Zearn Math–Teacher Edition: Course Guide, G7 : simplebooklet.com

Table of Contents ABOUT ZEARN MATH Vision 6 Learning principles 6 ABOUT SEVENTH GRADE MATH Approach 7 Scope sequence 7 Pacing 9 A TYPICAL LESSON IN ZEARN MATH Warm Up 11 Concept Exploration 11 Wrap Up 12 IMPLEMENTING ZEARN MATH Planning for a Mission 13 Planning your week 14 Core Days 14 Flex Day 14 Planning for a lesson 16 Preparing students for Independent Digital Lessons 17 SUPPORTING DIVERSE LEARNERS Commitment to accessibility 19 Design features that support all learners 19 Supporting multilingual learners 20 Elements of language 20 Mathematical language routines MLRs 20 Supporting students with disabilities 22 Accessible design features 22 Assistive technology 22 Instructional accommodations 23 ASSESSMENTS AND REPORTS Ongoing formative assessments Daily lesson level assessments The Tower of Power digital and Exit Tickets paper 24 24

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Table of Contents Mission level assessments paper 25 Interim assessments 26 Class and student reports 26 Class reports Progress Pace and Tower Alerts 26 Student Reports 27 Approach to unfinished learning 27 TERMINOLOGY REQUIRED MATERIALS LESSONS BY STANDARD STANDARDS BY LESSON APPENDIX I INSTRUCTIONAL ROUTINES Algebra Talk 42 Anticipate Monitor Select Sequence Connect 42 Notice and Wonder 43 Number Talk 43 Poll the Class 43 Take Turns 44 Think Pair Share 44 True or False 45 Which One Doesn t Belong 45 Group Presentations 46 APPENDIX II ACCESS FOR MULTILINGUAL LEARNERS Introduction 46 Theory Of Action 47 Design Principles for Promoting Mathematical Language Use and Development 48 Principle 1 Support Sense Making 48 Principle 2 Optimize Output 48 Principle 3 Cultivate Conversation 49 Principle 4 Maximize Meta awareness 49 Mathematical Language Routines 50 Mathematical Language Routine 1 Stronger and Clearer Each Time 50 Mathematical Language Routine 2 Collect and Display 51 Mathematical Language Routine 3 Clarify Critique Correct 52

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About Zearn Math G7 Course Guide About Zearn Math All Children Can Love Learning Math VISION Zearn Math was developed by Zearn a nonprofit educational organization We believe that an understanding and love of mathematics is critical to helping all children realize their potential and to creating a generation of engaged learners who can change the world In 2011 Zearn s team of educators and engineers created Zearn Math as an evidence based student centered curriculum that balances rich mathematical discourse collaborative problem solving and independent thinking and working time With Zearn Math students learn math as the progression of connected ideas over the course of the year grounded in visual problem solving with a concrete to pictorial to abstract approach LEARNING PRINCIPLES Zearn combines our own digital lessons and assessments with open source curricula in order to create an engaging accessible and coherent K 8 experience for all students We developed Zearn Math using learning principles drawn from teacher practice education research and brain science as well as extensive data from student engagement with our software over the years which we use to strengthen our materials and technology each year Math is a few big ideas We delve deeply into these ideas connecting and reinforcing them over the course of grades K 8 When kids learn math as a coherent discipline rather than a series of unrelated tricks and move from simple to 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 6 ZEARN MATH Teacher Edition

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G7 Course Guide About Seventh Grade Math Mistakes are magic We help teachers create inclusive math communities where students feel safe to struggle Students receive inthe moment feedback that precisely addresses areas of misconception both during independent learning and as they explore concepts with their peers Research on growth mindsets shows that children who believe that making mistakes is part of the learning process enjoy learning more and to be 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 digital lessons and 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 Seventh Grade Math APPROACH Guided by our learning principles Zearn Math s multimodal learning accommodates and celebrates learning differences and fosters positive math mindsets and social belonging so all students can love learning math With Zearn Math students will explore the same math concepts in two ways Alongside their peers and teacher students will model math with concrete manipulatives represent their work on paper discuss their reasoning aloud and receive direct feedback from their teacher as well as from peers Independently students will use self paced software based lessons to explore and practice concepts with concrete and digital manipulatives interactive videos and pictorial representations receiving precise digital feedback at the moment of misconception With this approach mathematics is not a spectator sport Students spend most of their time in math class actually doing mathematics rather than just listening to or watching it They work on mathematics problems together and independently often utilizing prior knowledge and skills with guidance from the teacher and with precise in the moment digital feedback that together ensure 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 SCOPE SEQUENCE The curriculum map below shows how students will cover a series of big mathematical ideas color coded to show the coherent structure of Zearn Math over the course of the grade and in other grades ZEARN MATH Teacher Edition 7

