GRADE 4 Mission 1 Add Subtract Round This Mission takes number sense and place value understanding from 2nd and 3rd grade a step further Students start by noticing patterns when bundling and unbundling groups of 10s 100s and 1 000s and they conclude by estimating and finding precise answers to addition and subtraction problems using the standard algorithm
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 052 0
Table of Contents MISSION OVERVIEW viii ASSESSMENTS xiii TOPIC A PLACE VALUE OF MULTI DIGIT WHOLE NUMBERS LESSON 1 3 LESSON 2 11 LESSON 3 19 LESSON 4 27 TOPIC B COMPARING MULTI DIGIT WHOLE NUMBERS LESSON 5 35 LESSON 6 43 TOPIC C ROUNDING MULTI DIGIT WHOLE NUMBERS LESSON 7 51 LESSON 8 57 LESSON 9 63 LESSON 10 69 TOPIC D MULTI DIGIT WHOLE NUMBER ADDITION LESSON 11 75 LESSON 12 85 TOPIC E MULTI DIGIT WHOLE NUMBER SUBTRACTION LESSON 13 93 LESSON 14 101 LESSON 15 107 LESSON 16 115 TOPIC F ADDITION AND SUBTRACTION WORD PROBLEMS LESSON 17 123 LESSON 18 131 LESSON 19 139 ZEARN MATH Teacher Edition iii
G4M1 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 Numbers to 10 Numbers to 5 Digital Activities 50 M1 G1 M1 G3 M2 Add Subtract Friendly Numbers Explore Length M1 Add Subtract Round 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 M2 Base Ten 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 M6 Equal Groups M4 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 Multiply and Divide Fractions Decimals Expressions Equations and Inequalities M7 M6 M5 M5 Arithmetic in Base Ten M8 Shapes Time Fractions Length Money Data Equivalent Fractions M5 M6 Add Subtract to 100 M7 Fractions as Numbers M4 Construct Lines Angles Shapes Multiply Divide Big Numbers M5 M4 Find the Area Numbers to 20 Digital Activities 35 Work with Shapes Add Subtract Big Numbers Multiply Divide Tricky Numbers M3 M1 M4 M5 M3 M2 Numbers to 15 Digital Activities 35 Add Subtract Big Numbers Add Subtract Solve Measure It M2 M1 M3 Measure Length M4 Counting Place Value Multiply Divide Friendly Numbers G4 G6 M3 Measure Solve G2 M2 Meet Place Value 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 Add Subtract Small Numbers M5 M4 Comparison of Length Weight Capacity Numbers to 10 2D 3D Shapes 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 G4M1 Topics and Lesson Objectives Objective Topic A Place Value of Multi Digit Whole Numbers Lesson 1 Interpret a multiplication equation as a comparison Lesson 2 Recognize a digit represents 10 times the value of what it represents in the place to its right Lesson 3 Name numbers within 1 million by building understanding of the place value chart and placement of commas for naming base thousand units Lesson 4 Read and write multi digit numbers using base ten numerals number names and expanded form Topic B Comparing Multi Digit Whole Numbers Lesson 5 Compare numbers based on meanings of the digits using
G4M1 Overview Topic E Multi Digit Whole Number Subtraction Lesson 13 Use place value understanding to decompose to smaller units once using the standard subtraction algorithm and apply the algorithm to solve word problems using tape diagrams Lesson 14 Use place value understanding to decompose to smaller units up to three times using the standard subtraction algorithm and apply the algorithm to solve word problems using tape diagrams Lesson 15 Use place value understanding to fluently decompose to smaller units multiple times in any place using the standard subtraction algorithm and apply the algorithm to solve word problems using tape diagrams Lesson 16 Solve two step word problems using the standard subtraction algorithm fluently modeled with tape diagrams and assess the reasonableness of answers using rounding Topic F Addition and Subtraction Word Problems Lesson 17 Solve additive compare word problems modeled with tape diagrams Lesson 18 Solve multi step word problems modeled with tape diagrams and assess the reasonableness of answers using rounding Lesson 19 Create and solve multi step word problems from given tape diagrams and equations End of Mission Assessment Topics D F Note on Pacing for Differentiation If you are using the Zearn Math recommended weekly schedule that consists of four Core Days when students learn grade level content and one Flex Day that can be tailored to meet students needs we recommend omitting the optional lesson in this mission during the Core Days Students who demonstrate a need for further support can explore these concepts with you and peers as part of a flex day as needed This schedule ensures students have sufficient time each week to work through grade level content and includes built in weekly time you can use to differentiate instruction to meet student needs Optional lesson for G4M1 Lesson 19 ZEARN MATH Teacher Edition vii
Overview G4M1 MISSION 1 OVERVIEW In this Grade 4 mission students extend their work with whole numbers They begin with large numbers using familiar units hundreds and thousands and develop their understanding of millions by building knowledge of the pattern of times ten in the base ten system on the place value chart They recognize that each sequence of three digits is read as hundreds tens and ones followed by the naming of the corresponding base thousand unit thousand million billion The place value chart is fundamental to Topic A Building upon their previous knowledge of bundling students learn that 10 hundreds can be composed into 1 thousand and therefore 30 hundreds can be composed into 3 thousands because a digit s value is 10 times what it would be one place to its right Students learn to recognize that in a number such as 7 777 each 7 has a value that is 10 times the value of its neighbor to the immediate right One thousand can be decomposed into 10 hundreds therefore 7 thousands can be decomposed into 70 hundreds Similarly multiplying by 10 shifts digits one place to the left and dividing by 10 shifts digits one place to the right 3 000 10 300 3 000 10 300 In Topic B students use place value as a basis for comparing whole numbers Although this is not a new concept it becomes more complex as the numbers become larger For example it becomes clear that 34 156 is 3 thousands greater than 31 156 34 156 31 156 Comparison leads directly into rounding where their skill with isolating units is applied and extended Rounding to the nearest ten and hundred with three digit numbers was a goal in Grade 3 Now Grade 4 students moving into Topic C learn to round to any place value initially using the vertical number line though ultimately moving away from the visual model altogether Topic C also includes word problems where students apply rounding to real life situations In Grade 4 students work on becoming fluent with the standard algorithms for addition and subtraction In Topics D and E students focus on single like unit calculations ones with ones thousands with thousands etc at times requiring the composition of greater units when adding 10 hundreds are composed into 1 thousand and decomposition into smaller units when subtracting 1 thousand is decomposed into 10 hundreds Throughout these topics students apply their algorithmic knowledge to solve word problems Students also use a variable to represent the unknown quantity The mission culminates with multi step word problems in Topic F Tape diagrams are used throughout the topic to model additive compare problems like the one exemplified below These diagrams facilitate deeper comprehension and serve as a way to support the reasonableness of an answer A goat produces 5 212 gallons of milk a year A cow produces 17 279 gallons of milk a year How much more milk does a goat need to produce to make the same amount of milk as a cow viii ZEARN MATH Teacher Edition
G4M1 Overview 17 279 5 212 A goat needs to produce more gallons of milk a year 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 18 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 G4M1 Terminology New or Recently Introduced Terms Millions ten millions hundred millions As places on the place value chart Ten thousands hundred thousands As places on the place value chart Variables Letters that stand for numbers and can be added subtracted multiplied and divided as numbers are 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 Familiar Terms and Symbols1 Equal to less than greater than Addend E g in 4 5 the numbers 4 and 5 are the addends Algorithm A step by step procedure to solve a particular type of problem Bundling making renaming changing exchanging regrouping trading E g exchanging 10 ones for 1 ten Compose E g to make 1 larger unit from 10 smaller units Decompose E g to break 1 larger unit into 10 smaller units Difference Answer to a subtraction problem Digit Any of the numbers 0 to 9 e g What is the value of the digit in the tens place 1 These are terms and symbols students have used or seen previously x ZEARN MATH Teacher Edition
G4M1 Overview Endpoint Used with rounding on the number line the numbers that mark the beginning and end of a given interval Equation E g 2 389 80 601 Estimate An approximation of a quantity or number Expanded form E g 100 30 5 135 Expression E g 2 thousands 10 Halfway With reference to a number line the midpoint between two numbers e g 5 is halfway between 0 and 10 Number line A line marked with numbers at evenly spaced intervals Number sentence E g 4 3 7 Place value The numerical value that a digit has by virtue of its position in a number Rounding Approximating the value of a given number Standard form A number written in the format 135 Sum Answer to an addition problem Tape diagram Bar diagram Unbundling breaking renaming changing regrouping trading E g exchanging 1 ten for 10 ones Word form E g one hundred thirty five Suggested Tools and Representations Number lines Vertical to represent rounding up and rounding down Personal white boards One per student Place value cards One large set per classroom including 7 units to model place value Place value chart Templates provided in lessons to insert into personal white boards ZEARN MATH Teacher Edition xi
Overview G4M1 Place value disks Can be concrete manipulatives or pictorial drawings such as the chip model to represent numbers Tape diagrams Drawn to model a word problem Place Value Chart with Headings used for numbers or the chip model Place Value Chart Without Headings used for place value disk manipulatives or drawings Place Value Disk Place Value Cards Vertical Number Line Personal White Boards Materials Needed for Personal White Boards 1 heavy duty clear sheet protector 1 piece of stiff red tag board 11 8 1 piece of stiff white tag board 11 8 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 G4 M1 Date 1 Compare the values of each 7 in the number 771 548 Use a picture numbers or words to explain 2 In the spaces provided write the following units in standard form Be sure to place commas where appropriate a 7 thousands 5 hundreds 6 ones b 2 ten thousands 8 thousands 3 hundreds 3 tens 9 ones c 9 hundred thousands 1 thousand 4 hundreds 7 ones 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 G4M1 Mid Mission Assessment 3 Complete the following chart Standard Form Word form Expanded form a Forty five thousand eighty seven b 7 802 c 50 000 900 70 5 d 620 320 4 Label the units in the place value chart Draw place value disks to represent each number in the place value chart Use or to compare the two numbers Write the correct symbol in the circle 34 321 34 032
PAGE 3 G4M1 Mid Mission Assessment 5 Compare using or Write your answer inside the circle a 100 000 10 000 b 204 000 240 000 c 95 347 95 357 6 Round to the nearest ten thousand Use the number line to model your thinking a 53 256 b 927 500
PAGE 1 ZEARN END OF MISSION ASSESSMENT Name G4 M1 Date 1 Solve each problem using the appropriate standard algorithm a 175 201 14 979 b 325 762 694 253 c 85 427 3 953 d 415 396 325 297 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
G4M1 End of Mission Assessment PAGE 2 2 Norfolk VA has a population of 242 628 people Baltimore MD has 376 865 more people than Norfolk Charleston SC has 496 804 less people than Baltimore a What is the total population of all three cities Draw a tape diagram to model the word problem Then solve the problem b Round to the nearest hundred thousand to check the reasonableness of your answer for the population of Charleston SC
PAGE 3 G4M1 End of Mission Assessment c Record each city s population in numbers in words and in expanded form d Compare the population of Norfolk and Charleston using
G4M1 Topic A TOPIC A Place Value of Multi Digit Whole Numbers In Topic A students build the place value chart to 1 million and learn the relationship between each place value as 10 times the value of the place to the right Students manipulate numbers to see this relationship such as 30 hundreds composed as 3 thousands They decompose numbers to see that 7 thousands is the same as 70 hundreds As students build the place value chart into thousands and up to 1 million the sequence of three digits is emphasized They become familiar with the base thousand unit names up to 1 billion Students fluently write numbers in multiple formats as digits in unit form as words and in expanded form up to 1 million Objective Topic A Place Value of Multi Digit Whole Numbers Lesson 1 Interpret a multiplication equation as a comparison Lesson 2 Recognize a digit represents 10 times the value of what it represents in the place to its right Lesson 3 Name numbers within 1 million by building understanding of the place value chart and placement of commas for naming base thousand units Lesson 4 Read and write multi digit numbers using base ten numerals number names and expanded form ZEARN MATH Teacher Edition 1
G4M1 Lesson 1 Topic A Lesson 1 YOUR NOTES Interpret a multiplication equation as a comparison Warm Up FLUENCY PRACTICE Place Value Materials S Personal white board Unlabeled Thousands Place Value Chart Fluency Template NOTE Reviewing and practicing place value skills in isolation prepares students for success in multiplying different place value units during today s Concept Exploration T Have students turn to the Unlabeled Thousands Place Value Chart in their student workbooks Project your place value chart to the thousands Show 4 ones as place value disks Write the number below it S Draw 4 ones disks and write 4 below it T Show 4 tens disks and write the number below it S Draw 4 tens disks and write 4 at the bottom of the tens column T Say the number in unit form S 4 tens 4 ones T Say the number in standard form S 44 Continue for the following possible sequence 2 tens 3 ones 2 hundreds 3 ones 2 thousands 3 hundreds 2 thousands 3 tens and 2 thousands 3 hundreds 5 tens and 4 ones MULTIPLE MEANS OF ACTION AND EXPRESSION For the Place Value fluency activity students may represent ones etc using counters rather than drawing Others may benefit from the opportunity to practice simultaneously speaking and showing units e g tens Provide sentence frames to support oral response such as tens ones is standard form ZEARN MATH Teacher Edition 3
G4M1 Topic A Lesson 1 YOUR NOTES WORD PROBLEM Ben has a rectangular area 9 meters long and 6 meters wide He wants a fence that will go around it as well as grass sod to cover it How many meters of fence will he need How many square meters of grass sod will he need to cover the entire area NOTE As the first lesson of the year this Word Problem reviews area perimeter multiplication and addition all important concepts from Grade 3 This problem can be extended after today s Concept Exploration by asking students to find an area 10 times as much as the grass sod or to find a perimeter 10 times as wide and 10 times as long MULTIPLE MEANS OF ENGAGEMENT Enhance the relevancy of the Word Problem by substituting names settings and tasks to reflect students and their experiences Set individual student goals and expectations Some students may successfully solve for area and perimeter in five minutes others may solve for one and others may solve for both and compose their own word problems Concept Exploration Materials T Place value disks ones tens hundreds and thousands Unlabeled Thousands Place Value Chart Fluency Template S Personal white board Unlabeled Thousands Place Value Chart Fluency Template PROBLEM 1 1 ten is 10 times as much as 1 one T Have a place value chart ready Draw or place 1 unit into the ones place T How many units do I have S 1 T What is the name of this unit S A one T Count the ones with me Draw ones as they do so S 1 one 2 ones 3 ones 4 ones 5 ones 10 ones 4 ZEARN MATH Teacher Edition
Topic A Lesson 1 G4M1 T 10 ones What larger unit can I make YOUR NOTES S 1 ten T I change 10 ones for 1 ten We say 1 ten is 10 times as much as 1 one Tell your partner what we say and what that means Use the model to help you S 10 ones make 1 ten 10 times 1 one is 1 ten or 10 ones We say 1 ten is 10 times as many as 1 one PROBLEM 2 One hundred is 10 times as much as 1 ten Quickly repeat the process from Problem 1 with 10 copies of 1 ten PROBLEM 3 One thousand is 10 times as much as 1 hundred Quickly repeat the process from Problem 1 with 10 copies of 1 hundred T Discuss the patterns you have noticed with your partner S 10 ones make 1 ten 10 tens make 1 hundred 10 hundreds make 1 thousand Every time we get 10 we bundle and make a bigger unit We copy a unit 10 times to make the next larger unit If we take any of the place value units the next unit on the left is ten times as many T Let s review in words the multiplication pattern that matches our models and 10 times as many Display the following information for student reference 1 ten 10 1 one Say 1 ten is 10 times as much as 1 one 1 hundred 10 1 ten Say 1 hundred is 10 times as much as 1 ten 1 thousand 10 1 hundred Say 1 thousand is 10 times as much as 1 hundred PROBLEM 4 Model 10 times as much as on the place value chart with an accompanying equation NOTE Place value disks are used as models throughout the curriculum and can be represented in two different ways A disk with a value labeled inside of it such as in Problem 1 should be drawn or placed on a place value chart with no headings The value of the disk in its appropriate column indicates the column heading A place value disk drawn as a dot should be used on place value ZEARN MATH Teacher Edition 5
G4M1 Topic A Lesson 1 YOUR NOTES charts with headings as in Problem 4 This type of representation is called the chip model The chip model is a faster way to represent place value disks and is used as students move away from a concrete stage of learning Model 2 tens is 10 times as much as 2 ones on the place value chart and as an equation T Draw place value disks as dots Because you are using dots label your columns with the unit value T Represent 2 ones Solve to find 10 times as many as 2 ones Work together S Work together T 10 times as many as 2 ones is S 20 ones 2 tens T Explain this equation to your partner using your model S 10 2 ones 20 ones 2 tens Repeat the process with 10 times as many as 4 tens is 40 tens is 4 hundreds and 10 times as many as 7 hundreds is 70 hundreds is 7 thousands 10 4 tens 40 tens 4 hundreds 10 7 hundreds 70 hundreds 7 thousands PROBLEM 5 Model as an equation 10 times as much as 9 hundreds is 9 thousands T Write an equation to find the value of 10 times as many as 9 hundreds Circulate and assist students as necessary T Show me your board Read your equation S 10 9 hundreds 90 hundreds 9 thousands T Yes Discuss whether this is true with your partner Write 10 9 hundreds 9 thousands S Yes it is true because 90 hundreds equals 9 thousands so this equation just eliminates that extra step Yes We know 10 of a smaller unit equals 1 of the next larger unit so we just avoided writing that step MULTIPLE MEANS OF REPRESENTATION Consider making a word wall for students to reference place value language throughout this mission You could include the words ones tens hundreds and thousands As students build sentences and write equations to describe the relationships in our base ten system encourage students to use the word wall as needed for additional language support 6 ZEARN MATH Teacher Edition
Topic A Lesson 1 G4M1 Independent Digital Lesson YOUR NOTES Lesson 1 Bundle Action 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 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 7
G4M1 Topic A Lesson 1 YOUR NOTES What are some ways you could model 10 times as many What are the benefits and drawbacks of each way of modeling Money base ten materials disks labeled drawings of disks dots on a labeled place value chart tape diagram Take two minutes to explain to your partner what we learned about the value of each unit as it moves from right to left on the place value chart Write and complete the following statements ten is times as many as hundred is thousand is times as many as times as many as one ten hundred EXIT TICKET After today s lesson instruct students to complete the Exit Ticket A review of their Exit Ticket as well as continuously monitoring your Digital Reports can help you assess your students understanding of the concepts explored in today s lesson and plan more effectively for future lessons The questions from the Exit Ticket may be read aloud to the students Task Use the disks in the place value chart below to complete the following problems 1 Label the place value chart 2 Tell about the movement of the disks in the place value chart by filling in the blanks to make the following equation match the drawing in the place value chart 10 8 ZEARN MATH Teacher Edition
G4M1 3 Write a statement about this place value chart using the words 10 times as many Topic A Lesson 1 YOUR NOTES Answers 1 Answers may vary Possible responses Hundreds Tens Ones Thousands Hundreds Tens 2 Answers may vary Possible responses 4 tens 40 tens 4 hundreds or 4 hundreds 40 hundreds 4 thousands 3 Possible responses 4 hundreds is 10 times as much as 4 tens or 4 thousands is 10 times as much as 4 hundreds ZEARN MATH Teacher Edition 9
Topic A Lesson 1 Fluency Template G4M1 UNLABELED THOUSANDS PLACE VALUE CHART FLUENCY TEMPLATE 10 ZEARN MATH Teacher Edition
