Zearn Math–Teacher Edition: Course Guide, K : simplebooklet.com

Table of ContentsABOUT ZEARN MATHABOUT KINDERGARTEN MATHApproach 6Scope & sequence 7Pacing 8A TYPICAL LESSON IN ZEARN MATHWarm-Up 9Concept Exploration 10Wrap-Up 11IMPLEMENTING ZEARN MATHPlanning for a Mission 11Planning your week 13Core Days 13Flex Day 13Planning for a lesson 14Preparing students for Independent Digital Lessons 17SUPPORTING DIVERSE LEARNERSCommitment to accessibility 18Design features that support all learners 18Supporting multilingual learners 19Elements of language 20Mathematical language routines (MLRs) 20Supporting students with disabilities 21Accessible design features 22Assistive technology 22Instructional accommodations 23ASSESSMENTS AND REPORTSOngoing formative assessments 24Daily lesson-level assessments: The Tower of Power (digital) and Exit Tickets (paper) 24Mission-level assessments (paper) 24Class and student reports 25

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Table of ContentsClass reports: Progress, Pace, Tower Alerts, and Sprint Alerts 25Student Reports 26Approach to unfinished learning 26TERMINOLOGYREQUIRED MATERIALSLESSONS BY STANDARDSTANDARDS BY LESSONAPPENDIX I: INSTRUCTIONAL ROUTINESWhite Board Exchange 38Anticipate, Monitor, Select, Sequence, Connect 38Take Turns 39Think Pair Share 39READ, DRAW, WRITE (RDW) 39APPENDIX II: ACCESS FOR MULTILINGUAL LEARNERSIntroduction 40Theory Of Action 40Design Principles for Promoting Mathematical Language Use and Development 42Principle 1: Support Sense-Making 42Principle 2: Optimize Output 42Principle 3: Cultivate Conversation 42Principle 4: Maximize Meta-awareness 43Mathematical Language Routines 43Mathematical Language Routine 1: Stronger and Clearer Each Time 44Mathematical Language Routine 2: Collect and Display 45Mathematical Language Routine 3: Clarify, Critique, Correct 45Mathematical Language Routine 4: Information Gap 46Mathematical Language Routine 5: Co-Craft Questions 46Mathematical Language Routine 6: Three Reads 47Mathematical Language Routine 7: Compare and Connect 48Mathematical Language Routine 8: Discussion Supports 49Sentence Frames 49REFERENCES

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About Zearn MathAll Children Can Love Learning MathVISIONZearn 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 PRINCIPLESZearn 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.GK Course Guide About Zearn MathZEARN MATH Teacher Edition 5

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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 Kindergarten MathAPPROACHGuided 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 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.GK Course GuideAbout Kindergarten MathZEARN MATH Teacher Edition6

