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COURSE GUIDE Grade 4 2022 Zearn Inc Portions of this work Zearn Math are derivative of Eureka Math and licensed by Great Minds 2021 Great Minds All rights reserved

2022 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 056 8

Table of Contents ABOUT ZEARN MATH ABOUT FOURTH GRADE MATH Approach 6 Pacing 8 A TYPICAL LESSON IN ZEARN MATH Warm Up 9 Concept Exploration 10 Wrap Up 11 IMPLEMENTING ZEARN MATH Planning for a Mission 11 Planning your week 12 Core Days 12 Flex Day 13 Planning for a lesson 14 SUPPORTING DIVERSE LEARNERS Commitment to accessibility 18 Design features that support all learners 18 Supporting multilingual learners 19 Elements of language 20 Mathematical language routines MLRs 20 Supporting students with disabilities 21 Accessible design features 22 Assistive technology 22 Instructional accommodations 23 ASSESSMENTS AND REPORTS Ongoing formative assessments 24 Daily lesson level assessments The Tower of Power digital and Exit Tickets paper 24 Mission level assessments paper 24 Class and student reports 26

Table of Contents Class reports Progress Pace Tower Alerts and Sprint Alerts 26 Student Reports 27 Approach to unfinished learning 27 TERMINOLOGY REQUIRED MATERIALS LESSONS BY STANDARD STANDARDS BY LESSON APPENDIX I INSTRUCTIONAL ROUTINES White Board Exchange 38 Anticipate Monitor Select Sequence Connect 38 Take Turns 39 Think Pair Share 39 READ DRAW WRITE RDW 39 APPENDIX II ACCESS FOR MULTILINGUAL LEARNERS Introduction 40 Theory Of Action 40 Design Principles for Promoting Mathematical Language Use and Development 42 Principle 1 Support Sense Making 42 Principle 2 Optimize Output 42 Principle 3 Cultivate Conversation 42 Principle 4 Maximize Meta awareness 43 Mathematical Language Routines 43 Mathematical Language Routine 1 Stronger and Clearer Each Time 44 Mathematical Language Routine 2 Collect and Display 45 Mathematical Language Routine 3 Clarify Critique Correct 45 Mathematical Language Routine 4 Information Gap 46 Mathematical Language Routine 5 Co craft Questions 47 Mathematical Language Routine 6 Three Reads 47 Mathematical Language Routine 7 Compare and Connect 48 Mathematical Language Routine 8 Discussion Supports 49 Sentence Frames 50 REFERENCES 4 ZEARN MATH Teacher Edition

G4 Course Guide About Zearn Math About Zearn Math All Children Can Love Learning Math VISION Zearn Math was developed by Zearn a nonprofit educational organization We believe that an understanding and love of mathematics is critical to helping all children realize their potential and to creating a generation of engaged learners who can change the world In 2011 Zearn s team of educators and engineers created Zearn Math as an evidence based student centered curriculum that balances rich mathematical discourse collaborative problem solving and independent thinking and working time With Zearn Math students learn math as the progression of connected ideas over the course of the year grounded in visual problem solving with a concrete to pictorial to abstract approach LEARNING PRINCIPLES Zearn combines our own digital lessons and assessments with open source curricula in order to create an engaging accessible and coherent K 8 experience for all students We developed Zearn Math using learning principles drawn from teacher practice education research and brain science as well as extensive data from student engagement with our software over the years which we use to strengthen our materials and technology each year Math is a few big ideas We delve deeply into these ideas connecting and reinforcing them over the course of grades K 8 When kids learn math as a coherent discipline rather than a series of unrelated tricks and move from a simple to a deeper understanding of the structures of math they build dense connections that can help them tackle any problem Schmidt et al 2005 Math is more than memorization We built Zearn Math using the proven Concrete to Pictorial to Abstract CPA approach in which students make sense of math using concrete materials then pictorial representations and finally abstract symbols to solve problems Leong and Cheng 2015 We also carry visual representations later into each year grade and lesson so students always have something they can reference when they are faced with a problem they don t know how to solve There are lots of right ways to solve problems We show students many options so they can find a way and move forward rather than getting stuck and feeling frustrated We used the Universal Design for Learning UDL principles to help teachers teach concepts in multiple ways with the whole class in groups with the teacher and their peers and on their own CAST n d This gives students more flexibility in how they learn and in how they demonstrate their understanding ZEARN MATH Teacher Edition 5

About Fourth Grade Math G4 Course Guide Mistakes are magic We help teachers create inclusive math communities where students feel safe to struggle Students receive in the moment feedback that precisely addresses areas of misconception both as they explore concepts with their peers and independently practice number sense concepts Research on growth mindsets shows that children who believe that making mistakes is part of the learning process enjoy learning more and are more resilient and self directed in their learning Paunesku et al 2015 Math is for everyone We think every kid should be able to see someone like themselves learning and persevering in math Scholars have found that members of historically excluded groups may feel belonging uncertainty undermining their motivation to learn Walton and Cohen 2007 To counter this our print based activities reflect the diversity found in classrooms across the country so that no one group is over or underrepresented or stereotyped within the context of a particular problem All students can see someone similar to themselves doing math and persevering through challenges About Fourth Grade Math APPROACH Guided by our learning principles Zearn Math s multimodal learning accommodates and celebrates learning differences and fosters positive math mindsets and social belonging so all students can love learning math During their daily math block students will explore the same math concepts in two ways Alongside their peers and teacher students will model math with concrete manipulatives represent their work on paper discuss their reasoning aloud and receive direct feedback from their teacher as well as from peers Independently students will use self paced software based lessons to explore and practice concepts with concrete and digital manipulatives interactive videos and pictorial representations receiving precise digital feedback at the moment of misconception With this approach mathematics is not a spectator sport Students spend most of their time in math class actually doing mathematics rather than just listening to or watching it They work on mathematics problems together and independently often utilizing prior knowledge and skills with guidance from the teacher and with precise in the moment digital feedback that together ensures all students understand each concept In the process they make sense of problems try different approaches select and use appropriate tools notice patterns explain their ideas and reasoning and listen to others and come to understand that mistakes are a valuable part of the mathematical learning process 6 ZEARN MATH Teacher Edition

G4 Course Guide About Fourth Grade Math SCOPE SEQUENCE The curriculum map below shows how students will cover a series of big mathematical ideas color coded to show the coherent structure of Zearn Math over the course of the grade and in other grades 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 K M3 M2 M1 2D 3D Shapes Numbers to 10 Numbers to 5 Digital Activities 50 M1 G1 M1 G3 M2 Add Subtract Friendly Numbers M1 G4 G5 Place Value with Decimal Fractions G7 G8 Key Base Ten Operations 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 M3 Rates and Percentages M4 Measuring Circles M2 Dilations Similarity and Introducing Slope M4 Dividing Fractions Proportional Relationships and Percentages M3 Linear Relationships Expanding Whole Numbers and Operations to Fractions and Decimals ZEARN MATH Teacher Edition Add Subtract Fractions M5 Rational Number Arithmetic M4 Linear Equations and Linear Systems M5 M5 M7 Functions and Volume Algebraic Thinking and Reasoning Leading to Functions M6 Associations in Data Geometry M6 M9 M8 Rational Numbers Angles Triangles and Prisms Multiply Measure The Coordinate Plane M7 Expressions and Equations M7 Decimal Fractions Volume Area Shapes M6 M6 Shapes Measurement Display Data M6 M4 Expressions Equations and Inequalities Shapes Time Fractions M7 M6 Fractions as Numbers Multiply and Divide Fractions Decimals Arithmetic in Base Ten M8 M7 Equivalent Fractions M5 M6 Add Subtract to 100 Length Money Data M5 Construct Lines Angles Shapes M3 M2 M6 Equal Groups M5 M4 M3 M5 M4 Find the Area Numbers to 20 Digital Activities 35 Work with Shapes M5 M3 Multiply Divide Big Numbers M1 M4 Add Subtract Big Numbers Multiply Divide Tricky Numbers Measure It Numbers to 15 Digital Activities 35 Add Subtract Big Numbers Add Subtract Solve M2 M2 M1 M3 Measure Length M4 Counting Place Value Multiply Divide Friendly Numbers Add Subtract Round G6 M3 Explore Length 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 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 7

About Fourth Grade Math G4 Course Guide Fourth grade math begins with a culmination of work students began in Kindergarten exploring number sense place value understanding and ultimately moving students towards the standard algorithm for whole number addition and subtraction Much of the rest of fourth grade is devoted to bridging students from third grade understanding of multiplication division and fractions to the work students will be expected to complete in fifth grade This includes multiplying and dividing beyond 100 both on paper and in their heads as well as extending their third grade understanding of fractions as numbers to fraction equivalence addition and subtraction of fractions with like denominators and multiplication of fractions by whole numbers This multiplication division and extensive fraction work will set students up for success in fifth grade where they extend each of these ideas Moreover in fourth grade students extend their understanding of fractions and the base ten number system to learn a new and special notation for fractions decimals Fourth grade concludes by providing students with an opportunity to synthesize what they ve learned throughout the year and apply it in complex measurement situations involving conversions Along with focusing on the big mathematical ideas of the grade Zearn Math gives students regular opportunities to engage in and develop the Standards for Mathematical Practice which are drawn from the National Council of Teachers of Mathematics and the National Research Council and describe varieties of expertise that mathematics educators should seek to develop in their K 12 students Common Core State Standards Initiative n d These MPs are MP1 Make sense of problems and persevere in solving them MP2 Reason abstractly and quantitatively MP3 Construct viable arguments and critique the reasoning of others MP4 Model with mathematics MP5 Use appropriate tools strategically MP6 Attend to precision MP 7 Look for and make use of structure MP8 Look for and express regularity in repeated reasoning PACING The fourth grade year will include seven units known in Zearn Math as Missions see details below Teachers should aim to cover four lessons per week with a fifth Flex day or equivalent time reserved for teachers to differentiate instruction and administer assessments so the full fourth grade curriculum should take about 36 weeks to complete This pace ensures students have sufficient time each week to work through grade level content with built in weekly time to assess and address student needs Each Mission will conclude with a paper based End of Mission assessment some longer Missions also contain a Mid Mission assessment Students also complete two formative assessments on each lesson a digital Tower of Power assessment and a paper Exit Ticket 8 Mission Title Lessons Weeks 1 Add Subtract and Round 18 5 ZEARN MATH Teacher Edition

G4 Course Guide A Typical Lesson in Zearn Math Mission Title Lessons Weeks 2 Measure and Solve 5 1 3 Multiply and Divide Big Numbers 34 9 4 Construct Lines Angles and Shapes 14 4 5 Equivalent Fractions 38 10 6 Decimal Fractions 15 4 7 Multiply and Measure 12 3 136 36 Totals Note Weeks are estimates based on 4 lessons completed per week Actual time will vary by student A Typical Lesson in Zearn Math In a typical math block with Zearn covering one lesson students will experience Warm Up Concept Exploration including Collaborative Concept Exploration with teacher and peers Independent Digital Lessons to explore concepts further on their own and Wrap Up Lesson Synthesis led by the teacher and the completion of an individual Exit Ticket WARM UP The first event in every lesson is the Warm Up which invites students into the day s lesson with a series of engaging activities The Warm Up gives students an opportunity to strengthen their number sense and procedural fluency and to get ready for the day s lesson by engaging with a real world problem Warm Ups include Fluency Practice Welcomes students into the day s lesson with a fun activity This activity helps students flex their mathematical muscles in order to stay sharp on previously learned skills prepare to practice and extend those skills in the current lesson and anticipate upcoming lessons As the opening activity of every lesson this should be welcoming and joyful with perfection neither expected nor required rather growth over time is the goal Teachers can help create a positive inclusive learning environment by ZEARN MATH Teacher Edition 9