G4M1 Lesson 2 Topic A Lesson 2 YOUR NOTES Recognize a digit represents 10 times the value of what it represents in the place to its right Warm Up FLUENCY PRACTICE Skip Counting NOTE Practicing skip counting on the number line builds a foundation for accessing higher order concepts throughout the year Direct students to count by threes forward and backward to 36 focusing on the crossing ten transitions Example 3 6 9 12 9 12 9 12 15 18 21 18 21 24 27 30 27 30 33 30 33 30 33 36 The purpose of focusing on crossing the ten transitions is to help students make the connection that for example when adding 3 to 9 9 1 is 10 and then 2 more is 12 There is a similar purpose in counting down by threes 12 2 is 10 and subtracting 1 more is 9 This work builds on the fluency work of previous grade levels Students should understand that when crossing the ten they are regrouping Direct students to count by fours forward and backward to 48 focusing on the crossing ten transitions Place Value Materials S Personal white board Unlabeled Thousands Place Value Chart Lesson 1 Fluency Template NOTE Reviewing and practicing place value skills in isolation prepares students for success in multiplying different place value units during today s Concept Exploration T Project the place value chart to the thousands place Show 5 tens as place value disks and write the number below it S Draw 5 tens Write 5 below the tens column and 0 below the ones column T Draw to correct student misunderstanding Say the number in unit form S 5 tens T Say the number in standard form S 50 ZEARN MATH Teacher Edition 11
Topic A Lesson 2 YOUR NOTES G4M1 Continue for the following possible sequence 3 tens 2 ones 4 hundreds 3 ones 1 thousand 2 hundreds 4 thousands 2 tens and 4 thousands 2 hundreds 3 tens 5 ones Multiply by 10 Materials S Personal white board NOTE This fluency activity reviews concepts learned in Lesson 1 T Project 10 ones 10 1 Fill in the blank S Write 10 ones 10 1 hundred T Say the multiplication sentence in standard form S 10 10 100 Repeat for the following possible sequence 10 2 hundreds 10 3 hundreds 10 7 hundreds 10 1 hundred 1 10 2 thousands 10 8 thousands 10 10 thousands WORD PROBLEM Amy is baking muffins Each baking tray can hold 6 muffins a If Amy bakes 4 trays of muffins how many muffins will she have in all b The corner bakery produced 10 times as many muffins as Amy baked How many muffins did the bakery produce Extension If the corner bakery packages the muffins in boxes of 100 how many boxes of 100 could they make NOTE This Word Problem builds on the concept from Lesson 1 of 10 times as many 12 ZEARN MATH Teacher Edition
G4M1 Concept Exploration Topic A Lesson 2 YOUR NOTES Materials T Unlabeled Millions Place Value Chart Concept Exploration Template S Personal white board Unlabeled Millions Place Value Chart Concept Exploration Template PROBLEM 1 Multiply single units by 10 to build the place value chart to 1 million Divide to reverse the process T Label ones tens hundreds and thousands on your place value chart T On your personal white board write the multiplication sentence that shows the relationship between 1 hundred and 1 thousand S Write 10 1 hundred 10 hundreds 1 thousand T Draw place value disks on your place value chart to find the value of 10 times 1 thousand T Circulate I saw that Tessa drew 10 disks in the thousands column What does that represent S 10 times 1 thousand equals 10 thousands 10 1 thousand 10 thousands T How else can 10 thousands be represented S 10 thousands can be bundled because when you have 10 of one unit you can bundle them and move the bundle to the next column T Point to the place value chart Can anyone think of what the name of our next column after the thousands might be Students share Label the ten thousands column T Now write a complete multiplication sentence to show 10 times the value of 1 thousand Show how you regroup S Write 10 1 thousand 10 thousands 1 ten thousand T On your place value chart show what 10 times the value of 1 ten thousand equals Circulate and assist students as necessary T What is 10 times 1 ten thousand S 10 ten thousands 1 hundred thousand T That is our next larger unit Write 10 1 ten thousand 10 ten thousands 1 hundred thousand T To move another column to the left what would be my next 10 times statement S 10 times 1 hundred thousand T Solve to find 10 times 1 hundred thousand Circulate and assist students as necessary T 10 hundred thousands can be bundled and represented as 1 million Title your column and write the multiplication sentence S Write 10 1 hundred thousand 10 hundred thousands 1 million After having built the place value chart by multiplying by ten quickly review the process simply moving from right to left on the place value chart and then reversing and moving left to right ZEARN MATH Teacher Edition 13
Topic A Lesson 2 YOUR NOTES G4M1 e g 2 tens times 10 equals 2 hundreds 2 hundreds times 10 equals 2 thousands 2 thousands divided by 10 equals 2 hundreds 2 hundreds divided by 10 equals 2 tens PROBLEM 2 Multiply multiple copies of one unit by 10 T Draw place value disks and write a multiplication sentence to show the value of 10 times 4 ten thousands T 10 times 4 ten thousands is S 40 ten thousands 4 hundred thousands T Write 10 4 ten thousands 40 ten thousands 4 hundred thousands Explain to your partner how you know this equation is true Repeat with 10 3 hundred thousands PROBLEM 3 Divide multiple copies of one unit by 10 T Write 2 thousands 10 What is the process for solving this division expression S Use a place value chart Represent 2 thousands on a place value chart Then change them for smaller units so we can divide T What would our place value chart look like if we changed each thousand for 10 smaller units S 20 hundreds 2 thousands can be changed to be 20 hundreds because 2 thousands and 20 hundreds are equal T Solve for the answer S 2 hundreds 2 thousands 10 is 2 hundreds because 2 thousands unbundled becomes 20 hundreds 20 hundreds divided by 10 is 2 hundreds 2 thousands 10 20 hundreds 10 2 hundreds Repeat with 3 hundred thousands 10 PROBLEM 4 Multiply and divide multiple copies of two different units by 10 T Draw place value disks to show 3 hundreds and 2 tens T Write 10 3 hundreds 2 tens Work in pairs to solve this expression I wrote 3 hundreds 2 tens in parentheses to show it is one number Circulate as students work Clarify that both hundreds and tens must be multiplied by 10 14 ZEARN MATH Teacher Edition
G4M1 T What is your product Topic A Lesson 2 YOUR NOTES S 3 thousands 2 hundreds T Write 10 3 hundreds 2 tens 3 thousands 2 hundreds How do we write this in standard form S 3 200 T Write 10 3 hundreds 2 tens 3 thousands 2 hundreds 3 200 T Write 4 ten thousands 2 tens 10 In this expression we have two units Explain how you will find your answer S We can use the place value chart again and represent the unbundled units and then divide Represent in the place value chart and record the number sentence 4 ten thousands 2 tens 10 4 thousands 2 ones 4 002 T Watch as I represent numbers in the place value chart to multiply or divide by ten instead of drawing disks Repeat with 10 4 thousands 5 hundreds and 7 hundreds 9 tens 10 MULTIPLE MEANS OF REPRESENTATION Scaffold student understanding of the place value pattern by recording the following sentence frames 10 1 one is 1 ten 10 1 ten is 1 hundred 10 1 hundred is 1 thousand 10 1 thousand is 1 ten thousand 10 1 ten thousand is 1 hundred thousand Students may benefit from speaking this pattern chorally Deepen understanding with prepared visuals ZEARN MATH Teacher Edition 15
Topic A Lesson 2 YOUR NOTES G4M1 Independent Digital Lesson Lesson 2 10 Times 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 16 ZEARN MATH Teacher Edition
G4M1 How did we use patterns to predict the increasing units on the place value chart up to 1 million Can you predict the unit that is 10 times 1 million 100 times 1 million What happens when you multiply a number by 10 1 ten thousand is what times 10 1 hundred thousand is what times 10 Gail said she noticed that when you multiply a number by 10 you shift the digits one place to the left and put a zero in the ones place Is she correct How can you use multiplication and division to describe the relationship between units on the place value chart Topic A Lesson 2 YOUR NOTES EXIT TICKET After today s lesson instruct students to complete the Exit Ticket A review of their Exit Ticket as well as continuously monitoring your Digital Reports can help you assess your students understanding of the concepts explored in today s lesson and plan more effectively for future lessons The questions from the Exit Ticket may be read aloud to the students Task 1 Fill in the blank to make a true number sentence Use standard form a 4 ten thousands 6 hundreds 10 b 8 thousands 2 tens 10 2 The Carson family saved up 39 580 for a new home The cost of their dream home is 10 times as much as they have saved How much does their dream home cost Answers 1 a 406 000 b 802 2 395 800 ZEARN MATH Teacher Edition 17
Topic A Lesson 2 Lesson Template G4M1 UNLABELED MILLIONS PLACE VALUE CHART CONCEPT EXPLORATION TEMPLATE 18 ZEARN MATH Teacher Edition
G4M1 Topic A Lesson 3 Lesson 3 YOUR NOTES Name numbers within 1 million by building understanding of the place value chart and placement of commas for naming base thousand units Warm Up FLUENCY PRACTICE Place Value and Value Materials T Unlabeled Millions Place Value Chart Lesson 2 Concept Exploration Template NOTE Reviewing and practicing place value skills in isolation prepares students for success in multiplying different place value units during today s Concept Exploration T Project the number 1 468 357 on a place value chart Underline the 5 Say the digit S 5 T Say the place value of the 5 S Tens T Say the value of 5 tens S 50 Repeat the process underlining 8 4 1 and 6 Base Ten Units NOTE This fluency activity bolsters students place value undestanding while reviewing multiplication concepts learned in Lessons 1 and 2 T Project 2 tens Say the number in standard form S 2 tens 20 Repeat for the following possible sequence 3 tens 9 tens 10 tens 11 tens 12 tens 19 tens 20 tens 30 tens 40 tens 80 tens 84 tens and 65 tens WORD PROBLEM The school library has 10 600 books The town library has 10 times as many books How many books does the town library have ZEARN MATH Teacher Edition 19
Topic A Lesson 3 G4M1 YOUR NOTES NOTE This Word Problem builds on the concept from Lesson 2 of determining 10 times as much as a number Concept Exploration Materials T Unlabeled Millions Place Value Chart Lesson 2 Concept Exploration Template S Personal white board Unlabeled Millions Place Value Chart Lesson 2 Concept Exploration Template NOTE Students will go beyond 1 million to establish a pattern within the base ten units INTRODUCTION Patterns of the base ten system T In the last lesson we extended the place value chart to 1 million Take a minute to label the place value headings on your place value chart Circulate and check all headings T Excellent Now talk with your partner about similarities and differences you see in those heading names S I notice some words repeat like ten hundred and thousand but ones appears once I notice the thousand unit repeats 3 times thousands ten thousands hundred thousands T That s right Beginning with thousands we start naming new place value units by how many one thousands ten thousands and hundred thousands we have What do you think the next unit might be called after 1 million S Ten millions T Extend chart to the ten millions And the next S Hundred millions T Extend chart again That s right Just like with thousands we name new units here in terms of how many one millions ten millions and hundred millions we have 10 hundred millions gets renamed as 1 billion Talk with your partner about what the next two place value units should be S Ten billions and hundred billions It works just like it does for thousands and millions 20 ZEARN MATH Teacher Edition
G4M1 PROBLEM 1 Placing commas in and naming numbers Topic A Lesson 3 YOUR NOTES This problem is optional T You ve noticed a pattern ones tens and hundreds one thousands ten thousands and hundred thousands one millions ten millions and hundred millions and so on We use commas to indicate this grouping of units taken 3 at a time For example ten billion would be written 10 000 000 000 T Write 608430325 Record this number and place the commas to show our groupings of units S Record the number and place the commas T Show 430 325 on a place value chart How many thousands are in this number S 430 T 430 what S 430 thousands T Correct We read this number as four hundred thirty thousand three hundred twenty five T Extend chart and show 608 430 325 How many millions are there in this number S 608 millions T Using what you know about our pattern in naming units talk with your partner about how to name this number S Six hundred eight million four hundred thirty thousand three hundred twenty five PROBLEM 2 Add to make 10 of a unit and bundling up to 1 million T What would happen if we combined 2 groups of 5 hundreds With your partner draw place value disks to solve Use the largest unit possible to express your answer S 2 groups of 5 hundreds equals 10 hundreds It would make 10 hundreds which can be bundled to make 1 thousand T Now solve for 5 thousands plus 5 thousands Bundle in order to express your answer using the largest unit possible S 5 thousands plus 5 thousands equals 10 thousands We can bundle 10 thousands to make 1 ten thousand T Solve for 4 ten thousands plus 6 ten thousands Express your answer using the largest unit possible S 4 ten thousands plus 6 ten thousands equals 10 ten thousands We can bundle 10 ten thousands to make 1 hundred thousand ZEARN MATH Teacher Edition 21
Topic A Lesson 3 YOUR NOTES G4M1 Continue renaming problems showing regrouping as necessary 3 hundred thousands 7 hundred thousands 23 thousands 4 ten thousands 43 ten thousands 11 thousands PROBLEM 3 10 times as many with multiple units T On your place value chart model 5 hundreds and 3 tens with place value disks What is 10 times 5 hundreds 3 tens S Show charts 5 thousands 3 hundreds T Model 10 times 5 hundreds 3 tens with digits on the place value chart Record your answer in standard form S Show 10 times 5 hundreds is 5 thousands and 10 times 3 tens is 3 hundreds as digits 5 300 T Check your partner s work and remind him of the comma s role in this number T Write 10 1 ten thousand 5 thousands 3 hundreds 9 ones solve this problem and write your answer in standard form With your partner S 10 15 309 153 090 MULTIPLE MEANS OF REPRESENTATION In this lesson students extend past 1 million to establish a pattern of ones tens and hundreds within each base ten unit thousands millions billions trillions Calculations in following lessons are limited to less than or equal to 1 million If students are not ready for this step omit establishing the pattern and internalize the units of the thousands period MULTIPLE MEANS OF REPRESENTATION Hide Zero Cards were used in 1st through 3rd grade and may be a helpful support to visualize the total amount of each unit For example in the number 3247 32 hundreds or 324 tens is easy to visualize when 3247 is written with Hide Zero cards In Grade 3 students understand 324 as 324 ones 32 tens 4 ones or 3 hundreds 2 tens 4 ones This flexible thinking allows for seeing simplifying strategies e g to solve 3247 623 rather than decompose 3 thousands students might subtract 6 hundreds from 32 hundreds 32 hundreds 6 hundreds 47 ones 23 ones is 26 hundreds and 24 ones or 2624 22 ZEARN MATH Teacher Edition
G4M1 Topic A Lesson 3 YOUR NOTES MULTIPLE MEANS OF ACTION AND EXPRESSION Scaffold partner talk with sentence frames such as I notice The place value headings are alike because The place value headings are not alike because The pattern I notice is I notice the units Independent Digital Lesson Lesson 3 Commas 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 23
Topic A Lesson 3 YOUR NOTES G4M1 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 does place value understanding and the role of commas help you to read the value in the millions period that is represented by the number of millions ten millions and hundred millions When might it be useful to omit commas Please refer to the notes on commas to guide your discussion 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 In the spaces provided write the following units in standard form Be sure to place commas where appropriate a 9 thousands 3 hundreds 4 ones b 6 ten thousands 2 thousands 7 hundreds 8 tens 9 ones c 1 hundred thousand 8 thousands 9 hundreds 5 tens 3 ones 24 ZEARN MATH Teacher Edition
G4M1 Topic A Lesson 3 2 Use digits or disks on the place value chart to write 26 thousands 13 hundreds millions hundred thousands ten thousands thousands hundreds tens YOUR NOTES ones How many thousands are in the number you have written Answers 1 a 9 304 b 62 789 c 108 953 2 27 300 accurately written 27 ZEARN MATH Teacher Edition 25
G4M1 Lesson 4 Topic A Lesson 4 YOUR NOTES Read and write multi digit numbers using base ten numerals number names and expanded form Warm Up FLUENCY PRACTICE Skip Counting NOTE Practicing skip counting on the number line builds a foundation for accessing higher order concepts throughout the year Direct students to skip count by fours forward and backward to 48 focusing on transitions crossing the ten Place Value Materials S Personal white board Unlabeled Millions Place Value Chart Lesson 2 Concept Exploration Template NOTE Reviewing and practicing place value skills in isolation prepares students for success in writing multi digit numbers in expanded form T Show 5 hundred thousands as place value disks and write the number below it on the place value chart S Draw 5 hundred thousands disks and write 500 000 below the chart T Say the number in unit form S 5 hundred thousands T Say it in standard form S 500 000 Continue for the following possible sequence 5 hundred thousands 3 ten thousands 5 hundred thousands 3 hundreds 5 ten thousands 3 hundreds 1 hundred thousand 3 hundreds 5 tens and 4 hundred thousands 2 ten thousands 5 tens 3 ones MULTIPLE MEANS OF REPRESENTATION Place value fluency supports language acquisition as it couples meaningful visuals with valuable practice speaking the standard and unit form of numbers to 1 million ZEARN MATH Teacher Edition 27
Topic A Lesson 4 YOUR NOTES G4M1 Numbers Expressed in Different Base Units Materials S Personal white board NOTE This fluency activity prepares students for success in writing multi digit numbers in expanded form Base Hundred Units T Project 3 hundreds Say the number in standard form S 300 Continue with a suggested sequence of 9 hundreds 10 hundreds 19 hundreds 21 hundreds 33 hundreds 30 hundreds 100 hundreds 200 hundreds 500 hundreds 530 hundreds 537 hundreds and 864 hundreds Base Thousand Units T Project 5 thousands Say the number in standard form S 5 000 Continue with a suggested sequence of 9 thousands 10 thousands 20 thousands 100 thousands 220 thousands and 347 thousands Base Ten Thousand Units T Project 7 ten thousands Say the number in standard form S 70 000 Continue with a suggested sequence of 9 ten thousands 10 ten thousands 12 ten thousands 19 ten thousands 20 ten thousands 30 ten thousands 80 ten thousands 81 ten thousands 87 ten thousands and 99 ten thousands Base Hundred Thousand Units T Project 3 hundred thousands Say the number in standard form S 300 000 Continue with a suggested sequence of 2 hundred thousands 4 hundred thousands 5 hundred thousands 7 hundred thousands 8 hundred thousands and 10 hundred thousands 28 ZEARN MATH Teacher Edition
G4M1 WORD PROBLEM Topic A Lesson 4 YOUR NOTES There are about forty one thousand Asian elephants and about four hundred seventy thousand African elephants left in the world About how many Asian and African elephants are left in total NOTE This Word Problem builds on Lesson 3 requiring students to name base thousand units It also builds from fluently adding and subtracting within 1000 Assist students by asking them to add using unit names similar to the example not the entire numbers as digits Concept Exploration Materials S Personal white board Unlabeled Millions Place Value Chart Lesson 2 Concept Exploration Template PROBLEM 1 Write a four digit number in expanded form This problem is optional T On your place value chart write 1 708 T What is the value of the 1 S 1 thousand T Record 1 000 under the thousands column What is the value of the 7 S 7 hundred T Record 700 under the hundreds column What value does the zero have S Zero Zero tens T What is the value of the 8 S 8 ones T Record 8 under the ones column What is the value of 1 000 and 700 and 8 S 1 708 T So 1 708 is the same as 1 000 plus 700 plus 8 T Record that as a number sentence S Write 1 000 700 8 1 708 ZEARN MATH Teacher Edition 29
Topic A Lesson 4 YOUR NOTES G4M1 PROBLEM 2 Write a five digit number in word form and expanded form T Now erase your values and write this number 27 085 T Show the value of each digit at the bottom of your place value chart S Write 20 000 7 000 80 and 5 T Why is there no term representing the hundreds S Zero stands for nothing Zero added to a number doesn t change the value T With your partner write an addition sentence to represent 27 085 S 20 000 7 000 80 5 27 085 T Now read the number sentence with me S Twenty thousand plus seven thousand plus eighty plus five equals twenty seven thousand eighty five T Write the number as you speak You said twenty seven thousand eighty five T What do you notice about where I placed a comma in both the standard form and word form S It is placed after 27 to separate the thousands in both the standard form and word form PROBLEM 3 Transcribe a number in word form to standard and expanded form Display two hundred seventy thousand eight hundred fifty T Read this number Students read Tell your partner how you can match the word form to the standard form S Everything you say you should write in words The comma helps to separate the numbers in the thousands from the numbers in the hundreds tens and ones T Write this number in your place value chart Now write this number in expanded form Tell your partner the number sentence S 200 000 plus 70 000 plus 800 plus 50 equals 270 850 Repeat with sixty four thousand three PROBLEM 4 Convert a number in expanded form to word and standard form Display 700 000 8 000 500 70 3 T Read this expression Students read Use digits to write this number in your place value chart T My sum is 78 573 Compare your sum with mine S Your 7 is in the wrong place The value of the 7 is 700 000 Your 7 has a value of 70 000 T Read this number in standard form with me 30 ZEARN MATH Teacher Edition