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SCOPE & SEQUENCEThe 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.M3Comparison of Length, Weight, Capacity, & Numbers to 10WEEK1 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 36KG1G2G3G4G5G6G7G8M1Numbers to 10M4Number Pairs, Addition, & Subtraction to 10M6Analyzing,Comparing, & Composing ShapesM1Add & Subtract Friendly NumbersM2Meet Place ValueM3Measure LengthM2Explore LengthM3Counting & Place ValueM1Add, Subtract, & RoundM1Multiply & Divide Friendly NumbersM2Measure ItM4Add & Subtract Big NumbersM5Work with ShapesM4Find the AreaM1Area and Surface AreaM1Scale DrawingsM3Measuring CirclesM6Add & Subtract to 100M4Add, Subtract, & SolveM5Add & Subtract Big NumbersM6EqualGroupsM7Length, Money, & DataM3Multiply & Divide Tricky NumbersM5Fractions as NumbersM6Display DataM7Shapes & MeasurementM3Multiply & Divide Big NumbersM5Equivalent FractionsM6Decimal FractionsM1Place Value with Decimal FractionsM7Multiply & MeasureM2Base Ten OperationsM3Add & Subtract FractionsM4Dividing FractionsM5Arithmetic in Base TenM4Multiply and Divide Fractions & DecimalsM5Volume, Area, & ShapesM6The Coordinate PlaneM2Introducing RatiosM2Introducing Proportional RelationshipsM1Rigid Transformations and CongruenceM4Proportional Relationships and PercentagesM4Linear Equations and Linear SystemsM3Rates and PercentagesM6Expressions and EquationsM6Associations in DataM3Linear RelationshipsM5Functions and VolumeM7Exponents and Scientific NotationM7Rational NumbersM8Data Sets and DistributionsM7Angles, Triangles, and PrismsM8Pythagorean Theorem and Irrational NumbersM6Expressions, Equations, and InequalitiesM5Rational Number ArithmeticM8Probability and SamplingM9Putting It ALL TogetherM4Construct Lines, Angles, & ShapesM2Measure & SolveM9Putting It ALL TogetherM9Putting It ALL TogetherM22D & 3D ShapesM5Numbers 10–20; Count to 100 by Ones and TensM8Shapes, Time, & FractionsM2Dilations, Similarity, and Introducing SlopeWhole Numbers and OperationsExpanding Whole Numbers and Operations to Fractions and DecimalsAlgebraic Thinking and Reasoning Leading to FunctionsGeometry Measurement, Statistics and ProbabilityM1Add & Subtract Small NumbersKeyGK Course Guide About Kindergarten MathZEARN MATH Teacher Edition 7

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Kindergarten is all about working concretely with numbers. Students will count, compose, decompose, compare, and begin to operate with numbers. Students also get the opportunity to apply mathematics to their everyday lives by exploring spatial concepts, measurement concepts, and how to use numbers to quantify an amount of an object. More learning time in Kindergarten will be devoted to numbers than to other topics. Fluency with addition and subtraction within 5 is a Kindergarten goal, and the building blocks start in Mission 1. Students learn the meaning of numbers to 10 by exploring counting sequences, cardinality, and one-to-correspondence. There is a focus on embedded numbers and relationships to 5. From there, students are introduced to two- and three-dimensional shapes and experiment with comparisons of length, weight, and capacity. Roughly half-way through the year, addition and subtraction are formally introduced, building from adding and subtracting within 5 to within 10. Additionally, students extend the count sequence all the way to 100, with a special emphasis on understanding teen numbers as “10 ones and some ones.” Kindergarten concludes the year with an exploration of shapes. Students build shapes from components, analyze and compare them, and discover that they can be composed of smaller shapes, just as larger numbers are composed of smaller numbers. The concrete exploration of numbers and shapes throughout Kindergarten establishes the foundation upon which all future grades will build.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.).1 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.PACINGThe kindergarten year will include six 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 kindergarten 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.1 Common Core State Standards Initiative (n.d.). Standards for Mathematical Practice. Retrieved December 7, 2021, from http://www.corestandards.org/Math/Practice/GK Course GuideAbout Kindergarten MathZEARN MATH Teacher Edition8

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Each Mission will conclude with a paper-based, End-of-Mission assessment; some longer Missions also contain a Mid-Mission assessment. 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.The table outlines the missions, lessons, and estimated duration of Kindergarten content on Zearn.Mission Title Lessons Weeks1 Numbers to 10 37 92 Two-Dimensional & Three-Dimensional Shapes 10 23 Comparison of Length, Weight, Capacity, & Numbers to 10 32 84 Number Pairs, Addition & Subtraction to 10 41 95 Numbers 10–20 & Counting to 100 24 66 Analyzing, Comparing, & Composing Shapes 8 2Totals 152 36A Typical Lesson in Zearn MathIn a typical math block with Zearn, covering one lesson, students will experience:Warm-UpConcept Exploration Collaborative Concept Exploration with teacher and peers, Independent Digital Lessons to explore concepts further on their own; andWrap-Up Lesson Synthesis led by the teacher and the completion of an individual Exit Ticket.WARM-UPThe 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 PracticeWelcomes students into the day’s lesson with a fun activity.GK Course Guide A Typical Lesson in Zearn MathZEARN MATH Teacher Edition 9