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About Seventh Grade Math G7 Course Guide As in grade 6 students start grade 7 by studying scale drawings an engaging geometric topic that supports the subsequent work on proportional relationships in the second and fourth units It also makes use of grade 6 arithmetic understanding and skill without arithmetic becoming the major focus of attention at this point Geometry and proportional relationships are also interwoven in the third unit on circles where the important 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 K M3 M2 M1 Numbers to 10 Numbers to 5 Digital Activities 50 M1 G3 M1 M2 M1 G5 Place Value with Decimal Fractions G8 Key Multiply Divide Big Numbers M1 M1 M2 Area and Surface Area Introducing Ratios M2 M1 Scale Drawings Introducing Proportional Relationships M1 Rigid Transformations and Congruence Whole Numbers and Operations M3 M2 Base Ten Operations M3 Rates and Percentages M4 M3 Add Subtract Fractions M4 Dividing Fractions Proportional Measuring Relationships Circles and Percentages M2 Dilations Similarity and Introducing Slope M3 Linear Relationships Expanding Whole Numbers and Operations to Fractions and Decimals M5 Rational Number Arithmetic M4 Linear Equations and Linear Systems M4 M5 M6 M5 M7 Functions and Volume Algebraic Thinking and Reasoning Leading to Functions M6 Associations in Data Geometry M6 M9 M8 Rational Numbers Angles Triangles and Prisms Multiply Measure The Coordinate Plane M7 Expressions and Equations M7 Decimal Fractions Volume Area Shapes M6 Expressions Equations and Inequalities Shapes Measurement Display Data M6 Multiply and Divide Fractions Decimals Arithmetic in Base Ten M7 M6 M5 Fractions as Numbers Equivalent Fractions M5 M8 Shapes Time Fractions Length Money Data M5 Construct Lines Angles Shapes Add Subtract to 100 M7 Equal Groups M4 Find the Area M4 M3 M6 Add Subtract Big Numbers Multiply Divide Tricky Numbers M6 Work with Shapes M5 M3 M2 Numbers to 20 Digital Activities 35 M5 Add Subtract Big Numbers Add Subtract Solve Measure It Numbers to 15 Digital Activities 35 M4 Measure Length M4 Counting Place Value Multiply Divide Friendly Numbers Add Subtract Round G7 M3 Explore Length G4 G6 8 M2 Add Subtract Friendly Numbers M3 Meet Place Value Measure Solve G2 M2 Add Subtract Small Numbers M6 Analyzing Comparing Composing Shapes Numbers 10 20 Count to 100 by Ones and Tens Number Pairs Addition Subtraction to 10 Numbers to 10 Digital Activities 50 M1 G1 M5 M4 Comparison of Length Weight Capacity Numbers to 10 2D 3D Shapes Putting It ALL Together 1 Data Sets and Distributions M8 Probability and Sampling M7 Exponents and Scientific Notation M9 Putting It ALL Together M8 Pythagorean Theorem and Irrational Numbers M9 Putting It ALL Together WEEK Measurement Statistics and Probability ZEARN MATH Teacher Edition

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G7 Course Guide About Seventh Grade Math proportional relationship between a circle s circumference and its diameter is studied By the time students reach the fifth unit on operations with rational numbers both positive and negative students have had time to brush up on and solidify their understanding and skill in grade 6 arithmetic The work on operations on rational numbers with its emphasis on the role of the properties of operations in determining the rules for operating with negative numbers is a natural lead in to the work on expressions and equations in the next unit Students then put their arithmetical and algebraic skills to work in the last two units on angles triangles and prisms and on probability and sampling In the Mission Overvieww of each unit there is a section called Progression of Disciplinary Language that explains the disciplinary language functions specific to that unit This level of detail assists teachers in planning and differentiation 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 PACING The seventh grade year will include nine units known in Zearn Math as Missions see details below Each course of Zearn Math for Middle School contains nine missions each of the first eight are anchored by a few big ideas in grade level mathematics and the optional Mission 9 contains lessons that help students apply and tie together big ideas from the year with no Independent Digital Lessons 1 ommon Core State Standards Initiative n d Standards for Mathematical Practice Retrieved December 7 2021 from http www corestandards C org Math Practice ZEARN MATH Teacher Edition 9

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A Typical Lesson in Zearn Math G7 Course Guide 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 seventh grade curriculum should take about 36 weeks to complete This pace ensures students have sufficient time each week to work through grade level content with built in weekly time to assess and address student needs Each Mission will conclude with a paper based End of Mission assessment some longer Missions also contain a Mid Mission assessment Students also complete two formative assessments on each lesson a digital Tower of Power assessment and a paper Exit Ticket Mission Title Lessons Weeks 1 Scale Drawings 13 3 2 Introducing Proportional Relationships 15 4 3 Measuring Circles 11 3 4 Proportional Relationships and Percentages 16 4 5 Rational Number Arithmetic 17 4 6 Expressions Equations and Inequalities 22 6 7 Angles Triangles and Prisms 17 4 8 Probability and Sampling 20 5 9 Putting It All Together 13 3 144 36 Total This mission is optional Note Weeks are estimates based on 4 lessons completed per week Actual time will vary by student A Typical Lesson in Zearn Math In a typical math block with Zearn covering one lesson students will experience Warm Up Concept Exploration Collaborative Concept Exploration with teacher and peers Independent Digital Lessons to explore concepts further on their own and Wrap Up Lesson Synthesis led by the teacher and the completion of an individual Exit Ticket Every lesson in Zearn Math for Seventh Grade is accompanied by an optional classroom presentation that contains the warm up collaborative concept exploration and wrap up activities and helps teachers with the 10 ZEARN MATH Teacher Edition

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G7 Course Guide A Typical Lesson in Zearn Math overall flow of the math block Each presentation is built to show students where in the lesson they should be at any given moment and includes cues that support the teacher s transitions if needed Additionally activities in all parts of a lesson identify the standards being addressed in the activity including building on addressing and building towards Oftentimes a particular standard requires weeks months or years to achieve in many cases building on work in prior grade levels When an activity reflects the work of prior grades but is being used to bridge to a grade level standard alignments are indicated as building on When an activity is laying the foundation for a grade level standard but has not yet reached the level of the standard the alignment is indicated as building towards When a task is focused on the grade level work the alignment is indicated as addressing For more standards alignment information see the sections below Standards by Lesson and Lessons by Standard WARM UP The first event in every lesson is a warm up which invites students into the day s lesson with a series of engaging activities A warm up either helps students get ready for the day s lesson or gives students an opportunity to strengthen their number sense or procedural fluency A warm up that helps students get ready for today s lesson might serve to remind them of a context they have seen before get them thinking about where the previous lesson left off or preview a calculation that will happen in the lesson so that the calculation doesn t get in the way of learning new mathematics A warm up that is meant to strengthen number sense or procedural fluency asks students to do mental arithmetic or reason numerically or algebraically It gives them a chance to make deeper connections or become more flexible in their thinking CONCEPT EXPLORATION Students have two opportunities to study the same concepts with their teacher and peers in Collaborative Concept Exploration and using self paced Independent Digital Lessons The intentional balance of learning with teachers and peers and learning independently in digital lessons ensures every student has multiple opportunities to represent engage with and express their math reasoning Concept exploration includes Collaborative Concept Exploration Built around a series of scaffolded math problems that move students towards the overall goal of the lesson Each collaborative classroom activity has three phases 1 Launch During the launch the teacher makes sure that students understand the context and what the problem is asking them to do This is not the same as making sure the students know how to do the problem part of the work that students should be doing for themselves is figuring out how to solve the problem 2 Student Work Time The launch for an activity frequently includes suggestions for grouping students This gives students the opportunity to work individually with a partner or in small groups ZEARN MATH Teacher Edition 11