G4M1 Topic A Lesson 4 S Seven hundred eight thousand five hundred seventy three YOUR NOTES T Write this number in words Remember to check for correct use of commas and hyphens Repeat with 500 000 30 000 10 3 MULTIPLE MEANS OF ACTION AND EXPRESSION Scaffold student composition of number words with the following options Provide individual cards with number words that can be easily copied Allow students to abbreviate number words Allow multilingual learners their language of choice for expressing number words Independent Digital Lesson Lesson 4 What s Your Name 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 31
Topic A Lesson 4 YOUR NOTES G4M1 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 Two students discussed the importance of zero Nate said that zero is not important while Jill said that zero is extremely important Who is right Why do you think so What role can zero play in a number How is the expanded form related to the standard form of a number When might you use expanded form to solve a calculation EXIT TICKET After today s lesson instruct students to complete the Exit Ticket A review of their Exit Ticket as well as continuously monitoring your Digital Reports can help you assess your students understanding of the concepts explored in today s lesson and plan more effectively for future lessons The questions from the Exit Ticket may be read aloud to the students Task 1 Use the place value chart below to complete the following a Label the units on the chart b Write the number 800 000 6 000 300 2 in the place value chart c Write the number in word form 2 Write one hundred sixty thousand five hundred eighty two in expanded form Answers 1 a Units accurately labeled b 806 302 written in chart c Eight hundred six thousand three hundred two 2 100 000 60 000 500 80 2 32 ZEARN MATH Teacher Edition
G4M1 Topic B TOPIC B Comparing Multi Digit Whole Numbers In Topic B students use place value to compare whole numbers Initially using the place value chart students compare the value of each digit to surmise which number is of greater value Moving away from dependency on models and toward fluency with numbers students compare numbers by observing across the entire number and noticing value differences For example in comparing 12 566 to 19 534 it is evident 19 thousands is greater than 12 thousands because of the value of the digits in the thousands unit Additionally students continue with number fluency by finding what is 1 10 or 100 thousand more or less than a given number Objective Topic B Comparing Multi Digit Whole Numbers Lesson 5 Compare numbers based on meanings of the digits using
G4M1 Lesson 5 Topic B Lesson 5 YOUR NOTES Compare numbers based on meanings of the digits using
Topic B Lesson 5 YOUR NOTES G4M1 T State the value of the 3 S 3 000 T 4 S 400 Repeat for the following possible sequence 59 607 287 493 and 742 952 WORD PROBLEM Draw and label the units on the place value chart to hundred thousands Use each of the digits 9 8 7 3 1 and 0 once to create a number that is between 7 hundred thousands and 9 hundred thousands In word form write the number you created Extension Create two more numbers following the same directions as above NOTE This Word Problem builds on the content of Lesson 4 requiring students to read and write multi digit numbers in expanded word and unit forms Concept Exploration Materials S Personal white board Unlabeled Hundred Thousands Place Value Chart Concept Exploration Template PROBLEM 1 Comparing two numbers with the same largest unit Display 3 010 2 040 T Let s compare two numbers Say the standard form to your partner and model each number on your place value chart S Three thousand ten Two thousand forty T What is the name of the unit with the greatest value S Thousands T Compare the value of the thousands S 3 thousands is greater than 2 thousands 2 thousands is less than 3 thousands 36 ZEARN MATH Teacher Edition
G4M1 Topic B Lesson 5 T Tell your partner what would happen if we only compared tens rather than the unit with the greatest value YOUR NOTES S We would say that 2 040 is greater than 3 010 but that isn t right The number with more of the largest unit being compared is greater We don t need to compare the tens because the thousands are different T Thousands is our largest unit 3 thousands is greater than 2 thousands so 3 010 is greater than 2 040 Write the comparison symbol in the circle Write this comparison statement on your board and say it to your partner in two different ways S Write 3 010 2 040 3 010 is greater than 2 040 2 040 is less than 3 010 PROBLEM 2 Comparing two numbers with an equal amount of the largest units Display 43 021 45 302 T Model and read each number How is this comparison different from our first comparison S Before our largest unit was thousands Now our largest unit is ten thousands In this comparison both numbers have the same number of ten thousands T If the digits of the largest unit are equal how do we compare S We compare the thousands We compare the next largest unit We compare the digit one place to the right T Write your comparison statement on your board Say the comparison statement in two ways S Write 43 021 45 302 and 45 302 43 021 43 021 is less than 45 302 45 302 is greater than 43 021 Repeat the comparison process using 2 305 and 2 530 and then 970 461 and 907 641 T Write your own comparison problem for your partner to solve Create a two number comparison problem in which the largest unit in both numbers is the same PROBLEM 3 Comparing values of multiple numbers using a place value chart This problem is optional Display 32 434 32 644 and 32 534 T Write these numbers in your place value chart Whisper the value of each digit as you do so T When you compare the value of these three numbers what do you notice ZEARN MATH Teacher Edition 37
Topic B Lesson 5 YOUR NOTES G4M1 S All three numbers have 3 ten thousands All three numbers have 2 thousands We can compare the hundreds because they are different T Which number has the greatest value S 32 644 T Tell your partner which number has the least value and how you know S 32 434 is the smallest of the three numbers because it has the least number of hundreds T Write the numbers from greatest to least Use comparison symbols to express the relationships of the numbers S Write 32 644 32 534 32 434 PROBLEM 4 Comparing numbers in different number forms Display Compare 700 000 30 000 20 8 and 735 008 T Discuss with your partner how to solve and write your comparison S I will write the numerals in my place value chart to compare Draw disks for each number I ll write the first number in standard form and then compare S Write 730 028 735 008 T Tell your partner which units you compared and why S I compared thousands because the larger units were the same 5 thousands are greater than 0 thousands so 735 008 is greater than 730 028 Repeat with 4 hundred thousands 8 thousands 9 tens and 40 000 8 000 90 MULTIPLE MEANS OF REPRESENTATION Provide sentence frames for students to refer to when using comparative statements For example I notice I compared because is greater than because is less than because MULTIPLE MEANS OF ACTION AND EXPRESSION For students who have difficulty converting numbers from expanded form into standard form demonstrate using a place value chart to show how each number can be represented and then how the numbers can be added together Alternatively use place value cards known as Hide Zero cards in the primary grades to allow students to see the value of each digit that composes a number The cards help students manipulate and visually display both the expanded form and the standard form of any number 38 ZEARN MATH Teacher Edition
G4M1 Topic B Lesson 5 Independent Digital Lesson YOUR NOTES Lesson 5 or 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 When comparing numbers which is more helpful to you lining up digits or lining up place value disks in a place value chart Explain ZEARN MATH Teacher Edition 39
Topic B Lesson 5 YOUR NOTES G4M1 How does your understanding of place value help to compare and order numbers How can ordering numbers apply to real life What challenges arise in comparing numbers when the numbers are written in different forms EXIT TICKET After today s lesson instruct students to complete the Exit Ticket A review of their Exit Ticket as well as continuously monitoring your Digital Reports can help you assess your students understanding of the concepts explored in today s lesson and plan more effectively for future lessons The questions from the Exit Ticket may be read aloud to the students Task 1 Use each of the digits 5 4 3 2 1 exactly once to create two different five digit numbers a Write each number on the line and compare the two numbers using the symbols or Write the correct symbol in the circle b Use words to write a comparison statement for the problem above Answers 1 a Answers will vary b Answers will vary 40 ZEARN MATH Teacher Edition
G4M1 Topic B Lesson 5 Lesson Template UNLABELED HUNDRED THOUSANDS PLACE VALUE CHART CONCEPT EXPLORATION TEMPLATE ZEARN MATH Teacher Edition 41
G4M1 Lesson 6 Topic B Lesson 6 YOUR NOTES Find 1 10 and 100 thousand more and less than a given number Warm Up FLUENCY PRACTICE Unit Skip Counting NOTE This activity applies skip counting fluency to the multiplying by ten lessons T Count by threes to 30 S 3 6 9 12 15 18 21 24 27 30 T Now count by 3 ten thousands to 30 ten thousands Stop counting and raise your hand when you see me raise my hand S 3 ten thousands 6 ten thousands 9 ten thousands T S Raise hand T Say the number in standard form S 90 000 Continue stopping students at 15 ten thousands 21 ten thousands and 30 ten thousands Repeat the process This time count by fours to 40 and by 4 hundred thousands to 40 hundred thousands MULTIPLE MEANS OF ACTION AND EXPRESSION Before directing the students to count by 3 ten thousands direct them first to count by 3 cats Then direct them to count by 3 hundreds Finally bridge the directions to counting by 3 ten thousands Rename the Units Materials S Personal white board NOTE This fluency activity applies students place value skills in a new context that helps them better access the content in today s Concept Exploration T Write 54 783 Say the number S 54 783 T How many thousands are in 54 783 ZEARN MATH Teacher Edition 43
Topic B Lesson 6 YOUR NOTES G4M1 S 54 thousands T Write 54 783 the equation thousands ones On your personal white board fill in S Write 54 783 54 thousands 783 ones T How many ten thousands are in 54 783 S 5 ten thousands T Write 54 783 ten thousands board fill in the equation hundreds ones On your S Write 54 783 5 ten thousands 47 hundreds 83 ones Follow the same process and sequence for 234 673 Compare Numbers Materials S Personal white board NOTE This fluency activity reviews comparing number concepts learned in Lesson 5 T Write 231 005 83 872 On your personal white board compare the numbers by writing the greater than less than or equal to symbol S Write 231 005 83 872 Repeat using the following sequence 6 thousands 4 hundreds 9 tens 4 hundreds 9 ones and 8 hundred thousands 7 thousands 8 hundreds 2 tens 5 ten thousands 807 820 WORD PROBLEM Use the digits 5 6 8 2 4 and 1 to create two six digit numbers Be sure to use each of the digits within both numbers Express the numbers in word form and use a comparison symbol to show their relationship NOTE This Word Problem builds on Lesson 4 and 5 Concept Exploration Materials T Unlabeled Hundred Thousands Place Value Chart Lesson 5 Concept Exploration Template S Personal white board Unlabeled Hundred Thousands Place Value Chart Lesson 5 Concept Exploration Template 44 ZEARN MATH Teacher Edition
G4M1 PROBLEM 1 Find 1 thousand more and 1 thousand less Topic B Lesson 6 YOUR NOTES T Draw 2 thousands disks in the place value chart How many thousands do you count S Two thousands T What number is one thousand more Draw 1 more thousand S Three thousands T Write 3 thousands 112 ones Model this number with disks and write its expanded and standard form S Write 3 000 100 10 2 3 112 T Draw 1 more unit of one thousand What number is 1 thousand more than 3 112 S 4 112 is 1 thousand more than 3 112 T 1 thousand less than 3 112 S 2 112 T Draw 1 ten thousands disk What number do you have now S 14 112 T Show 1 less unit of 1 thousand What number is 1 thousand less than 14 112 S 13 112 T 1 thousand more than 14 112 S 15 112 T Did the largest unit change Discuss with your partner S Discuss T Show 19 112 Pause as students draw What is 1 thousand less 1 thousand more than 19 112 S 18 112 20 112 T Did the largest unit change Discuss with your partner S Discuss T Show 199 465 Pause as they do so What is 1 thousand less 1 thousand more than 199 465 S 198 465 200 465 T Did the largest unit change Discuss with your partner S Discuss PROBLEM 2 Find 10 thousand more and 10 thousand less T Use numbers and disks to model 2 ten thousands 3 thousands Read and write the expanded form S Model read and write 20 000 3 000 23 000 ZEARN MATH Teacher Edition 45
Topic B Lesson 6 YOUR NOTES G4M1 T What number is 10 thousand more than 2 ten thousands 3 thousands Draw read and write the expanded form S Model read and write 20 000 10 000 3 000 33 000 T Display 100 000 30 000 4 000 Use disks and numbers to model the sum What number is 10 thousand more than 134 000 Say your answer as an addition sentence S 10 000 plus 134 000 is 144 000 T Display 25 130 10 000 What number is 10 thousand less than 25 130 Work with your partner to use numbers and disks to model the difference Write and whisper to your partner an equation in unit form to verify your answer S Model read and write 2 ten thousands 5 thousands 1 hundred 3 tens minus 1 ten thousand is 1 ten thousand 5 thousands 1 hundred 3 tens PROBLEM 3 Find 100 thousand more and 100 thousand less T Display 200 352 Work with your partner to find the number that is 100 thousand more than 200 352 Write an equation to verify your answer S Write 200 352 100 000 300 352 T Display 545 000 and 445 000 and 345 000 Read these three numbers to your partner Predict the next number in my pattern and explain your reasoning S I predict the next number will be 245 000 I notice the numbers decrease by 100 000 345 000 minus 100 000 is 245 000 I notice the hundred thousand units decreasing 5 hundred thousands 4 hundred thousands 3 hundred thousands I predict the next number will have 2 hundred thousands I notice the other units do not change so the next number will be 2 hundred thousands 4 ten thousands 5 thousands MULTIPLE MEANS OF ENGAGEMENT After students predict the next number in the pattern ask students to create their own pattern using the strategy of one thousand more or less ten thousand more or less or one hundred thousand more or less Then ask students to challenge their classmates to predict the next number in the pattern Independent Digital Lesson Lesson 6 Pattern Spotter 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 46 ZEARN MATH Teacher Edition
G4M1 Topic B Lesson 6 There are no notes for this digital lesson Go online to see the full digital lesson 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 does your understanding of place value help you add or subtract 1 000 10 000 and 100 000 What place value patterns have we discovered 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 Fill in the empty boxes to complete the pattern 468 235 471 235 472 235 Explain in pictures numbers or words how you found your answers 2 Fill in the blank for each equation a 1 000 56 879 b 324 560 100 000 c 456 080 10 000 d 10 000 786 233 ZEARN MATH Teacher Edition 47
Topic B Lesson 6 YOUR NOTES G4M1 3 The population of Rochester NY in the 2000 Census was 219 782 The 2010 Census found that the population decreased by about 10 000 About how many people lived in Rochester in 2010 Explain in pictures numbers or words how you found your answer Answers 1 469 235 470 235 473 235 explanations will vary 2 a 57 879 b 224 560 c 446 080 d 796 233 3 209 782 explanations will vary 48 ZEARN MATH Teacher Edition
G4M1 Topic C TOPIC C Rounding Multi Digit Whole Numbers In Topic C students round to any place using the vertical number line and approximation The vertical number line allows students to line up place values of the numbers they are comparing In Grade 3 students rounded to the nearest 10 or 100 using place value understanding Now they extend this understanding rounding to the nearest thousand ten thousand and hundred thousand Uniformity in the base ten system easily transfers understanding from Grade 3 to Grade 4 standard Rounding to the leftmost unit is easiest for students but Grade 4 students learn the advantages to rounding to any place value which increases accuracy Students move from dependency on the number line and learn to round a number to a particular unit To round 34 108 to the nearest thousand students find the nearest multiple 34 000 or 35 000 by seeing if 34 108 is more than or less than halfway between the multiples The final lesson of Topic C presents complex and real world examples of rounding including instances where the number requires rounding down but the context requires rounding up Objective Topic C Rounding Multi Digit Whole Numbers Lesson 7 Round multi digit numbers to the thousands place using the vertical number line Lesson 8 Round multi digit numbers to any place using the vertical number line Lesson 9 Use place value understanding to round multi digit numbers to any place value Lesson 10 Use place value understanding to round multi digit numbers to any place value using real world applications ZEARN MATH Teacher Edition 49
G4M1 Topic C Lesson 7 Lesson 7 YOUR NOTES Round multi digit numbers to the thousands place using the vertical number line Warm Up FLUENCY PRACTICE Change Place Value Materials S Personal white board Unlabeled Hundred Thousands Place Value Chart Lesson 5 Concept Exploration Template NOTE This fluency activity reviews Lesson 6 s content T Project place value chart Write 3 hundred thousands 5 ten thousands 2 thousands 1 hundred 5 tens and 4 ones On your personal white board draw place value disks and write the numbers beneath it S Draw disks and write 352 154 T Show 100 more S Draw 1 more 100 disk erase the number 1 in the hundreds place and replace it with a 2 so that their boards now read 352 254 Possible further sequence 10 000 less 100 000 more 1 less and 10 more Repeat with the following 7 385 297 084 and 306 032 Number Patterns Materials S Personal white board NOTE This activity synthesizes skip counting fluency with Lesson 6 s content and applies it in a context that lays a foundation for rounding multi digit numbers to the thousands place T Project 50 300 60 300 70 300 What is the place value of the digit that s changing S Ten thousand T Count with me saying the value of the digit I m pointing to Point at the ten thousand digit as students count S 50 000 60 000 70 000 T On your personal board write what number would come after 70 300 S Write 80 300 ZEARN MATH Teacher Edition 51
G4M1 Topic C Lesson 7 YOUR NOTES Repeat for the following possible sequence using place value disks if students are struggling 92 010 82 010 72 010 135 004 136 004 137 004 832 743 832 643 832 543 271 543 281 543 291 543 Find the Midpoint Materials S Personal white board NOTE Practicing this skill in isolation lays a foundation to conceptually understand rounding on a vertical number line and reviews Grade 3 skills in anticipation of today s Concept Exploration Project a vertical number line with endpoints 10 and 20 T What s halfway between 10 and 20 S 15 T Write 15 halfway between 10 and 20 Draw a second line with 1 000 and 2 000 as the endpoints How many hundreds are in 1 000 S 10 hundreds T Below 1 000 write 10 hundreds How many hundreds are in 2 000 S 20 hundreds T Write 20 hundreds below 2 000 What s halfway between 10 hundreds and 20 hundreds S 15 hundreds T Write 1 500 halfway between 1 000 and 2 000 Below 1 500 write 15 hundreds On your personal board draw a vertical number line with two endpoints and a midpoint S Draw number line with two endpoints and a midpoint T Label 31 000 and 32 000 as endpoints S Label 31 000 and 32 000 as endpoints T How many hundreds are in 31 000 S 310 hundreds T How many hundreds are in 32 000 S 320 hundreds T Identify the midpoint S Write 31 500 Repeat the process and procedure to find the midpoint of 831 000 and 832 000 63 000 and 64 000 264 000 and 265 000 and 99 000 and 100 000 52 ZEARN MATH Teacher Edition
G4M1 WORD PROBLEM Topic C Lesson 7 YOUR NOTES According to their pedometers Mrs Alsup s class took a total of 42 619 steps on Tuesday On Wednesday they took ten thousand more steps than they did on Tuesday On Thursday they took one thousand fewer steps than they did on Wednesday How many steps did Mrs Alsup s class take on Thursday NOTE This Word Problem builds on Lesson 6 requiring students to find 1 thousand 10 thousand or 100 thousand more or less than a given number Concept Exploration Materials S Personal white board PROBLEM 1 Use a vertical number line to round four digit numbers to the nearest thousand T Draw a vertical number line with 2 endpoints We are going to round 4 100 to the nearest thousand How many thousands are in 4 100 S 4 thousands T Mark the lower endpoint with 4 thousands And 1 more thousand would be S 5 thousands T Mark the upper endpoint with 5 thousands What s halfway between 4 thousands and 5 thousands S 4 500 T Label 4 500 on the number line Where should I label 4 100 Tell me where to stop Move your marker up the line ZEARN MATH Teacher Edition 53
