn He can make 4 smoothies 32 ZEARN MATH Teacher Edition

G3M1 Lesson 6 Topic B Lesson 6 YOUR NOTES Interpret the unknown in division using the array model Warm Up FLUENCY PRACTICE Group Counting NOTE Group counting reviews interpreting multiplication as repeated addition Counting by twos and threes in this activity supports work with those factors in Topic B T Let s count by twos Direct students to count forward and backward to 20 emphasizing the 8 to 10 10 to 12 and 18 to 20 transitions T Let s count by threes Direct students to count forward and backward to 30 periodically changing directions Emphasize the 9 to 12 18 to 21 and 27 to 30 transitions Divide Equal Groups Materials S Personal white board NOTE Students directly relate repeated addition to division They interpret the unknown in division This activity bridges Lesson 5 and today s Concept Exploration T Project an array with 3 groups of 5 Say the total as a repeated addition sentence S 5 5 5 15 T Write a division sentence for 15 divided into 3 equal groups S Write 15 3 5 Continue with the following possible sequence 5 groups of 3 4 groups of 3 3 groups of 4 9 groups of 2 and 2 groups of 9 Alternate between division sentences where the quotient represents either the number of objects in a group or the number of groups WORD PROBLEM Twenty children play a game There are 5 children on each team How many teams play the game Write a division sentence to represent the problem ZEARN MATH Teacher Edition 33

Topic B Lesson 6 G3M1 YOUR NOTES NOTE This problem reviews division from Lesson 5 where the unknown represents the number of groups It also leads into Problem 1 of today s Concept Exploration which relates division to the array model Concept Exploration Materials S Personal white board PROBLEM 1 Relate division to an array model Draw an array representing the Word Problem on the board Have students analyze the array and describe the following relationships Total number of children and total number of dots Number of children on each team and number of dots in each row Number of teams and number of rows Repeat the process with the following suggested examples This time guide students to draw the array from the division equations below Alternate between having the quotient represent the size of the groups and the number of groups 8 2 4 18 6 3 PROBLEM 2 Use an array to relate the unknown factor in multiplication to the quotient in division This problem is optional T Draw an array that shows the equation 15 3 5 where the quotient that means the answer represents the size of the groups S Draw array to the right T Now write both a division and a multiplication equation for the array S Write 15 3 5 3 5 15 T Where do you find the quotient in our multiplication equation S It s the second number It s the size of the groups It s a factor T Circle the size of the groups in both problems S Circle the 5 in both problems Repeat the process with the following suggested examples Alternate between having the quotient represent the size of the groups and the number of groups 34 ZEARN MATH Teacher Edition

G3M1 Topic B Lesson 6 4 rows of 2 7 rows of 3 YOUR NOTES T Use our equations to explain to your partner how the factors in a multiplication problem can help you find the quotient in division PROBLEM 3 Relate multiplication and division T Write 3 24 on the board Skip count and track the number of threes to solve S 3 6 9 12 15 18 21 24 Write 8 to complete the equation T How many threes make 24 Answer in a complete sentence S Eight threes make 24 T Write a related division equation where the quotient represents the unknown factor S Write 24 3 8 T Twenty four divided in threes makes how many groups Answer in a complete sentence S Twenty four divided in threes makes 8 groups T How are the unknown factor and the quotient related in these equations S The unknown factor is the same number as the quotient Repeat the process with the following suggested examples 2 18 and 18 2 9 27 and 27 9 T Write 3 24 and 24 3 threes are in 24 True or false Both equations ask how many S They look different but they mean the same thing In both we re talking about 8 groups of 3 and a total of 24 So it s true The quotient in a division equation is like finding the unknown factor in a multiplication equation MULTIPLE MEANS OF REPRESENTATION Problem 1 in this lesson introduces students to relating division to an array model In Lesson 2 students related the rows in an array to the number of equal groups and the number of dots in each row to the size of the group The same concept applies for division arrays but now the problems begin with the total number MULTIPLE MEANS OF ENGAGEMENT Some students may benefit from working with a partner They may underline each row to literally show division and circle each row to show the size of each group They should explain each step they take This may be particularly helpful for students who prefer visual or kinesthetic activities ZEARN MATH Teacher Edition 35

Topic B Lesson 6 YOUR NOTES G3M1 MULTIPLE MEANS OF ACTION AND EXPRESSION Some students may still benefit from the visual of an array in Problem 3 If necessary encourage students to draw an array Independent Digital Lesson Lesson 6 Ends with a Q 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 36 ZEARN MATH Teacher Edition

G3M1 Topic B Lesson 6 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 do arrays represent both multiplication and division Based on your observation of arrays what do multiplication and division have in common What is the relationship between the quotient in division and the unknown factor in a related multiplication equation 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 Cesar arranges 12 notecards into rows of 6 for his presentation a Draw an array to represent the problem 12 6 6 12 b What do the unknown factor and quotient represent Answers 1 a Array of 2 rows of 6 drawn 2 2 b The number of groups ZEARN MATH Teacher Edition 37

Topic C G3M1 TOPIC C Multiplication Using Units of 2 and 3 In Topic C students begin building fluency with facts of 2 and 3 using the array model and familiar skip counting strategies Lessons 7 and 8 introduce the new complexity of manipulating arrays to study the commutative property Students learn to distinguish rows from columns as they rotate arrays 90 degrees noticing that the meaning of the factors changes depending on the orientation of the array Students write two different multiplication sentences to interpret the same array These lessons emphasize the equivalence of facts by demonstrating for example that 2 groups of 8 and 8 groups of 2 have the same product Students observe the pattern and begin to recognize commutativity as a strategy for solving twice as many facts Lessons 9 and 10 introduce the distributive property as a strategy for multiplication In Lesson 9 students use arrays to decompose unknown facts as the sum or difference of two known facts For example they analyze an array to see that 7 3 can be decomposed as 2 rows of 3 5 rows of 3 In Lesson 10 students learn to write the decomposition as 5 3 2 3 21 They explain each step of the solving process in anticipation of the work they are expected to complete independently on the Mid Mission Assessment Objective Topic C Multiplication Using Units of 2 and 3 Lessons 7 8 Demonstrate the commutativity of multiplication and practice related facts by skip counting objects in array models Lesson 9 Find related multiplication facts by adding and subtracting equal groups in array models Lesson 10 Model the distributive property with arrays to decompose units as a strategy to multiply 38 ZEARN MATH Teacher Edition

G3M1 Lesson 7 Topic C Lesson 7 YOUR NOTES Demonstrate the commutativity of multiplication and practice related facts by skip counting objects in array models Warm Up FLUENCY PRACTICE Group Counting NOTE Group counting reviews interpreting multiplication as repeated addition Counting by twos and threes in this activity anticipates work with those factors in Topic C T Let s count by twos Direct students to count forward and backward to 20 emphasizing the 8 to 10 10 to 12 and 18 to 20 transitions T Let s count by threes Direct students to count forward and backward to 30 periodically changing directions Emphasize the 9 to 12 18 to 21 and 27 to 30 transitions Divide Equal Groups Materials S Personal white board NOTE Students directly relate repeated addition to division They interpret the unknown in division This activity reviews Lesson 6 T Project an array with 2 groups of 4 Say the total as a repeated addition sentence S 4 4 8 T Write a division sentence for 8 divided into 2 equal groups S Write 8 2 4 T Below that division sentence write a division sentence dividing 8 into 4 equal groups S Write 8 4 2 Continue with this possible sequence 5 groups of 3 3 groups of 4 and 6 groups of 2 Multiply with Twos Materials S Personal white board twos array Fluency Template blank paper NOTE Students unit count objects in an array and write multiplication sentences that match the count by in anticipation of today s lesson objective ZEARN MATH Teacher Edition 39

Topic C Lesson 7 YOUR NOTES G3M1 T Slip your twos array template from your workbook into your personal white board Twos Array Fluency Template T Turn your board so that it s vertical Use your blank paper to cover all but the first row of dots T How many twos show S 1 two T Say the multiplication sentence to represent the array that s shown and solve S 1 2 2 T Uncover another row Continue this sequence having students uncover twos for 2 2 3 2 10 2 4 2 5 2 6 2 7 2 9 2 and 8 2 WORD PROBLEM Anna picks 24 flowers She makes equal bundles of flowers and gives 1 bundle to each of her 7 friends She keeps a bundle for herself too How many flowers does Anna put in each bundle NOTE This problem reviews division from Lesson 5 where the unknown represents the size of the group The problem s complexity is in understanding that the flowers are divided equally into 8 bundles not 7 in order to include a bundle for Anna Students might choose to solve by drawing a division array learned in Lesson 6 or a number bond learned in Lesson 3 Concept Exploration Materials S Personal white board PROBLEM 1 Rotate arrays 90 degrees Personal White Board T Position your board so that the long side is horizontal Draw an array that shows 4 rows of 2 S Draw the array as shown 40 ZEARN MATH Teacher Edition

G3M1 T Write a skip count by twos to find the total Then write a multiplication sentence where the first factor represents the number of rows Topic C Lesson 7 YOUR NOTES S Write 2 4 6 8 and 4 2 8 as shown T Rotate your board 90 degrees so that the long side is vertical S Rotate T What happened to the array S It has 2 rows of 4 It has 4 groups of 2 but they re up and down instead of in rows T Now the twos are columns vertical groups in an array T I ll rotate my board You tell me if the twos are columns or rows T Show the twos as rows S Rows T Rotate your board and show the twos as columns S Columns T Skip count the rows by four S Point to the rows as students count 4 8 T Add that skip count to your board Allow time What multiplication sentence can represent this array S 2 4 8 T Write 4 2 8 and 2 4 8 on the board with their corresponding arrays drawn as shown What do you notice about the multiplication sentences S The 4 and the 2 switched places T What do the 4 and 2 represent in each Talk to your partner S In A the 4 represents the number of rows but in B it represents the size of the row The twos are rows in A but columns in B T Did the meaning of the 8 change S No T So factors can switch places and trade meanings but the total stays the same We call that the commutative property Talk to your partner about why the total stays the same S Discuss Continue with 2 5 and 3 4 arrays PROBLEM 2 Interpreting rows and columns in rotated arrays Ask students to draw an array that shows 8 rows of 2 They should write a skip count to find the total and a number sentence to represent the array See the example shown T What does the first factor the 8 in your equation represent ZEARN MATH Teacher Edition 41

Topic C Lesson 7 YOUR NOTES G3M1 S The number of equal groups in the array The number of rows T Can the 8 also represent the size of the group Talk to your partner S It can be the vertical group It can mean the size of the column T If we think of 8 as the size of the groups then how many groups does the array show S 2 groups T Are those 2 groups shown by columns or by rows S By columns T Does the total change if we think of 8 as the size of the groups and 2 as the number of groups S No the total is still 16 because you still have to multiply 8 and 2 T Talk with a partner Does 8 2 16 represent this array even if we think of 8 as the size of the groups and 2 columns as the number of groups S No it should be written as 2 8 16 We just learned that factors can trade meanings They can trade meanings but they also switch places The total stays the same so I think it works T Factors can trade meanings without always having to switch places in the equation It s okay to write 8 2 16 and think of 8 as the size of the groups and 2 columns as the number of groups In third grade we ll usually write multiplication sentences so that the first factor represents the number of groups That makes them a little easier to read But either factor can mean the size of the groups or the number of groups MULTIPLE MEANS OF REPRESENTATION The word column was originally introduced in Grade 2 Mission 6 but is treated as new vocabulary in this lesson MULTIPLE MEANS OF REPRESENTATION Students need not gain a deep understanding of the term commutative property However they will need to be familiar with the vocabulary moving forward in this mission Independent Digital Lesson Lesson 7 Flip It 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 42 ZEARN MATH Teacher Edition