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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 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 ProblemFocuses 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 EXPLORATIONNext, 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 ExplorationBuilt 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 LessonsStudents 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.GK Course GuideA Typical Lesson in Zearn MathZEARN MATH Teacher Edition10

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(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.)WRAP-UPAfter 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 SynthesisStudents 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 TicketStudents 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 MathPLANNING FOR A MISSIONThe story of Zearn Math for kindergarten is told in six Missions. Concepts are taught through the concrete-to-pictorial-to-abstract progression within each Mission and throughout the year to allow students ample time to GK Course Guide Implementing Zearn MathZEARN MATH Teacher Edition 11

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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.There are many materials you can use to plan for a Mission:Familiarize yourself with the mathematics of the Mission and how students will progress toward understanding 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.• 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.2 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.2 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.GK Course GuideImplementing Zearn MathZEARN MATH Teacher Edition12

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PLANNING YOUR WEEKWe 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 DaysIf 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 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 DayIn 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.)GK Course Guide Implementing Zearn MathZEARN MATH Teacher Edition 13

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• 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 grade-level 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.• 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 LESSONYou 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 lessonGain 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:• Fluency: Each Independent Digital Lesson starts with a short lesson-aligned fluency activity designed for students to develop and deepen number sense. Students practice prior concepts in activities such as Counting Train, Sum Snacks, Hop Skip Splash, Make and Break, Next Stop Top, Sprints, and Blasts. GK Course GuideImplementing Zearn MathZEARN MATH Teacher Edition14

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• Guided Practice: Students experience one of three different Guided Practice activities—Math Chat, Learning Lab, or Story Time. 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 complete problems in their paper Student Notes to transfer their software-based learning, check and correct their work, and strengthen knowledge retention. In Zearn Math for Kindergarten, students also have the option to follow along with the notes on-screen if they do not have their paper Student Notes available.• 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.• If 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, and 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; select 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 GK Course Guide Implementing Zearn MathZEARN MATH Teacher Edition 15

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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.• 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 challenges; 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; 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.GK Course GuideImplementing Zearn MathZEARN MATH Teacher Edition16

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PREPARING STUDENTS FOR INDEPENDENT DIGITAL LESSONSTo 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: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 kindergarten, these are:• 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. In Zearn Math for Kindergarten, all critical on-screen text is automatically read aloud and can be read again through clicking the audio buttons. 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.GK Course Guide Implementing Zearn MathZEARN MATH Teacher Edition 17

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• Interaction Hints: Pulsing buttons on screen encourage interaction with key buttons at precise moments. This is helpful for students who are unsure how to move forward in a lesson.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.3 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 LearnersCOMMITMENT TO ACCESSIBILITYZearn 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 LEARNERSTo 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.3 https://help.zearn.orgGK Course GuideSupporting Diverse LearnersZEARN MATH Teacher Edition18

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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 Math-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.4SUPPORTING MULTILINGUAL LEARNERSZearn 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 with opportunities to access grade-level 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 4 Zearn Math manipulative kits can be found at https://www.hand2mind.com/kits/publisher-aligned-kits/zearn.GK Course Guide Supporting Diverse LearnersZEARN MATH Teacher Edition 19

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additional expertise on how to support students’ language development as they learn math and encounter areas of struggle.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 languageDuring 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 problem solving 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:GK Course GuideSupporting Diverse LearnersZEARN MATH Teacher Edition20

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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.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 DISABILITIESStudents 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.”)GK Course Guide Supporting Diverse LearnersZEARN MATH Teacher Edition 21

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The following design elements, assistive technologies, and accommodations may help students with disabilities access Zearn Math.Accessible design featuresWe 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 technologyAssistive 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.GK Course GuideSupporting Diverse LearnersZEARN MATH Teacher Edition22