G4M1 Topic C Lesson 7 YOUR NOTES S Stop T Label 4 100 on the number line Is 4 100 nearer to 4 thousands or 5 thousands S 4 100 is nearer to 4 thousands T True We say 4 100 rounded to the nearest thousand is 4 000 T Label 4 700 on the number line What about 4 700 S 4 700 is nearer to 5 thousands T Therefore we say 4 700 rounded to the nearest thousand is 5 000 PROBLEM 2 Use a vertical number line to round five and six digit numbers to the nearest thousand T Let s round 14 500 to the nearest thousand How many thousands are there in 14 500 S 14 thousands T What s 1 more thousand S 15 thousands T Designate the endpoints on your number line What is halfway between 14 000 and 15 000 S 14 500 Hey that s the number that we are trying to round to the nearest thousand T True 14 500 is right in the middle It is the halfway point It is not closer to either number The rule is that we round up 14 500 rounded to the nearest thousand is 15 000 T With your partner mark 14 990 on your number line and round it to the nearest thousand S 14 990 is nearer to 15 thousands or 15 000 T Mark 14 345 on your number line Talk with your partner about how to round it to the nearest thousand S 14 345 is nearer to 14 thousands 14 345 is nearer to 14 000 14 345 rounded to the nearest thousand is 14 000 T Is 14 345 greater than or less than the halfway point S Less than T We can look to see if 14 345 is closer to 14 000 or 15 000 and we can also look to see if it is greater than or less than the halfway point If it is less than the halfway point it is closer to 14 000 Repeat using the numbers 215 711 and 214 569 Round to the nearest thousand and name how many thousands are in each number MULTIPLE MEANS OF REPRESENTATION For those students who have trouble conceptualizing halfway demonstrate halfway using students as models 54 ZEARN MATH Teacher Edition
G4M1 Topic C Lesson 7 Two students represent the thousands A third student represents halfway A fourth student represents the number being rounded Use the discussion questions Where do they belong To whom are they nearer To which number would they round YOUR NOTES Independent Digital Lesson Lesson 7 Round and Round Students also learn the concepts from this lesson in the Independent Digital Lesson The intentional balance of learning with teachers and peers and learning independently in digital lessons ensures every student has multiple opportunities to represent engage with and express their math reasoning See the digital lesson notes below for a glimpse of the paper to pencil transfer of these math ideas Go online to see the full digital lesson ZEARN MATH Teacher Edition 55
G4M1 Topic C Lesson 7 YOUR NOTES Wrap Up LESSON SYNTHESIS Guide students in a conversation to process today s lesson and surface any misconceptions or misunderstandings The questions below may be used to lead the discussion What makes 5 special in rounding How does the number line help you round numbers Is there another way you prefer Why What is the purpose of rounding When might we use rounding or estimation 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 Round to the nearest thousand Use the number line to model your thinking a 7 621 b 12 502 c 324 087 2 It takes 39 090 gallons of water to manufacture a new car Sammy thinks that rounds up to about 40 000 gallons Susie thinks it is about 39 000 gallons Who rounded to the nearest thousand Sammy or Susie Use pictures numbers or words to explain Answers 1 a 8 000 b 13 000 c 324 000 2 Susie explanations will vary 56 ZEARN MATH Teacher Edition
G4M1 Topic C Lesson 8 Lesson 8 YOUR NOTES Round multi digit numbers to any place using the vertical number line Warm Up FLUENCY PRACTICE Rename the Units Materials S Personal white board NOTE This fluency activity applies students place value skills in a new context that helps them better access today s Concept Exploration T Write 357 468 Say the number S 357 468 T Write 357 468 equation thousands 468 ones On your personal white boards fill in the S Write 357 468 357 thousands 468 ones Repeat process for 357 468 ten thousands 7 468 ones 357 468 hundreds 6 tens 8 ones and 357 468 tens 8 ones WORD PROBLEM Jose s parents bought a used car a new motorcycle and a used snowmobile The car cost 8 999 The motorcycle cost 9 690 The snowmobile cost 4 419 About how much money did they spend on the three items NOTE This Word Problem builds on the content of previous lessons Students are required to round and then to add base thousand units ZEARN MATH Teacher Edition 57
Topic C Lesson 8 YOUR NOTES G4M1 Concept Exploration Materials S Personal white board PROBLEM 1 Use a vertical number line to round five and six digit numbers to the nearest ten thousand This problem is optional Display a number line with endpoints 70 000 and 80 000 T We are going to round 72 744 to the nearest ten thousand How many ten thousands are in 72 744 S 7 ten thousands T Mark the lower endpoint with 7 ten thousands And 1 more ten thousand would be S 8 ten thousands T Mark the upper endpoint with 8 ten thousands What s halfway between 7 ten thousands and 8 ten thousands S 7 ten thousands 5 thousands 75 000 T Mark 75 000 on the number line Where should I label 72 744 Tell me where to stop Move your marker up the line S Stop T Mark 72 744 on the number line T Is 72 744 nearer to 70 000 or 80 000 S 72 744 is nearer to 70 000 T We say 72 744 rounded to the nearest ten thousand is 70 000 Repeat with 337 601 rounded to the nearest ten thousand PROBLEM 2 Use a vertical number line to round six digit numbers to the nearest hundred thousand This problem is optional T Draw a number line to round 749 085 to the nearest hundred thousand We are going to round 749 085 to the nearest hundred thousand How many hundred thousands are in 749 085 S 7 hundred thousands 58 ZEARN MATH Teacher Edition
G4M1 T What s 1 more hundred thousand Topic C Lesson 8 YOUR NOTES S 8 hundred thousands T Label your endpoints on the number line What is halfway between 7 hundred thousands and 8 hundred thousands S 7 hundred thousands 5 ten thousands 750 000 T Designate the midpoint on the number line With your partner mark 749 085 on the number line and round it to the nearest hundred thousand S 749 085 is nearer to 7 hundred thousands 749 085 is nearest to 700 000 749 085 rounded to the nearest hundred thousand is 700 000 Repeat with 908 899 rounded to the nearest hundred thousand PROBLEM 3 Estimating with addition and subtraction T Write 505 341 193 841 Without finding the exact answer I can estimate the answer by first rounding each addend to the nearest hundred thousand and then adding the rounded numbers T Use a number line to round both numbers to the nearest hundred thousand S Round 505 341 to 500 000 Round 193 841 to 200 000 T Now add 500 000 200 000 S 700 000 T So what s a good estimate for the sum of 505 341 and 193 841 S 700 000 T Write 35 555 26 555 How can we use rounding to estimate the answer S Let s round each number before we subtract T Good idea Discuss with your partner how you will round to estimate the difference S I can round each number to the nearest ten thousand That way I ll have mostly zeros in my numbers 40 000 minus 30 000 is 10 000 35 555 minus 26 555 is like 35 minus 26 which is 9 35 000 minus 26 000 is 9 000 It s more accurate to round up 36 000 minus 27 000 is 9 000 Hey it s the same answer T What did you discover S It s easier to find an estimate rounded to the largest unit We found the same estimate even though you rounded up and I rounded down We got two different estimates T Which estimate do you suppose is closer to the actual difference S I think 9 000 is closer because we changed fewer numbers when we rounded T How might we find an estimate even closer to the actual difference S We could round to the nearest hundred or ten ZEARN MATH Teacher Edition 59
Topic C Lesson 8 YOUR NOTES G4M1 MULTIPLE MEANS OF REPRESENTATION An effective scaffold when working in the thousands period is to first work with an analogous number in the ones period For example before rounding 72 744 to the nearest ten thousand in Problem 1 lead students through a discussion around rounding 72 to the nearest ten Ask students to consider how one could support the other T Let s round 72 to the nearest ten T How many tens are in 72 S 7 tens T What is 1 more ten S 8 tens T 7 tens and 8 tens are the endpoints of my number line T What is the value of the halfway point S 7 tens 5 ones Seventy five T Tell me where to stop on my number line Start at 70 and move up S 7 tens S Stop T Is 72 less than halfway or more than halfway to 8 tens or 80 S Less than halfway T We say 72 rounded to the nearest ten is 70 T We use the exact same process when rounding 72 thousand to the nearest ten thousand MULTIPLE MEANS OF ENGAGEMENT Make the lesson relevant to students lives Discuss everyday instances of estimation Elicit examples of when a general idea about a sum or difference is necessary rather than an exact answer Ask When is it appropriate to estimate When do we need an exact answer Independent Digital Lesson Lesson 8 Oh the Places You ll Round Students also learn the concepts from this lesson in the Independent Digital Lesson The intentional balance of learning with teachers and peers and learning independently in digital lessons ensures every student has multiple opportunities to represent engage with and express their math reasoning See the digital lesson notes below for a glimpse of the paper to pencil transfer of these math ideas Go online to see the full digital lesson 60 ZEARN MATH Teacher Edition
G4M1 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 questions below may be used to lead the discussion Tell your partner your steps for rounding a number Which step is most difficult for you Why Write and complete one of the following statements in your math journal The purpose of rounding addends is Rounding to the nearest is best when 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 61
Topic C Lesson 8 YOUR NOTES G4M1 Task 1 Round to the nearest ten thousand Use the number line to model your thinking a 35 124 b 981 657 2 Round to the nearest hundred thousand Use the number line to model your thinking a 89 678 b 999 765 3 Estimate the sum by rounding each number to the nearest hundred thousand 257 098 548 765 Answers 1 a 40 000 number line accurately models work b 980 000 number line accurately models work 2 a 100 000 number line accurately models work b 1 000 000 number line accurately models work 3 800 000 62 ZEARN MATH Teacher Edition
G4M1 Topic C Lesson 9 Lesson 9 YOUR NOTES Use place value understanding to round multi digit numbers to any place value Warm Up FLUENCY PRACTICE Multiply by Ten Materials S Personal white board NOTE This fluency activity deepens the students foundation of multiplying by ten T Write 10 10 Say the multiplication sentence S 10 10 100 T Write 10 ten 100 On your personal white boards fill in the blank S Write 10 1 ten 100 T Write ten ten 100 On your boards fill in the blanks S Write 1 ten 1 ten 100 T Write ten fill in the blanks ten hundred On your boards S Write 1 ten 1 ten 1 hundred Repeat process for possible sequence 1 ten 20 1 ten 700 and 4 tens 1 ten 1 ten 40 hundreds hundreds NOTE The use of the digit or a unit is intentional It builds understanding of multiplying by different units 6 ones times 1 ten equals 6 tens so 6 tens times 1 ten equals 6 hundreds not 6 tens Round to Different Place Values Materials S Personal white board NOTE This fluency activity reviews Lesson 8 s objective and lays a foundation for today s Concept Exploration T Write 63 941 Say the number S 63 941 T Round 63 941 to the nearest ten thousand Between what 2 ten thousands is 63 941 ZEARN MATH Teacher Edition 63
Topic C Lesson 9 YOUR NOTES G4M1 S 6 ten thousands and 7 ten thousands T On your boards draw a vertical number line with 60 000 and 70 000 as endpoints S Draw a vertical number line with 60 000 and 70 000 as the endpoints T What s halfway between 60 000 and 70 000 S 65 000 T Label 65 000 as the midpoint on your number line Label 63 941 on your number line S Label 63 941 below 65 000 on their number lines T Write 63 941 ten thousand On your boards fill in the blank rounding 63 941 to the nearest S Write 63 941 60 000 Repeat process for 63 941 rounded to the nearest thousand 47 261 rounded to the nearest ten thousand 47 261 rounded to the nearest thousand 618 409 rounded to the nearest hundred thousand 618 409 rounded to the nearest ten thousand and 618 409 rounded to the nearest thousand WORD PROBLEM 34 123 people attended a basketball game 28 310 people attended a football game About how many more people attended the basketball game than the football game Round to the nearest ten thousand to find the answer Does your answer make sense What might be a better way to compare attendance NOTE The Word Problem builds on the concept learned in Lesson 8 Students are required to round and then to subtract using base thousand units Students have not practiced an algorithm for subtracting with five digits Due to the rounded numbers you may show subtraction using unit form as an alternative method 34 thousand 28 thousand instead of 34 000 28 000 64 ZEARN MATH Teacher Edition
G4M1 Topic C Lesson 9 Concept Exploration YOUR NOTES Materials S Personal white board PROBLEM 1 Rounding to the nearest thousand without using a number line This problem is optional T Write 4 333 Round to the nearest thousand Between what two thousands is 4 333 S 4 thousands and 5 thousands T What is halfway between 4 000 and 5 000 S 4 500 T Is 4 333 less than or more than halfway S Less than T So 4 333 is nearer to 4 000 T Write 18 753 Round to the nearest thousand Tell your partner between what two thousands 18 753 is located S 18 thousands and 19 thousands T What is halfway between 18 thousands and 19 thousands S 18 500 T Round 18 753 to the nearest thousand Tell your partner if 18 753 is more than or less than halfway S 18 753 is more than halfway 18 753 is nearer to 19 000 18 753 rounded to the nearest thousand is 19 000 Repeat with 346 560 rounded to the nearest thousand PROBLEM 2 Rounding to the nearest ten thousand or hundred thousand without using a vertical line This problem is optional T Write 65 600 thousands is 65 600 Round to the nearest ten thousand Between what two ten S 6 ten thousands and 7 ten thousands T What is halfway between 60 000 and 70 000 S 65 000 ZEARN MATH Teacher Edition 65
Topic C Lesson 9 YOUR NOTES G4M1 T Is 65 600 less than or more than halfway S 65 600 is more than halfway T Tell your partner what 65 600 is when rounded to the nearest ten thousand S 65 600 rounded to the nearest ten thousand is 70 000 Repeat with 676 000 rounded to the nearest ten thousand T Write 676 000 Round 676 000 to the nearest hundred thousand First tell your partner what your endpoints will be S 600 000 and 700 000 T Determine the halfway point S 650 000 T Is 676 000 greater than or less than the halfway point S Greater than T Tell your partner what 676 000 is when rounded to the nearest hundred thousand S 676 000 rounded to the nearest hundred thousand is 700 000 T Write 203 301 hundred thousand Work with your partner to round 203 301 to the nearest T Explain to your partner how we use the midpoint to round without a number line S We can t look at a number line so we have to use mental math to find our endpoints and halfway point If we know the midpoint we can see if the number is greater than or less than the midpoint When rounding the midpoint helps determine which endpoint the rounded number is closer to PROBLEM 3 Rounding to any value without using a number line T Write 147 591 Whisper read this number to your partner in standard form Now round 147 591 to the nearest hundred thousand S 100 000 T Excellent Write 147 591 100 000 Point to 100 000 100 000 has zero ones in the ones place zero tens in the tens place zero hundreds in the hundreds place zero thousands in the thousands place and zero ten thousands in the ten thousands place I could add subtract multiply or divide with this rounded number much easier than with 147 591 True But what if I wanted a more accurate estimate Give me a number closer to 147 591 that has point a zero in the ones tens hundreds and thousands S 150 000 T Why not 140 000 S 147 591 is closer to 150 000 because it is greater than the halfway point 145 000 T Great 147 591 rounded to the nearest ten thousand is 150 000 Now let s round 147 591 to the nearest thousand 66 ZEARN MATH Teacher Edition
G4M1 Topic C Lesson 9 S 148 000 YOUR NOTES T Work with your partner to round 147 591 to the nearest hundred and then the nearest ten S 147 591 rounded to the nearest hundred is 147 600 147 591 rounded to the nearest ten is 147 590 T Compare estimates of 147 591 after rounding to different units What do you notice When might it be better to round to a larger unit When might it be better to round to a smaller unit S Discuss MULTIPLE MEANS OF REPRESENTATION In Problem 1 students who have difficulty visualizing 4 333 as having 4 thousands 3 hundreds could benefit from writing the number on their place value chart In doing so they will be able to see that 4 333 has 43 hundreds This strategy can be used throughout the Concept Exploration MULTIPLE MEANS OF ENGAGEMENT Challenge students who finish early to look at the many ways that they rounded the number 147 591 to different place values Have them discuss with a partner what they notice about the rounded numbers Students should notice that when rounding to the hundred thousands the answer is 100 000 but when rounding to all of the other places the answers are closer to 150 000 Have them discuss what this can teach them about rounding Independent Digital Lesson Lesson 9 Round 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 ZEARN MATH Teacher Edition 67
Topic C Lesson 9 YOUR NOTES G4M1 Wrap Up LESSON SYNTHESIS Guide students in a conversation to process today s lesson and surface any misconceptions or misunderstandings The questions below may be used to lead the discussion How is rounding without a number line easier How is it more challenging How does knowing how to round mentally assist you in everyday life What strategy do you use when observing a number to be rounded 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 Round 765 903 to the given place value Thousand Ten thousand Hundred thousand 2 There are 16 850 Star coffee shops around the world Round the number of shops to the nearest thousand and ten thousand Which answer is more accurate Explain your thinking using pictures numbers or words Answers 1 766 000 770 000 800 000 2 17 000 20 000 explanations will vary 68 ZEARN MATH Teacher Edition
G4M1 Topic C Lesson 10 Lesson 10 YOUR NOTES Use place value understanding to round multi digit numbers to any place value using real world applications Warm Up FLUENCY PRACTICE Multiply by 10 Materials S Personal white board NOTE This fluency activity deepens student understanding of base ten units T Write 10 10 Say the multiplication sentence S 10 10 100 T Write ten 10 100 On your personal white boards fill in the blank S Write 1 ten 10 100 T Write ten ten 100 On your boards fill in the blanks S Write 1 ten 1 ten 100 T Write ten ten hundred On your boards fill in the blanks S Write 1 ten 1 ten 1 hundred Repeat using the following sequence 1 ten 50 1 ten 600 and 3 tens 1 ten 1 ten 80 hundreds hundreds NOTE Watch for students who say 3 tens 4 tens is 12 tens rather than 12 hundreds WORD PROBLEM The post office sold 204 789 stamps last week and 93 061 stamps this week About how many more stamps did the post office sell last week than this week Explain how you got your answer NOTE This Word Problem builds on Lesson 9 rounding multi digit numbers to any place value and creates a bridge to the objective of today s Concept Exploration rounding using real world applications ZEARN MATH Teacher Edition 69
Topic C Lesson 10 YOUR NOTES G4M1 Concept Exploration Materials S Personal white board PROBLEM 1 Round one number to multiple units T Write 935 292 Read it to your partner and round to the nearest hundred thousand S 900 000 T It is 900 000 when we round to the largest unit What s the next largest unit we might round to S Ten thousands T Round to the ten thousands Then round to the thousands S 940 000 935 000 T What changes about the numbers when rounding to smaller and smaller units Discuss with your partner S When you round to the largest unit every other place will have a zero Rounding to the largest unit gives you the easiest number to add subtract multiply or divide As you round to smaller units there are not as many zeros in the number Rounding to smaller units gives an estimate that is closer to the actual value of the number PROBLEM 2 Determine the best estimate to solve a word problem Display In the year 2012 there were 935 292 visitors to the White House T Let s read together Assume that each visitor is given a White House map Now use this information to predict the number of White House maps needed for visitors in 2013 Discuss with your partner how you made your estimate S I predict 940 000 maps are needed I rounded to the nearest ten thousands place in order to make sure every visitor has a map It is better to have more maps than not enough maps I predict more people may visit the White House in 2013 so I rounded to the nearest ten thousand 940 000 the only estimate that is greater than the actual number Display In the year 2011 there were 998 250 visitors to the White House T Discuss with your partner how these data may change your estimate S These data show the number of visitors decreased from 2011 to 2012 It may be wiser to predict 935 000 or 900 000 maps needed for 2013 T How can you determine the best estimate in a situation S I can notice patterns or find data that might inform my estimate 70 ZEARN MATH Teacher Edition