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A Typical Lesson in Zearn Math G7 Course Guide 3 Activity Synthesis During the activity synthesis the teacher orchestrates some time for students to synthesize what they have learned This time is used to ensure that all students have an opportunity to understand the mathematical punch line of the activity and situate the new learning within students previous understanding Independent Digital Lessons Students complete self paced software based lessons on their own Students construct their mathematical thinking using visual models and have opportunities to test and confirm their reasoning with precise feedback to help them find and correct mistakes This self paced learning fosters students sense of ownership over their math learning and boosts students math mindsets because all students are able to take the amount of time they need to problem solve review content or receive scaffolded support The video player can be paused or rewound at any time For more on what students will experience during Independent Digital Lessons see Planning for a Lesson in the Implementing Zearn Math section below For more on addressing struggle see Addressing unfinished learning in the Assessments and Reports section below WRAP UP After the concept exploration phase of the lesson students move to the final phase of the lesson the wrap up This phase provides students with time to synthesize what they just learned during the concept exploration and gives teachers a chance to formatively assess whether students grasped the big idea of the lesson which can then inform the next lesson The wrap up includes two opportunities to formatively assess student understanding Lesson Synthesis Students incorporate new insights into big picture understanding and teachers get a sense of students understanding Each lesson includes suggested discussion starters that teachers can use to guide students in a conversation to process the lesson Teachers may pose questions verbally and call on volunteers to respond and could ask students to add a new component to a persistent display like a word wall Also this is the final moment of discourse for every lesson and unfinished learning may be evident by what students are saying or not saying However teachers should not use this moment to try and reteach the entire lesson but rather use this moment as one of many formative assessments provided in each lesson they can combine this data with their review of student work on the lesson s Exit Ticket and the Tower Alerts report to determine the effectiveness of the lesson For more on how to appropriately diagnose and respond to unfinished learning see the corresponding section below in Assessments and Reports Exit Ticket Students to 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 12 ZEARN MATH Teacher Edition

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G7 Course Guide Implementing Zearn Math Finally note that each Zearn Math for Middle School lesson includes an associated set of practice problems found in the Optional Practice Materials packet including a few problems from that day s lesson along with a mix of topics from previous lessons Teachers may assign some or all practice problems during class or for homework or not at all they may also decide to collect and score those problems or to provide students with answers ahead of time for self assessment or to score them together as a class Implementing Zearn Math PLANNING FOR A MISSION The story of Zearn Math for Seventh Grade is told in nine Missions Each course of Zearn Math for Middle School contains nine missions each of the first eight are anchored by a few big ideas in grade level mathematics and the optional Mission 9 contains lessons that help students apply and tie together big ideas from the year Concepts are taught through the concrete to pictorial to abstract progression within each Mission and throughout the year to allow students ample time to continue to build their developing understanding The table of contents in each Mission book shows you how the lessons of the Mission are divided into topics as well as the placement of the Mission level paper based assessments To plan for a Mission Familiarize yourself with the mathematics of the Mission and how students will progress toward understanding of the big ideas of the Mission Read through the Mission Overview in the Zearn Math Teacher Edition taking note of the progression of the mission key representations and strategies used and any moments that may be challenging for students The Mission Overviews provide an opportunity to deeply learn the big ideas of the Mission Complete the Mission level paper based assessments and study the assessment rubrics provided including the exemplar student work Take note of any lessons that are marked optional Mission 9 is optional and contains no Independent Digital Lessons 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 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 Send home the Family Materials packet which discusses key learning objectives and include sample problems for parents caregivers to try at home with their students ZEARN MATH Teacher Edition 13

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Implementing Zearn Math G7 Course Guide 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 web site 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 send home the Family Materials packet which discusses key learning objectives and include sample problems for parents caregivers to try at home with their students In addition the Student Report for their child and the assessment rubrics may provide additional insight to their student s progress and areas of misconception or struggle PLANNING YOUR WEEK We designed Zearn Math to include four Core Days when students learn grade level content as well as one Flex Day that you can tailor to meet students needs This weekly schedule ensures students have sufficient time each week to work through grade level content while also giving you additional time to address unfinished learning and or misconceptions that might be hindering student progress Core Days If you are using this Zearn Math recommended weekly schedule we recommend omitting the optional lessons in each Mission On Core Days you should plan for a balance of learning across multiple formats We designed this lesson structure to fit into a 50 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 5 minutes Concept Exploration includes about 20 minutes of Collaborative Concept Exploration and 20 minutes of Independent Digital Lessons for a total of 40 minutes These can be adjusted based on available time as long as students have daily opportunities to learn and practice in a variety of instructional settings with a variety of different learners Some teachers choose to have students rotate through these two stations while others have students complete Independent Digital Lessons during other flexible time during the day A few lessons do not include an Independent Digital Lesson Guidance on how best to handle each situation is detailed in your Zearn Math Teacher Edition Wrap Up including lesson synthesis and an Exit Ticket takes about 5 minutes Flex Day In addition to 4 Core Days if you are using the Zearn Math recommended weekly schedule and omitting optional lessons you will have time for a Flex Day each week Consider how you might use this time to continue addressing individual student needs you may have noticed during your Core Day lessons or while reviewing Zearn class and student reports 2 he 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 T at https about zearn org math resources parent caregiver support 14 ZEARN MATH Teacher Edition