A Typical Lesson in Zearn Math G4 Course Guide encouraging and praising students for participating and taking note of any unfinished learning as an opportunity to address later rather than something to resolve in the moment Word Problem Focuses on problem solving using previously learned math concepts Students solve word problems independently and then share their work with peers to provide opportunities for student to student math discussion Like the daily fluency activity the daily word problem primes students for the day s lesson by bringing to the surface math concepts that are applicable to the new learning of the lesson Teachers should focus on creating discourse rather than ensuring every student solves the problem correctly Consider this as an opportunity to identify any unfinished learning that may surface which you can address during Collaborative Concept Exploration CONCEPT EXPLORATION Next students have two opportunities to study the same concepts with their teacher and peers in Collaborative Concept Exploration and using self paced Independent Digital Lessons 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 Concept exploration includes Collaborative Concept Exploration Built around a series of scaffolded math problems that move students toward the overall goal of the lesson Teachers facilitate thoughtful mathematical discussions between students allowing them to refer to and build on each others ideas using sample vignettes provided by Zearn that illustrate how each problem should unfold and what rich discourse should look like during the learning Students will share their own thinking aloud and discuss classmates problem solving strategies Teachers can also assess individual students understanding as students model their math thinking using concrete manipulatives share their reasoning aloud and problem solve These moments of feedback also provide all students with valuable in the moment support so they can correct their misconceptions and continue learning Independent Digital Lessons Students complete self paced software based lessons on their own Students construct their mathematical thinking using visual models and have opportunities to test and confirm their reasoning with precise feedback to help them find and correct mistakes This self paced learning fosters students sense of ownership over their math learning and boosts students math mindsets because all students are able to take the amount of time they need to problem solve review content or receive scaffolded support The video player can be paused or rewound at any time For more on what students will experience during Independent Digital Lessons see Planning for a Lesson in the Implementing Zearn Math section below For more on addressing struggle see Addressing unfinished learning in the Assessments and Reports section below 10 ZEARN MATH Teacher Edition

G4 Course Guide Implementing Zearn Math WRAP UP After the concept exploration phase of the lesson students move to the final phase of the lesson the Wrap Up This phase provides students with time to synthesize what they just learned during the concept exploration and gives teachers a chance to formatively assess whether students grasped the big idea of the lesson which can then inform the next lesson The Wrap Up includes two opportunities to formatively assess student understanding Lesson Synthesis Students incorporate new insights into big picture understanding and teachers get a sense of students understanding Each lesson includes suggested discussion starters that teachers can use to guide students in a conversation to process the lesson Teachers may pose questions verbally and call on volunteers to respond and could ask students to add a new component to a persistent display like a word wall Also this is the final moment of discourse for every lesson and unfinished learning may be evident by what students are saying or not saying However teachers should not use this moment to try and reteach the entire lesson but rather use this moment as one of many formative assessments provided in each lesson they can combine this data with their review of student work on the lesson s Exit Ticket and the Tower Alerts report to determine the effectiveness of the lesson For more on how to appropriately diagnose and respond to unfinished learning see the corresponding section below in Assessments and Reports Exit Ticket Students demonstrate their understanding of the content of the lesson To get the most authentic and helpful data possible students should complete the un scaffolded practice problems on the paper Exit Ticket independently to the best of their ability Teachers can use Exit Tickets as formative assessments to identify students who may need extra help with a particular concept and provide appropriate support and or combine this information with observations from the Tower Alerts report to determine the extent of any misconception For more see Assessments and Reports below Implementing Zearn Math PLANNING FOR A MISSION The story of Zearn Math for fourth grade is told in seven Missions Concepts are taught through the concrete topictorial to abstract progression within each Mission and throughout the year to allow students ample time to continue to build their developing understanding The table of contents in each Mission book shows you how the lessons of the Mission are divided into topics as well as the placement of the Mission level paper based assessments If you have access to Curriculum Study Professional Development as part of your Zearn Math School Account it will guide your planning and understanding of each Mission including an in depth examination of the visual representations and strategies explored in that Mission it will also guide you through the assessments and a selection of Independent Digital Lessons curated based on our data about where students tend to encounter challenges If you don t have access to this resource there are many materials you can use to plan for a Mission ZEARN MATH Teacher Edition 11

Implementing Zearn Math G4 Course Guide Familiarize yourself with the mathematics of the Mission and how students will progress toward understanding of the big ideas of the Mission Read through the Mission Overview in the Zearn Math Teacher Edition taking note of the progression of the mission key representations and strategies used and any moments that may be challenging for students The Mission Overviews provide an opportunity to deeply learn the big ideas of the Mission Complete the Mission level paper based assessments and study the assessment rubrics provided including the exemplar student work Take note of any lessons that are marked optional You can omit these lessons to allow for a Flex Day each week and still complete all grade level content For more on Flex Days see below section on Planning for a week Work through a selection of the Independent Digital Lessons that students will complete during the Mission including the Guided and Independent Practice portions of the lessons This will help you deepen your understanding of how the previously studied concepts act as on ramps into the new learning as well as how the ideas will scaffold across the Mission For more on preparing for individual lessons see the Planning for a lesson section below At the start of each Mission Check Zearn Class Reports to review students progress and assign all students to the first Independent Digital Lesson of the Mission to ensure that they will have a chance to cover all the big mathematical ideas of the Mission in two ways both digitally and in person with their class For more see Assessments and Reports below Finally as you prepare for your first Mission keep in mind that parents caregivers may want to know how best to support their students To equip them go online to visit the Zearn Math Parent and Caregiver Support page of the Zearn website available in both English and Spanish 1 Ideas include Sending home our Learning with Zearn overview flyer Hosting a parent orientation or back to school night using our Zearn Math Parent Presentations Throughout the year consider sharing Mission Overviews with parents and caregivers so they know what big mathematical ideas students will be learning in addition the Student Report for their child and the assessment rubrics may provide additional insight into their student s progress and areas of misconception or struggle PLANNING YOUR WEEK We designed Zearn Math to include four Core Days when students learn grade level content as well as one Flex Day that you can tailor to meet students needs This weekly schedule ensures students have sufficient time each week to work through grade level content while also giving you additional time to address unfinished learning and or misconceptions that might be hindering student progress Core Days If you are using this Zearn Math recommended weekly schedule we recommend omitting the optional lessons in each Mission On Core Days you should plan for a balance of learning across multiple formats We designed The Zearn Help Center can be found at http help zearn org the Zearn Math Parent and Caregiver Support page of the Zearn web site can be found at https about zearn org math resources parent caregiver support 1 12 ZEARN MATH Teacher Edition

G4 Course Guide Implementing Zearn Math this lesson structure to fit into a 75 minute math block but all times are suggestions that can be modified to accommodate different schedules Warm Up with the whole class may take up to 10 minutes including fluency and word problems Concept Exploration includes about 30 minutes of Collaborative Concept Exploration and 30 minutes of Independent Digital Lessons for a total of 60 minutes These can be adjusted based on available time as long as students have daily opportunities to learn and practice in a variety of instructional settings with a variety of different learners Some teachers choose to have students rotate through these two stations while others have students complete Independent Digital Lessons during other flexible time during the day A few lessons do not include an Independent Digital Lesson Guidance on how best to handle each situation is detailed in your Zearn Math Teacher Edition Wrap Up including lesson synthesis and an Exit Ticket takes about 5 minutes Flex Day In addition to 4 Core Days if you are using the Zearn Math recommended weekly schedule and omitting optional lessons you will have time for a Flex Day each week Consider how you might use this time to continue addressing individual student needs you may have noticed during your Core Day lessons or while reviewing Zearn class and student reports Check Zearn class and student reports to determine what student needs you might address during this time The Pace report indicates which students may need more time to complete Independent Digital Lessons The Tower Alerts report indicates which students are struggling with particular concepts Decide how you will address the needs of different students during Flex Day or Flex time Use the Pace Report to identify any students who have completed fewer than four Independent Digital Lessons that week Some students may need more time to finish these digital lessons If these students are making progress and simply need more time allow these students to spend time during Flex Days finishing their Independent Digital Lessons so they can meet their goals Use the Tower Alerts report to identify groups of students struggling with the same concepts or misconceptions You could teach these groups mini lessons using the optional problems from the Zearn Math Teacher Edition If the Tower Alerts report identifies individual students struggling with a particular concept or misconception you could bookmark foundational content for them to complete For more see Addressing unfinished learning in the Assessments and Reports section below For students who are completing four Independent Digital Lessons each week and demonstrating full understanding on assessments you can use Flex time to provide opportunities for additional challenge and growth Zearn Math provides teachers with curricular materials for extending learning that are aligned to students current grade level work including Digital Bonuses Digital Bonuses are challenging problems students can work on after they complete an Independent Digital Lesson These problems enrich and extend their learning by going deeper into gradelevel mathematics often making connections between the topic at hand and other concepts Digital Bonuses do not appear automatically in the Student Feed so you can direct students to navigate to them from their Badges ZEARN MATH Teacher Edition 13

Implementing Zearn Math G4 Course Guide Optional enrichment problems The Zearn Math Teacher Edition highlights extra above grade level problems that you can point students to during Flex time for enrichment Some of these problems extend the work of the associated lesson while others may involve concepts covered in prior grades or Missions These problems are denoted by a green apple and marked Optional for Flex Day Enrichment When it is time for a Mission level assessment plan to have students complete these assessments during Flex time For more see Assessments and Reports below PLANNING FOR A LESSON You can use your Zearn Math Teacher Edition daily to plan and implement each lesson of the Mission To prepare for teaching each lesson within a Mission we recommend that teachers Read through the lesson to gain an understanding of how the big mathematical idea of the lesson unfolds across the lesson taking note of the discussion guidance and how it helps move students toward the lesson s objective Discussion guidance Every lesson includes a description of each problem as well as a sample vignette that shows potential dialogue between teacher and students As students share their reasoning are exposed to other perspectives and engage in mathematical sense making they are able to deepen their own understanding and become more creative and effective problem solvers These vignettes should not be viewed as a script that teachers and students must follow but rather an illustration of how each problem should unfold and of what rich discourse should look like during the learning Above all you ll want to be comfortable with the flow of the lesson how the big mathematical ideas unfold within it and the purpose of each problem in the lesson Complete the entire Independent Digital Lesson that students will complete As you do this focus on examining the learning progression and students move toward developing a full understanding of the big mathematical idea of the Mission We recommend intentionally making mistakes throughout the digital experience to see how students will be supported when making their own mistakes For students each lesson includes Adaptive fluency activities Every Independent Digital Lesson includes Number Gym an individually adaptive fluency experience that helps students build foundational number sense Number Gym activities are designed to bridge K 2 math foundations reinforce previously learned skills and address areas of unfinished learning Number Gym activities include Make and Break Next Stop Top Number Bond Dash Take From 10 Take from 10 Take Two Addition Magician Addition Magician Returns Form to Form the Counting Train Hop Skip Splash Sum Snacks Bundle the Sea Count the Cosmos and Polar Place Values Lesson aligned fluency activities Each Independent Digital Lesson includes a fluency activity aligned to the specific lesson the student is working on and preparing them for upcoming content Students practice prior concepts in lesson aligned fluency activities such as Sprints Pair Compare Totally Times Fraction Action Mix and Match and Blasts Guided Practice Students experience one of three different Guided Practice activities Math Chat Learning Lab or Z Squad Each activity creates a rich learning environment for students through interactive and multisensory videos featuring real on screen teachers and digital manipulatives Students are prompted to 14 ZEARN MATH Teacher Edition

G4 Course Guide Implementing Zearn Math complete problems in their paper Student Notes to transfer their software based learning check and correct their work and strengthen knowledge retention Independent Practice Tower of Power Students demonstrate their understanding of the content of an Independent Digital Lesson and unlock the next one by completing all problems correctly in the Tower of Power If students make a mistake in a Tower of Power problem a Boost breaks down the question into smaller steps with more supportive manipulatives to allow students to understand and correct their mistakes Students then have a chance to demonstrate their learning with a new problem I f students continue to struggle in the Tower of Power after multiple attempts their teacher receives an alert in the Tower Alerts Report enabling them to provide tailored differentiated support for that student Determine specific instructional routines you will use Zearn Math lesson plans often include information about instructional routines that may be suited to teaching a particular lesson The kind of instruction appropriate in any particular lesson depends on the learning goals of that lesson Some lessons may be devoted to developing a concept others to mastering a procedural skill yet others to applying mathematics to a real world problem These include White Board Exchange Students record their thinking on a personal white board and exchange their white boards with a partner to evaluate their partner s thinking and strategy Anticipate Monitor Select Sequence Connect These are the 5 Practices for Orchestrating Productive Mathematical Discussions Smith and Stein 2011 Teachers will want to prepare for and conduct whole class discussions anticipate likely student responses to challenging mathematical tasks monitor students actual responses to the tasks selecting particular students to present their mathematical work during discussion sequence the student responses that will be displayed in a specific order and connect different students responses to one another and to key mathematical ideas Take Turns Students work with a partner or group of peers taking turns in the work of the activity If they disagree they are expected to support their case and listen to their partner s arguments Think Pair Share Students have quiet time to think about a problem and work on it individually and then time to share their response or their progress with a partner Once these partner conversations have taken place some students are selected to share their thoughts with the class Read Draw Write RDW Students engage with word problems by first reading the problem then representing their thinking visually with a drawing and finally solving the problem and writing their answer in the form of a sentence For more detail and source information see Appendix I Instructional Routines Consider which strategies you will use to create access for all learners You will want to plan intentionally for how to meet the specific and varied needs of your students including those with unfinished learning those with disabilities and multilingual learners using data from Zearn reports and your own observations from the classroom The notes at the end of each Zearn Math lesson suggest strategies for ensuring that diverse learners can access specific activities without reducing the mathematical demand of the task Each strategy aligns to one of the three principles of UDL engagement representation and action and expression to increase access and eliminate barriers ZEARN MATH Teacher Edition 15