G4M1 Topic C Lesson 10 PROBLEM 3 Choose a unit of rounding to solve a word problem YOUR NOTES Display 2 837 students attend Lincoln Elementary school T Discuss with your partner how you would estimate the number of chairs needed in the school S I would round to the nearest thousand for an estimate of 3 000 chairs needed If I rounded to the nearest hundred 2 800 some students may not have a seat I disagree 3 000 is almost 200 too many I would round to the nearest hundred because some students might be absent T Compare the effect of rounding to the largest unit in this problem and Problem 2 S In Problem 2 rounding to the largest unit resulted in a number less than the actual number By contrast when we rounded to the largest unit in Problem 3 our estimate was greater T What can you conclude S Rounding to the largest unit may not always be a reliable estimate I will choose the unit based on the situation and what is most reasonable MULTIPLE MEANS OF REPRESENTATION Define words or experiences that may be challenging for students to understand Provide an alternate example using a more familiar reference to better to connect to your students MULTIPLE MEANS OF ENGAGEMENT If students are ready for a challenge prompt them to think of at least two situations similar to that of Problem 3 where choosing the unit to which to round is important to the outcome of the problem Have them share and discuss Independent Digital Lesson Lesson 10 Round the World 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 71
Topic C Lesson 10 G4M1 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 you choose a best estimate What is the advantage of rounding to smaller and larger units Why might you round up even though the numbers tell you to round down 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 72 ZEARN MATH Teacher Edition
G4M1 Topic C Lesson 10 Task YOUR NOTES 1 There are 598 500 Apple employees in the United States a Round the number of employees to the given place value Thousand Ten thousand Hundred thousand b Explain why two of your answers are the same 2 A company developed a student survey so that students could share their thoughts about school In 2011 78 234 students across the United States were administered the survey In 2012 the company planned to administer the survey to 10 times as many students as were surveyed in 2011 About how many surveys should the company have printed in 2012 Explain how you found your answer Answers 1 a 599 000 600 000 600 000 b Explanations will vary 2 Answers and explanations will vary ZEARN MATH Teacher Edition 73
G4M1 Topic D TOPIC D Multi Digit Whole Number Addition Moving away from special strategies for addition students develop fluency with the standard addition algorithm Students compose larger units to add like base ten units such as composing 10 hundreds to make 1 thousand and working across the numbers unit by unit ones with ones thousands with thousands Recording of regrouping occurs on the line under the addends as shown to the right For example in the ones column students do not record the 0 in the ones column and the 1 above the tens column instead students record 10 writing the 1 under the tens column and then a 0 in the ones column They practice and apply the algorithm within the context of word problems and assess the reasonableness of their answers using rounding When using tape diagrams to model word problems students use a variable to represent the unknown quantity Objective Topic D Multi Digit Whole Number Addition Lesson 11 Use place value understanding to fluently add multi digit whole numbers using the standard addition algorithm and apply the algorithm to solve word problems using tape diagrams Lesson 12 Solve multi step word problems using the standard addition algorithm modeled with tape diagrams and assess the reasonableness of answers using rounding 74 ZEARN MATH Teacher Edition
G4M1 Topic D Lesson 11 Lesson 11 YOUR NOTES Use place value understanding to fluently add multi digit whole numbers using the standard addition algorithm and apply the algorithm to solve word problems using tape diagrams Warm Up FLUENCY PRACTICE Round to Different Place Values Materials S Personal white board NOTE This fluency activity reviews rounding skills that are building toward understanding T Write 3 941 Say the number We are going to round this number to the nearest thousand T How many thousands are in 3 941 S 3 thousands T Label the lower endpoint of a vertical number line with 3 000 And 1 more thousand is S 4 thousands T Mark the upper endpoint with 4 000 Draw the same number line S Draw number line T What is halfway between 3 000 and 4 000 S 3 500 T Label 3 500 on your number line as I do the same Now label 3 941 on your number line S Label 3 500 and 3 941 T Is 3 941 nearer to 3 000 or 4 000 T Write 3 941 Write your answer on your personal white board S Write 3 941 4 000 Repeat the process for 3 941 rounded to the nearest hundred 74 621 rounded to the nearest ten thousand and nearest thousand and 681 904 rounded to the nearest hundred thousand nearest ten thousand and nearest thousand Multiply by 10 Materials S Personal white board NOTE This fluency activity deepens student understanding of base ten units ZEARN MATH Teacher Edition 75
Topic D Lesson 11 YOUR NOTES G4M1 T Write 10 100 Say the multiplication sentence S 10 10 100 T Write 10 1 ten On your personal white boards fill in the blank S Write 10 1 ten 10 tens T Write 10 tens T Write ten hundred On your personal white boards fill in the blank ten 1 hundred On your boards fill in the blanks S Write 1 ten 1 ten 1 hundred Repeat the process for the following possible sequence 1 ten 60 1 ten 30 hundreds 1 ten 900 and 7 tens 1 ten hundreds NOTE Watch for students who say 3 tens 4 tens is 12 tens rather than 12 hundreds Add Common Units Materials S Personal white board NOTE This mental math fluency activity prepares students for understanding the importance of the algorithm T Project 303 Say the number in unit form S 3 hundreds 3 ones T Write 303 202 Say the addition sentence and answer in unit form S 3 hundreds 3 ones 2 hundreds 2 ones 5 hundreds 5 ones T Write the addition sentence on your personal white boards S Write 303 202 505 Repeat the process and sequence for 505 404 5 005 5 004 7 007 4 004 and 8 008 5 005 WORD PROBLEM A county has three towns Town A has a population of 12 490 people Town B has a population of 14 295 people and Town C has a population of 11 116 people About how many people live in the county altogether Which of these estimates will produce a more accurate answer rounding to the nearest thousand or rounding to the nearest ten thousand Explain 76 ZEARN MATH Teacher Edition
G4M1 NOTE This problem reviews rounding from Lesson 10 Topic D Lesson 11 YOUR NOTES MULTIPLE MEANS OF REPRESENTATION For the Word Problem some students may need further guidance in putting together three addends Help them to break it down by putting two addends together and then adding the third addend to the total Use manipulatives to demonstrate Concept Exploration Materials T Labeled Millions Place Value Chart Concept Exploration Template S Personal white board Labeled Millions Place Value Chart Concept Exploration Template NOTE Using the template provided within this lesson in upcoming lessons provides students with space to draw a tape diagram and record an addition or a subtraction problem below the place value chart Alternatively the unlabeled millions place value chart template from Lesson 2 s Concept Exploration could be used along with paper and pencil PROBLEM 1 Add renaming once using place value disks in a place value chart T Project vertically 3 134 2 493 Say this problem with me S Three thousand one hundred thirty four plus two thousand four hundred ninety three T Draw a tape diagram to represent this problem What are the two parts that make up the whole S 3 134 and 2 493 T Record that in the tape diagram T What is the unknown S In this case the unknown is the whole T Show the whole above the tape diagram using a bracket and label the unknown quantity with an a When a letter represents an unknown number we call that letter a variable T Draw place value disks on the place value chart to represent the first part 3 134 Now it is your turn When you are done add 2 493 by drawing more disks on your place value chart ZEARN MATH Teacher Edition 77
Topic D Lesson 11 YOUR NOTES G4M1 T Point to the problem 4 ones plus 3 ones equals S 7 ones Count 7 ones in the chart and record 7 ones in the problem T Point to the problem 3 tens plus 9 tens equals S 12 tens Count 12 tens in the chart T We can bundle 10 tens as 1 hundred Circle 10 tens disks draw an arrow to the hundreds place and draw the 1 hundred disk to show the regrouping T We can represent this in writing Write 12 tens as 1 hundred crossing the line and 2 tens in the tens column so that you are writing 12 and not 2 and 1 as separate numbers Refer to the visual above T Point to the problem 1 hundred plus 4 hundreds plus 1 hundred equals S 6 hundreds Count 6 hundreds in the chart and record 6 hundreds in the problem T Point to the problem 3 thousands plus 2 thousands equals S 5 thousands Count 5 thousands in the chart and record 5 thousands in the problem T Say the equation with me 3 134 plus 2 493 equals 5 627 Label the whole in the tape diagram above the bracket with a 5 627 PROBLEM 2 Add renaming in multiple units using the standard algorithm and the place value chart T Project vertically 40 762 30 473 With your partner draw a tape diagram to model this problem labeling the two known parts and the unknown whole using the variable B to represent the whole Circulate and assist students T With your partner write the problem and draw disks for the first addend in your chart Then draw disks for the second addend T Point to the problem 2 ones plus 3 ones equals S 5 ones Count the disks to confirm 5 ones and write 5 in the ones column T 6 tens plus 7 tens equals S 13 tens We can group 10 tens to make 1 hundred We do not write two digits in one column We can change 10 tens for 1 hundred leaving us with 3 tens T Regroup the disks Watch me as I record the larger unit using the addition problem First record the 1 on the line in the hundreds place and then record the 3 in the tens so that you are writing 13 not 3 then 1 78 ZEARN MATH Teacher Edition
G4M1 T 7 hundreds plus 4 hundreds plus 1 hundred equals 12 hundreds Discuss with your partner how to record this Continue adding regrouping and recording across other units Topic D Lesson 11 YOUR NOTES T Say the equation with me 40 762 plus 30 473 equals 71 235 Label the whole in the tape diagram with 71 235 and write B 71 235 PROBLEM 3 Add renaming multiple units using the standard algorithm T Project 207 426 128 744 Draw a tape diagram to model this problem Record the numbers on your personal white board T With your partner add units right to left regrouping when necessary using the standard algorithm S 207 426 128 744 336 170 PROBLEM 4 Solve a one step word problem using the standard algorithm modeled with a tape diagram The Lane family took a road trip During the first week they drove 907 miles The second week they drove the same amount as the first week plus an additional 297 miles How many miles did they drive during the second week T What information do we know S We know they drove 907 miles the first week We also know they drove 297 miles more during the second week than the first week T What is the unknown information S We do not know the total miles they drove in the second week T Draw a tape diagram to represent the amount of miles in the first week 907 miles Since the Lane family drove an additional 297 miles in the second week extend the bar for 297 more miles What does the tape diagram represent S The number of miles they drove in the second week T Use a bracket and label the unknown with the variable m for miles T How do we solve for m S 907 297 m T Check student work to see they are recording the regrouping of 10 of a smaller unit for 1 larger unit T Solve What is m S m 1 204 Write m 1 204 T Write a statement that tells your answer S Write The Lane family drove 1 204 miles during the second week ZEARN MATH Teacher Edition 79
Topic D Lesson 11 YOUR NOTES G4M1 MULTIPLE MEANS OF ACTION AND EXPRESSION Students may benefit from further explanation of the Problem 4 word problem Have a conversation around the following What do we do if we do not understand a word in the problem What thinking can we use to figure out the answer anyway In this case students do not need to know what a road trip is in order to solve Discuss How is the tape diagram helpful to us It may be helpful to use the RDW approach Read important information Draw a picture Write an equation to solve Write the answer as a statement Independent Digital Lesson Lesson 11 Add It 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 80 ZEARN MATH Teacher Edition
G4M1 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 When we are writing a sentence to express our answer what part of the original problem helps us to tell our answer using the correct words and context What purpose does a tape diagram have How does it support your work What does a variable help us do when drawing a tape diagram If you have 2 addends can you ever have enough ones to make 2 tens or enough tens to make 2 hundreds or enough hundreds to make 2 thousands Try it out with your partner What if you have 3 addends How is recording the regrouped number in the next column when using the standard algorithm related to bundling disks EXIT TICKET After today s lesson instruct students to complete the Exit Ticket A review of their Exit Ticket as well as continuously monitoring your Digital Reports can help you assess your students understanding of the concepts explored in today s lesson and plan more effectively for future lessons The questions from the Exit Ticket may be read aloud to the students Task 1 Solve the addition problems below using the standard algorithm a 23 607 2 307 _____________ b 3 948 278 ____________ c ZEARN MATH Teacher Edition 5 983 2 097 81
Topic D Lesson 11 YOUR NOTES G4M1 2 The office supply closet had 25 473 large paperclips 13 648 medium paperclips and 15 306 small paperclips How many paperclips were in the closet Answers 1 a 25 914 b 4 226 c 8 080 2 54 427 82 ZEARN MATH Teacher Edition
G4M1 Topic D Lesson 11 Lesson Template LABELED MILLIONS PLACE VALUE CHART CONCEPT EXPLORATION TEMPLATE ZEARN MATH Teacher Edition 83
G4M1 Topic D Lesson 12 Lesson 12 YOUR NOTES Solve multi step word problems using the standard addition algorithm modeled with tape diagrams and assess the reasonableness of answers using rounding Warm Up FLUENCY PRACTICE Round to Different Place Values Materials S Personal white board NOTE This fluency activity reviews rounding skills that are building towards understanding T Project 726 354 Say the number S Seven hundred twenty six thousand three hundred fifty four T What digit is in the hundred thousands place S 7 T What is the value of the digit 7 S 700 000 T On your personal white boards round the number to the nearest hundred thousand S Write 726 354 700 000 Repeat the process rounding 726 354 to the nearest ten thousand thousand hundred and ten Follow the same process and sequence for 496 517 Find the Sum Materials S Personal white board NOTE This fluency activity prepares students for understanding the importance of the algorithm T Write 417 232 Solve by writing horizontally or vertically S Write 417 232 649 Repeat the process and sequence for 7 073 2 312 13 705 4 412 3 949 451 538 385 853 and 23 944 6 056 159 368 ZEARN MATH Teacher Edition 85
Topic D Lesson 12 YOUR NOTES G4M1 WORD PROBLEM A basketball team raised a total of 154 694 in September and 29 987 more in October than in September How much money did they raise in October Draw a tape diagram and write your answer in a complete sentence NOTE This is a comparative word problem that reviews the addition algorithm practiced in Lesson 11 MULTIPLE MEANS OF REPRESENTATION For students who have difficulty conceptualizing word problems use smaller numbers or familiar contexts Have students make sense of the problem and direct them through the process of creating a tape diagram A pizza shop sold five pepperoni pizzas on Friday They sold ten more sausage pizzas than pepperoni pizzas How many pizzas did they sell Have a discussion about the two unknowns in the problem and about which unknown needs to be solved first Students may draw a picture to help them solve Then relate the problem to that with bigger numbers and numbers that involve regrouping Relay the message that it is the same process The difference is that the numbers are bigger Concept Exploration Materials S Personal white board PROBLEM 1 Solve a multi step word problem using a tape diagram The city flower shop sold 14 594 pink roses on Valentine s Day They sold 7 857 more red roses than pink roses How many pink and red roses did the city flower shop sell altogether on Valentine s Day Use a tape diagram to show the work T Read the problem with me What information do we know S We know they sold 14 594 pink roses 86 ZEARN MATH Teacher Edition
G4M1 T To model this let s draw one tape to represent the pink roses Do we know how many red roses were sold Topic D Lesson 12 YOUR NOTES S No but we know that there were 7 857 more red roses sold than pink roses T A second tape can represent the number of red roses sold Model on the tape diagram T What is the problem asking us to find S The total number of roses T We can draw a bracket to the side of both tapes Let s label it R for pink and red roses T First solve to find how many red roses were sold S Solve 14 594 7 857 22 451 T What does the bottom tape represent S The bottom tape represents the number of red roses 22 451 T Bracket and label 22 451 to show the total number of red roses Now we need to find the total number of roses sold How do we solve for R S Add the totals for both tapes together 14 594 22 451 R T Solve with me What does R equal S R equals 37 045 T Write R 37 045 Let s write a statement of the answer S Write The city flower shop sold 37 045 pink and red roses on Valentine s Day PROBLEM 2 Solve a two step word problem using a tape diagram and assess the reasonableness of the answer On Saturday 32 736 more bus tickets were sold than on Sunday On Sunday only 17 295 tickets were sold How many people bought bus tickets over the weekend Use a tape diagram to show the work T Tell your partner what information we know S We know how many people bought bus tickets on Sunday 17 295 We also know how many more people bought tickets on Saturday But we do not know the total number of people that bought tickets on Saturday T Let s draw a tape for Sunday s ticket sales and label it How can we represent Saturday s ticket sales S Draw a tape the same length as Sunday s and extend it further for 32 736 more tickets T What does the problem ask us to solve for S The number of people that bought tickets over the weekend ZEARN MATH Teacher Edition 87
Topic D Lesson 12 YOUR NOTES G4M1 T With your partner finish drawing a tape diagram to model this problem Use B to represent the total number of tickets bought over the weekend T Before we solve estimate to get a general sense of what our answer will be Round each number to the nearest ten thousand S Write 20 000 20 000 30 000 70 000 About 70 000 tickets were sold over the weekend T Now solve with your partner to find the actual number of tickets sold over the weekend S Solve S B equals 67 326 T Write B 67 326 T Now let s look back at the estimate we got earlier and compare with our actual answer Is 67 326 close to 70 000 S Yes 67 326 rounded to the nearest ten thousand is 70 000 T Our answer is reasonable T Write a statement of the answer S Write There were 67 326 people who bought bus tickets over the weekend PROBLEM 3 Solve a multi step word problem using a tape diagram and assess reasonableness Last year Big Bill s Department Store sold many pairs of footwear 118 214 pairs of boots were sold 37 092 more pairs of sandals than pairs of boots were sold and 124 417 more pairs of sneakers than pairs of boots were sold How many pairs of footwear were sold last year T Discuss with your partner the information we have and the unknown information we want to find S Discuss T With your partner draw a tape diagram to model this problem How do you solve for P S The tape shows me I could add the number of pairs of boots 3 times and then add 37 092 and 124 417 You could find the number of pairs of sandals find the number of pairs of sneakers and then add those totals to the number of pairs of boots Have students then round each addend to get an estimated answer calculate precisely and compare to see if their answers are reasonable 88 ZEARN MATH Teacher Edition
G4M1 Topic D Lesson 12 MULTIPLE MEANS OF REPRESENTATION YOUR NOTES At this point in the Mission some students are still developing their fluency with adding multi digit whole numbers This should not keep them from engaging with and conceptualizing the word problems in this lesson If the numbers seem to be a barrier for students encourage students to solve the problems using a place value chart Alternatively students could start by rewriting the numbers in the problem by rounding them to the nearest thousand ten thousand or hundred thousand Once students solve the problem using the rounded numbers challenge them to complete the same process using the original numbers MULTIPLE MEANS OF REPRESENTATION Students may need direction in creating their answer in the form of a sentence Provide them with language support by displaying a number sentence example Direct them to be sure to provide a label for their numerical answer Independent Digital Lesson Lesson 12 Sum Sense Students also learn the concepts from this lesson in the Independent Digital Lesson The intentional balance of learning with teachers and peers and learning independently in digital lessons ensures every student has multiple opportunities to represent engage with and express their math reasoning See the digital lesson notes below for a glimpse of the paper to pencil transfer of these math ideas Go online to see the full digital lesson ZEARN MATH Teacher Edition 89