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G7 Course Guide Implementing Zearn Math 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 Activities found in the Enrichment section of the Optional Practice Materials packet These optional activities are included for topics where experience shows students often need some additional time to work with the ideas These activities are marked as optional because no new mathematics is covered so if a teacher were to skip them no new topics would be missed If the Tower Alerts report identifies individual students struggling with a particular concept or misconception you could bookmark foundational content for them to complete For more see Addressing unfinished learning in the Assessments and Reports section below For students who are completing four Independent Digital Lessons each week and demonstrating full understanding on assessments you can use Flex time to provide opportunities for additional challenge and growth Zearn Math provides teachers with curricular materials for extending learning that are aligned to students current grade level work including Digital Bonuses Digital Bonuses are challenging problems students can work on after they complete an Independent Digital Lesson These problems enrich and extend their learning by going deeper into 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 Enrichment Problems Also included in the Enrichment section of the Optional Practice Materials packet are Extension Problems which go deeper into grade level mathematics and often make connections between the topic at hand and other concepts at grade level or that are outside of the standard K 12 curriculum They are not routine or procedural and intended to be used on an opt in basis by students if they finish the main class activity early or want to do more mathematics on their own It is not expected that an entire class engages in extension problems and it is not expected that any student works on all of them which makes them well suited for Flex Days 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 ZEARN MATH Teacher Edition 15

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Implementing Zearn Math G7 Course Guide PLANNING FOR A LESSON You can use your Zearn Math Teacher Edition daily to plan and implement each lesson of the Mission To prepare for teaching each lesson within a Mission we recommend that teachers Read through the lesson Gain an understanding of how the big mathematical idea of the lesson unfolds across the lesson taking note of the discussion guidance and how it helps move students toward the lesson s objective Each lesson in the Mission has a narrative that contains a description of the mathematical content of the lesson and its place in the learning sequence the meaning of any new terms introduced in the lesson and how the mathematical practices come into play as appropriate Activities within lessons also have a narrative which explains the mathematical purpose of the activity and its place in the learning sequence what students are doing during the activity what teacher needs to look for while students are working on an activity to orchestrate an effective synthesis and connections to the mathematical practices when appropriate 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 Students warm up with a short fluency activity that supports the big ideas developed in that mission These activities activate prior knowledge of fractions operations and mental math strategies that students will need throughout the mission Regular practice through these activities helps all students access grade level math by enabling them to shift working memory from calculations to new concept development Fluency will be available in pilot form beginning in the 22 23 ASY Guided Practice Students experience one of three different Guided Practice activities Math Chat Learning Lab or Z Squad Each activity creates a rich learning environment for students through interactive and multisensory videos featuring real on screen teachers and digital manipulatives Students are prompted to complete problems in their paper Student Notes to transfer their software based learning reflect on the key idea in the lesson and strengthen knowledge retention Independent Practice Tower of Power Students demonstrate their understanding of the content of an Independent Digital Lesson and unlock the next one by completing all problems correctly in the Tower of Power If students make a mistake in a Tower of Power problem a Boost breaks down the question into smaller steps with more supportive manipulatives to allow students to understand and correct their mistakes Students then have a chance to demonstrate their learning with a new problem 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 yet others to applying mathematics to a real world problem For example four instructional routines frequently used in warm ups are Number Talks Notice and Wonder Which One Doesn t Belong and True or False In addition 16 ZEARN MATH Teacher Edition

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G7 Course Guide Implementing Zearn Math to the mathematical purposes these routines serve the additional purpose of strengthening students skills in listening and speaking about mathematics For a full list including when and how to use instructional routines 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 Supplemental instructional strategies labeled Support for English Language Learners and Support for Students with Disabilities are included in each lesson and are designed to increase access and eliminate barriers For more on the supports for multilingual learners visit Appendix II Access for Multilingual Learners Fore more on the design principles for the supports for students with disabilities and the cognitive functioning areas they address visit Appendix III Access for Students with Disabilities For more information and ideas see the next section on Supporting Diverse Learners including both 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 towards understanding the takeaway during the synthesis portion of each activity and Explicit connections to prior activities and or lessons Make sure to have on hand all of the required materials to successfully enact the lesson Required materials and required preparation are listed alongside the learning goals and standards alignment information on the first page of each lesson For a full list of required materials for the course see Required Materials section below PREPARING STUDENTS FOR INDEPENDENT DIGITAL LESSONS To ensure students are ready to complete Independent Digital Lessons you will want to do the following with them You should only have to do this during your first week of instruction unless you observe that a refresher is needed 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 seventh grade these are Fluency available in pilot form beginning in the 22 23 ASY Guided Practice Independent Practice Model completing paper Student Notes when prompted in the Guided Practice section ZEARN MATH Teacher Edition 17

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Implementing Zearn Math G7 Course Guide Discuss strategies for persevering through challenges like working through a Boost within a Tower of Power referencing Student Notes revisiting the Guided Practice and even guessing if needed and letting the digital lesson provide help Remind students that some struggle is both expected and useful and that you will not be helping them to complete these lessons Instead they should try their best to resolve challenges on their own with the support of the software s built in scaffolds and you will frequently check Pace Report and Tower Alerts Report to identify any students who may be struggling unproductively Show students how to work on their Next Up activity Students work through Independent Digital Lessons at their own pace and are always assigned to one of these activities as their Next Up assignment Students can only access the next digital activity in the sequence once they complete their currently assigned activity Show students the accessibility features including Closed captioning Closed captioning for all interactive student videos is available for all Missions for all grades Closed captioning allows students to turn on an English text transcription of all dialogue and other relevant audio information in the Zearn Math video player This accessibility feature is particularly useful for deaf and hard of hearing students as well as multilingual learners Audio support All instructional prompts students see in Independent Digital Lessons have audio support through either recorded audio or Zearn Math s text to speech feature Students can click on the audio button next to text questions or prompts to hear the words spoken aloud All math expressions in Zearn Math software based lessons are read correctly with Zearn Math s text to speech tool Additional audio support if needed can be accessed using supported browser text to speech tools These accessibility features are particularly important for students with cognitive impairments students with learning differences young students and multilingual learners Zoomability Students may resize digital pages up to 200 through browser settings to view images or text closer up without losing any content This accessibility feature is particularly important for students with visual impairments and students using devices with small screens On screen keypad As students work through Independent Digital Lessons they have the option to use an on screen keypad rather than a computer keyboard to type and submit answers This accessibility feature is particularly important for tablet users and young students who may not know how to use a computer keyboard 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 3 https help zearn org 18 ZEARN MATH Teacher Edition