G3M1 Wrap Up Topic C Lesson 7 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 How did rotating our boards help us see rows as columns and columns as rows What did you learn today about changing the order of the factors Factors can change their order without changing the total We call that the commutative property Let s test addition subtraction and division and see if the commutative property applies to them too 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 2 5 5 2 1 Do you agree or disagree with the statement above Draw arrays and use skip counting to explain your thinking Answers 1 Agree array of 2 rows of 5 and array of 5 rows of 2 drawn skip counts by fives or twos depending on the array written to show a total of 10 each ZEARN MATH Teacher Edition 43

Topic C Lesson 7 Fluency Template G3M1 TWOS ARRAY FLUENCY TEMPLATE 44 ZEARN MATH Teacher Edition

G3M1 Lesson 8 Topic C Lesson 8 YOUR NOTES Demonstrate the commutativity of multiplication and practice related facts by skip counting objects in array models Warm Up FLUENCY PRACTICE Group Counting NOTE Group counting reviews interpreting multiplication as repeated addition Counting by twos threes and fours in this activity supports work with units of 2 and 3 in this topic and anticipates work using units of 4 in Topic E T Let s count by twos to 20 Whisper the numbers and then speak them T Let s count by twos to 20 again This time hum the first number and then speak it As you hum think of the number T Let s count by twos to 20 This time instead of humming think every other number T What did we just count by S Twos T Let s count by fours Direct students to count forward and backward to 20 periodically changing directions T Let s count by threes Direct students to count forward and backward to 30 periodically changing directions Emphasize the 9 to 12 18 to 21 and 27 to 30 transitions Commutative Multiplying Materials S Personal white board NOTE Practicing this concept which was taught in Lesson 7 helps students build confidence and automaticity T Project a 3 2 array How many groups of 2 do you see S 3 groups of 2 T Write two different multiplication sentences for the array S Write 3 2 6 and 2 3 6 ZEARN MATH Teacher Edition 45

Topic C Lesson 8 YOUR NOTES G3M1 Continue with the following possible sequence 3 by 5 and 4 by 3 T Write 4 2 2 On your board fill in the blank S Write 4 2 2 4 Repeat the process for 9 5 5 and 3 6 6 WORD PROBLEM Children sit in 2 rows of 9 on the carpet for math time Erin says We make 2 equal groups Vittesh says We make 9 equal groups Who is correct Explain how you know using models numbers and words NOTE This problem reviews the commutativity of multiplication introduced in Lesson 7 and prepares students for Day 2 of the same concept in today s Concept Exploration Concept Exploration Materials S Personal white board PROBLEM 1 Rotate arrays 90 degrees This problem is optional T Turn your personal white board so that the long side is vertical Skip count by threes 4 times and write each number S 3 6 9 12 T Draw an array to match your count where the number of rows represents the number of groups T Discuss how many rows and columns you see S Students discuss that there are 4 rows and 3 columns T Turn your board so that the long side is horizontal How many rows and columns does it show now S Turn boards 90 degrees 3 rows and 4 columns T Tell your partner a different skip count that also represents the array S 4 8 12 46 ZEARN MATH Teacher Edition

G3M1 Topic C Lesson 8 T What is the difference between the vertical and horizontal arrays YOUR NOTES S In the vertical array the 4 threes were rows and in the horizontal array they were columns It s the same with the 3 fours They were columns then rows T Did the total number of dots change S No T So the total and the factors stay the same but the factors switch places Yesterday we learned a special name for that It s called S Commutative The commutative property T Use the commutative property to write two multiplication sentences for the array S Write 4 3 12 and 3 4 12 Students practice with partners using the following examples Partner A gives skip counting directions Partner B writes the count draws an array and writes multiplication sentences Then partners switch roles Skip count by twos 3 times Skip count by threes 6 times PROBLEM 2 Interpreting rows and columns in rotated arrays T Work with your partner to draw an array that shows 5 rows and 3 columns S Demonstrate one possible process Let s draw 5 circles going down to show the start of each row Then we can draw 3 circles to show the columns across the top Wait we already drew 1 column when we made the rows so we can just draw 2 more columns T Write an equation to match your array where the first factor represents the number of rows Don t solve it yet S Write 5 3 T I m going to change the problem slightly Listen carefully and rotate your array to match 3 rows and 5 columns S Turn boards 90 degrees T Write the equation for the new array Let the first factor represent the number of rows Don t solve it yet S Write 3 5 T Explain the difference between these problems to your partner S The array turned and the factors switched places T When we rotated the array we agreed the first factor would tell us the number of rows What did that do to the order of the factors S They switched ZEARN MATH Teacher Edition 47

Topic C Lesson 8 YOUR NOTES G3M1 T Did the total change S No T When we change the order of the factors we are using the commutative property T Solve each of your equations by skip counting Write each number as you say it S Write 3 6 9 12 15 and 5 10 15 Continue with the following possible examples 7 rows and 2 columns 3 rows and 9 columns T Once students have worked through the problem write the final example in groups language 3 groups of 9 and 9 groups of 3 Are these statements equal Use your array to discuss with your partner how you know MULTIPLE MEANS OF ENGAGEMENT If students are very comfortable with the way an array changes depending on how it is turned add a bit of complexity by having them imagine turning it horizontal rather than actually doing it in Problem 1 MULTIPLE MEANS OF ACTION AND EXPRESSION Students may not immediately recognize that they do not need to redraw the corner circle to make 3 columns After drawing rows they already have 1 column and for this problem only need to add 2 more columns If they make a mistake help them recognize it by encouraging them to recount their total columns MULTIPLE MEANS OF ENGAGEMENT Consider providing a challenge for students by having them cover the array as they skip count to solve Independent Digital Lesson Lesson 8 Flip It Well 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 48 ZEARN MATH Teacher Edition

G3M1 Topic C Lesson 8 YOUR NOTES Wrap Up LESSON SYNTHESIS Guide students in a conversation to process today s lesson and surface any misconceptions or misunderstandings The prompts below may be used to lead the discussion Discuss the meaning of the commutative property and how it relates to equal groups columns rows and arrays Discuss the usefulness of skip counting to solve multiplication problems Build fluency by having students skip count to find answers to the following expressions without the help of an array They can keep track of their count using fingers 3 sixes 6 threes 3 eights 8 threes 5 threes 3 fives ZEARN MATH Teacher Edition 49

Topic C Lesson 8 YOUR NOTES G3M1 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 Mary Beth organizes stickers on a page in her sticker book She arranges them in 3 rows and 4 columns a Draw an array to show Mary Beth s stickers b Use your array to write a multiplication sentence to find Mary Beth s total number of stickers c Label your array to show how you skip count to solve your multiplication sentence d Use what you know about the commutative property to write a different multiplication sentence for your array Answers 1 a Array of 3 rows of 4 drawn b 3 4 12 c Rows of array labeled 4 8 12 d 4 3 12 50 ZEARN MATH Teacher Edition

G3M1 Topic C Lesson 9 Lesson 9 YOUR NOTES Find related multiplication facts by adding and subtracting equal groups in array models Warm Up FLUENCY PRACTICE Multiply by 2 Materials S Multiply by 2 1 5 today s Pattern Sheet NOTE This activity builds fluency with multiplication facts using units of 2 It works toward students knowing from memory all products of two one digit numbers T Write 5 2 Let s skip count by twos to find the answer Count with fingers to 5 as students count Record skip count on the board S 2 4 6 8 10 T Circle 10 and write 5 2 10 above it Write 3 2 again Count with fingers to 3 as students count Let s skip count up by twos S 2 4 6 T Let s see how we can skip count down to find the answer too Start at 10 with 5 fingers 1 for each two Count down with your fingers as students say numbers S 10 5 fingers 8 4 fingers 6 3 fingers Repeat the process for 4 2 T Let s practice multiplying by 2 Directions for Administration of Multiply By Pattern Sheet Instruct students to find the Multiply By Pattern Sheet in their workbooks Allow a maximum of 2 minutes for students to complete as many problems as possible Direct students to work left to right across the page Encourage skip counting strategies to solve unknown facts ZEARN MATH Teacher Edition 51

Topic C Lesson 9 YOUR NOTES G3M1 Group Counting NOTE Group counting reviews interpreting multiplication as repeated addition Counting by threes and fours in this activity supports work with units of 3 in this topic and anticipates work using units of 4 in Topic E T Let s count by threes Direct students to count forward and backward to 30 emphasizing the transition from 18 to 21 T Let s count by fours Direct students to count forward and backward to 24 emphasizing the 16 to 20 transition Forms of Multiplication Materials S Personal white board NOTE Students directly relate repeated addition to multiplication in preparation for using the distributive property in today s Concept Exploration T Project a 3 5 array Represent this array as a repeated addition sentence using 5 as the size of the groups S Write 5 5 5 15 T Project a 3 4 array Write personal white board fours Complete the equation on your S Write 3 fours 12 T Project a 7 2 array Write two multiplication sentences for 7 groups of 2 S Write 7 2 14 and 2 7 14 T Project a 6 3 array Write 18 6 board Complete the equation on your personal white S Write 18 6 3 T Project a 5 3 array Write 5 threes white board Complete the equation on your personal S Write 5 threes 15 T Add one more group of 3 to the array Write 5 threes 1 three ones Complete the equation on your personal white board threes S Write 5 threes 1 three 6 threes 18 ones Concept Exploration Materials S Personal white board threes array no fill Concept Exploration Template blank paper NOTE Consider bringing in concrete objects to make Problem 1 come to life 52 ZEARN MATH Teacher Edition

G3M1 Topic C Lesson 9 PROBLEM 1 Add two known smaller facts to solve an unknown larger fact YOUR NOTES T Slip the template from your workbook into your board Cover part of the array with blank paper to show 5 rows of 3 Draw a box around the uncovered array Write and solve a multiplication sentence to describe it S Cover then box array and write 5 3 15 T Move the paper so the array shows 7 3 Shade the rows you added S Shade 2 rows T Write and solve a multiplication sentence to describe the shaded part of your array S Write 2 3 6 T How many threes are in 5 3 S 5 threes T How many threes did you add to 5 3 to make the array show 7 3 S 2 threes T Write 7 threes 5 threes 2 threes So 7 threes equals 5 threes plus 2 threes T Write 7 3 5 3 2 3 as shown Do you agree or disagree S I agree That s just adding the two parts of the array together 7 rows of three is the same as 5 rows of three plus 2 rows of three T We already wrote totals for the two parts of our array Let s add those to find the total for the whole array What is the total of 5 3 S 15 T Write 15 on the board What is the total of 2 3 S 6 T Add to the board so the equation reads Signal 15 6 Say the total at the signal S 21 Provide students with another example Have them use the template to add the totals of 4 3 and 4 3 to find the answer to 8 3 Teach them to double the total for 4 3 T Explain how we added to find 7 3 21 and 8 3 24 S We added the totals of smaller facts together to find the whole We used two facts we already knew to find one we didn t know ZEARN MATH Teacher Edition 53

Topic C Lesson 9 YOUR NOTES G3M1 PROBLEM 2 Subtract two known smaller facts to solve an unknown larger fact This problem is optional T Draw a box around an array that shows 9 3 Notice that 9 3 is very close to 10 3 10 3 is easier to solve because we can count by tens to get the total Let s do that now S 10 20 30 T Let s use 10 3 30 to help us solve 9 3 T Use your finger to trace 10 threes T What should we subtract to show 9 threes instead S 1 three T Write 10 threes 1 three on the board 10 threes equals S 30 T 30 3 equals S 27 Provide another example Have students subtract to find the answer to 8 3 10 3 is the basic fact so the subtraction to find 8 3 is 30 6 T Tell your partner how we used 10 3 to help us find the answer to 9 3 and 8 3 S Discuss MULTIPLE MEANS OF REPRESENTATION Decomposing this way naturally relates to the part whole relationship that students studied in Grades K 2 The vignette implies the relationship but a more formal connection to prior knowledge may be appropriate for some classes MULTIPLE MEANS OF REPRESENTATION Introduce the word distribute into everyday classroom language This will help with students understanding of the distributive property which is formally introduced in Lesson 16 For example Paper monitors please distribute the papers to the class MULTIPLE MEANS OF REPRESENTATION The second example for subtraction 8 3 is intentionally the same as the second example for addition Solving the same problem in two ways provides an opportunity for students to compare the strategies Students benefit from the opportunity to reflect and analyze how strategies helped them understand problems and processes that led to correct or incorrect answers 54 ZEARN MATH Teacher Edition