Implementing Zearn Math G4 Course Guide Engagement Students attitudes interests and values help to determine the ways in which they are most engaged and motivated to learn Supports that align to this principle provide students with multiple means of engagement and include suggestions that help provide access by leveraging curiosity and students existing interests leveraging choice around perceived challenge encouraging and supporting opportunities for peer collaboration providing structures that help students maintain sustained effort and persistence during a task providing tools and strategies that help students self motivate and become more independent Representation Teachers can reduce barriers and leverage students individual strengths by inviting students to engage with the same content in different ways Supports that align to this principle provide students with multiple means of representation and include suggestions that offer alternatives for the ways information is presented or displayed help develop students understanding and use of mathematical language and symbols illustrate connections between and across mathematical representations using color and annotations identify opportunities to activate or supply background knowledge and describe organizational methods and approaches designed to help students internalize learning Action and Expression Throughout the curriculum students are invited to share both their understanding and their reasoning about mathematical ideas with others Supports that align to this principle provide students with multiple means of action and expression and include suggestions that encourage flexibility and choice with the ways students demonstrate their understanding list sentence frames that support discourse or accompany writing prompts see Appendix II Access for Multilingual Learners indicate appropriate tools templates and assistive technologies support the development of organizational skills in problem solving and provide checklists that enable students to monitor their own progress For more information and ideas see the next section on Supporting Diverse Learners including students with disabilities and multilingual learners After reviewing the lesson materials and completing the Independent Digital Lesson you can annotate your Zearn Math Teacher Edition using the Your Notes section in the margin of each lesson Annotations may include Key ideas from each moment of the lesson Probing questions you may ask to move students toward understanding the takeaway during the synthesis portion of each activity Explicit connections to prior activities and or lessons and Optional problems you plan to use Some lessons contain optional activities that provide additional practice for you to use at your discretion These problems are denoted by a green apple in the teacher materials and marked Optional for Flex Day To identify which students may benefit from extra practice with a specific math idea teachers can check the Tower Alerts Report each week Make sure to have on hand all of the required materials to successfully enact the lesson Required materials are listed on the first page of each lesson and a full list is available in a later section of this course guide PREPARING STUDENTS FOR INDEPENDENT DIGITAL LESSONS To ensure students are ready to complete Independent Digital Lessons you will want to do the following with them You should only have to do this during your first week of instruction unless you observe that a refresher is needed 16 ZEARN MATH Teacher Edition

G4 Course Guide Implementing Zearn Math Complete 2 3 Independent Digital Lessons together as a whole class You can model a lesson from your account by using the Try lesson as a student feature on your Zearn Math Welcome Page and project or share your screen so students can follow along Be sure to Walk through each component of a digital lesson For fourth grade these are Adaptive Fluency Lesson Aligned Fluency Guided Practice Independent Practice Model completing paper Student Notes and correcting them when prompted in the Guided Practice section Discuss strategies for persevering through challenges like working through a Boost within a Tower of Power referencing Student Notes revisiting the Guided Practice and even guessing if needed and letting the digital lesson provide help Remind students that some struggle is both expected and useful and that you will not be helping them to complete these lessons Instead they should try their best to resolve challenges on their own with the support of the software s built in scaffolds and you will frequently check Pace Report and Tower Alerts Report to identify any students who may be struggling unproductively Show students how to work on their Next Up activity Students work through Independent Digital Lessons at their own pace and are always assigned to one of these activities as their Next Up assignment Students can only access the next digital activity in the sequence once they complete their currently assigned activity Show students the accessibility features including Closed captioning Closed captioning for all interactive student videos is available for all Missions for all grades Closed captioning allows students to turn on an English text transcription of all dialogue and other relevant audio information in the Zearn Math video player This accessibility feature is particularly useful for deaf and hard of hearing students as well as multilingual learners Audio support All instructional prompts students see in Independent Digital Lessons have audio support through either recorded audio or Zearn Math s text to speech feature Students can click on the audio button next to text questions or prompts to hear the words spoken aloud All math expressions in Zearn Math software based lessons are read correctly with Zearn Math s text to speech tool Additional audio support if needed can be accessed using supported browser text to speech tools These accessibility features are particularly important for students with cognitive impairments students with learning differences young students and multilingual learners Zoomability Students may resize digital pages up to 200 through browser settings to view images or text closer up without losing any content This accessibility feature is particularly important for students with visual impairments and students using devices with small screens On screen keypad As students work through Independent Digital Lessons they have the option to use an on screen keypad rather than a computer keyboard to type and submit answers This accessibility feature is particularly important for tablet users and young students who may not know how to use a computer keyboard ZEARN MATH Teacher Edition 17

Supporting Diverse Learners G4 Course Guide You may also use this time to introduce students to the Math Library noting that you might direct them here throughout the year for additional assignments For more on the Math Library see the Addressing unfinished learning section of Assessments and Reports below To find many additional resources that can help you and your students prepare for software based lessons go online to visit the Zearn Help Center 2 There you can find not only a getting started checklist a recommended schedule and technology requirements but also ideas for how to set up strong classroom systems and routines that will help students learn how to use Zearn Math and how to build the mindsets habits and confidence in math Supporting Diverse Learners COMMITMENT TO ACCESSIBILITY Zearn believes that with proper structures accommodations and support all children can learn mathematics As such we designed Zearn Math to be accessible for all students using the Universal Design for Learning UDL principles to maximize access and engagement for all students We have also added supports and structures throughout to help teachers accommodate the needs of diverse learners For more see above sections on Planning for a lesson as well as Preparing students for Independent Digital Lessons under Implementing Zearn Math DESIGN FEATURES THAT SUPPORT ALL LEARNERS To support a diverse range of learners including students with unfinished learning multilingual learners and students with disabilities Zearn Math design features include Consistent lesson structures The structure of every lesson is the same Warm Up Concept Exploration Wrap Up By keeping the components of each lesson similar from day to day the flow of work in class becomes predictable for students This reduces cognitive demand and enables students to focus on the mathematics at hand rather than the mechanics of the lesson Concepts developing over time from concrete to abstract Mathematical concepts are introduced simply concretely and repeatedly with complexity and abstraction developing over time Students begin with concrete examples and transition to diagrams and tables before relying on symbols to represent the mathematics they encounter Moreover this CPA approach is repeated throughout lessons Missions and across the grade to continually give students access to new ideas 2 https help zearn org 18 ZEARN MATH Teacher Edition

G4 Course Guide Supporting Diverse Learners Co constructing knowledge with students Providing students with time to think through a situation or question independently before engaging with others allows students to carry the weight of their own learning with support arriving just in time from the community of learners in Collaborative Concept Exploration as well as from the software based Independent Digital Lessons This progression allows students to start with what they already know and continue to build from this base with others Opportunities to apply mathematics to real world contexts Giving students opportunities to apply the mathematics they learn through word problems clarifies and deepens their understanding of core math concepts and skills while also providing motivation and support Mathematical modeling is a powerful activity for all students but especially for students with disabilities Centering instruction on these contextual situations right from the beginning of the lesson during the Warm Up can provide students with disabilities an anchor upon which to base their mathematical understandings Access strategies The Notes Page at the end of each lesson includes additional strategies for learners who might benefit from alternate access pathways These lesson specific supports can be used as needed to help students succeed with a specific activity without reducing the mathematical demand of the task and can be faded out as students gain understanding and fluency Each strategy aligns to one of the three principles of UDL Multiple Means of Engagement Multiple Means of Representation and Multiple Means of Action and Expression and includes a suggested strategy to increase access and eliminate barriers Physical Math Manipulatives Zearn Math notes required materials in the Mission Overview and in each Lesson Additionally Hand2Mind sells Zearn aligned kits to allow concept exploration to always start with the concrete Manipulative kits are designed to include all of the essential concrete manipulatives classrooms need and each grade level kit connects with Zearn Math activities and lessons for each Mission All kits are organized labeled and ready to drop off in classrooms 3 SUPPORTING MULTILINGUAL LEARNERS Zearn believes that language learners of all levels can and should engage with grade level content that is scaffolded with sufficient linguistic support Zearn Math provides students opportunities to access gradelevel mathematics using existing language skills and to extend their language development in the context of mathematical skill development Each day with Zearn Math students learn in a classroom model designed for daily differentiation experience inclusive environments of social belonging and build language skills as they learn with the whole class with peers and on their own with software based lessons In addition we provide teachers with a Zearn Math Teacher Edition that provides strategies on how to support students language development daily within the context of their math class For more see above section on Planning for a lesson under Implementing Zearn Math Teachers who have access to Curriculum Study Professional Development as part of their PD enabled Zearn Math School Account can use that tool to build additional expertise on how to support students language development as they learn math and encounter areas of struggle 3 Zearn Math manipulative kits can be found at https www hand2mind com kits publisher aligned kits zearn ZEARN MATH Teacher Edition 19

Supporting Diverse Learners G4 Course Guide While these features of Zearn Math support all students in building a deep understanding of grade level mathematics they are particularly critical for meeting the needs of multilingual learners Elements of language During their daily learning with Zearn Math students are exposed to many elements of language such as mathematics vocabulary and spoken language patterns In some situations multilingual learners may benefit from using their first language because processing math in their first language can create a safe space for deeper thinking Zearn Math supports students as they develop their mathematical skills by reinforcing Essential vocabulary Students are not expected to have prior knowledge of essential math vocabulary Language critical to students mathematical learning is explicitly introduced taught and repeated frequently which helps all students gain familiarity with new terminology and practice using it as they move through the curriculum Patterns of discourse As students engage in rich math discussions throughout the lesson they have opportunities to organize their language in discourse patterns such as compare and contrast or question and answer Teachers facilitate these structured conversations through instructional routines such as Think Pair Shares which allow students to make claims provide evidence communicate thinking and critique others reasoning The Zearn Math lessons include specific notes with conversation starters sentence frames and modeling guidance that can help enhance discussion quality for all students and ensure multilingual learners are supported in participating Math discussion Students share their own thinking aloud and discuss classmates problem solving strategies throughout daily Warm Up and Collaborative Concept Exploration Teachers facilitate thoughtful mathematical discussions between students that allow learners to refer to and build on each others ideas The Zearn Math Teacher Edition provides guidance on instructional routines that further math discussions for all students with additional notes on supporting multilingual learners Mathematical language routines MLRs To further support students language development Zearn recommends that teachers read and consider using the mathematical language routines MLRs listed below A mathematical language routine is a structured but adaptable format developed by the Stanford University UL SCALE team Zwiers et al 2017 for amplifying assessing and developing students language in order to provide various types of learners including multilingual learners with greater access by supporting them with the language demands of a specific activity without reducing the mathematical demand of the task These routines emphasize uses of language that are meaningful and purposeful rather than just getting correct answers These routines can be adapted and incorporated across lessons in each unit wherever there are productive opportunities to support students in using and improving their English and disciplinary language These eight routines were selected for inclusion in this curriculum because they are effective and practical for simultaneously learning mathematical practices content and language They are MLR 1 Stronger and Clearer Each Time Students think and write individually about a question use a structured pairing strategy to have multiple opportunities to refine and clarify their response through conversation and then finally revise their original written response 20 ZEARN MATH Teacher Edition

G4 Course Guide Supporting Diverse Learners MLR 2 Collect and Display Teachers listen for and scribe the language students use during discussions using written words diagrams and pictures This collected output can be organized re voiced or explicitly connected to other language in a display that all students can refer to build on or make connections with during future discussion or writing MLR 3 Clarify Critique Correct Teachers provide students with an incorrect incomplete or ambiguous written mathematical statement and students improve upon the written work by correcting errors and clarifying meaning MLR 4 Information Gap Teachers facilitate meaningful interactions by positioning some students as holders of information that is needed by other students to accomplish a goal such as solving a problem or winning a game MLR 5 Co Craft Questions Students use conversation skills to generate choose argue for the best one and improve questions and situations as well as develop meta awareness of the language used in mathematical questions and problems MLR 6 Three Reads Students read a mathematical text situation or word problem three times each with a particular focus The intended question or main prompt is intentionally withheld until the third read so that students can concentrate on making sense of what is happening in the text before rushing to a solution or method MLR 7 Compare and Connect Students make sense of mathematical strategies other than their own by creating visual displays and then relating and connecting other approaches to their own MLR 8 Discussion Supports This collection of instructional moves can be combined and used together with any of the other routines to help students make sense of complex language ideas and classroom communication and to invite and incentivize more student participation conversation and meta awareness of language To learn more about our approach to supporting multilingual learners including a full description of each MLR see Appendix 2 Access for Multilingual Learners Zearn is committed to offering comprehensive curriculum resources in Spanish As of the 2021 22 school year paper based teacher and student instructional materials have been fully translated into Spanish SUPPORTING STUDENTS WITH DISABILITIES Students with disabilities can and should engage with Zearn Math While a student s Individualized Education Plan should be the first resource teachers use when determining how to differentiate instruction for a student with a disability Zearn s curriculum also highlights patterns critical features and big math ideas in a way that supports such differentiation For more see above sections on Planning for a lesson as well as Preparing students for Independent Digital Lessons under Implementing Zearn Math ZEARN MATH Teacher Edition 21