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G7 Course Guide Supporting Diverse Learners Supporting Diverse Learners COMMITMENT TO ACCESSIBILITY Zearn believes that with proper structures accommodations and support all children can learn mathematics As such we designed Zearn Math to be accessible for all students using the Universal Design for Learning UDL principles to maximize access and engagement for all students We have also added supports and structures throughout to help teachers accommodate the needs of diverse learners For more see above sections on Planning for a lesson as well as Preparing students for Independent Digital Lessons under Implementing Zearn Math DESIGN FEATURES THAT SUPPORT ALL LEARNERS To support a diverse range of learners including students with unfinished learning multilingual learners and students with disabilities Zearn Math design features include Consistent lesson structures The structure of every lesson is the same Warm Up Concept Exploration Wrap Up By keeping the components of each lesson similar from day to day the flow of work in class becomes predictable for students This reduces cognitive demand and enables students to focus on the mathematics at hand rather than the mechanics of the lesson Concepts developing over time from concrete to abstract Mathematical concepts are introduced simply concretely and repeatedly with complexity and abstraction developing over time Students begin with concrete examples and transition to diagrams and tables before relying on symbols to represent the mathematics they encounter Moreover this CPA approach is repeated throughout lessons Missions and across the grade to continually give students access to new ideas 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 ZEARN MATH Teacher Edition 19

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Supporting Diverse Learners G7 Course Guide SUPPORTING MULTILINGUAL LEARNERS Zearn believes that language learners of all levels can and should engage with grade level content that is scaffolded with sufficient linguistic support Zearn Math provides students opportunities to access gradelevel mathematics using existing language skills and to extend their language development in the context of mathematical skill development Each day with Zearn Math students learn in a classroom model designed for daily differentiation experience inclusive environments of social belonging and build language skills as they learn with the whole class with peers and on their own with software based lessons In addition we provide teachers with a Zearn Math Teacher Edition that provides strategies on how to support students language development daily within the context of their math class For more see above section on Planning for a lesson under Implementing Zearn Math While these features of Zearn Math support all students in building a deep understanding of grade level mathematics they are particularly critical for meeting the needs of multilingual learners Elements of language During their daily learning with Zearn Math students are exposed to many elements of language such as mathematics vocabulary and spoken language patterns In some situations multilingual learners may benefit from using their first language because processing math in their first language can create a safe space for deeper thinking Zearn Math supports students as they develop their mathematical skills by reinforcing Essential vocabulary Students are not expected to have prior knowledge of essential math vocabulary Language critical to students mathematical learning is explicitly introduced taught and repeated frequently which helps all students gain familiarity with new terminology and practice using it as they move through the curriculum Patterns of discourse As students engage in rich math discussions throughout the lesson they have opportunities to organize their language in discourse patterns such as compare and contrast or question and answer Teachers facilitate these structured conversations through instructional routines such as Think Pair Shares which allow students to make claims provide evidence communicate thinking and critique others reasoning The Zearn Math lessons include specific notes with conversation starters sentence frames and modeling guidance that can help enhance discussion quality for all students and ensure multilingual learners are supported in participating Math discussion Students share their own thinking aloud and discuss classmates problem solving strategies throughout daily Warm Up and Collaborative Concept Exploration Teachers facilitate thoughtful mathematical discussions between students that allow learners to refer to and build on each others ideas The Zearn Math Teacher Edition provides guidance on instructional routines that further math discussions for all students with additional notes on supporting multilingual learners Mathematical language routines MLRs For instances where students need even more support than what s in the curriculum 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 20 ZEARN MATH Teacher Edition

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G7 Course Guide Supporting Diverse Learners of a specific activity without reducing the mathematical demand of the task These routines emphasize uses of language that are meaningful and purposeful rather than just getting correct answers These routines can be adapted and incorporated across lessons in each unit wherever there are productive opportunities to support students in using and improving their English and disciplinary language These eight routines were selected for inclusion in this curriculum because they are effective and practical for simultaneously learning mathematical practices content and language They are MLR 1 Stronger and Clearer Each Time Students think and write individually about a question use a structured pairing strategy to have multiple opportunities to refine and clarify their response through conversation and then finally revise their original written response MLR 2 Collect and Display Teacher listens for and scribes 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 Teacher provides 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 II 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 ZEARN MATH Teacher Edition 21

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Supporting Diverse Learners G7 Course Guide SUPPORTING STUDENTS WITH DISABILITIES Students with disabilities can and should engage with Zearn Math While a student s Individualized Education Plan should be the first resource teachers use when determining how to differentiate instruction for a student with a disability Zearn s curriculum also highlights patterns critical features and big math ideas in a way that supports such differentiation For more see above sections on Planning for a lesson as well as Preparing students for Independent Digital Lessons under Implementing Zearn Math The following design elements assistive technologies and accommodations may help students with disabilities access Zearn Math Accessible design features We developed Zearn Math with a wide range of students in mind and included accessibility features that ensure students with cognitive physical and communication challenges can easily use the self paced software based lessons These design features include Visual clarity All content in Independent Digital Lessons is visually clear and understandable These visual accessibility features help all learners but are particularly important for students with color blindness or any visual impairments Use of color Throughout Zearn Math Independent Digital Lessons color is never used as the only visual means of conveying information When a student receives precise feedback on an answer during Independent Digital Lessons that feedback is provided in multiple ways with color but also with clear iconography and specific messages such as Nice Try again or Check the answer Additionally where color is used to draw attention to a specific piece of information Zearn Math also uses words to convey the same information Color contrast Zearn Math aims to conform to minimum color contrast requirements Software based lessons use larger fonts that meet a minimum contrast ratio of 3 1 Font smaller than 18pt or 14pt bold meet a contrast ratio of 4 5 1 Where specific elements of Independent Digital Lessons do not meet contrast standards today Zearn is making improvements Font readability Throughout software based lessons Zearn Math avoids using fonts smaller than 10pt with most text using at least 16pt fonts Font types are simple clear and have limited variation in order to ensure all text is readable Volume consistency In order to provide a consistent and non disruptive audio experience for students there are no significant volume changes during Independent Digital Lessons Outside of Zearn Math s video content there is no audio that plays automatically for more than 3 seconds This accessibility feature is particularly important for students who are sensitive to changes in volume students who have difficulty focusing on visual content including text when audio is playing students on the autism spectrum and students with hearing impairments Assistive technology Assistive technology may be helpful to increase and maintain access for students with disabilities Many assistive technology features are embedded into Zearn s digital materials Text to Speech All instructional prompts and directions that students see in the Zearn Math digital program can be read aloud by selecting buttons 22 ZEARN MATH Teacher Edition