Topic D Lesson 12 G4M1 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 Explain why we should test to see if our answers are reasonable Show an example of one of the above lesson problems solved incorrectly to show how checking the reasonableness of an answer is important When might you need to use an estimate in real life What are the next steps if your estimate is not near the actual answer Consider the example we discussed earlier where the problem was solved incorrectly Because we had estimated an answer we knew that our solution was not reasonable EXIT TICKET After today s lesson instruct students to complete the Exit Ticket A review of their Exit Ticket as well as continuously monitoring your Digital Reports can help you assess your students understanding of the concepts explored in today s lesson and plan more effectively for future lessons The questions from the Exit Ticket may be read aloud to the students 90 ZEARN MATH Teacher Edition
G4M1 Topic D Lesson 12 Task YOUR NOTES Model the problem with a tape diagram Solve and write your answer as a statement 1 In January Scott earned 8 999 In February he earned 2 387 more than in January In March Scott earned the same amount as in February How much did Scott earn altogether during those three months Is your answer reasonable Explain Answers 1 31 771 explanations will vary ZEARN MATH Teacher Edition 91
G4M1 Topic E TOPIC E Multi Digit Whole Number Subtraction Following the introduction of the standard algorithm for addition in Topic D the standard algorithm for subtraction replaces special strategies for subtraction in Topic E Moving slowly from smaller to larger minuends students practice decomposing larger units into smaller units First only one decomposition is introduced where one zero may appear in the minuend As in Grades 2 and 3 students continue to decompose all necessary digits before performing the algorithm allowing subtraction from left to right or as taught in the lessons from right to left Students use the algorithm to subtract numbers from 1 million allowing for multiple decompositions The topic concludes with practicing the standard algorithm for subtraction in the context of two step word problems where students have to assess the reasonableness of their answers by rounding When using tape diagrams to model word problems students use a variable to represent the unknown quantity Objective Topic E Multi Digit Whole Number Subtraction Lesson 13 Use place value understanding to decompose to smaller units once using the standard subtraction algorithm and apply the algorithm to solve word problems using tape diagrams Lesson 14 Use place value understanding to decompose to smaller units up to three times using the standard subtraction algorithm and apply the algorithm to solve word problems using tape diagrams Lesson 15 Use place value understanding to fluently decompose to smaller units multiple times in any place using the standard subtraction algorithm and apply the algorithm to solve word problems using tape diagrams Lesson 16 Solve two step word problems using the standard subtraction algorithm fluently modeled with tape diagrams and assess the reasonableness of answers using rounding 92 ZEARN MATH Teacher Edition
G4M1 Topic E Lesson 13 Lesson 13 YOUR NOTES Use place value understanding to decompose to smaller units once using the standard subtraction algorithm and apply the algorithm to solve word problems using tape diagrams Warm Up FLUENCY PRACTICE Find the Sum Materials S Personal white board NOTE This math fluency activity prepares students for understanding the importance of the addition algorithm T Write 316 473 Solve by writing an addition sentence horizontally or vertically S Write 316 473 789 Repeat the process and sequence for 6 065 3 731 13 806 4 393 5 928 124 and 629 296 962 Subtract Common Units Materials S Personal white board NOTE This mental math fluency activity prepares students for understanding the importance of the subtraction algorithm T Project 707 Say the number in unit form S 7 hundreds 7 ones T Write 707 202 Say the subtraction sentence and answer in unit form S 7 hundreds 7 ones 2 hundreds 2 ones 5 hundreds 5 ones T Write the subtraction sentence on your personal white boards S Write 707 202 505 Repeat the process and sequence for 909 404 9 009 5 005 11 011 4 004 and 13 013 8 008 ZEARN MATH Teacher Edition 93
Topic E Lesson 13 YOUR NOTES G4M1 WORD PROBLEM A university received 5 849 applications in January In February the university received 1 263 more applications than in January What was the total number of applications the university received in the two months combined Explain how you know if the answer is reasonable NOTE This Word Problem reviews content from Lesson 12 of a multi step addition problem Concept Exploration Materials T Labeled Millions Place Value Chart Lesson 11 Concept Exploration Template S Personal white board Labeled Millions Place Value Chart Lesson 11 Concept Exploration Template PROBLEM 1 Use a place value chart and place value disks to model subtracting alongside the algorithm regrouping 1 hundred into 10 tens Display 4 259 2 171 vertically on the board T Say this problem with me Read problem together T Watch as I draw a tape diagram to represent this problem What is the whole S 4 259 T We record that above the tape as the whole and record the known part of 2 171 under the tape It is your turn to draw a tape diagram Mark the unknown part of the diagram with the variable A T Model the whole 4 259 using place value disks on your place value chart T Do we model the part we are subtracting S No just the whole T First let s determine if we are ready to subtract We look across the top number from right to left to see if there are enough units in each column Let s look at the ones column Are there enough ones in the top number to subtract the ones in the bottom number Point to the 9 and the 1 in the problem S Yes 9 is greater than 1 94 ZEARN MATH Teacher Edition
G4M1 T That means we are ready to subtract in the ones column Let s look at the tens column Are there enough tens in the top number to subtract the tens in the bottom number Topic E Lesson 13 YOUR NOTES S No 5 is less than 7 T Show regrouping on the place value chart We ungroup or unbundle 1 unit from the hundreds to make 10 tens I now have 1 hundred and 15 tens Let s rename and represent the change in writing using the algorithm Cross out the hundreds and tens to rename them in the problem T Show the change with your disks Cross off 1 hundred and change it for 10 tens as shown below T Are there enough hundreds in the top number to subtract the hundreds in the bottom number S Yes 1 is equal to 1 T Are there enough thousands in the top number to subtract the thousands in the bottom number S Yes 4 is greater than 2 T Are we ready to subtract S Yes we are ready to subtract T Point to the problem 9 ones minus 1 one S 8 ones T Cross off 1 disk write an 8 in the problem T 15 tens minus 7 tens S 8 tens T Cross off 7 disks write an 8 in the problem Continue subtracting through the hundreds and thousands T Say the number sentence S 4 259 2 171 2 088 T The value of the A in our tape diagram is 2 088 We write A 2 088 below the tape diagram What can be added to 2 171 to result in the sum of 4 259 S 2 088 Optional Repeat the Process Repeat the process for 6 314 3 133 ZEARN MATH Teacher Edition 95
Topic E Lesson 13 YOUR NOTES G4M1 PROBLEM 2 Regroup 1 thousand into 10 hundreds using the subtraction algorithm Display 23 422 11 510 vertically on the board T With your partner read this problem and draw a tape diagram Label the whole the known part and use the variable B for the unknown part T Record the problem on your personal white board T Look across the digits Are we ready to subtract S No T Are there enough ones in the top number to subtract the ones in the bottom number Point to the 2 and the 0 S Yes 2 is greater than 0 T Are there enough tens in the top number to subtract the tens in the bottom number S Yes 2 is greater than 1 T Are there enough hundreds in the top number to subtract the hundreds in the bottom number S No 4 is less than 5 T Tell your partner how to make enough hundreds to subtract S I unbundle 1 thousand to make 10 hundreds I now have 2 thousands and 14 hundreds I change 1 thousand for 10 hundreds I rename 34 hundreds as 20 hundreds and 14 hundreds T Watch as I record that Now it is your turn Repeat questioning for the thousands and ten thousands columns T Are we ready to subtract S Yes we are ready to subtract T 2 ones minus 0 ones S 2 ones Record 2 in the ones column Continue subtracting across the number from right to left always naming the units T Tell your partner what must be added to 11 510 to result in the sum of 23 422 T How do we check a subtraction problem S We can add the difference to the part we knew at first to see if the sum we get equals the whole T Please add 11 912 and 11 510 What sum do you get S 23 422 so our answer to the subtraction problem is correct T Label your tape diagram as B 11 912 Optional Repeat the Process Repeat for 29 014 7 503 96 ZEARN MATH Teacher Edition
G4M1 PROBLEM 3 Solve a subtraction word problem regrouping 1 ten thousand into 10 thousands Topic E Lesson 13 YOUR NOTES The paper mill produced 73 658 boxes of paper 8 052 boxes have been sold How many boxes remain T Draw a tape diagram to represent the boxes of paper produced and sold I will use the letter P to represent the boxes of paper remaining Record the subtraction problem Check to see that you lined up all units T Am I ready to subtract S No T Work with your partner asking if there are enough units in each column to subtract Regroup when needed Then ask Am I ready to subtract before you begin subtracting Use the standard algorithm Students work S 73 658 8 052 65 606 T The value of P is 65 606 In a statement tell your partner how many boxes remain S 65 606 boxes remain T To check and see if your answer is correct add the two values of the tape 8 052 and your answer of 65 606 to see if the sum is the value of the tape 73 658 S Add to find that the sum matches the value of the tape Repeat with the following The library has 50 819 books 4 506 are checked out How many books remain in the library MULTIPLE MEANS OF ENGAGEMENT Ask students to look at the numbers in the subtraction problem and to think about how the numbers are related Ask them how they might use their discovery to check to see if their answer is correct Use the tape diagram to show if 8 052 was subtracted from 73 658 to find the unknown part of the tape diagram the value of the unknown 65 606 can be added to the known part of the tape diagram 8 052 If the sum is the value of the whole tape diagram the answer is correct ZEARN MATH Teacher Edition 97
Topic E Lesson 13 YOUR NOTES G4M1 Independent Digital Lesson Lesson 13 Subtraction Action 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 98 ZEARN MATH Teacher Edition
G4M1 Topic E Lesson 13 YOUR NOTES Why do we ask Are we ready to subtract After we get our top number ready to subtract do we have to subtract in order from right to left When do we need to unbundle to subtract What are the benefits to modeling subtraction using place value disks Why must the units line up when subtracting How might our answer change if the digits were not aligned What happens when there is a zero in the top number of a subtraction problem What happens when there is a zero in the bottom number of a subtraction problem When you are completing word problems how can you tell that you need to subtract EXIT TICKET After today s lesson instruct students to complete the Exit Ticket A review of their Exit Ticket as well as continuously monitoring your Digital Reports can help you assess your students understanding of the concepts explored in today s lesson and plan more effectively for future lessons The questions from the Exit Ticket may be read aloud to the students Task 1 Use the standard algorithm to solve the following subtraction problems a 8 512 2 501 _____________ b 18 042 4 122 ______________ c 8 072 1 561 ____________ Draw a tape diagram to represent the following problem Use numbers to solve Write your answer as a statement Check your answer 2 What number must be added to 1 575 to result in a sum of 8 625 ZEARN MATH Teacher Edition 99
Topic E Lesson 13 YOUR NOTES G4M1 Answers 1 a 6 011 b 13 920 c 6 511 2 Tape diagram accurately drawn 7 050 must be added to 1 575 to result in a sum of 8 625 100 ZEARN MATH Teacher Edition
G4M1 Topic E Lesson 14 Lesson 14 YOUR NOTES Use place value understanding to decompose to smaller units up to three times using the standard subtraction algorithm and apply the algorithm to solve word problems using tape diagrams Warm Up FLUENCY PRACTICE Base Ten Thousand Units Materials S Personal white board NOTE This fluency activity helps students work towards understanding base ten units T Project 8 ten thousands Write the number in standard form S 80 000 Continue with the following possible sequence 9 ten thousands 10 ten thousands 13 ten thousands 19 ten thousands 20 ten thousands 30 ten thousands 70 ten thousands 71 ten thousands 90 ten thousands and 100 ten thousands Find the Difference Materials S Personal white board NOTE This math fluency activity prepares students for understanding the importance of the subtraction algorithm T Write 735 203 Write a subtraction sentence horizontally or vertically S Write 735 203 532 Repeat process and sequence for 7 045 4 003 845 18 5 725 915 and 34 736 2 806 Convert Units NOTE Reviewing the relationship between meters and centimeters learned in Grade 3 helps prepare students to solve problems with metric measurement and to understand metric measurement s relationship to place value T Write 1 m cm How many centimeters are in a meter S 1 m 100 cm ZEARN MATH Teacher Edition 101
Topic E Lesson 14 YOUR NOTES G4M1 Repeat the process for 2 m 3 m 8 m 8 m 50 cm 7 m 50 cm and 4 m 25 cm T Write 100 cm m Say the answer S 100 cm 1 m T Write 150 cm m cm Say the answer S 150 cm 1 m 50 cm Repeat the process for 250 cm 350 cm 950 cm and 725 cm WORD PROBLEM In one year the animal shelter bought 25 460 pounds of dog food That amount was 10 times the amount of cat food purchased in the month of July How much cat food was purchased in July Extension If the cats ate 1 462 pounds of the cat food how much cat food was left NOTE This Word Problem incorporates prior knowledge of 10 times as many with the objective of decomposing to smaller units in order to subtract Concept Exploration Materials S Personal white board PROBLEM 1 Subtract decomposing twice Write 22 397 3 745 vertically on the board T Let s read this subtraction problem together Watch as I draw a tape diagram labeling the whole the known part and the unknown part using a variable A Now it is your turn T Record the problem on your personal white board T Look across the digits Am I ready to subtract S No T We look across the top number to see if I have enough units in each column Are there enough ones in the top number to subtract the ones in the bottom number S Yes 7 ones is greater than 5 ones T Are there enough tens in the top number to subtract the tens in the bottom number 102 ZEARN MATH Teacher Edition
G4M1 S Yes 9 tens is greater than 4 tens Topic E Lesson 14 YOUR NOTES T Are there enough hundreds in the top number to subtract the hundreds in the bottom number S No 3 hundreds is less than 7 hundreds We can unbundle 1 thousand as 10 hundreds to make 1 thousand and 13 hundreds I can subtract the hundreds column now T Watch as I record that Now it is your turn to record the change T Are there enough thousands in the top number to subtract the thousands in the bottom number S No 1 thousand is less than 3 thousands We can unbundle 1 ten thousand to 10 thousands to make 1 ten thousand and 11 thousands I can subtract in the thousands column now T Watch as I record Now it is your turn to record the change T Are there enough ten thousands in the top number to subtract the ten thousands in the bottom number S Yes T Are we ready to subtract S Yes we are ready to subtract T 7 ones minus 5 ones S 2 ones Record 2 in the ones column Continue subtracting across the problem always naming the units T Say the equation with me S 22 397 minus 3 745 equals 18 652 T Check your answer using addition S Our answer is correct because 18 652 plus 3 745 equals 22 397 T What is the value of A in the tape diagram S A equals 18 652 PROBLEM 2 Subtract decomposing three times Write 210 290 45 720 vertically on the board T With your partner draw a tape diagram to represent the whole the known part and the unknown part T Record the subtraction problem on your board T Look across the digits Are we ready to subtract S No T Look across the top number s digits to see if we have enough units in each column Are there enough ones in the top number to subtract the ones in the bottom number Point to the zeros in the ones column S Yes 0 equals 0 T We are ready to subtract in the ones column Are there enough tens in the top number to subtract the tens in the bottom number S Yes 9 is greater than 2 ZEARN MATH Teacher Edition 103
Topic E Lesson 14 YOUR NOTES G4M1 T We are ready to subtract in the tens column Are there enough hundreds in the top number to subtract the hundreds in the bottom number S No 2 hundreds is less than 7 hundreds T There are no thousands to unbundle so we look to the ten thousands We can unbundle 1 ten thousand to 10 thousands Unbundle 10 thousands to make 9 thousands and 12 hundreds Now we can subtract the hundreds column Repeat questioning for the thousands ten thousands and hundred thousands place recording the renaming of units in the problem T Are we ready to subtract S Yes we are ready to subtract T 0 ones minus 0 ones S 0 ones T 9 tens minus 2 tens S 7 tens Have partners continue using the algorithm reminding them to work right to left always naming the units T Read the equation to your partner and complete your tape diagram by labeling the variable S 210 290 minus 45 720 is 164 570 A 164 570 PROBLEM 3 Use the subtraction algorithm to solve a word problem modeled with a tape diagram decomposing units 3 times This problem is optional Bryce needed to purchase a large order of computer supplies for his company He was allowed to spend 859 239 on computers However he ended up only spending 272 650 How much money was left T Read the problem with me Tell your partner the information we know S We know he can spend 859 239 and we know he only spent 272 650 T Draw a tape diagram to represent the information in the problem Label the whole the known part and the unknown part using a variable T Tell me the problem we must solve and write it on your board S 859 239 272 650 T Work with your partner to move across the digits Are there enough in each column to subtract Regroup when needed Then ask Are we ready to subtract before you begin subtracting Use the standard algorithm S 859 239 272 650 586 589 104 ZEARN MATH Teacher Edition
G4M1 Topic E Lesson 14 T Say your answer as a statement YOUR NOTES S 586 589 was left MULTIPLE MEANS OF ENGAGEMENT Use flexible groupings based on the learning of the day and your knowledge of your students For example you may want to group students together who are most comfortable using the place value chart and separately group students using the standard algorithm for subtraction Alternatively you may choose to partner a student who uses the place value chart with a student who uses the standard algorithm so they can draw connections between the two representations Independent Digital Lesson Lesson 14 Take It Away 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 105
Topic E Lesson 14 YOUR NOTES G4M1 Wrap Up LESSON SYNTHESIS Guide students in a conversation to process today s lesson and surface any misconceptions or misunderstandings The questions below may be used to lead the discussion How is the complexity of this lesson different from the complexity of Lesson 13 In which column can you begin subtracting when you are ready to subtract Any column You are using a variable or a letter to represent the unknown in each tape diagram Tell your partner how you determine what variable to use and how it helps you to solve the problem How can you check a subtraction 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 Use the standard algorithm to solve the following problems 1 19 350 2 32 010 2 546 5 761 Draw a tape diagram to represent the following problem Use numbers to solve and write your answer as a statement Check your answer 3 A doughnut shop sold 1 232 doughnuts in one day If they sold 876 doughnuts in the morning how many doughnuts were sold during the rest of the day Answers 1 13 589 2 29 464 3 Tape diagram accurately drawn 356 donuts were sold during the rest of the day 106 ZEARN MATH Teacher Edition
G4M1 Topic E Lesson 15 Lesson 15 YOUR NOTES Use place value understanding to fluently decompose to smaller units multiple times in any place using the standard subtraction algorithm and apply the algorithm to solve word problems using tape diagrams Warm Up FLUENCY PRACTICE Place Value Materials T Personal white board NOTE Practicing these skills in isolation helps lay a foundation for conceptually understanding the content from today s Concept Exploration T Write 4 598 Say the number S 4 598 T What digit is in the tens place S 9 T Underline 9 What is the value of the 9 S 90 T State the value of the digit 4 S 4 000 T 5 S 500 Repeat using the following possible sequence 69 708 398 504 and 853 967 Find the Difference Materials S Personal white board NOTE This math fluency activity prepares students for understanding the importance of the subtraction algorithm T Write 846 304 Write a subtraction sentence horizontally or vertically S Write 846 304 542 Repeat process and sequence for 8 056 5 004 935 17 4 625 815 and 45 836 2 906 ZEARN MATH Teacher Edition 107