G3M1 Topic C Lesson 9 Independent Digital Lesson YOUR NOTES Lesson 9 Fun Friendly Facts 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 55

Topic C Lesson 9 YOUR NOTES G3M1 Wrap Up LESSON SYNTHESIS Guide students in a conversation to process today s lesson and surface any misconceptions or misunderstandings The prompts below may be used to lead the discussion Review the strategy of adding and subtracting the totals of known easy facts for solving unknown facts Differentiate between when to apply addition or subtraction through analysis of the example 8 3 from the lesson Students solved 8 3 using both addition and subtraction Ask students to apply the strategy to solve 8 4 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 9 2 20 18 9 2 Answers 1 18 20 2 2 18 56 ZEARN MATH Teacher Edition

G3M1 Topic C Lesson 9 Pattern Sheet MULTIPLY BY 2 1 5 PATTERN SHEET ZEARN MATH Teacher Edition 57

Topic C Lesson 9 Lesson Template G3M1 THREES ARRAY NO FILL CONCEPT EXPLORATION TEMPLATE 58 ZEARN MATH Teacher Edition

G3M1 Topic C Lesson 10 Lesson 10 YOUR NOTES Model the distributive property with arrays to decompose units as a strategy to multiply Warm Up FLUENCY PRACTICE Multiply by 2 Materials S Multiply by 2 6 10 today s Pattern Sheet NOTE This activity builds fluency with multiplication facts using units of 2 It works toward students knowing from memory all products of two one digit numbers See Lesson 9 for the directions for administering a Multiply By Pattern Sheet T Write 7 2 Let s skip count up by twos Count with fingers to 7 as students count S 2 4 6 8 10 12 14 T This time let s start from 10 to find our answer more quickly Show 5 fingers all at once to show 10 S Show 5 fingers T Now count by twos from 10 Raise another finger for each two you count Model as students count S 10 12 14 Raise a sixth finger at 12 and a seventh finger at 14 T Let s see how we can skip count down to find the answer too Start at 20 Show 10 fingers to represent 20 Hide one finger at a time as students say numbers S 20 18 16 14 Repeat the process for 9 2 and 8 2 T Instruct students to find the Multiply By 2 Pattern Sheet in their workbooks Let s get some practice multiplying by 2 Be sure to work left to right across the page Group Counting NOTE Group counting reviews interpreting multiplication as repeated addition Counting by threes and fours in this activity supports work with units of 3 in this topic and anticipates work using units of 4 in Topic E T Let s count by threes Direct students to count forward and backward to 30 emphasizing the transition from 18 to 21 ZEARN MATH Teacher Edition 59

Topic C Lesson 10 YOUR NOTES G3M1 T Let s count by fours Direct students to count forward and backward to 24 emphasizing the 16 to 20 transition WORD PROBLEM A guitar has 6 strings How many strings are there on 3 guitars Write a multiplication equation to solve NOTE This problem leads into today s Concept Exploration Students will compare their multiplication equation with the new equations presented in the Concept Exploration Concept Exploration Materials S Personal white board 1 sheet of blank paper T On your personal white board draw an array to represent the total number of guitar strings Let the number of strings on one guitar be 1 row S Draw a 3 6 array as shown T Make a dotted line below the first row to show just one guitar S Draw line as shown T Write and solve a multiplication sentence to describe each part of your array S Write 1 6 6 and 2 6 12 as shown T Write 6 12 3 sixes Why is this true S 1 six is 6 2 sixes are 12 When I add 6 and 12 I get 18 which is 3 sixes T Write 1 6 2 6 3 sixes on the board as shown How do you know this equation is true 60 ZEARN MATH Teacher Edition

G3M1 S 1 6 is the same as 1 six 2 6 is the same as 2 sixes 1 six plus 2 sixes is the same as 3 sixes 1 6 6 and 2 6 12 12 6 18 3 sixes 18 so the equation is true Topic C Lesson 10 YOUR NOTES T Write 1 6 2 6 6 With your partner discuss what number completes the equation S 1 6 equals 6 That s how the teacher got 6 To get the other number we do 2 6 That s 12 I know it s 12 because you need the same amount on each side of the equal sign On the left the value is 6 12 if you solve the multiplication That s what it should be on the right too T Write 12 to fill in the equation T Notice the symbols around my multiplication expressions They are called parentheses Let s say that word together S Parentheses T Write 1 6 2 6 and 1 2 6 below it as shown My parentheses show how I make groups How did I rearrange the groups S You added the number of rows Then you multiplied by 6 T Look back at the array you drew Do the 1 and 2 represent the number of groups or the size of groups S The number of groups T What does the 6 represent S The size of the groups T Use that language the number of groups and the size of groups to tell your partner about my second equation S The teacher added the number of groups first That s 1 2 Then she multiplied the number of groups times the size of the groups which is 6 T 1 2 equals S 3 T Write 3 6 under the second equation Look back at the work you did on today s Word Problem How does this equation compare with what you did S It s the same It s the number of groups times the size of groups just like we did T Rewrite each equation on your personal white board and solve What is the answer to all three equations S 18 T Fill in the equations on the board Think back to the problem we re solving 18 what S 18 strings T Write 1 6 2 6 3 6 on the board True or false S True T In your own words tell your partner how we got 3 6 and why it s equal to 1 6 2 6 Use the three equations you just solved to help you explain S Retell the steps using the three equations and solutions to guide them ZEARN MATH Teacher Edition 61

Topic C Lesson 10 YOUR NOTES G3M1 MULTIPLE MEANS OF ENGAGEMENT This lesson begins at the pictorial level and quickly advances to the more abstract numerical form Some students may need to begin with concrete materials If so have students use linking cubes to show how to distribute the rows of 6 MULTIPLE MEANS OF REPRESENTATION In this lesson students are not responsible for the vocabulary distributive property They revisit the distributive property as a strategy for multiplication and division in Topics E and F In those lessons they begin referring to it as the break apart and distribute strategy MULTIPLE MEANS OF ENGAGEMENT Give students the option of working independently or with a partner to solve the equations Independent Digital Lesson Lesson 10 Yes and Know 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 and prompt below may be used to lead the discussion Review the vocabulary term parentheses Why might breaking an array into two parts to multiply add and then solve be easier than just multiplying the total number of groups times their size 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

G3M1 Topic C Lesson 10 Task YOUR NOTES 1 6 3 4 3 2 3 4 3 2 3 6 3 3 2 7 3 3 3 5 3 2 3 7 3 3 Answers 1 18 12 6 12 6 12 6 6 18 2 21 5 15 2 6 15 6 15 6 7 21 ZEARN MATH Teacher Edition 63

Topic C Lesson 10 Pattern Sheet G3M1 MULTIPLY BY 2 6 10 PATTERN SHEET 64 ZEARN MATH Teacher Edition

G3M1 Topic D TOPIC D Division Using Units of 2 and 3 In Topic D students solve two types of division situations partitive group size unknown and measurement number of groups unknown using factors of 2 and 3 Students build on their background knowledge of tape diagrams and apply it to represent division In Lesson 11 the tape diagram is used as a tool to help students recognize and distinguish between types of division By the end of Lessons 11 and 12 students independently draw and label tape diagrams that help them to compare and analyze problems that may use the same division sentence but have quotients representing different things Lesson 13 solidifies growing understanding that the unknown can also be found from the related multiplication sentence Students initially work through word problems using arrays and tape diagrams to practice solving the two types of division and then transition to problem solving using abstract division and multiplication equations Objective Topic D Division Using Units of 2 and 3 Lesson 11 Model division as the unknown factor in multiplication using arrays and tape diagrams Lesson 12 Interpret the quotient as the number of groups or the number of objects in each group using units of 2 Lesson 13 Interpret the quotient as the number of groups or the number of objects in each group using units of 3 ZEARN MATH Teacher Edition 65

G3M1 Topic D Lesson 11 Lesson 11 YOUR NOTES Model division as the unknown factor in multiplication using arrays and tape diagrams Warm Up FLUENCY PRACTICE Multiply by 3 Materials S Multiply by 3 1 5 today s Pattern Sheet NOTE This activity builds fluency with multiplication facts using units of 3 It works toward students knowing from memory all products of two one digit numbers See Lesson 9 for the directions for administering a Multiply By Pattern Sheet T Write 5 3 Let s skip count up by threes to solve Raise a finger for each number to track the count Record the skip count answers on the board S 3 6 9 12 15 T Circle 15 and write 5 3 15 above it Write 4 3 find the answer Track with fingers as students count Skip count up by threes to S 3 6 9 12 T Let s count down to find the answer to 4 3 too Start at 15 Count down with fingers as students say numbers S 15 12 T Let s practice multiplying by 3 Be sure to work left to right across the page Instruct students to find the Multiply By 3 Pattern Sheet in their workbooks MULTIPLE MEANS OF REPRESENTATION Use this activity to teach skip counting as a strategy for building automaticity with multiplication facts Once students know that 3 5 15 they can flash 5 fingers to show 15 and then count on the other hand How solving 3 8 looks and sounds is illustrated Group Counting NOTE Group counting reviews interpreting multiplication as repeated addition Counting by twos and fours in this activity reviews multiplication with units of 2 from Topic C and anticipates using units of 4 in Topic E ZEARN MATH Teacher Edition 67

Topic D Lesson 11 YOUR NOTES G3M1 T Let s count by twos Direct students to count forward and backward to 20 T Let s count by fours Direct students to count forward and backward to 36 emphasizing the 20 to 24 and 28 to 32 transitions WORD PROBLEM Rosie puts 2 lemon slices in each cup of iced tea She uses a total of 8 slices How many cups of iced tea does Rosie make NOTE Students may have solved the problem as shown or by using division 8 2 4 This problem leads into modeling with tape diagrams which is introduced in today s Concept Exploration MULTIPLE MEANS OF ENGAGEMENT The numbers in the Word Problem may be too simple They were chosen to complement the introduction of the tape diagram in the Concept Exploration If needed change the numbers in the Word Problem to meet the needs of the class and adjust the opening language of the Concept Exploration accordingly Concept Exploration Materials S Personal white board PROBLEM 1 Relate arrays to tape diagrams modeling division where the quotient represents the number of groups T Draw or project a 2 4 array The columns in this array show the number of lemon slices in 1 cup of Rosie s iced tea Reread the Word Problem and tell your partner what the unknown represents S The unknown is the number of cups or groups T How might this array help us solve 8 2 S We can count the number of columns to find how many cups 2 times 4 equals 8 so 8 2 4 T Draw a rectangle around the array What is the total number of lemon slices S 8 lemon slices T Bracket the rectangle and label the whole 8 lemon slices The question asks how many cups of iced tea Rosie makes Do the cups represent the number of groups or the number of lemon slices in each group 68 ZEARN MATH Teacher Edition