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G7 Course Guide Supporting Diverse Learners 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 Keyboard accessibility While Zearn Math requires the use of a mouse trackpad or touchscreen device today Zearn has made keyboard accessibility a priority In the coming years Zearn will be adding new features to ensure that students can use keyboards for all interactive elements in Independent Digital Lessons This accessibility feature is particularly important for students with impaired mobility or dexterity or students with low vision Instructional accommodations Teachers can and should provide student specific accommodations for students with disabilities The following accommodations may increase access for students Translated Materials All of Zearn s core student facing paper based instructional materials will be available during the 2022 2023 school year in various accessible formats including large print Braille and tactile from APH org American Printing House Educators will be able to search APH s Louis catalog and place orders for the Zearn Math materials they need These materials will also be on file with the National Instructional Materials Accessibility Center NIMAC Guided Notes and Graphic Organizers All Zearn Math lessons include Student Notes to help keep students focused and organized Zearn also uses graphic organizers in digital content and in paper based materials to help students organize and internalize information Read Aloud Students who struggle with word decoding and or reading comprehension may benefit from having question prompts read aloud Students who are blind or have limited sight may benefit from hearing oral descriptions of graphs and of other visual representations of problems or math concepts Scribe Students with scribe accommodation will need support transferring their math thinking problem solving and answers into digital form or as a written answer when prompted to write or input an answer Separate Location or Quiet Space When completing digital lessons some students may benefit from working in a separate space where they can process out loud work without headphones and input text or numerical answers with their voice Breaks Students may benefit from structured breaks when completing Zearn Math lessons in order to rest or refocus All Zearn Math digital lessons can be paused rewound or restarted Checklists and Other Self Monitoring Activities Self monitoring checklists may be helpful for students to use in determining the best approach to solve a problem guiding problem solving processes or evaluating work habits or progress made toward a goal ZEARN MATH Teacher Edition 23

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Assessments and Reports G7 Course Guide 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 Assessments and Reports Zearn offers a series of formative assessments designed to provide teachers with precise and actionable feedback they can use to inform instruction and respond to the needs of each student as well as student and class level reports that provide teachers with real time data and insights into student pace progress and areas of struggle during Zearn Math digital lessons To address areas of unfinished learning Zearn Math contains both embedded supports within each Independent Digital Lesson as well as foundational lessons that teachers may assign as interventions ONGOING FORMATIVE ASSESSMENTS Assessments focus on the big ideas of mathematics and allow students to demonstrate their understanding across multiple modalities through a thoughtful balance of software and paper based experiences All assessments are designed to fit into the classroom model and allocated time and to enhance rather than distract from instruction Daily lesson level assessments The Tower of Power digital and Exit Tickets paper Lesson level assessments are embedded into the curriculum and occur as part of recommended daily core instructional time not in addition to it Tower of Power digital This scaffolded assessment focuses on the content of a single lesson and is administered automatically at the end of each Independent Digital Lesson If students make a mistake they receive real time support at the point of misconception allowing them to correct their understanding and continue through the assessment Each Tower of Power contains two to four stages of problems that increase in complexity and decrease in scaffolding as students progress The problems in each stage are carefully designed to focus on the big ideas of each lesson mirroring the progression of learning students have just completed Students are not permitted to move on to their next Independent Digital lesson without successful completion of the Tower of Power Since the Tower of Power is software based teachers can access a report to determine how well students are progressing through the Tower of Power assessments enabling them to adjust instruction to support students progress See next section on Reports Exit Ticket paper This assessment also focuses on the content of a single lesson and it is administered at the culmination of each Lesson to help teachers monitor daily learning As the companion to the Tower of Power the Exit Ticket uses a single problem or multiple problems where appropriate to determine if the student can transfer their thinking and work from the Concept Exploration to an open response item that requires students to show their thinking and work including drawing models and or writing explanations Exit Ticket problems are designed to highlight the big mathematical idea of each lesson or a piece thereof and as such should not be edited 24 ZEARN MATH Teacher Edition

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G7 Course Guide Assessments and Reports Mission level assessments paper Mission level assessments take an average of 30 minutes to complete and should be administered at the end of a Mission during built in weekly Flex time longer Missions will sometimes be broken into a Mid Mission Assessment roughly halfway through the Mission and an end of Mision assessment at the end both of similar length All questions assess student understanding of content within the specific Mission and do not include questions related to other Missions Each assessment includes a carefully selected number of problems that give teachers rich feedback on student learning while limiting the time students spend on any given assessment and teachers spend analyzing assessments These paper assessments consist of open response items that require students to show their work or explain their thinking in a variety of ways including drawing models and writing explanations similar to an Exit Ticket Some assessment items highlight a student s understanding of a big mathematical idea while others focus on students procedural fluency Each part of any multi step problem has a clear objective is aligned to the explicit expectations of the target standards and allows teachers to identify whether students are struggling with the foundational math concept or the multi step aspect of the problem Zearn provides teachers with an answer key for each Mission level assessment that contains an exemplar student response for each item as well as specific standards alignment information Exemplar student responses can be used to inform teacher feedback but are not the only correct answer or solution method many of the problems on a Mission level assessment allow students multiple entry points and acceptable solution paths or strategies Zearn also offers assessment rubrics to provide teachers with actionable feedback they can use to respond to the learning and misconceptions students demonstrate on the Mission level assessment Each rubric models a progression towards understanding offering detailed examples of where students might go wrong along with guidance on what incorrect answers may indicate about a student s unfinished learning The rubrics also include guidance on scoring each item Scoring guidance helps teachers assess the depth of students learning and provide students with the precise feedback they need to continue to develop their understanding Each rubric is designed to produce a score out of 100 so that teachers can more easily input that score into their gradebooks To help create inclusive classroom math communities in which all students feel they belong and can deeply learn the math content of their grade Zearn s scoring guidance raises the floor for grades ensuring that any student who is at least initiating understanding on all items is guaranteed a minimum score of 60 or higher When connecting possible scores to the Progression Towards Understanding scores now have meaning a student s score communicates where they are in the progression from initial understanding to full understanding A student scoring above 90 points on an assessment should be considered as having full understanding of the content of the Mission A student scoring between 80 and 90 points on an assessment should be considered as nearing full understanding of the content of the Mission A student scoring between 70 and 80 points on an assessment should be considered as developing understanding of the content of the Mission A student scoring between 60 and 70 points on an assessment should be considered as initiating understanding of the content of the Mission ZEARN MATH Teacher Edition 25