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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 accommodationsTeachers 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: In Zearn Math for Kindergarten, all critical on-screen text is automatically read aloud and can be read again through clicking the audio buttons. 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. GK Course Guide Supporting Diverse LearnersZEARN MATH Teacher Edition 23

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Assessments and ReportsZearn 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 ASSESSMENTSAssessments 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. In Kindergarten, we recommend reading the Exit Ticket out loud to create access as students are building their early reading skills. 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)GK Course GuideAssessments and ReportsZEARN MATH Teacher Edition24

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Mid-Mission and End-of-Mission assessments are formative assessments, administered roughly halfway through the Mission and at the conclusion of the Mission respectively. In kindergarten, teachers should administer this paper-based assessment in interview style, recording their observations of the student’s work and thinking. The assessment items vary in their focus, ranging from items that highlight a student’s understanding of a big mathematical idea to items that are more focused on students’ procedural fluency. Zearn Math provides a rubric for each Mission-level assessment that contains a progression towards understanding for each item, as well as specific standards-alignment information. Each rubric offers detailed examples of where students might go wrong as well as guidance on what incorrect answers indicate about a student’s unfinished learning. These rubrics help teachers leverage the Mission-level assessments by providing actionable feedback they can use to respond to students’ demonstrated learning and misconceptions. *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 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 REPORTSZearn 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.5 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 AlertsProgress 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.5 To learn about the Zearn Class Reports and Student Reports you may access, visit https://help.zearn.org/hc/en-us/articles/4403432402071-Teacher-ReportsGK Course Guide Assessments and ReportsZEARN MATH Teacher Edition 25

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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 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, 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 ReportsZearn 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 LEARNINGZearn Math for Kindergarten provides support for every starting point, 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, so that students can strengthen foundational understanding while learning grade-level concepts. These built-in supports GK Course GuideAssessments and ReportsZEARN MATH Teacher Edition26

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allow all kindergarten students to begin the year with the first Mission of Zearn Math for Kindergarten, even if it is their first experience with mathematics.• 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.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 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.GK Course Guide Assessments and ReportsZEARN MATH Teacher Edition 27

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• Cylinder solid shape • Endpoint with reference to alignment for direct comparison• Exactly the same, not exactly the same, and the same, but… ways to analyze objects to match or sort• Faceflat side of a solid• First, second, third, fourth, h, sixth, seventh, eighth, ninth, tenthordinal numbers • Flattwo-dimensional shape• Heavier than/lighter thanweight comparison• Heightvertical distance measurement from bottom to top• Hexagonflat figure enclosed by six straight sides• Hidden partnersembedded numbers • Hide Zero cardscalled Place Value cards in later grades, pictured to the rightHide Zero card (front)Hide Zero card (back) • How many?with reference to counting quantities or sets • Length distance measurement from end to end; in a rectangular shape, length can be used to describe any of the four sidesGK Course Guide TerminologyZEARN MATH Teacher Edition 29

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• Regular counting by tens to 100e.g., ten, twenty, thirty, forty, fifty, sixty, seventy, eighty, ninety, one hundred• Rows and Columnslinear configuration types • Say Ten counting by tens to 100e.g., 1 ten, 2 tens, 3 tens, 4 tens, 5 tens, 6 tens, 7 tens, 8 tens, 9 tens, 10 tens• Solidthree-dimensional shape• Sortgroup objects according to a particular attribute • Spheresolid shape• Squareflat figure enclosed by four straight, equal sides• Subtraction specifically using take from with result unknown• Take apartdecompose• Take awaysubtract• Taller than/shorter thanheight comparison• Teen numbers• The same ascomparative term• Triangleflat figure enclosed by three straight sides• Weightheaviness measurement• Wholetotal • Zerounderstand the meaning of, write, and recognizeGK Course Guide TerminologyZEARN MATH Teacher Edition 31