G3M1 Topic D Lesson 11 S The number of groups YOUR NOTES T Under 8 lemon slices label the unknown as cups T Watch how I show the number of slices in one cup Draw lines to divide columns and label 1 unit as 2 slices Where do we see the cups in our diagram S You made 4 cups with the dividing lines T By adding lines and labels to our array we made a tape diagram Each boxed column shows 1 unit One unit represents 1 cup and has a value of 2 slices Notice that I labeled the diagram with all of the known and unknown information from the problem as we solved That made it a helpful tool for understanding the problem T Write 8 2 and 2 8 Talk to your partner about how the tape diagram helps you see the unknown in both equations S Discuss In Problem 1 the quotient represents the number of groups Repeat the process using the following examples reminding students to label known and unknown information from the problem on every tape diagram 10 2 5 18 3 6 PROBLEM 2 Use arrays to draw tape diagrams modeling division where the quotient represents the number of objects in each group This problem is optional Write or project the following problem Ms Alves puts 21 papers in 7 piles How many papers are in each pile T Read the problem What is unknown S The number of objects in each group T Model the problem on your personal white board as an array where each column represents 1 pile S Draw array as shown T Count to find how many papers are in each of Ms Alves s piles S Count to find 3 papers T Work with a partner to model the problem as a tape diagram Be sure to label the diagram with known and unknown information Use your array to help S Draw tape diagram shown T Use the tape diagram to write multiplication and division equations that show the unknown S Write 7 21 and 21 7 ZEARN MATH Teacher Edition 69

Topic D Lesson 11 YOUR NOTES G3M1 In Problem 2 the quotient represents the number of objects in each group Repeat the process using the following examples 16 2 8 24 3 8 T Compare models What are the similarities and differences between arrays and tape diagrams S The tape diagram is like a labeled and boxed array They both show the 7 piles 3 papers in each pile and 21 papers total The labels make the tape diagram a little easier to use MULTIPLE MEANS OF ENGAGEMENT The numbers in the Word Problem may be too simple They were chosen to complement the introduction of the tape diagram in the Concept Exploration Lowering the arithmetic demand of the problem frees up students working memory to focus on the new learning of the lesson If this is not the right choice for your students you could change the numbers in the Word Problem to meet the needs of the class and adjust the opening language of the Concept Exploration accordingly MULTIPLE MEANS OF REPRESENTATION Students are familiar with tape diagrams from Grade 2 They use tape diagrams to represent the information given in a problem and then analyze the model to help determine the unknown and solve As tape diagrams are reviewed ask why the diagram might have that name Guide students to make connections that help them remember the name MULTIPLE MEANS OF REPRESENTATION Keep math vocabulary such as arrays and tape diagram posted in the math classroom with a picture and a number sentence Allow students who need extra language supports the opportunity to reference the chart as needed such as when explaining their thinking to a partner or the class Independent Digital Lesson Lesson 11 Hi I m Unit 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 70 ZEARN MATH Teacher Edition

G3M1 Topic D Lesson 11 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 Compare how units are represented in tape diagrams and in arrays How can each model represent both types of unknowns Compare the way you solved the Word Problem with the tape diagram model we learned today 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 71

Topic D Lesson 11 YOUR NOTES G3M1 Task 1 Ms McCarthy has 18 stickers She puts 2 stickers on each homework paper and has no more left How many homework papers does she have Model the problem with both an array and a labeled tape diagram Answers 1 9 array and tape diagram drawn showing 9 groups of 2 is 18 72 ZEARN MATH Teacher Edition

G3M1 Topic D Lesson 11 Pattern Sheet MULTIPLY BY 3 1 5 PATTERN SHEET ZEARN MATH Teacher Edition 73

G3M1 Topic D Lesson 12 Lesson 12 YOUR NOTES Interpret the quotient as the number of groups or the number of objects in each group using units of 2 Warm Up FLUENCY PRACTICE Multiply by 3 Materials S Multiply by 3 6 10 today s Pattern Sheet NOTE This activity builds fluency with multiplication facts using units of 3 It works toward students knowing from memory all products of two one digit numbers See Lesson 9 for the directions for administering a Multiply By Pattern Sheet T Write 6 3 students count Let s skip count up by threes to solve Count with fingers to 6 as S 3 6 9 12 15 18 T Let s skip count down to find the answer too Start at 30 Count down with fingers as students count S 30 27 24 21 18 Repeat the process for 8 3 and 7 3 T Let s practice multiplying by 3 Be sure to work left to right across the page Instruct students to find the Multiply By 3 Pattern Sheet in their workbooks Group Counting NOTE Group counting reviews interpreting multiplication as repeated addition Counting by twos and fours in this activity reviews multiplication with units of 2 from Topic C and anticipates using units of 4 in Topic E T Let s count by twos Direct students to count forward and backward to 20 T Let s count by fours Direct students to count forward and backward to 36 emphasizing the 20 to 24 and 28 to 32 transitions ZEARN MATH Teacher Edition 75

Topic D Lesson 12 YOUR NOTES G3M1 Divide Materials S Personal white board NOTE This activity builds fluency with multiplication and division It works toward the goal of students knowing from memory all products of two one digit numbers and reviews the objective of Lesson 11 T Project a 2 by 4 array of objects Draw an array to match my picture S Draw 2 by 4 array T Skip count by twos to find how many total objects there are Point as students count S 2 4 6 8 T How many groups of 2 are there S 4 T Say the total as a multiplication sentence starting with the number of groups S 4 2 8 T Write 4 2 8 Below it write 8 4 Fill in the blank to make a true division sentence Then divide your array into 4 equal groups to find the answer S Draw lines separating the array into 4 groups of 2 and write 8 4 2 T Erase the lines that divided the array S Erase lines T Show 8 4 by making groups of 4 S Circle 2 groups of 4 Repeat process for the following possible sequence 9 3 12 2 and 12 3 WORD PROBLEM A chef arranges 4 rows of 3 red peppers on a tray He adds 2 more rows of 3 yellow peppers How many peppers are there altogether NOTE Students might solve using an array to model the distributive property Lesson 10 or a tape diagram Lesson 11 If they use the latter strategy it is likely their first use of a tape diagram to solve multiplication The problem is a review that provides an exploratory opportunity for students to select and use appropriate tools 76 ZEARN MATH Teacher Edition

G3M1 Concept Exploration Topic D Lesson 12 YOUR NOTES Materials S Personal white board PROBLEM 1 Model division where the unknown represents the number of objects in each group T Two students equally share 8 crackers How many crackers does each student get Draw to model and solve the problem Then explain your thinking to your partner S Draw and solve I gave 1 cracker to each student until I drew 8 4 4 8 so I drew 4 crackers for each student It s a multiplication problem with an unknown factor T Write a division sentence to represent your model S Write 8 2 4 T Draw a rectangle This diagram represents the total 8 crackers In your mind visualize where we would divide it to make 2 equal parts S Visualize T Say Stop when I get to the spot you have in mind Move finger from left edge toward middle S Stop T How does the diagram represent the students S 2 students 2 parts T What is our unknown S The number of crackers each student gets T Watch how I label the unknown on the diagram Bracket and label as shown Tell your partner a strategy for finding the unknown using the diagram S I would draw 1 cracker in each part until I drew 8 Each part has to be equal 4 4 8 so 1 part is 4 I would think 2 8 The question mark is 4 T Look at the division sentence you wrote for your first model Does it represent this diagram too Explain to your partner S Discuss Repeat the process with the following suggested expressions to model division where the quotient represents the number of objects in each group 12 2 18 2 ZEARN MATH Teacher Edition 77

Topic D Lesson 12 YOUR NOTES G3M1 PROBLEM 2 Model division where the unknown represents the number of groups T Let s go back to our original problem this time changing it a bit There are 8 crackers but this time each student gets 2 How many students get crackers T Do we know the size of the groups or the number of groups S The size of the groups T We can draw 1 unit of the diagram to represent a group of 2 crackers Draw 1 unit of two What other information does the problem tell us S The total T Estimate the whole and label it 8 crackers Notice that I drew a dotted line to show the whole diagram What is our unknown S The number of groups T Bracket the top part of the diagram and label with a question mark Let s find the number of groups by drawing more units of 2 How will we know when we ve drawn enough units S We ll get to the total 8 T Draw along with me on your personal white board Skip count by two drawing to add 3 more units S Draw T Whisper to your partner the number of students that get crackers S 4 students T Write a division sentence to match the diagram S Write 8 2 4 Repeat the process with the following suggested expressions to model division where the unknown represents the number of groups 12 2 18 2 In this lesson three division sentences are each modeled with two types of division Use one pair of division sentences for the following reflective dialogue The dialogue is modeled with 8 2 4 T The two division sentences for these diagrams are the same but the tape diagrams are different Turn and talk to your partner about why S The 2 and the 4 represent different things in each problem In the first diagram we knew how many groups and in the second we knew how many in each group T When we divide we always know the total number of objects We divide either to find the size of the groups like in the first problem or the number of groups like in the second problem 78 ZEARN MATH Teacher Edition

G3M1 Topic D Lesson 12 MULTIPLE MEANS OF REPRESENTATION YOUR NOTES Students draw to model before or as they solve problems so that the diagram assists them with analysis The model provides a place aside from the words to think about the problem It should guide their understanding of the problem and how to find the unknown They might ask themselves the following questions as they draw Am I looking for a part Am I looking for a number of parts Am I looking for the whole amount What is my model showing me Erasers are important for drawing tape diagrams to model division where the unknown represents the number of groups Students may find they have very incorrectly determined the length of the whole Encourage them to erase and redraw MULTIPLE MEANS OF REPRESENTATION If a natural opportunity presents itself teach students the word bracket so they have specific language with which to refer to the diagram This may be especially useful for multilingual learners MULTIPLE MEANS OF ENGAGEMENT Gradually release responsibility to students as the process is repeated with additional examples By the third example students should be working nearly independently Independent Digital Lesson Lesson 12 Tape Diagrams Awesome 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 79

Topic D Lesson 12 G3M1 YOUR NOTES 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 does what the quotient represents affect the way a tape diagram is drawn 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 80 ZEARN MATH Teacher Edition

G3M1 Topic D Lesson 12 Task YOUR NOTES 1 There are 14 mints in 1 box Cecilia eats 2 mints each day How many days does it take Cecilia to eat 1 box of mints Draw and label a tape diagram to solve It takes Cecilia days to eat 1 box of mints Answers 1 7 tape diagram drawn and labeled to represent the problem showing 7 groups of 2 ZEARN MATH Teacher Edition 81

Topic D Lesson 12 Pattern Sheet G3M1 MULTIPLY BY 3 6 10 PATTERN SHEET 82 ZEARN MATH Teacher Edition

G3M1 Topic D Lesson 13 Lesson 13 YOUR NOTES Interpret the quotient as the number of groups or the number of objects in each group using units of 3 Warm Up FLUENCY PRACTICE Group Counting NOTE Group counting reviews interpreting multiplication as repeated addition Counting by threes and fours in this activity reviews multiplication with units of 3 from Topic C and anticipates using units of 4 in Topic E T Let s count by threes Direct students to count forward and backward to 30 T Let s count by fours Direct students to count forward and backward to 40 emphasizing the 20 to 24 28 to 32 and 36 to 40 transitions Divide Materials S Personal white board NOTE This activity builds fluency with multiplication and division It works toward students knowing from memory all products of two one digit numbers T Write 2 3 Say the multiplication sentence S 2 3 6 T Write 2 3 6 Directly below it write the equation and fill in the blank 3 2 On your personal white board write S Write 6 3 2 Repeat the process for the following possible sequence 3 3 5 3 and 9 3 WORD PROBLEM Mark spends 16 on 2 video games Each game costs the same amount Find the cost of each game ZEARN MATH Teacher Edition 83