Topic E Lesson 15 YOUR NOTES G4M1 Convert Units NOTE This material is a review of Grade 2 and Grade 3 concepts and helps prepare students to solve problems with meters and centimeters in Grade 4 Mission 2 Topic A Materials S Personal white board T Count by 20 centimeters When you get to 100 centimeters say 1 meter When you get to 200 centimeters say 2 meters S 20 cm 40 cm 60 cm 80 cm 1 m 120 cm 140 cm 160 cm 180 cm 2 m Repeat process this time pulling out the meter e g 1 m 20 cm 1 m 40 cm T Write 130 cm m cm On your personal white boards fill in the blanks S Write 130 cm 1 m 30 cm Repeat process for 103 cm 175 cm 345 cm and 708 cm for composing to meters WORD PROBLEM When the amusement park opened the number on the counter at the gate read 928 614 At the end of the day the counter read 931 682 How many people went through the gate that day NOTE At times students are asked to use a specific strategy and at other times their independent work is observed Concept Exploration Materials T Labeled Millions Place Value Chart Lesson 11 Concept Exploration Template S Personal white board Labeled Millions Place Value Chart Lesson 11 Concept Exploration Template PROBLEM 1 Regroup units 5 times to subtract This problem is optional Write 253 421 75 832 vertically on the board 108 ZEARN MATH Teacher Edition
G4M1 T Say this problem with me Topic E Lesson 15 YOUR NOTES T Work with your partner to draw a tape diagram representing this problem T What is the whole amount S 253 421 T What is the part S 75 832 T Look across the top number 253 421 to see if we have enough units in each column to subtract 75 832 Are we ready to subtract S No T Are there enough ones in the top number to subtract the ones in the bottom number Point to the 1 and 2 in the ones column S No 1 one is less than 2 ones T What should we do S Change 1 ten for 10 ones That means you have 1 ten and 11 ones T Are there enough tens in the top number to subtract the tens in the bottom number Point to tens column S No 1 ten is less than 3 tens T What should we do S Change 1 hundred for 10 tens You have 3 hundreds and 11 tens T The tens column is ready to subtract Have partners continue questioning if there are enough units to subtract in each column regrouping where needed T Are we ready to subtract S Yes we are ready to subtract T Go ahead and subtract State the difference to your partner Label the unknown part in your tape diagram S The difference between 253 421 and 75 832 is 177 589 Label A 177 589 T Add the difference to the part you knew to see if your answer is correct S It is The sum of the parts is 253 421 PROBLEM 2 Decompose numbers from 1 thousand and 1 million into smaller units to subtract modeled with place value disks NOTE Be sure to discuss multiple ways of solving these problems The standard algorithm may be the least efficient strategy in some problems A more efficient strategy for some students may be using the arrow way or another mental math strategy ZEARN MATH Teacher Edition 109
Topic E Lesson 15 YOUR NOTES G4M1 Write 1 000 528 vertically on the board T With your partner read this problem and draw a tape diagram Label what you know and the unknown T Record the problem on your personal white board T Look across the units in the top number Are we ready to subtract S No T Are there enough ones in the top number to subtract the ones in the bottom number Point to 0 and 8 in the ones column S No 0 ones is less than 8 ones T I need to ungroup 1 unit from the tens What do you notice S There are no tens to ungroup T We can look to the hundreds There are no hundreds to ungroup either T In order to get 10 ones we need to regroup 1 thousand Watch as I represent the ungrouping in my subtraction problem Model using place value disks and rename units in the problem simultaneously Now it is your turn T Are we ready to subtract S Yes we are ready to subtract T Solve for 9 hundreds 9 tens 10 ones minus 5 hundreds 2 tens 8 ones S 1 000 528 is 472 T Check our answer S The sum of 472 and 528 is 1 000 Write 1 000 000 345 528 vertically on the board T Read this problem and draw a tape diagram to represent the subtraction problem T Record the subtraction problem on your board T What do you notice when you look across the top number 110 ZEARN MATH Teacher Edition
G4M1 S There are a lot more zeros We will have to regroup 6 times We are not ready to subtract We will have to regroup 1 million to solve the problem Topic E Lesson 15 YOUR NOTES T Work with your partner to get 1 000 000 ready to subtract Rename your units in the subtraction problem S 9 hundred thousands 9 ten thousands 9 thousands 9 hundreds 9 tens 10 ones We are ready to subtract S 1 000 000 minus 345 528 equals 654 472 T To check your answer add the parts to see if you get the correct whole amount S We did We got one million when we added the parts PROBLEM 3 Solve a word problem decomposing units multiple times Last year there were 620 073 people in attendance at a local parade This year there were 456 795 people in attendance How many more people were in attendance last year T Read with me T Represent this information in a tape diagram T Work with your partner to write a subtraction problem using the information in the tape diagram T Look across the units in the top number Are you ready to subtract S No I do not have enough ones in the top number I need to unbundle 1 ten to make 10 ones Then I have 6 tens and 13 ones T Continue to check if you are ready to subtract in each column When you are ready to subtract solve S 620 073 minus 456 795 equals 163 278 There were 163 278 more people in attendance last year MULTIPLE MEANS OF ENGAGEMENT Students benefit from using addition to check subtraction Students should see that if the sum does not match the whole the subtraction or calculation is faulty They must subtract again and then check with addition Challenge students to think about how they use this check strategy in everyday life We use it all of the time when we add up to another number MULTIPLE MEANS OF ACTION AND EXPRESSION Encourage students who notice a pattern of repeated nines when subtracting across multiple zeros to express this pattern in writing Allow students to identify why this happens using manipulatives or in writing Allow students to slowly transition into recording this particular unbundling across zeros as nines as they become fluent with using the algorithm ZEARN MATH Teacher Edition 111
Topic E Lesson 15 YOUR NOTES G4M1 Independent Digital Lesson Lesson 15 Unbundling Bonanza Students also learn the concepts from this lesson in the Independent Digital Lesson The intentional balance of learning with teachers and peers and learning independently in digital lessons ensures every student has multiple opportunities to represent engage with and express their math reasoning There are no notes for this digital lesson Go online to see the full digital lesson Wrap Up LESSON SYNTHESIS Guide students in a conversation to process today s lesson and surface any misconceptions or misunderstandings The questions below may be used to lead the discussion How do you know when you are ready to subtract across the problem How can you check your answer when subtracting Is there a number that you can subtract from 1 000 000 without decomposing across to the ones other than 1 000 000 100 000 10 000 How can decomposing multiple times be challenging How does the tape diagram help you determine which operation to use to find the answer EXIT TICKET After today s lesson instruct students to complete the Exit Ticket A review of their Exit Ticket as well as continuously monitoring your Digital Reports can help you assess your students understanding of the concepts explored in today s lesson and plan more effectively for future lessons The questions from the Exit Ticket may be read aloud to the students 112 ZEARN MATH Teacher Edition
G4M1 Topic E Lesson 15 Task YOUR NOTES Draw a tape diagram to model each problem and solve 1 956 204 780 169 2 A construction company was building a stone wall on Main Street 100 000 stones were delivered to the site On Monday they used 15 631 stones How many stones remain for the rest of the week Write your answer as a statement Answers 1 176 035 2 84 369 stones remain for the rest of the week ZEARN MATH Teacher Edition 113
G4M1 Lesson 16 Topic E Lesson 16 YOUR NOTES Solve two step word problems using the standard subtraction algorithm fluently modeled with tape diagrams and assess the reasonableness of answers using rounding WARM UP FLUENCY PRACTICE Compare Numbers Materials S Personal white board NOTE Reviewing this concept helps students work toward understanding comparing numbers T Project 342 006 94 983 On your personal white boards compare the numbers by writing the greater than less than or equal symbol S Write 342 006 94 893 Repeat with the following possible sequence 7 thousands 5 hundreds 8 tens 6 ten thousands 5 hundreds 8 ones and 9 hundred thousands 8 thousands 9 hundreds 3 tens 807 820 WORD PROBLEM For the weekend basketball playoffs a total of 61 941 tickets were sold 29 855 tickets were sold for Saturday s games The rest of the tickets were sold for Sunday s games How many tickets were sold for Sunday s games 32 086 tickets were sold for Sunday s games NOTE This Word Problem reviews content from Lesson 15 of using the subtraction algorithm with multiple regroupings ZEARN MATH Teacher Edition 115
Topic E Lesson 16 YOUR NOTES G4M1 Concept Exploration Materials S Personal white board PROBLEM 1 Solve a two step word problem modeled with a tape diagram assessing reasonableness of the answer using rounding A company has 3 locations with 70 010 employees altogether The first location has 34 857 employees The second location has 17 595 employees How many employees work in the third location T Read with me Take 2 minutes to draw and label a tape diagram Circulate and encourage the students Can you draw something What can you draw T After 2 minutes Tell your partner what you understand and what you still do not understand S We know the total number of employees and the employees at the first and second locations We do not know how many employees are at the third location T Use your tape diagram to estimate the number of employees at the third location Explain your reasoning to your partner S I rounded the number of employees 30 000 20 000 50 000 and I know that the total number of employees is about 70 000 That means that there would be about 20 000 employees at the third location T Now find the precise answer Work with your partner to do so Give students time to work T Label the unknown part on your diagram and make a statement of the solution S There are 17 558 employees at the third location T Is your answer reasonable S Yes because 17 558 rounded to the nearest ten thousand is 20 000 and that was our estimate PROBLEM 2 Solve two step word problems modeled with a tape diagram assessing reasonableness of the answer using rounding This problem is optional Owen s goal is to have 1 million people visit his new website within the first four months of it being launched Below is a chart showing the number of visitors each month How many more visitors does he need in Month 4 to reach his goal 116 ZEARN MATH Teacher Edition
G4M1 Topic E Lesson 16 Month Month 1 Month 2 Month 3 Visitors 228 211 301 856 299 542 Month 4 YOUR NOTES T With your partner draw a tape diagram Tell your partner your strategy for solving this problem S We can find the sum of the number of visitors during the first 3 months Then we subtract that from 1 million to find how many more visitors are needed to reach his goal T Make an estimate for the number of visitors in Month 4 Explain your reasoning to your partner S I can round to the nearest hundred thousand and estimate Owen will need about 200 000 visitors to reach his goal I rounded to the nearest ten thousand to get a closer estimate of 170 000 visitors T Find the total for the first 3 months What is the precise sum S 829 609 T Compare the actual and estimated solutions Is your answer reasonable S Yes because our estimate of 200 000 is near 170 391 Rounded to the nearest hundred thousand 170 391 is 200 000 170 391 rounded to the nearest ten thousand is 170 000 which was also our estimate so our solution is reasonable PROBLEM 3 Solve a two step compare with smaller unknown word problem There were 12 345 people at a concert on Saturday night On Sunday night there were 1 795 fewer people at the concert than on Saturday night How many people attended the concert on both nights T For 2 minutes with your partner draw a tape diagram Circulate and encourage students as they work You might choose to call two pairs of students to draw on the board while others work at their seats Have the pairs then present their diagrams to the class T Now how can you calculate to solve the problem S We can find the number of people on Sunday night and then add that number to the people on Saturday night T Make an estimate of the solution Explain your reasoning to your partner ZEARN MATH Teacher Edition 117
Topic E Lesson 16 G4M1 YOUR NOTES S Rounding to the nearest thousand the number of people on Saturday night was about 12 000 The number of people fewer on Sunday night can be rounded to 2 000 so the estimate for the number of people on Sunday is 10 000 12 000 10 000 is 22 000 T Find the exact number of people who attended the concert on both nights What is the exact sum S 22 895 T Compare the actual and estimated solutions Is your answer reasonable S Yes because 22 895 is near our estimate of 22 000 T Be sure to write a statement of your solution MULTIPLE MEANS OF ACTION AND EXPRESSION Students who need additional support with this activity may not consider whether their answer makes sense Encourage students to reread the problem after solving and to ask themselves Does my answer make sense If not ask What else can I try MULTIPLE MEANS OF ENGAGEMENT If there are students who are ready for a challenge prompt them to expand their thinking and figure out another way to solve the two step problem Is there another strategy that would work Independent Digital Lesson Lesson 16 Break It and Tape 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 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 118 ZEARN MATH Teacher Edition
G4M1 Topic E Lesson 16 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 you determine what place value to round to when finding an estimate What is the benefit of checking the reasonableness of your answer Describe the difference between rounding and estimating 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 119
Topic E Lesson 16 YOUR NOTES G4M1 Task 1 Quarterback Brett Favre passed for 71 838 yards between the years 1991 and 2011 His all time high was 4 413 passing yards in 1995 In 1992 he threw 4 212 passing yards a About how many passing yards did he throw in the remaining years Estimate by rounding each value to the nearest thousand and then compute b Exactly how many passing yards did he throw in the remaining years c Assess the reasonableness of your answer in b Use your estimate from a to explain Answers 1 a 64 000 b 63 213 c Explanations will vary 120 ZEARN MATH Teacher Edition
G4M1 Topic F TOPIC F Addition and Subtraction Word Problems Mission 1 culminates with multi step addition and subtraction word problems in Topic F In these lessons the format for the Concept Exploration is different from the traditional vignette Instead of following instruction the Problem Set facilitates the problems and discussion of the Concept Exploration Throughout the mission tape diagrams are used to model word problems and students continue to use tape diagrams to solve additive comparative word problems Students also continue using a variable to represent an unknown quantity To culminate the mission students are given tape diagrams or equations and are encouraged to use creativity and the mathematics learned during this mission to write their own word problems to solve using place value understanding and the algorithms for addition and subtraction The mission facilitates deeper comprehension and supports determining the reasonableness of an answer Solving multi step word problems using multiplication and division is addressed in later missions Objective Topic F Addition and Subtraction Word Problems Lesson 17 Solve additive compare word problems modeled with tape diagrams Lesson 18 Solve multi step word problems modeled with tape diagrams and assess the reasonableness of answers using rounding Lesson 19 Create and solve multi step word problems from given tape diagrams and equations Note on Pacing for Differentiation If you are using the Zearn Math recommended weekly schedule that consists of four Core Days when students learn grade level content and one Flex Day that can be tailored to meet students needs we recommend omitting the optional lesson in this mission during the Core Days Students who demonstrate a need for further support can explore these concepts with you and peers as part of a flex day as needed This schedule ensures students have sufficient time each week to work through grade level content and includes built in weekly time you can use to differentiate instruction to meet student needs Optional lesson for Topic F Lesson 19 ZEARN MATH Teacher Edition 121
G4M1 Topic F Lesson 17 Lesson 17 YOUR NOTES Solve additive compare word problems modeled with tape diagrams TIP There is no Independent Digital Lesson corresponding to today s Concept Exploration Students should use digital time to complete other digital lessons in this Mission If a student has already completed 4 digital lessons this week they should complete digital bonuses from this Mission Warm Up FLUENCY PRACTICE Change Place Value Materials S Personal white board Labeled Millions Place Value Chart Lesson 11 Concept Exploration Template NOTE This fluency activity helps students work toward using place value skills to add and subtract different units T Project the place value chart to the millions place Write 4 hundred thousands 6 ten thousands 3 thousands 2 hundreds 6 tens 5 ones On your personal white board write the number S Write 463 265 T Show 100 more S Write 463 365 Possible further sequence 10 000 less 100 000 more 1 less and 10 more T Write 400 90 3 On your place value chart write the number Possible further sequence 7 000 300 80 5 20 000 700 000 5 80 30 000 600 000 3 20 Convert Units NOTE This fluency activity strengthens understanding of the relationship between kilograms and grams learned in Grade 3 and prepares students to use this relationship to solve problems in Mission 2 Topic A Use a number bond to support understanding the relationship of grams and kilograms ZEARN MATH Teacher Edition 123
Topic F Lesson 17 YOUR NOTES G4M1 T Write 1 kg g How many grams are in 1 kilogram S 1 kg 1 000 g Repeat the process for 2 kg 3 kg 8 kg 8 kg 500 g 7 kg 500 g and 4 kg 250 g T Write 1 000 g kg Say the answer S 1 000 grams equals 1 kilogram T Write 1 500 g kg g Say the answer S 1 500 grams equals 1 kilogram 500 grams Repeat the process for 2 500 g 3 500 g 9 500 g and 7 250 g WORD PROBLEM A bakery used 12 674 kg of flour Of that 1 802 kg was whole wheat and 888 kg was rice flour The rest was all purpose flour How much all purpose flour did they use Solve and check the reasonableness of your answer NOTE This problem leads into Lesson 17 and acts as a bridge as it goes back into the work from Lesson 16 Concept Exploration NOTE Today s Concept Exploration uses the Problem Set Solutions for each problem are included below Materials S Problem Set Suggested Delivery of Instruction for Solving Topic F s Word Problems NOTE In Lessons 17 19 the Problem Set comprises word problems from the lesson and is therefore to be used during the lesson itself Have students turn to the Problem Set in their student workbooks 1 Model the problem 124 ZEARN MATH Teacher Edition
G4M1 Topic F Lesson 17 Have two pairs of students choose as models those students who are likely to successfully solve the problem work at the board while the others work independently or in pairs at their seats Review the following questions before solving the first problem Can you draw something What can you draw What conclusions can you make from your drawing YOUR NOTES As students work circulate Reiterate the questions above After two minutes have the two pairs of students share only their labeled diagrams For about one minute have the demonstrating students receive and respond to feedback and questions from their peers 2 Calculate to solve and write a statement Give everyone two minutes to finish work on the problem sharing their work and thinking with a peer All should then write their equations and statements for the answer 3 Assess the solution for reasonableness Give students one to two minutes to assess and explain the reasonableness of their solutions PROBLEM 1 Solve a single step word problem using how much more Sean s school raised 32 587 Leslie s school raised 18 749 How much more money did Sean s school raise Support students in realizing that though the question is asking How much more the tape diagram shows that the unknown is a missing part and therefore subtraction is necessary to find the answer PROBLEM 2 Solve a single step word problem using how many fewer At a parade 97 853 people sat in bleachers 388 547 people stood along the street How many fewer people were in the bleachers than standing along the street Circulate and support students to realize that the unknown number of how many fewer people is the difference between the two tape diagrams Encourage them to write a statement using the word fewer when talking about separate things For example I have fewer apples than you do and less juice ZEARN MATH Teacher Edition 125