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Assessments and Reports G7 Course Guide The points possible for each item vary based on the amount of understanding a student can demonstrate in any single item in addition to the mathematical focus of the item and the extent to which it connects to the big ideas of the Mission Note Given the coherent structure of Zearn Math if unfinished learning is evident on Mission level assessments teachers should move forward with additional supports and address misconceptions during collaborative Concept Exploration and on Flex Days understanding that the unfinished learning may best be completed by connecting it to new ideas presented in the latter half of a Mission or a subsequent Mission Students with 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 Interim assessments Zearn Math has partnered with The Achievement Network ANet to build a series of three interim assessments per grade These assessments measure learning across multiple Missions complementing the daily and Missionlevel assessments Each interim assessment is designed to focus on the big mathematical ideas of several Missions Zearn has worked side by side with ANet to ensure that all vocabulary visual representations contexts and numerical choices will be familiar to students using the Zearn Math curriculum while still challenging students to express that learning in new ways To learn more about this partnership including frequently asked questions sample assessments and an ondemand Webinar go online to the Zearn partnership page of ANet s website 4 CLASS AND STUDENT REPORTS Zearn provides teachers with reports that provide real time visibility into student pace progress and areas of struggle during software based learning which they can use to differentiate instruction and ensure all students receive the support and enrichment they need Go online to Zearn s Help Center to find information about all of these reports including video overviews 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 and Tower Alerts Progress Report This report shows teachers where each student is in the digital sequence of all grade level content Teachers can view the percentage of Independent Digital Lessons students have completed for each Mission By checking the Progress Report teachers can understand how far along students are in exploring grade level math content Pace Report This report helps teachers keep students on track each week to complete the recommended four Independent Digital Lessons Teachers can access a real time view of how many lessons students have completed the time it took to complete each lesson and whether students have completed any bookmarked foundational lessons if applicable to learn more about foundational lessons see the section on Addressing unfinished learning 4 5 he Zearn partnership page of the ANet website can be found at https www achievementnetwork org anet zearn partnership learn more T To learn about the Zearn Class Reports and Student Reports you may access visit https help zearn org hc en us articles 4403432402071Teacher Reports 26 ZEARN MATH Teacher Edition

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G7 Course Guide Assessments and Reports below By checking the Pace Report teachers can identify groups of students who need more time to meet weekly learning goals with Independent Digital Lessons and students who have already met their goal and can begin working on Bonuses for an extra challenge Teachers can also use the Pace Report to track student progress on any foundation lessons the teacher has bookmarked and can filter by lesson grade level to monitor how many still remain Tower Alerts Report This report allows teachers to identify the part of the lesson where the student struggled and whether or not the student was able to complete the independent practice portion of an Independent Digital Lesson and move on to the next Independent Digital Lesson Mistakes are magic and not all struggle is bad If a student struggles in the Tower of Power the student receives scaffolded support at the precise moment of misconception called a Boost If the Boost allows the student to move past their initial point of struggle this struggle was productive If a student struggles multiple times it s a sign that they have moved past the point of productive struggle to unproductive struggle and their teacher receives a Tower Alert Teachers can then use the Tower Alerts Report to identify which students need additional support on specific concepts and can bookmark 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 Student Reports Zearn also offers Student Reports that contain real time data and insights into student pace progress and areas of struggle during Independent Digital Lessons Teachers can use these reports along with other formative assessment data to gain insight into individual student learning including topics where that student excels and topics where they may still struggle Within a Student Report teachers can see the breakdown of Pace Progress and Tower Alerts as well as all the activities that the student has completed and when they did so Combined with Zearn s automated recommendations on foundational lessons that support students with unfinished learning see next section this report gives teachers the information they need to choose deeper interventions when necessary APPROACH TO UNFINISHED LEARNING Zearn Math helps teachers address students unfinished learning in the context of new learning setting students up for success with just in time supports built into daily digital lessons as well as targeted foundational lessons that are coherently aligned to their grade s core content Embedded supports Each Zearn Math grade level digital lesson includes built in support on concepts from previous topics and grades so that students can strengthen foundational understanding while learning grade level concepts In lesson adaptive support All Independent Digital Lessons contain built in supportive pathways that teach new concepts through concrete and pictorial representations that help students make sense of new concepts ZEARN MATH Teacher Edition 27

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Assessments and Reports G7 Course Guide 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 lLibrary 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 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 28 ZEARN MATH Teacher Edition

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G7 Course Guide Terminology Terminology Adjacent angles Adjacent angles share a side and a vertex C In this diagram angle ABC is adjacent to angle DBC A D B Area of a circle The area of a circle whose radius is r units is r2 square units A circle has radius 3 inches Its area is 32 9 square inches which is approximately 28 3 square inches Chance experiment A chance experiment is something you can do over and over again and you don t know what will happen each time Y For example each time you spin the spinner it could land on red yellow blue or green B G R Circle A circle is made out of all the points that are the same distance from a given point C m E 5c For example every point on this circle is 5 cm away from point A which is the center of the circle G A B F D Circumference The circumference of a circle is the distance around the circle If you imagine the circle as a piece of string it is the length of the string If the circle has radius r then the circumference is 2 r The circumference of a circle of radius 3 is 2 3 6 which is about 18 85 Complementary Complementary angles have measures that add up to 90 degrees For example a 15 angle and a 75 angle are complementary 75 75 15 ZEARN MATH Teacher Edition 15 29