Topic D Lesson 13 YOUR NOTES G3M1 NOTE This problem reviews equal groups division from Lesson 12 where the unknown is the number of objects in each group Concept Exploration Materials S Personal white board PICTORIAL Draw and analyze tape diagrams to determine the unknown Write or project the following story and the tape diagram shown Three students equally share a pack of 12 pencils T What information do we know from reading the story S The total pencils and the number of students T How does the tape diagram show the story S The whole diagram represents 12 pencils and it s divided into 3 parts Those are the students We don t know how many pencils each student gets That s what the question mark represents T Write a division equation to find how many pencils each student gets S Write 12 3 T Draw my tape diagram on your personal white board Then draw to share the 12 pencils equally among the 3 students Fill in your division equation S Draw 4 in each unit on the tape diagram Write 12 3 4 Students can check their work by writing a multiplication sentence Write or project the following problem and the first tape diagram shown A school buys 12 boxes of pencils Each classroom gets 3 boxes How many classrooms get boxes of pencils T What information do we know from the problem S The total boxes and the number of boxes each classroom gets T The box drawn with a solid line represents the number of boxes 1 class gets I used the dotted line to estimate the total boxes How should I label the unknown on this diagram S It s the number of classrooms that get boxes T Where can I record my question mark S Under 12 boxes write classrooms 84 ZEARN MATH Teacher Edition

G3M1 T Label the unknown On your board skip count by threes to draw more units in the tape diagram How will you know when to stop Topic D Lesson 13 YOUR NOTES S We stop when we get to 12 Draw and count 6 9 12 T Use the tape diagram to write and solve a division equation that represents the problem S Write 12 3 4 It s the same division problem as before T What does the 4 represent in this problem S It s the number of classrooms that get boxes of pencils It s the number of groups Repeat the process showing division with both types of unknowns using the following suggested expressions 18 3 21 3 ABSTRACT Interpret tape diagrams to determine the unknown and write division problems Draw or project the tape diagrams shown Students work in pairs Write division sentences to represent each diagram Division sentences should be the same for both diagrams Label each tape diagram including the unknown The tape diagrams and division sentences show solutions Write a word problem to match each solution Save the word problems to compare with other groups during the Lesson Synthesis MULTIPLE MEANS OF ACTION AND EXPRESSION This lesson is similar to Lesson 12 Depending on how students are doing on dividing with tape diagrams modify guidance so that students work through pictorial examples quickly in pairs or independently Meet with groups or individuals who need support Alternatively maximize support by skipping the abstract example in favor of slowly working the class through the pictorial As an additional scaffold ask students to create tape diagrams with drawings inside each unit to show the value Students have used tape diagrams drawn with and without this feature in Grade 2 ZEARN MATH Teacher Edition 85

Topic D Lesson 13 YOUR NOTES G3M1 MULTIPLE MEANS OF REPRESENTATION For the abstract portion of the lesson some pairs may benefit from looking at word problems completed the previous day to gather ideas and examples upon which to model their work Independent Digital Lesson Lesson 13 Lunch Crunch 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 prompt below may be used to lead the discussion Share word problems from the abstract activity in the lesson The class may solve or simply discuss which is the unknown factor Guide students to notice how different the contexts are but that each pair of problems always shows the same two unknowns 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 86 ZEARN MATH Teacher Edition

G3M1 Topic D Lesson 13 Task YOUR NOTES 1 Andrea has 21 apple slices She uses 3 apple slices to decorate 1 pie How many pies does Andrea make Draw and label a tape diagram to solve 2 There are 24 soccer players on the field They form 3 equal teams How many players are on each team Answers 1 7 tape diagram drawn and labeled to represent problem showing 7 groups of 3 2 8 ZEARN MATH Teacher Edition 87

Topic E G3M1 TOPIC E Multiplication and Division Using Units of 4 Topic E begins by introducing students to multiplication by 4 through skip counting objects in array models in Lesson 14 Students revisit the commutative property in Lesson 15 this time modeling commutativity using both arrays and tape diagrams For example students might initially draw a 2 4 array and a 4 2 array Then they see 2 bars of equal length one with 4 equal parts and the other with 2 equal parts Now they have arrays that show 2 4 4 2 as well as tape diagrams that reflect the equality In Lesson 16 students examine the distributive property in greater depth This lesson introduces the 5 n pattern as a strategy for finding unknown facts involving 4 For example students know that 4 5 is 20 so 4 6 is the same as 20 4 more which totals 24 By Lesson 17 practice of multiplication and division facts is dedicated to modeling the relationship between operations using facts of 4 Objective Topic E Multiplication and Division Using Units of 4 Lesson 14 Skip count objects in models to build fluency with multiplication facts using units of 4 Lesson 15 Relate arrays to tape diagrams to model the commutative property of multiplication Lesson 16 Use the distributive property as a strategy to find related multiplication facts Lesson 17 Model the relationship between multiplication and division 88 ZEARN MATH Teacher Edition

G3M1 Lesson 14 Topic E Lesson 14 YOUR NOTES Skip count objects in models to build fluency with multiplication facts using units of 4 Warm Up FLUENCY PRACTICE Read Tape Diagrams Materials S Personal white board NOTE Students practice reading the difference between the value of the unit the size of the groups and the number of units The activity anticipates using the tape diagram as a model for commutativity T Project a tape diagram partitioned into 5 equal units drawing 2 stars in the first unit What is the value of each unit S 2 stars T How many units are there S 5 units T Write a multiplication sentence for this tape diagram S Write 5 2 10 Repeat the process alternating between finding the number of groups and the size of the groups for 4 3 12 8 4 2 and 15 3 5 WORD PROBLEM Jackie buys 21 pizzas for a party She places 3 pizzas on each table How many tables are there NOTE This problem reviews division from Lesson 13 where the unknown is the number of groups In preparation for today s Concept Exploration the teacher might choose to have students solve by skip counting to add units until they reach the total of 21 ZEARN MATH Teacher Edition 89

Topic E Lesson 14 YOUR NOTES G3M1 Concept Exploration Materials S Personal white board fours array Concept Exploration Template in workbook PROBLEM 1 Skip count by fours using an array to multiply Instruct students to turn to the fours array Concept Exploration Template in their workbooks T Let s count to 40 using the array Hum the number you count as you point to each dot For the last dot in each row say the number out loud and write it to the right of the row S Hum hum hum 4 Write 4 Continue counting in this manner to 40 T At the signal tell what unit we counted by Signal S Fours T I will say a multiplication expression You find the answer on your array Write the expression and an equal sign next to the answer to make an equation Say expressions that correspond to the array out of order for example 4 4 9 4 etc S Write expressions and equal signs next to each answer T I will say the answer you say the equation 20 S 20 5 4 PROBLEM 2 Use a tape diagram to model and solve multiplication T Draw a tape diagram that represents the number of groups shown on the array template S Draw a rectangle partitioned into 10 units and label it as 10 groups T Tell your partner the number of objects in each group and then draw and label that information on your diagram S There are 4 objects in each group Label 1 unit as 4 objects T Label the unknown on your diagram Check your work with your partner s S Label the total unknown and check with a partner T Skip count units to find the total value of your tape diagram S 4 8 12 16 20 24 28 32 36 40 T Write and solve an equation to represent the problem S Write 10 4 40 90 ZEARN MATH Teacher Edition

G3M1 Topic E Lesson 14 Repeat the process using 7 4 and 4 5 Consider asking students to draw the arrays or vary practice by adding context to one or both of these problems YOUR NOTES MULTIPLE MEANS OF REPRESENTATION Use the template for Problem 1 to guide information processing and visualization The template helps learners connect spoken numbers with their physical value It illustrates the relationship between counting by fours and multiplying with units of 4 MULTIPLE MEANS OF REPRESENTATION This lesson offers an opportunity to use a tape diagram to model multiplication If students need additional help identifying known and unknown information prompt them to look back at the array and then have them articulate the meaning of each factor Connections between the array and tape diagram may encourage students to progress to the tape diagram Independent Digital Lesson Lesson 14 Funky Fours 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 and prompt below may be used to lead the discussion Discuss differences between the tape diagrams and unknowns in each problem you solved How does an array help you skip count How is that similar and different from how a tape diagram helps you skip count ZEARN MATH Teacher Edition 91

Topic E Lesson 14 YOUR NOTES G3M1 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 Arthur has 4 boxes of chocolates Each box has 6 chocolates inside How many chocolates does Arthur have altogether Draw and label a tape diagram to solve Answers 1 24 tape diagram drawn and labeled to represent problem showing 4 groups of 6 92 ZEARN MATH Teacher Edition

G3M1 Topic E Lesson 14 Lesson Template FOURS ARRAY CONCEPT EXPLORATION TEMPLATE ZEARN MATH Teacher Edition 93

G3M1 Topic E Lesson 15 Lesson 15 YOUR NOTES Relate arrays to tape diagrams to model the commutative property of multiplication Warm Up FLUENCY PRACTICE Multiply by 4 Materials S Multiply by 4 1 5 today s Pattern Sheet NOTE This activity builds fluency with multiplication facts using units of 4 It works toward the goal of students knowing from memory all products of two one digit numbers See Lesson 9 for the directions for administering a Multiply By Pattern Sheet T Write 5 4 Let s skip count up by fours to find the answer Count with fingers to 5 as students count Record the skip count answers on the board S 4 8 12 16 20 T Circle 20 and write 5 4 20 above it Write 4 4 again Count with fingers to 4 as students count Let s skip count up by fours S 4 8 12 16 T Let s see how we can skip count down to find the answer to 4 4 Start at 20 Count down with fingers as students say numbers S 20 16 Repeat the process for 3 4 T Let s practice multiplying by 4 Be sure to work left to right across the page Instruct students to find the Multiply By 4 Pattern Sheet in their workbooks Group Counting NOTE Group counting reviews interpreting multiplication as repeated addition Counting by twos and threes in this activity reviews multiplication with units of 2 and 3 from Topics C and D T Let s count by twos Direct students to count forward and backward to 20 T Let s count by threes Direct students to count forward and backward to 30 ZEARN MATH Teacher Edition 95

Topic E Lesson 15 YOUR NOTES G3M1 WORD PROBLEM A cell phone is about 4 inches long About how long are 9 cell phones laid end to end NOTE This problem reviews multiplication using units of 4 from Lesson 14 It provides an opportunity to review using tape diagrams as tools for solving multiplication problems Concept Exploration Materials S Personal white board blank paper with 1 3 folded as shown PICTORIAL Relate arrays to tape diagrams Each student starts with one piece of blank folded paper as shown T Draw an array with 2 rows and 4 columns above the fold on your paper Use the array to remind your partner about what the commutative property is Turn your paper if you need to S May rotate array 90 degrees The factors can switch places or trade meanings but the total stays the same T Use the commutative property to write two multiplication equations for the array Write them on the left side of the paper below the fold one above the other S Write 2 4 8 and 4 2 8 T Next to each equation draw and label a tape diagram to match Make sure the diagrams are the same size because they both represent the same total S Draw two diagrams as shown T Explain to a partner how your tape diagrams relate to the array S Discuss T The array shows commutativity and so do the tape diagrams as we compare them Why is that true S What the factors represent in the tape diagrams changes to number of units or size of units It depends on what the factors represent in the equations or in the array The tape diagrams are just a different way to represent the multiplication 96 ZEARN MATH Teacher Edition

G3M1 Topic E Lesson 15 Repeat the process with 9 4 To facilitate comparing tape diagrams remind students to draw diagrams of the same size YOUR NOTES PICTORIAL ABTRACT Model commutativity using arrays and tape diagrams Provide students with two examples 5 4 and 4 7 Make further practice less guided Ask students to do the following Draw arrays to match the expressions Write two equations for each array Draw and label tape diagrams to represent the commutativity for each set of facts After they have completed both examples invite students to share and discuss their work T Why is it that an array can show two multiplication sentences but a tape diagram can only show one multiplication sentence S Because if you turn the tape diagram the number of units and their size doesn t change They just look different That s why we need two tape diagrams to model the commutativity of one array MULTIPLE MEANS OF ENGAGEMENT For the Pictorial Abstract problems encourage students to follow the progression of arrays to equations to tape diagrams If students are struggling to represent both problems in all 3 ways consider giving students the option to select their preferred representation and then share with a partner who chose a different representation Independent Digital Lesson Lesson 15 Two for One 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 15 G3M1 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 do the array and the two tape diagrams show commutativity How does the commutative property help us learn new multiplication facts 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 98 ZEARN MATH Teacher Edition