Supporting Diverse Learners G4 Course Guide The following design elements assistive technologies and accommodations may help students with disabilities access Zearn Math Accessible design features We developed Zearn Math with a wide range of students in mind and included accessibility features that ensure students with cognitive physical and communication challenges can easily use the self paced software based lessons These design features include Visual clarity All content in Independent Digital Lessons is visually clear and understandable These visual accessibility features help all learners but are particularly important for students with color blindness or any visual impairments Use of color Throughout Zearn Math Independent Digital Lessons color is never used as the only visual means of conveying information When a student receives precise feedback on an answer during Independent Digital Lessons that feedback is provided in multiple ways with color but also with clear iconography and specific messages such as Nice Try again or Check the answer Additionally where color is used to draw attention to a specific piece of information Zearn Math also uses words to convey the same information Color contrast Zearn Math aims to conform to minimum color contrast requirements Software based lessons use larger fonts that meet a minimum contrast ratio of 3 1 Fonts smaller than 18pt or 14pt bold meet a contrast ratio of 4 5 1 Where specific elements of Independent Digital Lessons do not meet contrast standards today Zearn is making improvements Font readability Throughout software based lessons Zearn Math avoids using fonts smaller than 10pt with most text using at least 16pt fonts Font types are simple clear and have limited variation in order to ensure all text is readable Volume consistency In order to provide a consistent and non disruptive audio experience for students there are no significant volume changes during Independent Digital Lessons Outside of Zearn Math s video content there is no audio that plays automatically for more than 3 seconds This accessibility feature is particularly important for students who are sensitive to changes in volume students who have difficulty focusing on visual content including text when audio is playing students on the autism spectrum and students with hearing impairments Assistive technology Assistive technology may be helpful to increase and maintain access for students with disabilities Many assistive technology features are embedded into Zearn s digital materials Text to Speech All instructional prompts and directions that students see in the Zearn Math digital program can be read aloud by selecting buttons Screen Reader and Braille Translation Software Zearn Math can be accessed by screen reading software All student facing PDFs are screen reader accessible Screen readers enable blind students to read the text that is displayed on the computer screen with a speech synthesizer or braille display However students who are blind or have limited sight will need teacher caregiver or screen reader assistance in understanding Zearn Math s dynamic digital manipulatives within the Guided Practice given the nature of how they are built 22 ZEARN MATH Teacher Edition

G4 Course Guide Supporting Diverse Learners Keyboard accessibility While Zearn Math requires the use of a mouse trackpad or touchscreen device today Zearn has made keyboard accessibility a priority In the coming years Zearn will be adding new features to ensure that students can use keyboards for all interactive elements in Independent Digital Lessons This accessibility feature is particularly important for students with impaired mobility or dexterity or students with low vision Instructional accommodations Teachers can and should provide student specific accommodations for students with disabilities The following accommodations may increase access for students Translated Materials All of Zearn s core student facing paper based instructional materials are available in various accessible formats including large print Braille and tactile from APH org American Printing House Educators can search APH s Louis catalog and place orders for the Zearn Math materials they need These materials are also on file with the National Instructional Materials Accessibility Center NIMAC Guided Notes and Graphic Organizers All Zearn Math lessons include Student Notes to help keep students focused and organized Zearn also uses graphic organizers in digital content and in paper based materials to help students organize and internalize information Read Aloud Students who struggle with word decoding and or reading comprehension may benefit from having question prompts read aloud Students who are blind or have limited sight may benefit from hearing oral descriptions of graphs and of other visual representations of problems or math concepts Scribe Students with scribe accommodation will need support transferring their math thinking problem solving and answers into digital form or as a written answer when prompted to write or input an answer Separate Location or Quiet Space When completing digital lessons some students may benefit from working in a separate space where they can process out loud work without headphones and input text or numerical answers with their voice Breaks Students may benefit from structured breaks when completing Zearn Math lessons in order to rest or refocus All Zearn Math digital lessons can be paused rewound or restarted Checklists and Other Self Monitoring Activities Self monitoring checklists may be helpful for students to use in determining the best approach to solve a problem guiding problem solving processes or evaluating work habits or progress made toward a goal Physical Math Manipulatives All students benefit from access to physical manipulatives Zearn Math notes required materials in the Mission Overview and in each Lesson For some students more work with physical manipulatives may be beneficial ZEARN MATH Teacher Edition 23

Assessments and Reports G4 Course Guide Assessments and Reports Zearn offers a series of formative assessments designed to provide teachers with precise and actionable feedback they can use to inform instruction and respond to the needs of each student as well as student and class level reports that provide teachers with real time data and insights into student pace progress and areas of struggle during Zearn Math digital lessons To address areas of unfinished learning Zearn Math contains both embedded supports within each Independent Digital Lesson as well as foundational lessons that teachers may assign as interventions ONGOING FORMATIVE ASSESSMENTS Assessments focus on the big ideas of mathematics and allow students to demonstrate their understanding across multiple modalities through a thoughtful balance of software and paper based experiences All assessments are designed to fit into the classroom model and allocated time and to enhance rather than distract from instruction Daily lesson level assessments The Tower of Power digital and Exit Tickets paper Lesson level assessments are embedded into the curriculum and occur as part of recommended daily core instructional time not in addition to it Tower of Power digital This scaffolded assessment focuses on the content of a single lesson and is administered automatically at the end of each Independent Digital Lesson If students make a mistake they receive real time support at the point of misconception allowing them to correct their understanding and continue through the assessment Each Tower of Power contains two to four stages of problems that increase in complexity and decrease in scaffolding as students progress The problems in each stage are carefully designed to focus on the big ideas of each lesson mirroring the progression of learning students have just completed Students are not permitted to move on to their next Independent Digital lesson without successful completion of the Tower of Power Since the Tower of Power is software based teachers can access a report to determine how well students are progressing through the Tower of Power assessments enabling them to adjust instruction to support students progress See next section on Reports Exit Ticket paper This assessment also focuses on the content of a single lesson and it is administered at the culmination of each Lesson to help teachers monitor daily learning As the companion to the Tower of Power the Exit Ticket uses a single problem or multiple problems where appropriate to determine if the student can transfer their thinking and work from the Concept Exploration to an open response item that requires students to show their thinking and work including drawing models and or writing explanations Exit Ticket problems are designed to highlight the big mathematical idea of each lesson or a piece thereof and as such should not be edited Mission level assessments paper Mission level assessments take an average of 30 minutes to complete and should be administered at the end of a Mission during built in weekly Flex time longer Missions will sometimes be broken into a Mid Mission Assessment roughly halfway through the Mission and an end of Mision assessment at the end both of similar length All questions assess student understanding of content within the specific Mission and do not include 24 ZEARN MATH Teacher Edition

G4 Course Guide Assessments and Reports questions related to other Missions Each assessment includes a carefully selected number of problems that give teachers rich feedback on student learning while limiting the time students spend on any given assessment and teachers spend analyzing assessments These paper assessments consist of open response items that require students to show their work or explain their thinking in a variety of ways including drawing models and writing explanations similar to an Exit Ticket Some assessment items highlight a student s understanding of a big mathematical idea while others focus on students procedural fluency Each part of any multi step problem has a clear objective is aligned to the explicit expectations of the target standards and allows teachers to identify whether students are struggling with the foundational math concept or the multi step aspect of the problem Zearn provides teachers with an answer key for each Mission level assessment that contains an exemplar student response for each item as well as specific standards alignment information Exemplar student responses can be used to inform teacher feedback but are not the only correct answer or solution method many of the problems on a Mission level assessment allow students multiple entry points and acceptable solution paths or strategies Zearn also offers assessment rubrics to provide teachers with actionable feedback they can use to respond to the learning and misconceptions students demonstrate on the Mission level assessment Each rubric models a progression towards understanding offering detailed examples of where students might go wrong along with guidance on what incorrect answers may indicate about a student s unfinished learning The rubrics also include guidance on scoring each item Scoring guidance helps teachers assess the depth of students learning and provide students with the precise feedback they need to continue to develop their understanding Each rubric is designed to produce a score out of 100 so that teachers can more easily input that score into their gradebooks To help create inclusive classroom math communities in which all students feel they belong and can deeply learn the math content of their grade Zearn s scoring guidance raises the floor for grades ensuring that any student who is at least initiating understanding on all items is guaranteed a minimum score of 60 or higher When connecting possible scores to the Progression Towards Understanding scores now have meaning a student s score communicates where they are in the progression from initial understanding to full understanding A student scoring above 90 points on an assessment should be considered as having full understanding of the content of the Mission A student scoring between 80 and 90 points on an assessment should be considered as nearing full understanding of the content of the Mission A student scoring between 70 and 80 points on an assessment should be considered as developing understanding of the content of the Mission A student scoring between 60 and 70 points on an assessment should be considered as initiating understanding of the content of the Mission The points possible for each item vary based on the amount of understanding a student can demonstrate in any single item in addition to the mathematical focus of the item and the extent to which it connects to the big ideas of the Mission Note Given the coherent structure of Zearn Math if unfinished learning is evident on Mission level assessments teachers should move forward with additional supports and address misconceptions during collaborative Concept Exploration and on Flex Days understanding that the unfinished learning may best be completed by connecting it to new ideas presented in the latter half of a Mission or a subsequent Mission Students with ZEARN MATH Teacher Edition 25

Assessments and Reports G4 Course Guide unfinished learnings should also be supported during flexible math time or other specific intervention time with work on foundational lessons For more information on Zearn Math s approach to unfinished learning see the Approach to Unfinished Learning section CLASS AND STUDENT REPORTS Zearn provides teachers with reports that provide real time visibility into student pace progress and areas of struggle during software based learning which they can use to differentiate instruction and ensure all students receive the support and enrichment they need Go online to Zearn s Help Center to find information about all of these reports including video overviews 4 Zearn encourages teachers to check reports at least twice a week to stay up to date on students learning and to use the insights to inform instruction Class reports Progress Pace Tower Alerts and Sprint Alerts Progress Report This report shows teachers where each student is in the digital sequence of all grade level content Teachers can view the percentage of Independent Digital Lessons students have completed for each Mission By checking the Progress Report teachers can understand how far along students are in exploring grade level math content Pace Report This report helps teachers keep students on track each week to complete the recommended four Independent Digital Lessons Teachers can access a real time view of how many lessons students have completed the time it took to complete each lesson and whether students have completed any bookmarked foundational lessons if applicable to learn more about foundational lessons see the section on Addressing unfinished learning below By checking the Pace Report teachers can identify groups of students who need more time to meet weekly learning goals with Independent Digital Lessons and students who have already met their goal and can begin working on Bonuses for an extra challenge Teachers can also use the Pace Report to track student progress on any foundation lessons the teacher has bookmarked and can filter by lesson grade level to monitor how many still remain Tower Alerts Report This report allows teachers to identify the part of the lesson where the student struggled and whether or not the student was able to complete the independent practice portion of an Independent Digital Lesson and move on to the next Independent Digital Lesson Mistakes are magic and not all struggle is bad If a student struggles in the Tower of Power the student receives scaffolded support at the precise moment of misconception called a Boost If the Boost allows the student to move past their initial point of struggle this struggle was productive If a student struggles multiple times it s a sign that they have moved past the point of productive struggle to unproductive struggle and their teacher receives a Tower Alert Teachers can then use the Tower Alerts Report to identify which students need additional support on specific concepts and can bookmark To learn about the Zearn Class Reports and Student Reports you may access visit https help zearn org hc en us articles 4403432402071Teacher Reports 4 26 ZEARN MATH Teacher Edition