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Lessons by StandardStandard LessonK.CC.1K.5.13, K.5.15, K.5.16, K.5.17, K.5.18K.CC.2K.5.13, K.5.16, K.5.17, K.5.18K.CC.3K.1.12, K.1.13, K.1.14, K.1.15, K.1.16, K.1.17, K.1.18, K.1.19, K.1.20, K.1.21, K.1.22, K.1.24, K.1.26, K.1.27, K.1.28, K.1.29, K.1.30, K.1.31, K.1.32, K.1.33, K.1.34, K.1.35, K.1.37, K.4.1, K.4.2, K.4.3, K.4.4, K.4.5, K.4.6, K.4.7, K.4.8, K.4.9, K.4.10, K.4.11, K.4.12, K.4.25, K.4.27, K.5.1, K.5.2, K.5.3, K.5.4, K.5.6, K.5.9, K.5.10, K.5.11, K.5.12, K.5.13K.CC.4K.1.5, K.1.6, K.1.7, K.1.8, K.1.9, K.1.10, K.1.11, K.1.12, K.1.13, K.1.14, K.1.15, K.1.16, K.1.17, K.1.18, K.1.19, K.1.20, K.1.21, K.1.22, K.1.23, K.1.24, K.1.25, K.1.26, K.1.27, K.1.28, K.1.29, K.1.30, K.1.31, K.1.32, K.1.33, K.1.34, K.1.35, K.1.36, K.1.37, K.4.38K.CC.5K.1.8, K.1.9, K.1.10, K.1.11, K.1.12, K.1.13, K.1.14, K.1.15, K.1.16, K.1.17, K.1.18, K.1.19, K.1.20, K.1.21, K.1.22, K.1.23, K.1.24, K.1.25, K.1.26, K.1.27, K.1.28, K.1.29, K.1.31, K.1.32, K.1.33, K.1.34, K.1.35, K.1.36, K.1.37, K.3.23, K.3.24, K.5.1, K.5.2, K.5.3, K.5.4, K.5.5, K.5.6, K.5.10, K.5.11, K.5.12, K.5.13, K.5.14, K.5.18, K.5.19, K.5.22Standard LessonK.CC.6K.3.17, K.3.18, K.3.19, K.3.20, K.3.21, K.3.22, K.3.23, K.3.24, K.3.25, K.3.26, K.3.27, K.3.28K.CC.7K.3.20, K.3.25, K.3.26, K.3.27, K.3.28K.OA.1K.4.13, K.4.14, K.4.15, K.4.16, K.4.20, K.4.21, K.4.22, K.4.23, K.4.24, K.4.29, K.4.30, K.4.33, K.4.38K.OA.2K.4.16, K.4.17, K.4.18, K.4.19, K.4.21, K.4.31, K.4.34, K.4.35, K.4.36, K.4.37K.OA.3K.1.9, K.1.10, K.1.11, K.1.14, K.1.15, K.4.2, K.4.4, K.4.5, K.4.6, K.4.7, K.4.8, K.4.9, K.4.10, K.4.11, K.4.12, K.4.22, K.4.23, K.4.24, K.4.25, K.4.26, K.4.27, K.4.28, K.4.32K.OA.4K.4.39, K.4.40K.OA.5K.4.34, K.4.35, K.4.36, K.4.37, K.4.39, K.6.1, K.6.2, K.6.5K.NBT.1K.5.2, K.5.3, K.5.4, K.5.5, K.5.6, K.5.7, K.5.8, K.5.9, K.5.10, K.5.11, K.5.12, K.5.13, K.5.20, K.5.21, K.5.23K.MD.1K.3.1, K.3.2, K.3.8, K.3.13, K.3.16K.MD.2K.3.1, K.3.2, K.3.3, K.3.4, K.3.5, K.3.6, K.3.7, K.3.8, K.3.9, K.3.10, K.3.11, K.3.12, K.3.13, K.3.14, K.3.15, K.3.20, K.3.28, K.3.29, K.3.30, K.3.31, K.3.32K.MD.3K.1.1, K.1.2, K.1.3, K.1.4, K.1.5, K.1.6, K.1.7, K.2.1, K.2.7Standard LessonK.G.1K.2.5, K.2.8, K.2.10K.G.2K.2.2, K.2.3, K.2.4, K.2.5, K.2.7, K.2.8, K.2.9, K.2.10K.G.3K.2.1, K.2.6, K.2.9, K.2.10K.G.4K.2.1, K.2.2, K.2.3, K.2.4, K.2.6, K.2.7, K.2.9, K.2.10, K.6.3K.G.5K.6.1, K.6.2, K.6.3K.G.6K.6.5, K.6.6, K.6.7GK Course Guide Lessons by StandardZEARN MATH Teacher Edition 33