Topic F Lesson 17 YOUR NOTES G4M1 PROBLEM 3 Solve a two step problem using how much more A pair of hippos weighs 5 201 kilograms together The female weighs 2 038 kilograms How much more does the male weigh than the female Many students may want to draw this as a single tape showing the combined weight to start That works However the second step most likely requires a new double tape to compare the weights of the male and female If no one comes up with the model pictured it can be shown quickly Students generally do not choose to draw a bracket with the known total to the side until they are very familiar with two step comparison models However be aware that students have modeled this problem type since Grade 2 PROBLEM 4 Solve a three step problem using how much longer A copper wire was 240 meters long After 60 meters was cut off it was double the length of a steel wire How much longer was the copper wire than the steel wire at first T Read the problem draw a model write equations both to estimate and calculate precisely and write a statement I ll give you five minutes Circulate using the bulleted questions to guide students When students get stuck encourage them to focus on what they can learn from their drawings Show me the copper wire at first In your model show me what happened to the copper wire In your model show me what you know about the steel wire What are you comparing Where is that difference in your model Notice the number size is quite small here The calculations are not the issue but rather the relationships Students will eventually solve similar problems with larger numbers but they will begin here at a simple level numerically 126 ZEARN MATH Teacher Edition
G4M1 MULTIPLE MEANS OF ACTION AND EXPRESSION Topic F Lesson 17 YOUR NOTES Make manipulatives available and encourage their use Some students may continue to need additional support in subtracting numbers using place value charts or disks MULTIPLE MEANS OF ACTION AND EXPRESSION Challenge students to think about how reasonableness can be associated with rounding If the actual answer does not round to the estimate does it mean that the answer is not reasonable Ask students to explain their thinking For example 376 134 242 Rounding to the nearest hundred would result with an estimate of 400 100 300 The actual answer of 242 rounds to 200 not 300 MULTIPLE MEANS OF ACTION AND EXPRESSION For students who may find Problem 4 challenging remind them of the work done earlier in this mission with multiples of 10 For example 180 is ten times as much as 18 If 18 divided by 2 is 9 then 180 divided by 2 is 90 Wrap Up LESSON SYNTHESIS Guide students in a conversation to process today s lesson and surface any misconceptions or misunderstandings The questions below may be used to lead the discussion How are your tape diagrams for Problem 1 and Problem 2 similar How did your tape diagrams vary across all problems In Problem 3 how did drawing a double tape diagram help you to visualize the problem What was most challenging about drawing the tape diagram for Problem 4 What helped you find the best diagram to solve the problem What different ways are there to draw a tape diagram to solve comparative problems What does the word compare mean What phrases do you notice repeated through many of today s problems that help you to see the problem as a comparative problem ZEARN MATH Teacher Edition 127
Topic F Lesson 17 YOUR NOTES G4M1 EXIT TICKET After the Student Debrief instruct students to complete the Exit Ticket A review of their work will help with assessing students understanding of the concepts that were presented in today s lesson and planning more effectively for future lessons The questions may be read aloud to the students Task Draw a tape diagram to represent the problem Use numbers to solve and write your answer as a statement A mixture of 2 chemicals measures 1 034 milliliters It contains some of Chemical A and 755 milliliters of Chemical B How much less of Chemical A than Chemical B is in the mixture Answers Tape diagram accurately drawn There are 476 ml less of Chemical A than of Chemical B in the mixture 128 ZEARN MATH Teacher Edition
G4M1 Topic F Lesson 17 Problem Set PROBLEM SET Name Date Draw a tape diagram to represent each problem Use numbers to solve and write your answer as a statement PROBLEM 1 Sean s school raised 32 587 Leslie s school raised 18 749 How much more money did Sean s school raise PROBLEM 2 At a parade 97 853 people sat in bleachers and 388 547 people stood along the street How many fewer people were in the bleachers than standing on the street ZEARN MATH Teacher Edition 129
Topic F Lesson 17 Problem Set G4M1 PROBLEM 3 A pair of hippos weighs 5 201 kilograms together The female weighs 2 038 kilograms How much more does the male weigh than the female PROBLEM 4 A copper wire was 240 meters long After 60 meters was cut off it was double the length of a steel wire How much longer was the copper wire than the steel wire at first 130 ZEARN MATH Teacher Edition
Topic F Lesson 18 G4M1 Lesson 18 YOUR NOTES Solve multi step word problems modeled with tape diagrams and assess the reasonableness of answers using rounding Warm Up FLUENCY PRACTICE Number Patterns Materials S Personal white board NOTE This fluency activity bolsters students place value understanding and helps them apply these skills to a variety of concepts T Project 40 100 50 100 60 100 What is the place value of the digit that s changing S Ten thousand T Count with me saying the value of the digit I m pointing to S Point at the ten thousand digit as students count 40 000 50 000 60 000 T On your personal white board write what number would come after 60 100 S Write 70 100 Repeat with the following possible sequence 82 030 72 030 62 030 215 003 216 003 217 003 943 612 943 512 943 412 and 372 435 382 435 392 435 Convert Units Materials S Personal white board NOTE This fluency activity strengthens understanding of the relationship between kilograms and grams learned in Grade 3 preparing students to use this relationship to solve problems in Mission 2 Topic A Use a number bond to support understanding of the relationship between grams and kilograms T Count by 200 grams starting at 0 grams and counting up to 2 000 grams When you get to 1 000 grams say 1 kilogram When you get to 2 000 grams say 2 kilograms S 0 g 200 g 400 g 600 g 800 g 1 kg 1 200 g 1 400 g 1 600 g 1 800 g 2 kg Repeat the process this time pulling out the kilogram e g 1 kg 200 g 1 kg 400 g ZEARN MATH Teacher Edition 131
Topic F Lesson 18 YOUR NOTES G4M1 T Write 1 300 g number sentence kg g On your board fill in the blanks to make a true S Write 1 300 g 1 kg 300 g Repeat the process for 1 003 g 1 750 g 3 450 g and 7 030 g WORD PROBLEM In all 30 436 people went skiing in February and January 16 009 went skiing in February How many fewer people went skiing in January than in February NOTE This comparison subtraction problem reviews content from Lesson 17 Concept Exploration NOTE Today s Concept Exploration uses the Problem Set Solutions for each problem are included below Materials S Problem Set Suggested Delivery of Instruction for Solving Topic F s Word Problems NOTE In Lessons 17 19 the Problem Set comprises word problems from the lesson and is therefore to be used during the lesson itself Have students turn to the Problem Set in their student workbooks 1 Model the problem 132 Have two pairs of students choose as models those students who are likely to successfully solve the problem work at the board while the others work independently or in pairs at their seats Review the following questions before solving the first problem Can you draw something What can you draw What conclusions can you make from your drawing ZEARN MATH Teacher Edition
G4M1 As students work circulate Reiterate the questions above After two minutes have the two pairs of students share only their labeled diagrams For about one minute have the demonstrating students receive and respond to feedback and questions from their peers Topic F Lesson 18 YOUR NOTES 2 Calculate to solve and write a statement Give everyone two minutes to finish work on the problem sharing their work and thinking with a peer All should then write their equations and statements for the answer 3 Assess the solution for reasonableness Give students one to two minutes to assess and explain the reasonableness of their solutions PROBLEM 1 Solve a multi step word problem requiring addition and subtraction modeled with a tape diagram and check the reasonableness of the answer using estimation This problem is optional In one year a factory used 11 650 meters of cotton 4 950 fewer meters of silk than cotton and 3 500 fewer meters of wool than silk How many meters in all were used of the three fabrics This problem is a step forward for students as they subtract to find the amount of wool from the amount of silk Students also might subtract the sum of 4 950 and 3 500 from 11 650 to find the meters of wool and add that to the amount of silk It is a longer method but makes sense Circulate and look for other alternate strategies which can be quickly mentioned or explored more deeply as appropriate Be advised however not to emphasize creativity but rather analysis and efficiency Ingenious shortcuts might be highlighted After students have solved the problem ask them to check their answers for reasonableness T How can you know if 21 550 is a reasonable answer Discuss with your partner S Well I can see by looking at the diagram that the amount of wool fits in the part where the amount of silk is unknown so the answer is a little less than double 12 000 Our answer makes sense S Another way to think about it is that 11 650 can be rounded to 12 thousands 12 thousands plus 7 thousands for the silk since 12 thousands minus 5 thousands is 7 thousands plus about 4 thousands for the wool That s 23 thousands ZEARN MATH Teacher Edition 133
Topic F Lesson 18 YOUR NOTES G4M1 PROBLEM 2 Solve an additive multi step word problem using a tape diagram modeled with a tape diagram and check the reasonableness of the answer using estimation This problem is optional The shop sold 12 789 chocolate and 9 324 cookie dough cones It sold 1 078 more peanut butter cones than cookie dough cones and 999 more vanilla cones than chocolate cones What was the total number of ice cream cones sold The solution above shows calculating the total number of cones of each flavor and then adding Students may also add like units before adding the extra parts After students have solved the problem ask them to check their answers for reasonableness T How can you know if 46 303 is a reasonable answer Discuss with your partner S By looking at the tape diagram I can see we have 2 thirteen thousands units That s 26 thousands We have 2 nine thousands units So 26 thousands and 18 thousands is 44 thousands Plus about 2 thousands more That s 46 thousands That s close S Another way to see it is that I can kind of see 2 thirteen thousands and the little extra pieces with the peanut butter make 11 thousands That is 37 thousands plus 9 thousands from cookie dough is 46 thousands That s close PROBLEM 3 Solve a multi step word problem requiring addition and subtraction modeled with a tape diagram and check the reasonableness of the answer using estimation In the first week of June a restaurant sold 10 345 omelets In the second week 1 096 fewer omelets were sold than in the first week In the third week 2 thousand more omelets were sold than in the first week In the fourth week 2 thousand fewer omelets were sold than in the first week How many omelets were sold in all in June 134 ZEARN MATH Teacher Edition
Topic F Lesson 18 G4M1 This problem is interesting because 2 thousand more and 2 thousand less mean that there is one more unit of 10 345 We therefore simply add in the omelets from the second week to three units of 10 345 YOUR NOTES T How can you know if 40 284 is a reasonable answer Discuss with your partner S By looking at the tape diagram it s easy to see it is like 3 ten thousands plus 9 thousands That s 39 thousands That is close to our answer S Another way to see it is just rounding one week at a time starting at the first week 10 thousands plus 9 thousands plus 12 thousands plus 8 thousands That s 39 thousands MULTIPLE MEANS OF ACTION AND EXPRESSION Give students support organizing their written workspace Some students may benefit from a dedicated box for drawing tape diagrams and or a written prompt reminding them to check their answer for reasonableness Independent Digital Lesson Lesson 18 Reflect on Reasonableness 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 135
Topic F Lesson 18 YOUR NOTES G4M1 Wrap Up LESSON SYNTHESIS Guide students in a conversation to process today s lesson and surface any misconceptions or misunderstandings The questions below may be used to lead the discussion How are the problems alike How are they different How was your solution the same and different from those that were demonstrated by your peers Why is there more than one right way to solve for example Problem 3 Did you see other solutions that surprised you or made you see the problem differently In Problem 1 was the part unknown or the total unknown What about in Problems 2 and 3 Why is it helpful to assess for reasonableness after solving How were the tape diagrams helpful in estimating to test for reasonableness Why is that 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 Draw a tape diagram to represent the problem Use numbers to solve and write your answer as a statement 1 Park A covers an area of 4 926 square kilometers It is 1 845 square kilometers larger than Park B Park C is 4 006 square kilometers larger than Park A a What is the area of all three parks b Assess the reasonableness of your answer Answers 1 a 16 939 sq km b Answers will vary 136 ZEARN MATH Teacher Edition
Topic F Lesson 18 Problem Set G4M1 PROBLEM SET Name Date Draw a tape diagram to represent each problem Use numbers to solve and write your answer as a statement PROBLEM 1 In one year the factory used 11 650 meters of cotton 4 950 fewer meters of silk than cotton and 3 500 fewer meters of wool than silk How many meters in all were used of the three fabrics PROBLEM 2 The shop sold 12 789 chocolate and 9 324 cookie dough cones It sold 1 078 more peanut butter cones than cookie dough cones and 999 more vanilla cones than chocolate cones What was the total number of ice cream cones sold ZEARN MATH Teacher Edition 137
Topic F Lesson 18 Problem Set G4M1 PROBLEM 3 In the first week of June a restaurant sold 10 345 omelets In the second week 1 096 fewer omelets were sold than in the first week In the third week 2 thousand more omelets were sold than in the first week In the fourth week 2 thousand fewer omelets were sold than in the first week How many omelets were sold in all in June 138 ZEARN MATH Teacher Edition
G4M1 Topic F Lesson 19 Lesson 19 YOUR NOTES Create and solve multi step word problems from given tape diagrams and equations TIP Students explore these concepts in their Independent Digital Lesson The teacher materials are optional for this lesson and we recommend that you continue your instruction with the next lesson Students who demonstrate a need for further support can explore these concepts with you and peers as part of a flex day as needed Warm Up FLUENCY PRACTICE Rename Units to Subtract NOTE This fluency activity supports further practice of decomposing a larger unit to make smaller units in order to subtract T Write 1 ten 6 ones Am I ready to subtract S No T Rename 1 ten as 10 ones Say the entire number sentence S 10 ones minus 6 ones is 4 ones Repeat with 2 tens 6 ones 2 tens 1 ten 6 ones 1 hundred 6 tens 2 hundreds 4 tens 3 hundreds 1 hundred 4 tens 5 thousands 3 hundreds 5 thousands 3 thousands 3 hundreds 2 ten thousands 3 hundreds Add Up to the Next Unit NOTE This fluency activity strengthens students ability to make the next unit a skill used when using the arrow way to add or subtract This activity also anticipates students use of the arrow way to solve mixed measurement unit addition and subtraction in Mission 2 T Write 8 How many more to make 10 S 2 T Write 80 How many more to make 100 S 20 ZEARN MATH Teacher Edition 139
Topic F Lesson 19 YOUR NOTES G4M1 T Write 84 How many more to make 100 S 16 Repeat with the following numbers to make 1000 200 250 450 475 600 680 700 720 800 805 855 and 945 Convert Units NOTE Reviewing unit conversions that were learned in Grade 3 helps prepare students to solve problems with centimeters and meters in Topic A of Mission 2 Materials S Personal white board T Write 1 m cm How many centimeters are in a meter S 1 m 100 cm Repeat the process for 2 m 3 m 8 m 8 m 50 cm 7 m 50 cm and 4 m 25 cm T Write 100 cm m Say the answer S 100 cm 1 m T Write 150 cm m cm Say the answer S 150 cm 1 m 50 cm Repeat the process for 250 cm 350 cm 950 cm and 725 cm WORD PROBLEM For Jordan to get to his grandparents house he has to travel through Albany and Plattsburgh From Jordan s house to Albany is 189 miles From Albany to Plattsburgh is 161 miles If the total distance of the trip is 508 miles how far from Plattsburgh do Jordan s grandparents live NOTE This problem reviews two step problems from the previous lessons 140 ZEARN MATH Teacher Edition
G4M1 Topic F Lesson 19 Concept Exploration YOUR NOTES NOTE Today s Concept Exploration uses the Problem Set Solutions for each problem are included below Materials S Problem Set Suggested Delivery of Instruction for Solving Topic F s Word Problems NOTE In Lessons 17 19 the Problem Set comprises word problems from the lesson and is therefore to be used during the lesson itself Have students turn to the Problem Set in their student workbooks 1 Model the problem Have two pairs of students choose as models those students who are likely to successfully solve the problem work at the board while the others work independently or in pairs at their seats Review the following questions before solving the first problem Can you draw something What can you draw What conclusions can you make from your drawing As students work circulate Reiterate the questions above After two minutes have the two pairs of students share only their labeled diagrams For about one minute have the demonstrating students receive and respond to feedback and questions from their peers 2 Calculate to solve and write a statement Give everyone two minutes to finish work on the problem sharing their work and thinking with a peer All should then write their equations and statements for the answer 3 Assess the solution for reasonableness Give students one to two minutes to assess and explain the reasonableness of their solutions PROBLEM 1 Create and solve a simple two step word problem from the tape diagram below Suggested context people at a football game ZEARN MATH Teacher Edition 141
Topic F Lesson 19 YOUR NOTES G4M1 PROBLEM 2 Create and solve a two step addition word problem from the tape diagram below Suggested context cost of two houses PROBLEM 3 Create and solve a three step word problem involving addition and subtraction from the tape diagram below Suggested context weight in kilograms of three different whales PROBLEM 4 Students use equations to model and solve multi step word problems Display the equation 26 854 17 729 3 731 A T Draw a tape diagram that models this equation T Compare with your partner Then create a word problem that uses the numbers from the equation Remember to first create a context Then 142 ZEARN MATH Teacher Edition
G4M1 Topic F Lesson 19 write a statement about the total and a question about the unknown Finally tell the rest of the information YOUR NOTES Students work independently Students can share problems in partners to solve or select word problems to solve as a class MULTIPLE MEANS OF REPRESENTATION Provide pictures of the suggested context or consider acting out the context for multilingual learners It might be helpful to go step by step while drawing a tape diagram Read a sentence and ask what can we draw to model what we know Consider working with multilingual learners in a small group and encourage them to explain their solutions in their language of choice Independent Digital Lesson Lesson 19 Tale of the Tape Students also learn the concepts from this lesson in the Independent Digital Lesson The intentional balance of learning with teachers and peers and learning independently in digital lessons ensures every student has multiple opportunities to represent engage with and express their math reasoning There are no notes for this digital lesson Go online to see the full digital lesson Wrap Up LESSON SYNTHESIS Guide students in a conversation to process today s lesson and surface any misconceptions or misunderstandings The questions below may be used to lead the discussion How does a tape diagram help when solving a problem What is the hardest part about creating a context for a word problem To write a word problem what must you know There are many different contexts for Problem 2 but everyone found the same answer How is that possible What have you learned about yourself as a mathematician over the past mission ZEARN MATH Teacher Edition 143
Topic F Lesson 19 YOUR NOTES G4M1 How can you use this new understanding of addition subtraction and solving word problems in the future 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 Using the diagram below create your own word problem Solve for the value of the variable 2 Using the equation below draw a tape diagram and create your own word problem Solve for the value of the variable 248 798 113 205 A 99 937 Answers 1 Word problems will vary 60 209 2 Tape diagram models the equation word problems will vary 35 656 144 ZEARN MATH Teacher Edition
G4M1 Topic F Lesson 19 Problem Set PROBLEM SET Name Date Using the diagrams below create your own word problem Solve for the value of the variable PROBLEM 1 PROBLEM 2 ZEARN MATH Teacher Edition 145
Topic F Lesson 19 Problem Set G4M1 PROBLEM 3 PROBLEM 4 Draw a tape diagram to model the following equation Create a word problem Solve for the value of the variable 26 854 17 729 3 731 A 146 ZEARN MATH Teacher Edition
Math Math TEACHER EDITION GRADE 4 TEACHER EDITION Mission 1 1 Mission 1 Add Subtract Round Mission 2 Measure and Solve Mission 3 Multiply and Divide Big Numbers Mission 4 Construct Lines Angles Shapes Mission 5 Equivalent Fractions Mission 6 Decimal Fractions 4 5 6 7 4 GRADE Mission 7 Multiply and Measure Grade 4 Mission 1 Zearnmath_TE_Grade4_M1 indd 1 3 TEACHER EDITION GRADE 4 2 1 27 23 1 20 PM