G4 Course Guide Assessments and Reports recommended foundational lessons for each of these students to complete For more see the next section on unfinished learning By checking the report at least twice each week teachers can ensure no students are stuck with unproductive struggle in a Tower for long periods of time before they can move on to the next lesson and continue learning Sprint Alerts Report This report allows teachers to see which students are struggling with Sprints lesson aligned fluency activities that appear in some Independent Digital Lessons to help students build and strengthen foundational knowledge and skills If students answer fewer than 10 questions correctly in a Sprint their teacher receives a Sprint Alert These students may need additional support during Flex time Students are timed during Sprints however the timer is not emphasized in the student experience Beginning in the 2022 23 school year there will be an option to turn the timer off for students Student Reports Zearn also offers Student Reports that contain real time data and insights into student pace progress and areas of struggle during Independent Digital Lessons Teachers can use these reports along with other formative assessment data to gain insight into individual student learning including topics where that student excels and topics where they may still struggle Within a Student Report teachers can see the breakdown of Pace Progress Tower Alerts and Sprint Alerts as well as all the activities that the student has completed and when they did so Combined with Zearn s automated recommendations on foundational lessons that support students with unfinished learning see next section this report gives teachers the information they need to choose deeper interventions when necessary APPROACH TO UNFINISHED LEARNING Zearn Math helps teachers address students unfinished learning in the context of new learning setting students up for success with just in time supports built into daily digital lessons as well as targeted foundational lessons that are coherently aligned to their grade s core content Embedded supports Each Zearn Math grade level digital lesson includes built in support on concepts from previous topics and grades so that students can strengthen foundational understanding while learning grade level concepts In lesson adaptive support All Independent Digital Lessons contain built in supportive pathways that teach new concepts through concrete and pictorial representations that help students make sense of new concepts by anchoring to ideas they already know or intuitively make sense to them This approach emphasizes the big ideas in mathematics and strengthens conceptual and procedural knowledge to address unfinished learning so that students can move smoothly to and make connections with other mathematics Boosts help during struggle In addition the Tower of Power Zearn s embedded daily diagnostic assesses each student s understanding and automatically launches a Boost exactly when kids need it with support and scaffolding they need from prior grades or prior units Thus Zearn continually assesses diagnoses and gives kids the Boost they need built into their grade level learning ZEARN MATH Teacher Edition 27

Terminology G4 Course Guide Foundational lessons to address significant unfinished learning If a student continues to struggle teachers receive a notification in their Tower Alerts Report which they should monitor regularly Teachers can then check the Student Report to see precisely which topics a student may be excelling in which topics a student may be struggling with and how deep the struggle is The information in the Student Reports empowers teachers to assess struggle side by side with other information such as productivity of the struggle where in the scope and sequence struggle is occurring and other formative assessment data so that teachers are empowered with the full information they need to choose deeper interventions when necessary In addition to alerts and reports Zearn helps teachers address misconceptions and unfinished learning through a recommendation engine that suggests precise targeted foundational content that will be most supportive based on an individual student s area of struggle Bookmark foundational lessons Teachers can bookmark foundational lessons recommended by Zearn as an additional assignment to be completed outside of the core math block The Zearn team has identified foundational lessons based on an analysis of data on student struggle from all problems completed in our digital lessons Each foundational lesson focuses on the big math idea that connects with and promotes the same grade level content students are learning during their math block Direct to Math Library Students can then access their bookmarked foundational lessons alongside their grade level assignments in their Math Library and spend flexible math time or other specific intervention time working on these foundational lessons in a way that is directly tied to core grade level learning Students can access both their foundational and grade level assignments on Zearn s online math platform with the same login Zearn s student experience is designed to feel safe and supportive so students do not see the word intervention or the grade level of the bookmarked lessons Zearn Math s database provides the essential foundational lessons for understanding specific grade level math concepts as well as an additional layer of support lessons that may be helpful to students In addition to guided and independent practice this option provides students with additional lesson aligned fluency work to build automaticity and deepen number sense Monitor student progress Teachers and administrators can log in to their Zearn Accounts to track student progress on unfinished learning In their digital reports teachers and administrators can see progress on a student s lesson assignments including grade level and bookmarked foundational lessons and areas of struggle Administrators will be able to see this same information for the school not just the class and student This targeted and coherent approach maximizes effectiveness by allowing students to move fluidly between grade level and intervention content as needed in order to fill conceptual gaps and get back to grade level learning as quickly as possible Terminology Acute angle Angle with a measure of less than 90 Acute triangle Triangle with all interior angles measuring less than 90 28 ZEARN MATH Teacher Edition

G4 Course Guide Terminology Adjacent angle Two angles AOC and COB with a common side OC are adjacent angles if C is in the interior of AOB Angle Union of two different rays sharing a common vertex e g ABC Arc Connected portion of a circle Associative property E g 96 3 4 8 3 4 8 Benchmark Standard or reference point by which something is measured Collinear Three or more points are collinear if there is a line containing all of the points otherwise the points are non collinear Composite number Positive integer having three or more whole number factors Common denominator When two or more fractions have the same denominator Complementary angles Two angles with a sum of 90 Convert Express a measurement in a different unit rename units Cup c Customary unit of measure for liquid volume Customary system of measurement Measurement system commonly used in the United States that includes such units as yards pounds and gallons Customary unit E g foot ounce quart Decimal expanded form e g 2 10 4 1 5 0 1 9 0 01 24 59 Decimal fraction A fraction with a denominator of 10 100 1 000 etc Decimal number A number written using place value units that are powers of 10 Decimal point A period used to separate the whole number part from the fractional part of a decimal number ZEARN MATH Teacher Edition 29

Terminology G4 Course Guide Degree degree measure of an angle Subdivide the length around a circle into 360 arcs of equal length A central angle for any of these arcs is called a one degree angle and is said to have an angle measure of 1 Denominator 3 E g the 5 in 5 names the fractional unit as fifths Diagonal Straight lines joining two opposite corners of a straight sided shape Distributive property E g 64 27 60 20 60 7 4 20 4 7 Divisible 1 12 ft Divisor The number by which another number is divided Equilateral triangle Triangle with three equal sides Fraction expanded form e g 2 10 4 1 5 Fraction greater than 1 A fraction with a numerator that is greater than the denominator Figure Set of points in the plane Formula A mathematical rule expressed as an equation with numbers and or variables Gallon gal Customary unit of measure for liquid volume Hundredth A place value unit such that 100 hundredths equals 1 one Interior of an angle The convex region defined by the angle Intersecting lines Lines that contain at least one point in common Isosceles triangle Triangle with at least two equal sides Kilometer km a unit of measure for length 30 1 1 59 9 100 24 100 10 ZEARN MATH Teacher Edition

G4 Course Guide Terminology Long division Process of dividing a large dividend using several recorded steps Length of an arc Circular distance around the arc Line Straight path with no thickness that extends in both directions without end e g AB Line of symmetry Line through a figure such that when the figure is folded along the line two halves are created that match up exactly Line segment Two points A and B together with the set of points on AB between A and B e g AB Line plot Display of data on a number line using an x or another mark to show frequency Mass The measure of the amount of matter in an object Metric system of measurement Base ten system of measurement used internationally that includes such units as meters kilograms and liters Metric unit E g kilometer gram milliliter Milliliter mL a unit of measure for liquid volume Millions ten millions hundred millions As places on the place value chart Mixed units E g 3 m 43 cm Mixed number Number made up of a whole number and a fraction Numerator E g the 3 in Obtuse angle Angle with a measure greater than 90 but less than 180 Obtuse triangle Triangle with an interior obtuse angle Ounce oz Customary unit of measure for weight 3 5 indicates 3 fractional units are selected ZEARN MATH Teacher Edition 31

Terminology G4 Course Guide Parallel Two lines in a plane that do not intersect e g AB CD Partial product E g 24 6 20 6 4 6 120 24 Perpendicular Two lines are perpendicular if they intersect and any of the angles formed between the lines is a 90 angle e g AB CD Point Precise location in the plane Prime number Positive integer greater than 1 having whole number factors of only 1 and itself Pint pt Customary unit of measure for liquid volume Pound lb Customary unit of measure for weight Protractor Instrument used in measuring or sketching angles Quart qt Customary unit of measure for liquid volume Ray The OA is the point O and the set of all points on OA that are on the same side of O as the point A Remainder The number left over when one integer is divided by another Right angle Angle formed by perpendicular lines measuring 90 Right triangle Triangle that contains one 90 angle Scalene triangle Triangle with no sides or angles equal Straight angle Angle that measures 180 Supplementary angle Two angles with a sum of 180 Ten thousands hundred thousands As places on the place value chart 32 ZEARN MATH Teacher Edition

G4 Course Guide Required Materials Triangle A triangle consists of three non collinear points and the three line segments between them The three segments are called the sides of the triangle and the three points are called the vertices Tenth A place value unit such that 10 tenths equals 1 one Variables Letters that stand for numbers and can be added subtracted multiplied and divided as numbers are Vertex A point often used to refer to the point where two lines meet such as in an angle or the corner of a triangle Vertical angles When two lines intersect any two non adjacent angles formed by those lines are called vertical angles or vertically opposite angles Required Materials Customary Weight Set Whole Number Place Value Cards or Strips Decimal Place Value Cards or Strips Graduated Cylinder 1000 ml 360 Circle Protractors Gallon Measurement Set Place Value Disks Decimal Disks 4 Protractors Platform Scale Bullseye Compass ZEARN MATH Teacher Edition 33

Lessons by Standard G4 Course Guide Lessons by Standard Standards Lessons 4 OA 1 4 1 1 4 OA 2 4 3 2 4 3 3 4 3 5 4 3 6 4 3 9 4 3 10 4 3 11 4 3 12 4 3 13 4 3 26 4 5 39 4 5 40 4 7 4 4 7 14 4 OA 3 4 OA 4 4 OA 5 4 NBT 1 4 NBT 2 4 NBT 3 4 NBT 4 4 NBT 5 34 4 3 12 4 3 13 4 3 14 4 3 19 4 3 31 4 3 12 4 3 13 4 3 14 4 3 19 4 3 31 4 3 32 4 3 22 4 3 23 4 3 24 4 3 25 4 5 41 4 1 2 4 1 3 4 1 3 4 1 4 4 1 5 4 1 6 4 1 7 4 1 8 4 1 9 4 1 10 4 1 12 4 1 16 4 1 17 4 1 19 4 1 11 4 1 12 4 1 13 4 1 14 4 1 15 4 1 16 4 1 17 4 1 18 4 1 19 4 3 4 4 3 5 4 3 6 4 3 7 4 3 8 4 3 9 4 3 10 4 3 11 4 3 34 4 3 35 4 3 36 4 3 37 4 3 38 Standards 4 NBT 6 4 NF 1 4 NF 2 4 NF 3 4 NF 4 4 NF 5 4 NF 6 Lessons 4 3 14 4 3 15 4 3 16 4 3 17 4 3 18 4 3 19 4 3 20 4 3 21 4 3 26 4 3 27 4 3 28 4 3 29 4 3 30 4 3 31 4 3 32 4 3 33 4 5 7 4 5 8 4 5 9 4 5 10 4 5 11 4 5 14 4 5 15 4 5 21 4 5 27 4 6 5 4 6 12 4 5 12 4 5 13 4 5 14 4 5 15 4 5 26 4 5 27 4 5 1 4 5 2 4 5 3 4 5 4 4 5 5 4 5 6 4 5 16 4 5 17 4 5 18 4 5 19 4 5 20 4 5 21 4 5 22 4 5 23 4 5 24 4 5 25 4 5 29 4 5 30 4 5 31 4 5 32 4 5 33 4 5 34 4 5 3 4 5 5 4 5 6 4 5 23 4 5 24 4 5 25 4 5 35 4 5 36 4 5 37 4 5 38 4 5 39 4 5 40 4 6 4 4 6 12 4 6 13 4 6 14 4 6 1 4 6 2 4 6 3 4 6 4 4 6 5 4 6 6 4 6 11 4 6 12 4 6 13 4 6 14 4 6 15 Standards 4 NF 7 4 MD 1 4 MD 2 4 MD 3 4 MD 4 4 MD 5 4 MD 6 4 MD 7 4 G 1 4 G 2 4 G 3 Lessons 4 6 9 4 6 10 4 6 11 4 4 4 4 7 1 4 7 2 4 7 3 4 7 6 4 7 7 4 7 8 4 7 9 4 7 12 4 7 13 4 5 40 4 6 14 4 6 15 4 6 16 4 7 1 4 7 2 4 7 3 4 7 4 4 7 5 4 7 6 4 7 7 4 7 8 4 7 9 4 7 10 4 7 11 4 7 14 4 3 1 4 3 2 4 3 3 4 7 15 4 7 16 4 5 28 4 5 40 4 4 1 4 4 5 4 4 6 4 4 7 4 4 5 4 4 6 4 4 7 4 4 8 4 4 9 4 4 10 4 4 11 4 4 1 4 4 2 4 4 3 4 4 4 4 4 13 4 4 14 4 4 15 4 4 13 4 4 14 4 4 15 4 4 12 4 4 12 ZEARN MATH Teacher Edition