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Standards by LessonLesson StandardLesson 15K.CC.3, K.CC.4, K.CC.5, and K.OA.3Lesson 16K.CC.3, K.CC.4, and K.CC.5Lesson 17K.CC.3, K.CC.4, and K.CC.5Lesson 18K.CC.3, K.CC.4, and K.CC.5Lesson 19K.CC.3, K.CC.4, and K.CC.5Lesson 20K.CC.3, K.CC.4, and K.CC.5Lesson 21K.CC.3, K.CC.4, and K.CC.5Lesson 22K.CC.3, K.CC.4, and K.CC.5Lesson 23K.CC.4 and K.CC.5Lesson 24K.CC.3, K.CC.4, and K.CC.5Lesson 25K.CC.4 and K.CC.5Lesson 26K.CC.3, K.CC.4, and K.CC.5Lesson StandardLesson 27K.CC.3, K.CC.4, and K.CC.5Lesson 28K.CC.3, K.CC.4, and K.CC.5Lesson 29K.CC.3, K.CC.4, and K.CC.5Lesson 30K.CC.3 and K.CC.4Lesson 31K.CC.3, K.CC.4, and K.CC.5Lesson 32K.CC.3, K.CC.4, and K.CC.5Lesson 33K.CC.3, K.CC.4, and K.CC.5Lesson 34K.CC.3, K.CC.4, and K.CC.5Lesson 35K.CC.3, K.CC.4, and K.CC.5Lesson 36K.CC.3, K.CC.4, and K.CC.5Lesson 37K.CC.3, K.CC.4, and K.CC.5Mission 1Lesson StandardLesson 1K.MD.3*Lesson 2K.MD.3*Lesson 3K.MD.3*Lesson 4K.MD.3Lesson 5K.CC.4 and K.MD.3Lesson 6K.CC.4 and K.MD.3Lesson 7K.CC.4 and K.MD.3Lesson 8K.CC.4 and K.CC.5Lesson 9K.CC.4, K.CC.5, and K.OA.3Lesson 10K.CC.4, K.CC.5, and K.OA.3Lesson 11K.CC.4, K.CC.5, and K.OA.3Lesson 12K.CC.3, K.CC.4, and K.CC.5Lesson 13K.CC.3, K.CC.4, and K.CC.5Lesson 14K.CC.3, K.CC.4, K.CC.5, and K.OA.3* While not representative of the full scope of the standard, this lesson is building towards full understanding of K.MD.3. GK Course GuideStandards by LessonZEARN MATH Teacher Edition34