G3M1 Topic E Lesson 15 Task YOUR NOTES 1 Write 2 different multiplication equations that represent this tape diagram Answers 1 4 x 6 24 and 6 x 4 24 ZEARN MATH Teacher Edition 99

Topic E Lesson 15 Pattern Sheet G3M1 MULTIPLY BY 4 1 5 PATTERN SHEET 100 ZEARN MATH Teacher Edition

G3M1 Topic E Lesson 16 Lesson 16 YOUR NOTES Use the distributive property as a strategy to find related multiplication facts Warm Up FLUENCY PRACTICE Multiply by 4 Materials S Multiply by 4 6 10 today s Pattern Sheet NOTE This activity builds fluency with multiplication facts using units of 4 It works toward the goal of students knowing from memory all products of two one digit numbers See Lesson 9 for the directions for administering a Multiply By Pattern Sheet T Write 7 4 students count Let s skip count up by fours to solve Count with fingers to 7 as S 4 8 12 16 20 24 28 T Let s skip count up by fours starting at 5 fours or 20 S Show 5 fingers to represent 5 fours or 20 20 24 28 Count with fingers up to 7 fours as students count T Let s skip count down to find the answer to 7 4 Start at 10 fours or 40 Count down with fingers as students say numbers S 40 36 32 28 Repeat the process of skip counting up from 5 fours and down from 10 fours to solve 9 4 and 8 4 T Let s practice multiplying by 4 Be sure to work left to right across the page Instruct students to find the Multiply By 4 6 10 Pattern Sheet in their workbooks Group Counting NOTE Group counting reviews interpreting multiplication as repeated addition Counting by twos and threes in this activity reviews multiplication with units of 2 and 3 from Topics C and D T Let s count by twos Direct students to count forward and backward to 20 T Let s count by threes Direct students to count forward and backward to 30 Whisper the numbers between threes and speak each three out loud For example whisper 1 whisper 2 say 3 whisper 4 whisper 5 say 6 and so on ZEARN MATH Teacher Edition 101

Topic E Lesson 16 YOUR NOTES G3M1 Read Tape Diagrams Materials S Personal white board NOTE Students practice reading the difference between the value of the unit the size of the groups and the number of units The activity reviews using the tape diagram as a model for commutativity T Project a tape diagram partitioned into 2 equal units Draw 8 stars in each unit and bracket the total with a question mark Say the addition sentence S 8 8 16 T Say the multiplication sentence starting with the number of groups S 2 8 16 T Draw the tape diagram and label units with numbers instead of stars Label the missing total Beneath the diagram write a multiplication sentence S Draw a tape diagram with 8 written inside both units and 16 written as the total Beneath the diagram write 2 8 16 Repeat the process for 3 7 and 4 6 WORD PROBLEM Ms Williams draws the array pictured to show the class seating chart She sees the students in 4 rows of 7 when she teaches at Board 1 Use the commutative property to show how Ms Williams sees the class when she teaches at Board 2 Extension On Monday 6 students are absent How many students are in class on Monday NOTE This problem reviews the commutative property from Lesson 15 Students may use a tape diagram to show their solution If appropriate for the class present the extension 102 ZEARN MATH Teacher Edition

G3M1 Topic E Lesson 16 Concept Exploration YOUR NOTES Materials S Personal white board fours array Lesson 14 Concept Exploration Template PROBLEM 1 Model the 5 n pattern as a strategy for multiplying using units of 4 Distribute a fours array Lesson 14 Concept Exploration Template to each student T Shade the part of the array that shows 5 4 S Shade 5 rows of 4 T Talk to your partner about how to box an array that shows 5 4 1 4 and then box it S The box should have one more row than what s shaded Box 6 4 T What expression does the boxed array represent S 6 4 T Label the shaded and un shaded arrays in your box with equations S Write 5 4 20 and 1 4 4 T How can we combine our two multiplication equations to find the total number of dots S 6 4 24 or 20 4 24 Repeat the process with the following suggested examples 5 4 and 2 4 to model 7 4 5 4 and 4 4 to model 9 4 T What expression did we use to help us solve all three problems S 5 4 T Talk to your partner Why do you think I asked you to solve using 5 4 each time S You can just count by fives to solve it It equals 20 It s easy to add other numbers to 20 T Compare using 5 4 to solve your fours with 5 6 to solve your sixes and 5 8 to solve your eights S Discuss Identify the ease of skip counting and that the products are multiples of 10 T Now that you know how to use your fives you have a way to solve 7 sixes as 5 sixes and 2 sixes or 7 eights as 5 eights and 2 eights PROBLEM 2 Apply the 5 n pattern to decompose and solve larger facts Students work in pairs T Fold the template so that only 8 of the 10 rows are showing We ll use the array that s left What multiplication expression are we finding ZEARN MATH Teacher Edition 103

Topic E Lesson 16 YOUR NOTES G3M1 S Fold two rows away 8 4 T Use the strategy we practiced today to solve 8 4 S Demonstrate one possible solution Let s shade and label 5 4 Then we can label the un shaded part That s 3 4 5 4 20 and 3 4 12 20 12 32 There are 32 in total T Write 8 4 5 4 3 4 Talk with your partner about how you know this is true S Discuss T We can break a larger fact into two smaller facts to help us solve it Draw number bond shown Here we broke apart 8 fours into 5 fours and 3 fours to solve So we can write an equation 8 fours 5 fours 3 fours Write equation on the board T 5 3 4 is another way of writing 5 4 3 4 Talk with your partner about why these expressions are the same T Discuss T True or false In 5 4 and 3 4 the size of the groups is the same S True T Four represents the size of the groups The expression 5 4 3 4 shows how we distribute the groups of 4 Since the size of the groups is the same we can add the 5 fours and 3 fours to make 8 fours Repeat the process with the following suggested example 10 4 modeled by doubling the product of 5 4 MULTIPLE MEANS OF REPRESENTATION Keep track of the equations for all three examples As students reflect they can refer to the visual on the class board to see that 5 4 is the consistent expression MULTIPLE MEANS OF ENGAGEMENT For Problem 2 have students who are ready for an additional challenge decompose the same problem using facts other than 5 4 They should see that other strategies work as well Compare strategies to prove the efficiency of 5 4 MULTIPLE MEANS OF ACTION AND EXPRESSION Minimize instructional changes as you repeat with different numbers Scaffolding problems using the same method allows students to generalize skills more easily 104 ZEARN MATH Teacher Edition

G3M1 Topic E Lesson 16 Independent Digital Lesson YOUR NOTES Lesson 16 Facts of Five 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 Review vocabulary term distribute ZEARN MATH Teacher Edition 105

Topic E Lesson 16 YOUR NOTES G3M1 Explain the following sequence 5 3 4 5 4 3 4 5 fours 3 fours 8 fours 8 4 How does the sequence above show a number being distributed Why would the strategy we learned today be helpful for solving an even larger fact like 15 4 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 Destiny says I can use 5 4 to find the answer to 7 4 Use the array below to explain Destiny s strategy using words and numbers 7 4 5 4 2 4 Answers 1 8 20 8 28 7 fours broken into two smaller facts 5 fours and 2 fours sum of two smaller facts equals larger fact 106 ZEARN MATH Teacher Edition

G3M1 Topic E Lesson 16 Pattern Sheet MULTIPLY BY 4 6 10 PATTERN SHEET ZEARN MATH Teacher Edition 107

G3M1 Topic E Lesson 17 Lesson 17 YOUR NOTES Model the relationship between multiplication and division TIP This lesson may not take an entire day to complete If you finish early consider moving on to Topic F as that topic may be more challenging Warm Up WORD PROBLEM Mrs Peacock bought 4 packs of yogurt She had exactly enough to give each of her 24 students 1 yogurt cup How many yogurt cups are there in 1 pack NOTE This problem is designed to lead into today s Concept Exploration In Problem 1 students will analyze how a number bond represents the division expression 24 4 Concept Exploration Materials S Personal white board PROBLEM 1 Use the number bond to relate multiplication and division This problem is optional for Extra Support T Draw or project the number bond shown The number bond represents the division equation you wrote to solve the Word Problem Turn and tell your partner how it shows 24 4 S Discuss T Look back at the Word Problem Is the unknown in the number bond the same as the unknown in the division problem What does it represent ZEARN MATH Teacher Edition 109

Topic E Lesson 17 YOUR NOTES G3M1 S They re the same The unknown represents the size of the groups T Project a second number bond where the total and one part are drawn Write 4 24 Skip count by fours to find the unknown factor Each time you say a four I will make a new part of my number bond Draw the parts as students count S 4 8 12 16 20 24 T How many fours make 24 S 6 fours T So 24 4 equals S 6 T The division equations are the same How do the quotients in the two number bonds represent different things S The 6 in the first number bond represents the size of the groups The 6 in the second number bond represents the number of groups Repeat the process with 32 4 Model how the quotient can represent the number of groups or the size of the groups T How do the multiplication and division equations relate in each example S I thought of the division equation like a multiplication equation with an unknown factor and skip counted by fours until I reached the total PROBLEM 2 Solve word problems to illustrate the relationship between multiplication and division Write or project the following problem A classroom has tables that seat a total of 20 students Four students are seated at each table How many tables are in the classroom T Draw and label a tape diagram to represent the problem S Draw diagram shown T Without solving write a division equation and a multiplication equation with an unknown factor to represent your drawing S Write 20 4 and 4 20 T What does the unknown in both problems represent S The number of groups T Tell your partner your strategy for solving each equation S To solve the division I will add units of 4 to the tape diagram until I get to 20 That is just skip counting by fours Skip counting is a way to solve the multiplication too The strategies are the same for both equations because you can use one to solve the other T Solve both equations now Repeat the process with 16 4 Problem 2 models division where the quotient represents the number of groups 110 ZEARN MATH Teacher Edition

G3M1 Topic E Lesson 17 MULTIPLE MEANS OF ACTION AND EXPRESSION YOUR NOTES Preview and display examples of number bonds and tape diagrams Independent Digital Lesson Lesson 17 Working Together 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 ZEARN MATH Teacher Edition 111

Topic E Lesson 17 YOUR NOTES G3M1 How can a number bond show both multiplication and division Discuss Division is an unknown factor problem 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 Mr Thomas organizes 16 binders into stacks of 4 How many stacks does he make Draw and label a number bond to solve 2 The chef uses 28 avocados to make 4 batches of guacamole How many avocados are in 2 batches of guacamole Draw and label a tape diagram to solve Answers 1 4 number bond drawn showing 4 units of 4 equals 16 2 14 tape diagram drawn and labeled to represent the problem 112 ZEARN MATH Teacher Edition

G3M1 Topic F TOPIC F Distributive Property and Problem Solving Using Units of 2 5 and 10 Topic F introduces the factors 5 and 10 familiar from skip counting in Grade 2 Students apply the multiplication and division strategies they have learned to mixed practice with all of the factors included in Mission 1 Students model relationships between factors and decompose numbers as they further explore the relationship between multiplication and division This culminates in Lessons 18 and 19 as students decompose the dividend in a division sentence to practice the distributive property with division For example students decompose 28 4 as 20 4 8 4 5 2 7 In the final lessons of the mission students apply the tools representations and concepts they have learned to solve multi step word problems They demonstrate the flexibility of their thinking as they assess the reasonableness of their answers for a variety of problem types Lesson 20 focuses on word problems involving multiplication and division while Lesson 21 increases the complexity of problem solving by including word problems involving all four operations Objective Topic F Distributive Property and Problem Solving Using Units of 2 5 and 10 Lessons 18 19 Apply the distributive property to decompose units Lesson 20 Solve two step word problems involving multiplication and division and assess the reasonableness of answers Lesson 21 Solve two step word problems involving all four operations and assess the reasonableness of answers ZEARN MATH Teacher Edition 113