G4 Course Guide Standards by Lesson Standards by Lesson Mission 2 Mission 1 Mission 3 Lesson Standard Lesson Standard Lesson Standard Lesson 1 4 OA 1 and 4 OA 2 Lesson 1 4 MD 1 and 4 MD 2 Lesson 1 4 MD 3 Lesson 2 4 OA 2 and 4 NBT 1 Lesson 2 4 MD 1 and 4 MD 2 Lesson 2 4 OA 2 and 4 MD 3 Lesson 3 4 NBT 1 and 4 NBT 2 Lesson 3 4 MD 1 and 4 MD 2 Lesson 3 4 OA 2 and 4 MD 3 Lesson 4 4 NBT 2 Lesson 4 4 MD 1 Lesson 4 4 NBT 5 Lesson 5 4 NBT 2 Lesson 5 4 MD 2 Lesson 5 4 OA 2 and 4 NBT 5 Lesson 6 4 NBT 2 Lesson 6 4 OA 2 and 4 NBT 5 Lesson 7 4 NBT 3 Lesson 7 4 NBT 5 Lesson 8 4 NBT 3 Lesson 8 4 NBT 5 Lesson 9 4 NBT 3 Lesson 9 4 OA 2 and 4 NBT 5 Lesson 10 4 NBT 3 Lesson 10 4 OA 2 and 4 NBT 5 Lesson 11 4 NBT 4 Lesson 11 4 OA 2 and 4 NBT 5 Lesson 12 4 OA 3 4 NBT 3 and 4 NBT 4 Lesson 12 4 OA 2 and 4 OA 3 Lesson 13 4 NBT 4 Lesson 13 4 OA 2 and 4 OA 3 Lesson 14 4 NBT 4 Lesson 14 4 OA 3 and 4 NBT 6 Lesson 15 4 NBT 4 Lesson 15 4 NBT 6 Lesson 16 4 OA 3 4 NBT 3 and 4 NBT 4 Lesson 16 4 NBT 6 Lesson 17 4 OA 3 4 NBT 3 and 4 NBT 4 Lesson 17 4 NBT 6 Lesson 18 Lesson 18 4 NBT 6 4 OA 3 and 4 NBT 4 4 OA 3 4 NBT 3 and 4 NBT 4 Lesson 19 4 OA 3 and 4 NBT 6 Lesson 19 Lesson 20 4 NBT 6 Lesson 21 4 NBT 6 Lesson 22 4 OA 4 Lesson 23 4 OA 4 Lesson 24 4 OA 4 Lesson 25 4 OA 4 ZEARN MATH Teacher Edition 35

Standards by Lesson G4 Course Guide Mission 4 Lesson Standard Lesson Standard Lesson Standard Lesson 26 4 OA 2 and 4 NBT 6 Lesson 1 4 MD 5 and 4 G 1 Lesson 1 4 NF 3 Lesson 27 4 NBT 6 Lesson 2 4 G 1 Lesson 2 4 NF 3 Lesson 28 4 NBT 6 Lesson 3 4 G 1 Lesson 3 4 NF 3 and 4 NF 4 Lesson 29 4 NBT 6 Lesson 4 4 G 1 Lesson 4 4 NF 3 Lesson 30 4 NBT 6 Lesson 5 4 MD 5 and 4 MD 6 Lesson 5 4 NF 3 and 4 NF 4 Lesson 31 4 OA 3 and 4 NBT 6 Lesson 6 4 MD 5 and 4 MD 6 Lesson 6 4 NF 3 and 4 NF 4 Lesson 32 4 OA 3 and 4 NBT 6 Lesson 7 4 MD 5 and 4 MD 6 Lesson 7 4 NF 1 Lesson 33 4 NBT 6 Lesson 8 4 MD 6 Lesson 8 4 NF 1 Lesson 34 4 NBT 5 Lesson 9 4 MD 7 Lesson 9 4 NF 1 Lesson 35 4 NBT 5 Lesson 10 4 MD 7 Lesson 10 4 NF 1 Lesson 36 4 NBT 5 Lesson 11 4 MD 7 Lesson 11 4 NF 1 Lesson 37 4 NBT 5 Lesson 12 4 G 3 Lesson 12 4 NF 2 Lesson 38 4 NBT 5 Lesson 13 4 G 1 and 4 G 2 Lesson 13 4 NF 2 Lesson 14 4 G 1 4 G 2 and 4 G 3 Lesson 14 4 NF 1 and 4 NF 2 Lesson 15 4 G 1 and 4 G 2 Lesson 15 4 NF 1 and 4 NF 2 Lesson 16 4 NF 3 Lesson 17 4 NF 3 Lesson 18 4 NF 3 Lesson 19 4 NF 3 Lesson 20 4 NF 3 Lesson 21 4 NF 1 and 4 NF 3 Lesson 22 4 NF 3 Lesson 23 4 NF 3 and 4 NF 4 Lesson 24 4 NF 3 and 4 NF 4 Lesson 25 4 NF 3 and 4 NF 4 Lesson 26 4 NF 2 Lesson 27 4 NF 1 and 4 NF 2 Lesson 16 36 Mission 5 ZEARN MATH Teacher Edition

G4 Course Guide Standards by Lesson Mission 6 Mission 7 Lesson Standard Lesson Standard Lesson Standard Lesson 28 4 MD 4 Lesson 1 4 NF 6 Lesson 1 4 MD 1 and 4 MD 2 Lesson 29 4 NF 3 Lesson 2 4 NF 6 Lesson 2 4 MD 1 and 4 MD 2 Lesson 30 4 NF 3 Lesson 3 4 NF 6 Lesson 3 4 MD 1 and 4 MD 2 Lesson 31 4 NF 3 Lesson 4 4 NF 5 4 NF 6 and 4 MD 1 Lesson 4 4 OA 2 and 4 MD 2 Lesson 32 4 NF 3 Lesson 5 4 NF 1 and 4 NF 6 Lesson 5 4 MD 2 Lesson 33 4 NF 3 Lesson 6 4 NF 6 Lesson 6 4 MD 1 and 4 MD 2 Lesson 34 4 NF 3 Lesson 7 Lesson 7 4 MD 1 and 4 MD 2 Lesson 35 4 NF 4 Lesson 8 Lesson 8 4 MD 1 and 4 MD 2 Lesson 36 4 NF 4 Lesson 9 4 NF 7 Lesson 9 4 MD 1 and 4 MD 2 Lesson 37 4 NF 4 Lesson 10 4 NF 7 Lesson 10 4 MD 2 Lesson 38 4 NF 4 Lesson 11 4 NF 6 and 4 NF 7 Lesson 11 4 MD 2 Lesson 39 4 OA 2 and 4 NF 4 Lesson 12 4 NF 1 4 NF 5 and 4 NF 6 Lesson 12 4 MD 1 Lesson 40 4 OA 2 4 NF 4 4 MD 2 and 4 MD 4 Lesson 13 4 NF 5 and 4 NF 6 Lesson 13 4 MD 1 Lesson 41 4 OA 5 Lesson 14 4 NF 5 4 NF 6 and 4 MD 2 Lesson 14 4 OA 2 and 4 MD 2 Lesson 15 4 NF 6 Lesson 15 4 MD 3 and 4 MD 8 Lesson 16 4 MD 2 Lesson 16 4 MD 3 and 4 MD 8 Lesson 17 Lesson 18 ZEARN MATH Teacher Edition 37

Appendix I Instructional Routines G4 Course Guide Appendix I Instructional Routines The kind of instruction appropriate in any particular lesson depends on the learning goals of that lesson Some lessons may be devoted to developing a concept others to mastering a procedural skill yet others to applying mathematics to a real world problem These aspects of mathematical proficiency are interwoven into Zearn Math The Zearn Math Teacher Edition includes a small set of activity structures that become more and more familiar to teachers and students as the year progresses WHITE BOARD EXCHANGE What Students record their thinking on a personal white board and exchange their white boards with a partner to evaluate their partner s thinking and strategy 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 within the white board for easy access and reuse Where Warm Up and Concept Exploration Why Using personal white boards allows students to quickly work and if needed re work problems while also efficiently sharing their work with their teacher and peers The white boards allow students the opportunity to quickly erase and move to a new problem This is particularly helpful when looking for repeated reasoning within a new concept ANTICIPATE MONITOR SELECT SEQUENCE CONNECT What Fans of 5 Practices for Orchestrating Productive Mathematical Discussions Smith and Stein 2011 will recognize these as the 5 Practices In this curriculum much of the work of anticipating sequencing and connecting is modeled by the materials in the discussion guidance Teachers will need to develop their capacity to prepare for and conduct whole class discussions Where Warm Up Concept Exploration Wrap Up Why In Zearn Math many activities can be described as do math and talk about it but the 5 Practices lend more structure to these activities so that they more reliably result in students making connections and learning new mathematics 38 ZEARN MATH Teacher Edition

G4 Course Guide Appendix I Instructional Routines TAKE TURNS What Students work with a partner or small group They take turns in the work of the activity whether it be spotting matches explaining justifying agreeing or disagreeing or asking clarifying questions If they disagree they are expected to support their case and listen to their partner s arguments The first few times students engage in these activities the teacher should demonstrate with a partner how the discussion is expected to go Once students are familiar with these structures less set up will be necessary While students are working the teacher can ask students to restate their question more clearly or paraphrase what their partner said Where Concept Exploration Why Building in an expectation through the routine that students explain the rationale for their choices and listen to another s rationale deepens the understanding that can be achieved through these activities Specifying that students take turns deciding explaining and listening limits the phenomenon where one student takes over and the other does not participate Taking turns can also give students more opportunities to construct logical arguments and critique others reasoning THINK PAIR SHARE What Students have quiet time to think about a problem and work on it individually and then time to share their response or their progress with a partner Once these partner conversations have taken place some partnerships are selected to share their thoughts with the class Where Warm Up and Concept Exploration Why This is a teaching routine useful in many contexts whose purpose is to give all students enough time to think about a prompt and form a response before they are expected to try to verbalize their thinking First they have an opportunity to share their thinking in a low stakes way with one partner so that when they share with the class they can feel calm and confident as well as say something meaningful that might advance everyone s understanding Additionally the teacher has an opportunity to eavesdrop on the partner conversations and can purposefully select students to share with the class READ DRAW WRITE RDW What Students engage with word problems by first reading the problem identifying any relevant information needed to solve the problem Next students represent their thinking and solution strategy through visualization drawing something connected to the problem Finally students solve the problem and write an answer to contextualize their solution ZEARN MATH Teacher Edition 39

Appendix II Access for Multilingual Learners G4 Course Guide Where Warm Up Concept Exploration Wrap Up Why Solving word problems can be difficult for students for many reasons not least of which is not knowing where to start Zearn believes that problem solving starts with visualization giving all students an entry point into the problem Drawings do not have to be mathematical in nature and creativity should be encouraged and celebrated This problem solving routine also helps teachers identify misconceptions that might be holding students back from progressing in their grade level learning Appendix II Access for Multilingual Learners INTRODUCTION Zearn Math for Fourth Grade builds on foundational principles for supporting language development for all students This appendix aims to provide guidance to help teachers recognize and support students language development in the context of mathematical sense making Embedded within the Zearn Math Teacher Edition are instructional supports and practices to help teachers address the specialized academic language demands in math when planning and delivering lessons including the demands of reading writing speaking listening conversing and representing in math Aguirre Bunch 2012 Therefore while these instructional supports and practices can and should be used to support all students learning mathematics they are particularly wellsuited to meet the needs of linguistically and culturally diverse students who are learning mathematics while simultaneously acquiring English This table reflects the attention and support for language development at each level of the Zearn Math curriculum Course Mission Lesson foundation of curriculum theory of action and design principles that drive a continuous focus on language development student terminology Mission specific progression of language development included in each Mission Overview definitions of new terminology additional supports for multilingual learners based on language demands of the activity THEORY OF ACTION Zearn believes that language development can be built into teachers instructional practice and students classroom experience through intentional design of materials teacher commitments administrative support and professional development Our theory of action is grounded in the interdependence of language learning and content learning the importance of scaffolding routines that foster students independent participation 40 ZEARN MATH Teacher Edition