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Mission 3Lesson StandardLesson 1K.MD.1 and K.MD.2Lesson 2K.MD.1 and K.MD.2Lesson 3K.MD.2Lesson 4K.MD.2Lesson 5K.MD.2Lesson 6K.MD.2Lesson 7K.MD.2Lesson 8K.MD.1 and K.MD.2Lesson 9K.MD.2Lesson 10K.MD.2Lesson 11K.MD.2Lesson 12K.MD.2Lesson 13K.MD.1 and K.MD.2Lesson 14K.MD.2Lesson 15K.MD.2Lesson 16K.MD.1Lesson 17K.CC.6Lesson 18K.CC.6Lesson 19K.CC.6Lesson 20K.CC.6, K.CC.7, and K.MD.2Lesson StandardLesson 21K.CC.6Lesson 22K.CC.6Lesson 23K.CC.5 and K.CC.6Lesson 24K.CC.5 and K.CC.6Lesson 25K.CC.6 and K.CC.7Lesson 26K.CC.6 and K.CC.7Lesson 27K.CC.6 and K.CC.7Lesson 28K.CC.6, K.CC.7, and K.MD.2Lesson 29K.MD.2Lesson 30K.MD.2Lesson 31K.MD.2Lesson 32K.MD.1 and K.MD.2Mission 2Lesson StandardLesson 1K.MD.3, K.G.3, and K.G.4Lesson 2K.G.2 and K.G.4Lesson 3K.G.2 and K.G.4Lesson 4K.G.2 and K.G.4Lesson 5K.G.1 and K.G.2Lesson 6K.G.3 and K.G.4Lesson 7K.MD.3, K.G.2, and K.G.4Lesson 8K.G.1 and K.G.2Lesson 9K.G.2, K.G.3, and K.G.4Lesson 10K.G.1, K.G.2, K.G.3, and K.G.4GK Course Guide Standards by LessonZEARN MATH Teacher Edition 35

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Lesson StandardLesson 23K.OA.1 and K.OA.3Lesson 24K.OA.1 and K.OA.3Lesson 25K.CC.3 and K.OA.3Lesson 26K.OA.3Lesson 27K.CC.3 and K.OA.3Lesson 28K.OA.3Lesson 29K.OA.1Lesson 30K.OA.1Lesson 31K.OA.2Lesson 32K.OA.3Lesson 33K.OA.1Lesson 34K.OA.2 and K.OA.5Lesson 35K.OA.2 and K.OA.5Lesson 36K.OA.2 and K.OA.5Lesson 37K.OA.2 and K.OA.5Lesson 38K.CC.4 and K.OA.1Lesson 39K.OA.4 and K.OA.5Lesson 40K.OA.4Lesson 41Mission 5Lesson StandardLesson 1K.CC.3 and K.CC.5Lesson 2K.CC.3, K.CC.5, and K.NBT.1Lesson 3K.CC.3, K.CC.5, and K.NBT.1Lesson 4K.CC.3, K.CC.5, and K.NBT.1Lesson 5K.CC.5 and K.NBT.1Lesson 6K.CC.3, K.CC.5, and K.NBT.1Lesson 7K.NBT.1Lesson 8K.NBT.1Lesson 9K.CC.3 and K.NBT.1Lesson 10K.CC.3, K.CC.5, and K.NBT.1Lesson 11K.CC.3, K.CC.5, and K.NBT.1Lesson 12K.CC.3, K.CC.5, and K.NBT.1Lesson 13K.CC.1, K.CC.2, K.CC.3, K.CC.5, and K.NBT.1Lesson 14K.CC.5Lesson 15K.CC.1Lesson 16K.CC.1 and K.CC.2Lesson 17K.CC.1 and K.CC.2Mission 4Lesson StandardLesson 1K.CC.3Lesson 2K.CC.3 and K.OA.3Lesson 3K.CC.3Lesson 4K.CC.3 and K.OA.3Lesson 5K.CC.3 and K.OA.3Lesson 6K.CC.3 and K.OA.3Lesson 7K.CC.3 and K.OA.3Lesson 8K.CC.3 and K.OA.3Lesson 9K.CC.3 and K.OA.3Lesson 10K.CC.3 and K.OA.3Lesson 11K.CC.3 and K.OA.3Lesson 12K.CC.3 and K.OA.3Lesson 13K.OA.1Lesson 14K.OA.1Lesson 15K.OA.1Lesson 16K.OA.1 and K.OA.2Lesson 17K.OA.2Lesson 18K.OA.2Lesson 19K.OA.2Lesson 20K.OA.1Lesson 21K.OA.1 and K.OA.2Lesson 22K.OA.1 and K.OA.3GK Course GuideStandards by LessonZEARN MATH Teacher Edition36