G3M1 Lesson 18 Topic F Lesson 18 YOUR NOTES Apply the distributive property to decompose units Warm Up WORD PROBLEM A parking structure has 10 levels There are 3 cars parked on each level How many cars are parked in the structure NOTE 10 3 30 is the same problem used in Problem 2 of today s Concept Exploration only without the context provided here Solving the problem ahead of time de emphasizes the answer so that students more easily focus attention on the new concept of decomposing with number bonds Concept Exploration NOTE This lesson may be particularly hard for students who did not learn decomposition in 1st and 2nd grade There is more overlap than usual between this Concept Exploration and the Independent Digital Lesson We recommend that you teach both problems as well as the varied numbers under Repeat the process Materials S Personal white board PROBLEM 1 Use number bonds to decompose numbers and apply the distributive property Project an array for 7 3 with a line drawn as shown Write 7 3 next to the array T How many threes S 7 threes ZEARN MATH Teacher Edition 115

Topic F Lesson 18 YOUR NOTES G3M1 T The dotted line shows a way to break apart the array The 7 threes are broken into S 5 threes and 2 threes T Let s draw our number bonds S Draw the number bond shown T Write the equation that shows how to add the two parts S Write 5 threes 2 threes 7 threes T Whisper to a partner the two multiplication sentences you used to help you solve 7 3 S Whisper 5 3 15 and 2 3 6 T Draw a second number bond using the expressions 5 3 and 2 3 The number bond is another way to show breaking apart This shows how we partitioned the array and wrote the number bond using our number sentences T Let s rewrite this as the addition of two products using my frame Point to the equation below 3 3 3 S Write 5 3 2 3 7 3 15 6 21 T How does the number sentence show the number bond S It shows the 7 broken into 5 and 2 And the threes are shared with both parts Yes 5 threes and 2 threes One part has 5 threes and the other part has 2 threes Repeat the process with 9 4 T Let s call it the break apart and distribute strategy The number bond helps us see that we can find the total by adding two smaller parts together PROBLEM 2 Use number bonds and the distributive property T Write 10 3 How many threes S 10 threes T What are some ways we can break apart 10 116 ZEARN MATH Teacher Edition

G3M1 Topic F Lesson 18 YOUR NOTES S 5 and 5 6 and 4 7 and 3 8 and 2 T So if we were counting apples that would be 5 apples and 5 apples or 6 apples and 4 apples S Yes T But we aren t counting apples What are we counting S Threes T So that would be 6 threes and S 4 threes T Let s draw our number bonds S Draw number bond shown T Write the equation that shows how to add the two parts Start with 6 threes and 4 threes S Write 6 threes 4 threes 10 threes T Rewrite this as the addition of two products using my frame Point to the equation below 3 3 3 S Write 6 3 4 3 10 3 18 12 30 Repeat the process with 8 4 MULTIPLE MEANS OF ACTION AND EXPRESSION Encourage students who need extra support to draw an array before using the number bond to decompose Independent Digital Lesson Lesson 18 Break It Up Number Bonds 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 ZEARN MATH Teacher Edition 117

Topic F Lesson 18 YOUR NOTES G3M1 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 118 Compare the number bond and array models for showing the break apart and distribute strategy Why do you think we use the number bond as a method for breaking a total into two parts In anticipation of using the distributive property with division in Lesson 19 ask the following Do you think the break apart and distribute strategy can be used with division What might that look like ZEARN MATH Teacher Edition

G3M1 Topic F Lesson 18 EXIT TICKET YOUR NOTES 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 Dylan used the break apart and distribute strategy to solve a multiplication problem Look at his work below write the multiplication problem Dylan solved and complete the number bond Dylan s work 5 4 1 4 20 4 24 Answers 1 6 4 1 4 6 4 24 ZEARN MATH Teacher Edition 119

G3M1 Topic F Lesson 19 Lesson 19 YOUR NOTES Apply the distributive property to decompose units Warm Up FLUENCY PRACTICE Group Counting NOTE Group counting reviews interpreting multiplication as repeated addition Counting by threes fours fives and sixes in this activity reviews multiplication with units of 3 4 and 5 and anticipates multiplication with units of 6 in Mission 3 T Let s count by fives Direct students to count forward and backward to 50 T Let s count by fours Direct students to count forward and backward to 40 T Let s count by threes Direct students to count forward and backward to 30 T Let s count by sixes Direct students to count forward and backward to 36 emphasizing the 24 to 30 transition Commutative Multiplying NOTE This activity reviews the commutativity of multiplication learned in Lessons 7 8 and 15 T Write 3 2 Say the multiplication sentence S 3 2 6 T Flip it S 2 3 6 Repeat the process for 5 2 5 3 3 4 2 8 and 3 7 Decompose and Multiply Materials S Personal white board NOTE This activity anticipates multiplication using units of 6 7 8 and 9 by decomposing larger facts into smaller known facts It reviews the break apart and distribute strategy T Write 7 4 S Write 7 fours Rewrite the equation in unit form ZEARN MATH Teacher Edition 121

Topic F Lesson 19 YOUR NOTES G3M1 T Write 7 fours 5 fours fours 7 fours is the same as 5 fours and how many fours S 2 fours T Write 5 fours 2 fours write 20 Fill in the blanks Below it S Write 20 8 28 T 7 4 equals S 28 Repeat for the following possible sequence 8 3 9 2 and 6 4 Change the unknowns that students need to fill in Compose and Multiply Materials S Personal white board NOTE This activity anticipates multiplication using units of 6 7 8 and 9 by composing smaller known facts into larger unknown facts It reviews the break apart and distribute strategy T Write 5 3 2 3 Fill in the blank to write a true multiplication sentence on your personal white board Below the multiplication sentence write an addition sentence S Write 5 3 2 3 21 Below it write 15 6 21 T Write 5 3 2 3 as a single multiplication sentence S Write 7 3 21 Repeat for the following possible sequence 8 2 and 9 4 WORD PROBLEM Henrietta works in a shoe store She uses 2 shoelaces to lace each pair of shoes She has a total of 24 laces How many pairs of shoes can Henrietta lace NOTE This problem reviews material from Lesson 18 but intentionally previews 24 2 which is used in the first example of today s Concept Exploration Students may choose to solve the Word Problem with division or as an unknown factor multiplication problem Use these variations in method to spark discussion 122 ZEARN MATH Teacher Edition

G3M1 Topic F Lesson 19 YOUR NOTES Concept Exploration NOTE This lesson may be particularly hard for students who did not learn decomposition in 1st and 2nd grade There is more overlap than usual between this Concept Exploration and the Independent Digital Lesson We recommend that you teach both problems as well as the varied numbers under Repeat the process Materials S Personal white board PROBLEM 1 Model break apart and distribute using an array as a strategy for division Draw or project a 12 2 array and write 24 2 above it T Let s use the array to help us solve 24 2 There are 24 dots total Draw a line after the tenth row This shows one way to break apart the array T Write division equations to represent the part of the array above the line and the part of the array below the line S Write 20 2 10 and 4 2 2 T How many twos are above the line S 10 twos T How many twos are below the line S 2 twos T Let s rewrite this as the addition of two quotients Use my equations 2 2 2 S Line 1 Fill in totals Line 2 Write 10 2 12 T Explain to your partner the process we used to solve 24 2 S We added the quotients of two smaller facts to find the quotient of a larger one Repeat the process with a 13 2 array to show 26 2 Break it into 20 2 and 6 2 PROBLEM 2 Use break apart and distribute as a strategy for division T Write 27 3 What are we focused on when we break apart to divide Breaking up the number of groups or rows like in multiplication or breaking up the total ZEARN MATH Teacher Edition 123

Topic F Lesson 19 YOUR NOTES G3M1 S Breaking up the total T Let s break up 27 into 15 and another number Fifteen plus what equals 27 S 12 T Work with a partner to draw an array that shows 27 3 where 3 is the number of columns S Draw a 9 3 array T Box the part of your array that shows a total of 15 S Box the first 5 rows T Write a division equation for the boxed portion to the right of the array S Write 15 3 5 T Box the part of your array that shows a total of 12 S Box the remaining 4 rows T Now write a division equation for that part of the array S Write 12 3 4 T Tell your partner how you will use the equations to help you solve the original equation 27 3 S I ll add the quotients of the two smaller facts T Write the following Complete the following sequence to solve 27 3 with your partner 27 3 15 3 12 3 Repeat the process with 33 3 Students can break apart 33 by using the number pair 30 and 3 MULTIPLE MEANS OF ENGAGEMENT Add a challenge by asking students to think about other ways of breaking apart 27 A student will most likely choose parts that are not evenly divisible by 3 This will lead to a discussion that gets students to realize that with division the strategy relies on the decomposition being such that the dividends must be evenly divisible by the divisor 124 ZEARN MATH Teacher Edition

G3M1 Topic F Lesson 19 Independent Digital Lesson YOUR NOTES Lesson 19 Break It Up Arrays 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 In Lesson 18 we used the break apart and distribute strategy with multiplication How is the method we learned today similar ZEARN MATH Teacher Edition 125

Topic F Lesson 19 YOUR NOTES G3M1 How is the break apart and distribute strategy different for multiplication than for division This strategy works for division when the total is broken into 2 parts that are evenly divisible by the divisor For example to solve 33 8 decomposing 33 into 25 and 8 is not effective at this level because neither 25 nor 8 is evenly divisible by 3 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 equations below to solve 22 2 20 2 2 22 2 20 2 2 Answers 1 11 10 2 1 2 10 1 11 126 ZEARN MATH Teacher Edition

G3M1 Lesson 20 Topic F Lesson 20 YOUR NOTES Solve two step word problems involving multiplication and division and assess the reasonableness of answers Warm Up WORD PROBLEM Red orange and blue scarves are on sale for 4 each Nina buys 2 scarves of each color How much does she spend altogether NOTE This problem reviews multiplication using units of 4 It also leads into Problem 1 of today s Concept Exploration Concept Exploration Materials S Personal white board PROBLEM 1 Model a two step problem with a tape diagram This problem is optional Write or project the following story Red orange and blue scarves are on sale for 4 each Nina buys 2 scarves of each color She also buys a hat that costs 4 How much does she spend altogether T Compare this new problem with the Word Problem you just solved What is different S The question is still the same but the new problem adds the cost of a hat to the total ZEARN MATH Teacher Edition 127

Topic F Lesson 20 YOUR NOTES G3M1 T Turn and talk to your partner How can we use our answer from the Word Problem to help solve the new problem S In our Word Problem we found the cost of the 6 scarves We just have to add the cost of the hat to the total T Draw tape diagram This tape diagram shows the Word Problem T Each of these boxes is 1 unit Tell me what 1 unit represents S 1 scarf T What is the value of 1 unit S 4 T What do the 6 units represent S 6 scarves T How did you label the 6 units S With a question mark T What equation did you use to find the total of all the items S 6 4 24 T Watch as I add to our model to represent the new problem T Draw and label diagram as shown Now I add the cost of the hat 4 to the total cost of the scarves 24 write 4 24 which is S 28 T How many units did we add together to find the total of both items S 7 units 1 unit 6 units T Tell your partner a multiplication sentence you could use to find the total cost of the scarves and hat without finding the value of the scarves first S 7 units of 4 28 7 4 28 PROBLEM 2 Use the tape diagram to solve a two step problem Write or project the following story Mr Lim buys 7 plants for his garden Each plant costs 5 The next day he buys a rose bush that also costs 5 How much more do the 7 plants cost than the rose bush T What information is known from reading the story S The cost of each plant is 5 We also know the rose bush costs 5 T What information is unknown S We don t know the total cost of the 7 plants so we don t know how much more the plants cost than the rose bush 128 ZEARN MATH Teacher Edition