G4 Course Guide Appendix II Access for Multilingual Learners the value of instructional responsiveness in the teaching process and the central role of student agency in the learning process Mathematical understandings and language competence develop interdependently Deep conceptual learning is gained through language Ideas take shape through words texts illustrations conversations debates examples etc Teachers peers and texts serve as language resources for learning Instructional attention to academic language development historically limited to vocabulary instruction has now shifted to also include instruction around the demands of argumentation explanation generalization analyzing the purpose and structure of the text and other mathematical discourse Scaffolding provides temporary supports that foster student autonomy Learners with emerging language at any level can engage deeply with central mathematical ideas under specific instructional conditions Mathematical language development occurs when students use their developing language to make meaning and engage with challenging problems that are beyond students mathematical ability to solve independently and therefore require interaction with peers However these interactions should be structured with temporary supports that students can use to make sense of what is being asked of them to help organize their own thinking and to give and receive feedback Instruction supports learning when teachers respond to students verbal and written work Eliciting student thinking through language allows teachers and students to respond formatively to the language students generate Formative peer and teacher feedback creates opportunities for revision and refinement of both content understandings and language Students are agents in their own mathematical and linguistic sense making Mathematical language proficiency is developed through the process of actively exploring and learning mathematics Language is action by engaging with mathematics content students have naturally occurring opportunities to need learn and notice mathematical ways of making sense and talking about ideas and the world These experiences support learners in using as well as expanding their existing language toolkits Additional supports for multilingual learners Are embedded within lessons in the Zearn Math Teacher Edition these offer instructional strategies for teachers to meet the individual needs of a diverse group of learners when support beyond existing strategies embedded in Zearn Math is required These lesson specific supports examples found below provide students with access to the mathematics by supporting them with the language demands of a specific activity without reducing the mathematical demand of the task Using these supports will help maintain student engagement in mathematical discourse and ensure that the struggle remains productive All of the supports are designed to be used as needed and use should be faded out as students develop understanding and fluency with the English language Teachers should use their professional judgment about which supports to use and when based on their knowledge of the individual needs of students in their classroom Based on their observations of student language teachers can make adjustments to their teaching and provide additional language support where necessary Teachers should take into account the language demands of the specific activity and the language needed to engage the content more broadly concerning their students current ways of using language to communicate ideas as well as their students English language proficiency ZEARN MATH Teacher Edition 41

Appendix II Access for Multilingual Learners G4 Course Guide DESIGN PRINCIPLES FOR PROMOTING MATHEMATICAL LANGUAGE USE AND DEVELOPMENT The framework for supporting multilingual learners in Zearn Math includes four design principles for promoting mathematical language use and development in curriculum and instruction The design principles and related routines work to make language development an integral part of planning and delivering instruction while guiding teachers to amplify the most important language that students are expected to bring to bear on the central mathematical ideas of each Mission Principle 1 Support Sense Making Scaffold tasks and amplify language so students can make their own meaning Students do not need to understand a language completely before they can engage with academic content in that language Language learners of all levels can and should engage with grade level content that is appropriately scaffolded Students need multiple opportunities to talk about their mathematical thinking negotiate meaning with others and collaboratively solve problems with targeted guidance from the teacher Teachers can make language more accessible for students by amplifying rather than simplifying speech or text Simplifying includes avoiding the use of challenging words or phrases Amplifying means anticipating where students might need support in understanding concepts or mathematical terms and providing multiple ways to access them Providing visuals or manipulatives demonstrating problem solving engaging in think alouds and creating analogies synonyms or context are all ways to amplify language so that students are supported in taking an active role in their own sense making of mathematical relationships processes concepts and terms Principle 2 Optimize Output Strengthen opportunities and supports for students to describe their mathematical thinking to others orally visually and in writing Linguistic output is the language that students use to communicate their ideas to others oral written visual etc and refers to all forms of student linguistic expressions except those that include significant back and forth negotiation of ideas That type of conversational language is addressed in the third principle All students benefit from repeated strategically optimized and supported opportunities to articulate mathematical ideas into linguistic expression Opportunities for students to produce output should be strategically optimized for both a important concepts of the Mission or grade level and b important disciplinary language functions for example making conjectures and claims justifying claims with evidence explaining reasoning critiquing the reasoning of others making generalizations and comparing approaches and representations The focus for optimization must be determined in part by how students are currently using language to engage with important disciplinary concepts When opportunities to produce output are optimized in these ways students will get spiraled practice in pairing their thinking with more robust reasoning and examples and with more precise language and visuals Principle 3 Cultivate Conversation Strengthen opportunities and supports for constructive mathematical conversations pairs groups and whole class Conversations are back and forth interactions with multiple turns that build up ideas about math Conversations act as scaffolds for students developing mathematical language because they provide opportunities to simultaneously make meaning communicate that meaning and refine the way content understandings are communicated 42 ZEARN MATH Teacher Edition

G4 Course Guide Appendix II Access for Multilingual Learners When students have a purpose for talking and listening to each other communication is more authentic During effective discussions students pose and answer questions clarify what is being asked and what is happening in a problem build common understandings and share experiences relevant to the topic As mentioned in Principle 2 learners must be supported in their use of language including when having conversations making claims justifying claims with evidence making conjectures communicating reasoning critiquing the reasoning of others engaging in other mathematical practices and above all when making mistakes Meaningful conversations depend on the teacher using lessons and activities as opportunities to build a classroom culture that motivates and values efforts to communicate Principle 4 Maximize Meta awareness Strengthen the meta connections and distinctions between mathematical ideas reasoning and language Language is a tool that not only allows students to communicate their math understanding to others but also to organize their own experiences ideas and learning for themselves Meta awareness is consciously thinking about one s own thought processes or language use Meta awareness develops when students and teachers engage in classroom activities or discussions that bring explicit attention to what students need to do to improve communication and reasoning about mathematical concepts When students are using language in ways that are purposeful and meaningful for themselves in their efforts to understand and be understood by each other they are motivated to think of ways in which language can be both clarified and clarifying Meta awareness in students can be strengthened when for example teachers ask students to explain to each other the strategies they brought to bear to solve a challenging problem They might be asked How does yesterday s method connect with the method we are learning today or What ideas are still confusing to you These questions are metacognitive because they help students to reflect on their own and others learning Students can also reflect on their expanding use of language for example by comparing the language they used to clarify a mathematical concept with the language used by their peers in a similar situation This is called metalinguistic awareness because students reflect on English as a language their own growing use of that language and the particular ways ideas are communicated in mathematics Students learning English benefit from being aware of how language choices are related to the purpose of the task and the intended audience especially if oral or written work is required Both metacognitive and metalinguistic awareness are powerful tools to help students self regulate their academic learning and language acquisition These four principles are guides for curriculum development as well as for planning and execution of instruction including the structure and organization of interactive opportunities for students They also serve as guides for observation analysis and reflection on student language and learning MATHEMATICAL LANGUAGE ROUTINES To further support students language development Zearn recommends that teachers read and consider using the mathematical language routines MLRs listed below MLR 1 Stronger and Clearer Each Time MLR 2 Collect and Display MLR 3 Clarify Critique Correct MLR 4 Information Gap ZEARN MATH Teacher Edition 43

Appendix II Access for Multilingual Learners MLR 5 Co Craft Questions MLR 6 Three Reads MLR 7 Compare and Connect MLR 8 Discussion Supports G4 Course Guide The mathematical language routines MLRs were selected because they are effective and practical for simultaneously learning mathematical practices content and language A mathematical language routine is a structured but adaptable format for amplifying assessing and developing students language The routines emphasize the uses of language that are meaningful and purposeful rather than about just getting answers These routines can be adapted and incorporated across lessons in each Mission to fit the mathematical work wherever there are productive opportunities to support students in using and improving their English and disciplinary language use Each MLR facilitates attention to student language in ways that support in the moment teacher peer and selfassessment for all learners The feedback enabled by these routines will help students revise and refine not only the way they organize and communicate their own ideas but also ask questions to clarify their understanding of others ideas Mathematical Language Routine 1 Stronger and Clearer Each Time Purpose To provide a structured and interactive opportunity for students to revise and refine both their ideas and their verbal and written output Zwiers 2014 This routine also provides a purpose for student conversation through the use of a discussion worthy and iteration worthy prompt The main idea is to have students think and write individually about a question use a structured pairing strategy to have multiple opportunities to refine and clarify their response through conversation and then finally revise their original written response Subsequent conversations and second drafts should naturally show evidence of incorporating or addressing new ideas and language They should also show evidence of refinement in precision communication expression examples and reasoning about mathematical concepts How it happens PROMPT This routine begins by providing a thought provoking question or prompt The prompt should guide students to think about a concept or big idea connected to the content goal of the lesson and should be answerable in a format that is connected with the activity s primary disciplinary language function RESPONSE FIRST DRAFT Students draft an initial response to the prompt by writing or drawing their initial thoughts in a first draft Responses should attempt to align with the activity s primary language function It is not necessary that students finish this draft before moving to the structured pair meetings step However students should be encouraged to write or draw something before meeting with a partner This encouragement can come over time as class culture is developed strategies and supports for getting started are shared and students become more comfortable with the low stakes of this routine 2 3 min STRUCTURED PAIR MEETINGS Next use a structured pairing strategy to facilitate students having 2 3 meetings with different partners Each meeting gives each partner an opportunity to be the speaker and an opportunity to be the listener As the speaker each student shares their ideas without looking at their first 44 ZEARN MATH Teacher Edition

G4 Course Guide Appendix II Access for Multilingual Learners draft when possible As a listener each student should a ask questions for clarity and reasoning b press for details and examples and c give feedback that is relevant for the language goal 1 2 min each meeting RESPONSE SECOND DRAFT Finally after meeting with 2 3 different partners students write a second draft This draft should naturally reflect borrowed ideas from partners as well as refinement of initial ideas through repeated communication with partners This second draft will be stronger with more or better evidence of mathematical content understanding and clearer more precision organization and features of disciplinary language function After students are finished their first and second drafts can be compared 2 3 min Mathematical Language Routine 2 Collect and Display Purpose To capture a variety of students oral words and phrases into a stable collective reference The intent of this routine is to stabilize the varied and fleeting language in use during mathematical work in order for students own output to become a reference in developing mathematical language The teacher listens for and scribes the language students use during partner small group or whole class discussions using written words diagrams and pictures This collected output can be organized revoiced or explicitly connected to other language in a display that all students can refer to build on or make connections with during future discussion or writing Throughout the course of a Mission and beyond teachers can reference the displayed language as a model update and revise the display as student language changes and make bridges between prior student language and new disciplinary language Zwiers et al 2017 This routine provides feedback for students in a way that supports sense making while simultaneously increasing meta awareness of language How it happens COLLECT During this routine circulate and listen to student talk during paired group or as a whole class discussion Jot down the words phrases drawings or writing students use Capture a variety of uses of language that can be connected to the lesson content goals as well as the relevant disciplinary language function s Collection can happen digitally with a clipboard or directly onto poster paper capturing on a whiteboard is not recommended due to risk of erasure DISPLAY Display the language collected visually for the whole class to use as a reference during further discussions throughout the lesson and Mission Encourage students to suggest revisions updates and connections be added to the display as they develop over time both new mathematical ideas and new ways of communicating ideas The display provides an opportunity to showcase connections between student ideas and new vocabulary and also highlights examples of students using disciplinary language functions beyond just vocabulary words Mathematical Language Routine 3 Clarify Critique Correct Purpose To give students a piece of mathematical writing that is not their own to analyze reflect on and develop The intent is to prompt student reflection with an incorrect incomplete or ambiguous written mathematical statement and for students to improve upon the written work by correcting errors and clarifying meaning Teachers can demonstrate how to effectively and respectfully critique the work of others with meta think alouds and pressing for details when necessary This routine fortifies output and engages students in meta awareness More than just error analysis this routine purposefully engages students in considering both the author s mathematical thinking as well as the features of their communication ZEARN MATH Teacher Edition 45