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Appendix I: Instructional RoutinesThe 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 EXCHANGEWhat: 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 ExplorationWhy: 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, CONNECTWhat: 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-UpWhy: 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.GK Course GuideAppendix I: Instructional RoutinesZEARN MATH Teacher Edition38

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TAKE TURNSWhat: 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 setup 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 ExplorationWhy: 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 SHAREWhat: 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 ExplorationWhy: 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 and 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.GK Course Guide Appendix I: Instructional RoutinesZEARN MATH Teacher Edition 39

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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 LearnersINTRODUCTIONZearn Math for First 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 well-suited 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• foundation of curriculum: theory of action and design principles that drive a continuous focus on language development• student terminologyMission • Mission-specific progression of language development included in each Mission OverviewLesson• definitions of new terminology• additional supports for multilingual learners based on language demands of the activityTHEORY OF ACTIONZearn 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, the value GK Course GuideAppendix II: Access for Multilingual LearnersZEARN MATH Teacher Edition40

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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 understanding 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.GK Course Guide Appendix II: Access for Multilingual LearnersZEARN MATH Teacher Edition 41

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DESIGN PRINCIPLES FOR PROMOTING MATHEMATICAL LANGUAGE USE AND DEVELOPMENTThe 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-MakingScaffold 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 OutputStrengthen 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 ConversationStrengthen 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.GK Course GuideAppendix II: Access for Multilingual LearnersZEARN MATH Teacher Edition42

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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-awarenessStrengthen 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 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 the 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 ROUTINESTo 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 GapGK Course Guide Appendix II: Access for Multilingual LearnersZEARN MATH Teacher Edition 43

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• MLR 5: Co-Craft Questions• MLR 6: Three Reads• MLR 7: Compare and Connect• MLR 8: Discussion SupportsThe 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 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 self-assessment 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 TimePurpose: 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 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)GK Course GuideAppendix II: Access for Multilingual LearnersZEARN MATH Teacher Edition44

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• 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 DisplayPurpose: 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, CorrectPurpose: 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.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 GK Course Guide Appendix II: Access for Multilingual LearnersZEARN MATH Teacher Edition 45

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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 GapPurpose: 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.• 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 QuestionsGK Course GuideAppendix II: Access for Multilingual LearnersZEARN MATH Teacher Edition46

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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 ReadsPurpose: 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 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,” GK Course Guide Appendix II: Access for Multilingual LearnersZEARN MATH Teacher Edition 47

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“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 ConnectPurpose: 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 sense-making (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 self-guided, 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, 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.GK Course GuideAppendix II: Access for Multilingual LearnersZEARN MATH Teacher Edition48

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Mathematical Language Routine 8: Discussion SupportsPurpose: 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)].SENTENCE FRAMESSentence 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.GK Course Guide Appendix II: Access for Multilingual LearnersZEARN MATH Teacher Edition 49

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Language function Sample sentence framesdescribe• 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 casecritique• 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 dierent because…• One thing that is the same is…• One thing that is dierent is…• How are _____ and _____ dierent?• What do _____ and _____ have in common?represent • _____ represents _____.• _____ stands for _____.• _____ corresponds to _____.• Another way to show _____ is…• How else could we show this?GK Course GuideAppendix II: Access for Multilingual LearnersZEARN MATH Teacher Edition50

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ReferencesAguirre, 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. Celedón-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.pdfPaunesku 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/10.1177/0956797615571017Schmidt, 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/10.1080/0022027042000294682Smith, 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/10.1037/0022-3514.92.1.82Zwiers, J. (2014). Building academic language: Meeting Common Core Standards across disciplines, grades 5–12 (2nd ed.). San Francisco, CA: Jossey-BassZwiers, 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-additional-resourcesGK Course Guide ReferencesZEARN MATHTeacher Edition52

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