G3M1 T Notice there are two unknowns in our problem Let s first draw and label a tape diagram to model the unknown as the cost of the 7 plants Topic F Lesson 20 YOUR NOTES S Draw and label tape diagram T Tell me how to find the cost of the plants S We multiply 7 5 T The plants cost S 35 T Have we answered the question S No T What is the question we are trying to answer S How much more the plants cost than the rose bush T Label the second question mark Tell your partner what strategy you might use to answer the question S I might subtract the cost of the rose bush from the total cost of the 7 plants I might do 6 5 because the plants have 6 units more than the rose bush I ll skip count the 6 extra fives on the plants diagram T Write an equation and solve the problem on your personal white board S Possibly write 35 5 30 6 5 30 5 5 5 5 5 5 30 T Reread the question Have we answered it S Reread and confirm T Is 30 a reasonable answer Why or why not S Yes 7 plants are expensive 5 is a lot less than 35 so 30 less makes sense I checked with addition 30 5 35 T Erase the first diagram and the 35 that marks the total value on the second diagram We first drew two models because the problem has two steps How does this model represent the whole problem on its own S Discuss T We know that 1 unit is 5 How many units represent the additional cost of the plants S 6 units T Given what you know is it necessary to find the total cost of the plants Why or why not S You can just do 6 5 without having to know about 35 T Explain to your partner the difference between the two ways of solving this problem ZEARN MATH Teacher Edition 129

Topic F Lesson 20 YOUR NOTES G3M1 PROBLEM 3 Work with a partner to model and solve a two step problem This problem is optional Write or project the following story Ten children equally share 40 almonds How many almonds will 3 children get T What information is known S The total amount of almonds and the number of children T What is unknown S How many almonds 3 children get T In order to solve what do you need to find first S The amount of almonds 1 child gets T With a partner model and solve the problem Make sure to reread the question to see if you have answered the question Then think about whether or not the answer makes sense This is how we check the reasonableness of the answer PROBLEM 4 Work with a partner to model and solve a two step problem Write or project the following story There are 25 blue balloons and 15 red balloons at a party Five children are given an equal number of each color balloon How many blue and red balloons does each child get T What information is known S The number of blue balloons the number red balloons and the number of children T What is unknown S How many of each color balloon each child gets T With a partner model and solve the problem Make sure to reread the question to see if you have answered the question Then think about whether or not the answer makes sense This is how we check the reasonableness of the answer MULTIPLE MEANS OF REPRESENTATION This lesson offers flexibility in its delivery Adjust the level of support for each problem according to the needs of students For example you could guide students through the first problem or choose to have them work with a partner and debrief the process after MULTIPLE MEANS OF REPRESENTATION Scaffold Problem 3 in the Concept Exploration by providing a tape diagram with no labels This allows students to see the problem and analyze the steps they need to take to solve the problem 130 ZEARN MATH Teacher Edition

G3M1 Topic F Lesson 20 Independent Digital Lesson YOUR NOTES Lesson 20 Tackle the Two Step 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 question below may be used to lead the discussion How did you check the reasonableness of your answers to each problem ZEARN MATH Teacher Edition 131

Topic F Lesson 20 YOUR NOTES G3M1 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 Thirty two jelly beans are shared by 8 students a How many jelly beans will each student get b How many jelly beans will 4 students get 2 The teacher has 30 apple slices and 20 pear slices Five children equally share all of the fruit slices How many fruit slices does each child get Answers 1 Tape diagram labeled a 4 b 16 2 10 132 ZEARN MATH Teacher Edition

G3M1 Topic F Lesson 21 Lesson 21 YOUR NOTES Solve two step word problems involving all four operations and assess the reasonableness of answers Warm Up FLUENCY PRACTICE Group Counting NOTE Group counting reviews interpreting multiplication as repeated addition Counting by threes fours and sixes in this activity reviews multiplication with units of 3 and 4 and anticipates multiplication with units of 6 in Mission 3 T Let s count by threes Direct students to count forward and backward to 30 T Let s count by fours think talk forward and backward Direct students to count forward and backward to 40 Think 1 2 3 say 4 Think 5 6 7 say 8 etc T Let s count by sixes Direct students to count forward and backward to 48 emphasizing the 24 to 30 and 36 to 42 transitions Multiply by 5 Materials S Multiply by 5 1 5 today s Pattern Sheet NOTE This activity builds fluency with multiplication facts using units of 5 It works toward students knowing from memory all products of two one digit numbers See Lesson 9 for the directions for administering a Multiply By Pattern Sheet T Let s count by threes Direct students to count forward and backward to 30 T Write 5 5 Let s skip count up by fives to solve Count with fingers to 5 as students count Record skip count answers on the board S 5 10 15 20 25 T Circle 25 and write 5 5 25 above it Write 3 5 again Count with fingers to 3 as students count Let s skip count up by fives S 5 10 15 T Let s see how we can skip count down to find the answer too Start at 25 Count down with fingers as students say numbers S 25 20 15 Repeat the process for 9 5 and 8 5 ZEARN MATH Teacher Edition 133

Topic F Lesson 21 YOUR NOTES G3M1 T Let s practice multiplying by 5 Be sure to work left to right across the page Instruct students to find the Multiply By 5 Pattern Sheet in their workbooks Commutative Multiplying NOTE This activity reviews the commutativity of multiplication learned in Lessons 7 8 and 15 T Write 4 2 Say the multiplication sentence S 4 2 8 T Flip it S 2 4 8 Repeat the process for 5 3 9 2 4 3 2 7 and 3 8 WORD PROBLEM There are 4 boxes with 6 binders in each one Three brothers share the binders How many binders does each brother get NOTE This two step problem reviews Lesson 20 s objective Students self select an approach and independently solve Practicing a two step problem here scaffolds the difference between the structured practice in Lesson 20 and the open ended practice in today s Concept Exploration Guide students to evaluate their methods for solving and assess the reasonableness of their answers Concept Exploration NOTE Today s lesson uses the Problem Set in student workbooks Solutions for each problem are included below Materials S Chart paper markers paper strips optional for representing tape diagrams glue Problem Set in student workbooks Today s lesson is a culminating exploration that follows the following process 134 Divide the class into groups no larger than four students Assign each group one word problem from the Problem Set ZEARN MATH Teacher Edition

G3M1 Each group collaborates to model and solve their assigned problem Each group prepares to present their problem to the class describing their method for solving and explaining the reasonableness of their answer Topic F Lesson 21 YOUR NOTES Each group needs one set of the materials listed in the materials section Directions similar to RDW process 1 Read and analyze together to determine known and unknown information 2 Discuss how to model 3 Model and label diagrams 4 Discuss and agree on the steps needed to solve 5 Write equations and solve 6 Assess the reasonableness of the solution Ask Does our answer make sense How do we know 7 Write a complete sentence to answer the question 8 Prepare a mini presentation to explain each step of your work Prepare to answer clarifying questions from the group Each group presents to the class Audience members should be prepared to ask clarifying questions challenge each other s work and offer compliments If more than one group solves the same problem discussion might include similarities and differences between problemsolving approaches PROBLEM 1 This problem is optional Jason earns 6 per week for doing all his chores On the fifth week he forgets to take out the trash so he only earns 4 Write and solve an equation to show how much Jason earns in 5 weeks PROBLEM 2 Miss Lianto orders 4 packs of 7 markers After passing out 1 marker to each student in her class she has 6 left Label the tape diagram to find how many students are in Miss Lianto s class ZEARN MATH Teacher Edition 135

Topic F Lesson 21 YOUR NOTES G3M1 PROBLEM 3 Orlando buys a box of 18 fruit snacks Each box comes with an equal number of strawberry cherry and grape flavored snacks He eats all of the grape flavored snacks Draw and label a tape diagram to find how many fruit snacks he has left PROBLEM 4 Eudora buys 21 meters of ribbon She cuts the ribbon so that each piece measures 3 meters in length a How many pieces of ribbon does she have b If Eudora needs a total of 12 pieces of the shorter ribbon how many more pieces of the shorter ribbon does she need MULTIPLE MEANS OF ACTION AND EXPRESSION The first two problems on the Problem Set have diagrams drawn to scaffold instructions These diagrams may be removed for the exploration to adjust the level of support for the groups who solve them MULTIPLE MEANS OF ENGAGEMENT Consider assigning roles so that group members participate and each student knows how best to contribute to group success This is particularly important with regard to each group s presentation Consider a rubric that encourages partnership demonstration of understanding and the use of precise language e g equation product and quotient 136 ZEARN MATH Teacher Edition

G3M1 Topic F Lesson 21 Independent Digital Lesson YOUR NOTES Lesson 21 Step Up 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 activity below may be used to lead the discussion Students are seated with a personal white board Select one student to stand behind someone seated Say an expression or give a word problem Of the pair the first student to solve it ZEARN MATH Teacher Edition 137

Topic F Lesson 21 YOUR NOTES G3M1 correctly and lift his board wins the round That student rotates one seat to the right The goal is for a single child to work her way back to the seat behind which she originally stood The game is very fast paced to build excitement Given the time constraint the game is unlikely to finish The winner can be the student who moves the most spaces Sample expressions or word problems How many legs are there on 5 dogs 4 3 6 2 Write a related division fact for 5 3 18 3 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 Ms Egeregor buys 27 books for her classroom library She buys an equal number of fiction nonfiction and poetry books She shelves all of the poetry books first Draw and label a tape diagram to show how many books Ms Egeregor has left to shelve Answers 1 Tape diagram drawn and labeled to represent problem 18 138 ZEARN MATH Teacher Edition

G3M1 Topic F Lesson 21 Problem Set PROBLEM SET Name Date PROBLEM 1 Jason earns 6 per week for doing all his chores On the fifth week he forgets to take out the trash so he only earns 4 Write and solve an equation to show how much Jason earns in 5 weeks Jason earns PROBLEM 2 Miss Lianto orders 4 packs of 7 markers After passing out 1 marker to each student in her class she has 6 left Label the tape diagram to find how many students are in Miss Lianto s class There are ZEARN MATH Teacher Edition students in Miss Lianto s class 139

Topic F Lesson 21 Problem Set G3M1 PROBLEM 3 Orlando buys a box of 18 fruit snacks Each box comes with an equal number of strawberry cherry and grapeflavored snacks He eats all of the grape flavored snacks Draw and label a tape diagram to find how many fruit snacks he has left PROBLEM 4 Eudora buys 21 meters of ribbon She cuts the ribbon so that each piece measures 3 meters in length a How many pieces of ribbon does she have b If Eudora needs a total of 12 pieces of the shorter ribbon how many more pieces of the shorter ribbon does she need 140 ZEARN MATH Teacher Edition

G3M1 Topic F Lesson 21 Pattern Sheet MULTIPLY BY 5 1 5 PATTERN SHEET ZEARN MATH Teacher Edition 141

Math Math TEACHER EDITION GRADE 3 TEACHER EDITION Mission 1 1 Mission 1 Multiply and Divide Friendly Numbers Mission 2 Measure It Mission 3 Multiply and Divide Tricky Numbers Mission 4 Find the Area Mission 5 Fractions as Numbers 4 5 6 7 3 GRADE Mission 6 Display Data Mission 7 Shapes and Measurement Grade 3 Mission 1 Zearnmath_TE_Grade3_M1 indd 1 3 TEACHER EDITION GRADE 3 2 12 9 22 10 19 AM