Appendix II Access for Multilingual Learners G4 Course Guide How it happens ORIGINAL STATEMENT Create or curate a written mathematical statement that intentionally includes conceptual or common errors in mathematical thinking as well as ambiguities in language The mathematical errors should be driven by the content goals of the lesson and the language ambiguities should be driven by common or typical challenges with the relevant disciplinary language function This mathematical text is read by the students and used as the draft or original statement that students improve 1 2 min DISCUSSION WITH PARTNER Next students discuss the original statement in pairs The teacher provides guiding questions for this discussion such as What do you think the author means Is anything unclear or Are there any reasoning errors In addition to these general guiding questions 1 2 questions can be added that specifically address the content goals and disciplinary language function relevant to the activity 2 3 min IMPROVED STATEMENT Students individually revise the original statement drawing on the conversations with their partners to create an improved statement In addition to resolving any mathematical errors or misconceptions clarifying ambiguous language other requirements can be added as parameters for the improved response These specific requirements should be aligned with the content goals and disciplinary language function of the activity 3 5 min Mathematical Language Routine 4 Information Gap Purpose To create a need for students to communicate Gibbons 2002 This routine allows teachers to facilitate meaningful interactions by positioning some students as holders of information that is needed by other students The information is needed to accomplish a goal such as solving a problem or winning a game An information gap creates a need for students to orally or visually share ideas and information in order to bridge a gap and accomplish something that they could not have done alone Teachers should demonstrate how to ask for and share information how to justify a request for information and how to clarify and elaborate on the information This routine cultivates conversation How it happens PROBLEM DATA CARDS Students are paired into Partner A and Partner B Partner A is given a card with a problem that must be solved and Partner B has the information needed to solve it on a data card Data cards can also contain diagrams tables graphs etc Neither partner should read nor show their cards to their partner Partner A determines what information they need and prepares to ask Partner B for that specific information Partner B should not share the information unless Partner A specifically asks for it and justifies the need for the information Because partners don t have the same information Partner A must work to produce clear and specific requests and Partner B must work to understand more about the problem through Partner A s requests and justifications BRIDGING THE GAP First Partner B asks What specific information do you need Then Partner A asks for specific information from Partner B Before sharing the requested information Partner B asks Partner A for a justification Why do you need that information Partner A explains how they plan to use the information Finally Partner B asks clarifying questions as needed and then provides the information These four steps are repeated until Partner A is satisfied that they have the information they need to solve the problem 46 ZEARN MATH Teacher Edition

G4 Course Guide Appendix II Access for Multilingual Learners SOLVING THE PROBLEM First Partner A shares the problem card with Partner B Partner B does not share the data card Then both students solve the problem independently then discuss their strategies Finally Partner B can share the data card after discussing their independent strategies Mathematical Language Routine 5 Co craft Questions Purpose To allow students to get inside of a context before feeling pressure to produce answers to create space for students to produce the language of mathematical questions themselves and to provide opportunities for students to analyze how different mathematical forms and symbols can represent different situations Through this routine students can use conversation skills to generate choose argue for the best one and improve questions and situations as well as develop meta awareness of the language used in mathematical questions and problems How it happens HOOK Begin by presenting students with a hook a context or a stem for a problem with or without values included The hook can also be a picture video or list of interesting facts STUDENTS WRITE QUESTIONS Next students write down possible mathematical questions that might be asked about the situation These should be questions that they think are answerable by doing math and could be questions about the situation information that might be missing and even assumptions that they think are important 1 2 minutes STUDENTS COMPARE QUESTIONS Students compare the questions they generated with a partner 1 2 minutes before sharing questions with the whole class Demonstrate or ask students to demonstrate identifying specific questions that are aligned to the content goals of the lesson as well as the disciplinary language function If there are no clear examples teachers can demonstrate adapting a question or ask students to adapt questions to align with specific content or function goals 2 3 minutes ACTUAL QUESTION S REVEALED IDENTIFIED Finally the actual questions students are expected to work on are revealed or selected from the list that students generated Mathematical Language Routine 6 Three Reads Purpose To ensure that students know what they are being asked to do create opportunities for students to reflect on the ways mathematical questions are presented and equip students with tools used to actively make sense of mathematical situations and information Kelemanik Lucenta Creighton 2016 This routine supports reading comprehension sense making and meta awareness of mathematical language It also supports negotiating information in a text with a partner through mathematical conversation How it happens In this routine students are supported in reading a mathematical text situation or word problem three times each with a particular focus The intended question or main prompt is intentionally withheld until the third read so that students can concentrate on making sense of what is happening in the text before rushing to a solution or method READ 1 SHARED READING ONE PERSON READS ALOUD WHILE EVERYONE ELSE READS WITH THEM The first read focuses on the situation context or main idea of the text After a shared reading ask students what ZEARN MATH Teacher Edition 47

Appendix II Access for Multilingual Learners G4 Course Guide is this situation about This is the time to identify and resolve any challenges with any non mathematical vocabulary 1 minute READ 2 INDIVIDUAL PAIRS OR SHARED READING After the second read students list any quantities that can be counted or measured Students are encouraged not to focus on specific values Instead they focus on naming what is countable or measurable in the situation It is not necessary to discuss the relevance of the quantities just to be specific about them examples number of people in her family rather than people number of markers after instead of markers Some of the quantities will be explicit example 32 apples while others are implicit example the time it takes to brush one tooth Record the quantities as a reference to use when solving the problem after the third read 3 5 minutes READ 3 INDIVIDUAL PAIRS OR SHARED READING During the third read the final question or prompt is revealed Students discuss possible solution strategies referencing the relevant quantities recorded after the second read It may be helpful for students to create diagrams to represent the relationships among quantities identified in the second read or to represent the situation with a picture Asturias 2015 1 2 minutes Mathematical Language Routine 7 Compare and Connect Purpose To foster students meta awareness as they identify compare and contrast different mathematical approaches and representations This routine leverages the powerful mix of disciplinary representations available in mathematics as a resource for language development In this routine students make sense of mathematical strategies other than their own by relating and connecting other approaches to their own Students should be prompted to reflect on and linguistically respond to these comparisons for example exploring why or when one might do or say something a certain way identifying and explaining correspondences between different mathematical representations or methods or wondering how a certain concept compares or connects to other concepts Be sure to demonstrate asking questions that students can ask each other rather than asking questions to test understanding Use think alouds to demonstrate the trial and error or fits and starts of sensemaking similar to the way teachers think aloud to demonstrate reading comprehension This routine supports metacognition and metalinguistic awareness and also supports constructive conversations How it happens STUDENTS PREPARE DISPLAYS OF THEIR WORK Students are given a problem that can be approached and solved using multiple strategies or a situation that can be modeled using multiple representations Students are assigned the job of preparing a visual display of how they made sense of the problem and why their solution makes sense Variation is encouraged and supported among the representations that different students use to show what makes sense COMPARE Students investigate each others work by taking a tour of the visual displays Tours can be selfguided a travelers and tellers format or the teacher can act as a docent by providing questions for students to ask of each other pointing out important mathematical features and facilitating comparisons Comparisons focus on the typical structures purposes and affordances of the different approaches or representations what worked well in this or that approach or what is especially clear in this or that representation During this discussion listen for and amplify any comments about what might make this or that approach or representation more complete or easy to understand CONNECT The discussion then turns to identifying correspondences between different representations Students are prompted to find correspondences in how specific mathematical relationships operations 48 ZEARN MATH Teacher Edition

G4 Course Guide Appendix II Access for Multilingual Learners quantities or values appear in each approach or representation Guide students to refer to each other s thinking by asking them to make connections between specific features of expressions tables graphs diagrams words and other representations of the same mathematical situation During the discussion amplify the language students use to communicate about mathematical features that are important for solving the problem or modeling the situation Call attention to the similarities and differences between the ways those features appear Mathematical Language Routine 8 Discussion Supports Purpose To support rich and inclusive discussions about mathematical ideas representations contexts and strategies Chapin O Connor Anderson 2009 Rather than another structured format the examples provided in this routine are instructional moves that can be combined and used together with any of the other routines They include multimodal strategies for helping students make sense of complex language ideas and classroom communication The examples can be used to invite and incentivize more student participation conversation and meta awareness of language Eventually as teachers continue to demonstrate students should begin using these strategies themselves to prompt each other to engage more deeply in discussions How it happens Unlike the other routines this support is a collection of strategies and moves that can be combined and used to support discussion during almost any activity Examples of possible strategies Revoice student ideas to demonstrate mathematical language use by restating a statement as a question in order to clarify apply appropriate language and involve more students Press for details in students explanations by requesting for students to challenge an idea elaborate on an idea or give an example Show central concepts multi modally by using different types of sensory inputs acting out scenarios or inviting students to do so showing videos or images using gestures and talking about the context of what is happening Practice phrases or words through choral response Think aloud by talking through thinking about a mathematical concept while solving a related problem or doing a task Demonstrate uses of disciplinary language functions such as detailing steps describing and justifying reasoning and questioning strategies Give students time to make sure that everyone in the group can explain or justify each step or part of the problem Then make sure to vary who is called on to represent the work of the group so students get accustomed to preparing each other to fill that role Prompt students to think about different possible audiences for the statement and about the level of specificity or formality needed for a classmate vs a mathematician for example Convince Yourself Convince a Friend Convince a Skeptic Mason Burton Stacey 2010 ZEARN MATH Teacher Edition 49

Appendix II Access for Multilingual Learners G4 Course Guide SENTENCE FRAMES Sentence frames can support student language production by providing a structure to communicate about a topic Helpful sentence frames are open ended so as to amplify language production not constrain it The table shows examples of generic sentence frames that can support common disciplinary language functions across a variety of content topics Some of the lessons in these materials include suggestions for additional sentence frames that could support the specific content and language functions of that lesson language function sample sentence frames describe It looks like I notice that I wonder if Let s try A quantity that varies is _____ What do you notice What other details are important explain First I _____ because Then Next I I noticed _____ so I I tried _____ and what happened was How did you get What else could we do justify I know _____ because I predict _____ because If _____ then _____ because Why did you How do you know Can you give an example generalize _____ reminds me of _____ because _____ will always _____ because _____ will never _____ because Is it always true that Is _____ a special case critique That could couldn t be true because This method works doesn t work because We can agree that _____ s idea reminds me of Another strategy would be _____ because Is there another way to say do compare and contrast Both _____ and _____ are alike because _____ and _____ are different because One thing that is the same is One thing that is different is How are _____ and _____ different What do _____ and _____ have in common 50 ZEARN MATH Teacher Edition

G4 Course Guide Appendix II Access for Multilingual Learners language function sample sentence frames represent _____ represents _____ _____ stands for _____ _____ corresponds to _____ Another way to show _____ is How else could we show this interpret We are trying to We will need to know We already know It looks like _____ represents Another way to look at it is What does this part of _____ mean Where does _____ show ZEARN MATH Teacher Edition 51

G4 Course Guide References References Aguirre J M Bunch G C 2012 What s language got to do with it Identifying language demands in mathematics instruction for English language learners In S Celed n Pattichis N Ramirez Eds Beyond good teaching Advancing mathematics education for ELLs pp 183 194 Reston VA National Council of Teachers of Mathematics Asturias Mendez Luis Harold 2015 Feb Access for All Linked Learning and Language Three Reads and Problem Stem Strategies Presentation at the English Learner Leadership Conference Sonoma CA CAST n d About Universal Design for Learning Retrieved December 7 2021 from https www cast org impact universal design for learning udl Chapin S O Connor C Anderson N 2009 Classroom discussions Using math talk to help students learn grades K 6 second edition Sausalito CA Math Solutions Publications Common Core State Standards Initiative n d Standards for Mathematical Practice Retrieved December 7 2021 from http www corestandards org Math Practice Gibbons P 2002 Scaffolding language scaffolding learning Teaching second language learners in the mainstream classroom Portsmouth NH Heinemann Kelemanik G Lucenta A Creighton S J 2016 Routines for reasoning Fostering the mathematical practices in all students Portsmouth NH Heinemann Leong Y H Ho W K Cheng L P 2015 Concrete Pictorial Abstract Surveying its origins and charting its future https repository nie edu sg bitstream 10497 18889 1 TME 16 1 1 pdf Paunesku D Walton GM Romero C Smith EN Yeager DS Dweck CS Mind Set Interventions Are a Scalable Treatment for Academic Underachievement Psychological Science 2015 26 6 784 793 https doi org 10 1177 0956797615571017 Schmidt W H Wang H C McKnight C C 2005 Curriculum coherence An examination of US mathematics and science content standards from an international perspective J Curriculum Studies 37 5 525 559 https doi org 10 1080 0022027042000294682 Smith M S Stein M K 2011 5 practices for orchestrating productive mathematics discussions Reston VA National Council of Teachers of Mathematics Stacey K Burton L Mason J 1982 Thinking mathematically Addison Wesley Walton G M Cohen G L 2007 A question of belonging race social fit and achievement J Pers Soc Psychol 92 1 82 https doi org 10 1037 0022 3514 92 1 82 Zwiers J 2014 Building academic language Meeting Common Core Standards across disciplines grades 5 12 2nd ed San Francisco CA Jossey Bass Zwiers J Dieckmann J Rutherford Quach S Daro V Skarin R Weiss S Malamut J 2017 Principles for the Design of Mathematics Curricula Promoting Language and Content Development Retrieved from Stanford University UL SCALE website http ell stanford edu content mathematics resources additionalresources ZEARN MATH Teacher Edition 52

Math TEACHER EDITION Math TEACHER EDITION GRADE 4 Course Guide 4 GRADE Zearnmath_CC_Grade4_CG indd 1 12 10 22 2 40 PM