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Terminology G7 Course Guide Constant of proportionality In a proportional relationship the values for one quantity are each multiplied by the same number to get the values for the other quantity This number is called the constant of proportionality In this example the constant of proportionality is 3 because 2 3 6 3 3 9 and 5 3 15 This means that there are 3 apples for every 1 orange in the fruit salad Number of oranges Number of apples 2 6 3 9 5 15 Corresponding When part of an original figure matches up with part of a copy we call them corresponding parts These could be points segments angles or distances A C D F For example point B in the first triangle corresponds to point E in the second triangle Segment AC corresponds to segment DF B E Cross section A cross section is the new face you see when you slice through a three dimensional figure For example if you slice a rectangular pyramid parallel to the base you get a smaller rectangle as the cross section Deposit When you put money into an account it is called a deposit For example a person added 60 to their bank account Before the deposit they had 435 After the deposit they had 495 because 435 60 495 Diameter A diameter is a line segment that goes from one edge of a circle to the other and passes through the center A diameter can go in any direction Every diameter of the circle is the same length We also use the word diameter to mean the length of this segment d O For example d is the diameter of this circle with center O 30 Equivalent ratios Two ratios are equivalent if you can multiply each of the numbers in the first ratio by the same factor to get the numbers in the second ratio For example 8 6 is equivalent to 4 3 because 8 21 4 and 6 21 3 Cups of Water Number of Lemons 8 6 4 3 ZEARN MATH Teacher Edition

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G7 Course Guide Terminology A recipe for lemonade says to use 8 cups of water and 6 lemons If we use 4 cups of water and 3 lemons it will make half as much lemonade Both recipes taste the same because 8 6 and 4 3 are equivalent ratios Event An event is a set of one or more outcomes in a chance experiment For example if we roll a number cube there are six possible outcomes Examples of events are rolling a number less than 3 rolling an even number or rolling a 5 Interquartile range IQR The interquartile range is one way to measure how spread out a data set is We sometimes call this the IQR To find the interquartile range we subtract the first quartile from the third quartile 22 29 30 Q1 31 32 43 44 Q2 45 50 50 59 Q3 For example the IQR of this data set is 20 because 50 30 20 Mean The mean is one way to measure the center of a data set We can think of it as a balance point For example for the data set 7 9 12 13 14 the mean is 11 To find the mean add up all the numbers in the data set Then divide by how many numbers there are 7 9 12 13 14 55 and 55 5 11 Mean absolute deviation MAD The mean absolute deviation is one way to measure how spread out a data set is Sometimes we call this the MAD For example for the data set 7 9 12 13 14 the MAD is 2 4 This tells us that these travel times are typically 2 4 minutes away from the mean which is 11 To find the MAD add up the distance between each data point and the mean Then divide by how many numbers there are 4 2 1 2 3 12 and 12 5 2 4 ZEARN MATH Teacher Edition 31

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Terminology G7 Course Guide Measurement error Measurement error is the positive difference between a measured amount and the actual amount For example Diego measures a line segment and gets 5 3 cm The actual length of the segment is really 5 32 cm The measurement error is 0 02 cm because 5 32 5 3 0 02 Median The median is one way to measure the center of a data set It is the middle number when the data set is listed in order For the data set 7 9 12 13 14 the median is 12 For the data set 3 5 6 8 11 12 there are two numbers in the middle The median is the average of these two numbers 6 8 14 and 14 2 7 Mode The mode is a measure of center that identifies the value that occurs most frequently in a data set The mode is easily identifiable in most visual displays of numerical data including line plots dot plots and stem plots as a peak in the data For the data set2 2 3 5 8 9 9 9 the mode is 9 For the data set 1 1 3 6 7 7 7 10 11 15 17 17 17 there are two numbers that occur most often 7 and 17 This data set would be considered bimodal or having two modes and a visual display would show two peaks Origin The origin is the point 0 0 in the coordinate plane This is where the horizontal axis and the vertical axis cross y 2 1 2 1 0 0 1 2 x 1 2 Outcome An outcome of a chance experiment is one of the things that can happen when you do the experiment For example the possible outcomes of tossing a coin are heads and tails Percent error Percent error is a way to describe error expressed as a percentage of the actual amount 32 ZEARN MATH Teacher Edition

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G7 Course Guide Terminology For example a box is supposed to have 150 folders in it Clare counts only 147 folders in the box This is an error of 3 folders The percent error is 2 because 3 is 2 of 150 3 150 0 02 Percentage decrease A percentage decrease tells how much a quantity went down expressed as a percentage of the starting amount For example a store had 64 hats in stock on Friday They had 48 hats left on Saturday The amount went down by 16 100 This was a 25 decrease because 16 is 25 of 64 16 64 0 25 48 16 75 25 Percentage increase A percentage increase tells how much a quantity went up expressed as a percentage of the starting amount For example Elena had 50 in the bank on Monday She had 56 on Tuesday The amount went up by 6 This was a 12 increase because 6 is 12 of 50 6 50 0 12 Pi There is a proportional relationship between the diameter and circumference of any circle The constant of proportionality is pi The symbol for pi is We can represent this relationship with the equation C d where C represents the circumference and d represents the diameter Some approximations for are 22 3 14 and 3 14159 7 Population A population is a set of people or things that we want to study 100 12 50 6 112 C 12 10 8 6 4 1 2 1 2 3 4 5 6 d For example if we want to study the heights of people on different sports teams the population would be all the people on the teams Probability The probability of an event is a number that tells how likely it is to happen A probability of 1 means the event will always happen A probability of 0 means the event will never happen For example the probability of selecting a moon block at random from this bag is 45 Proportion A proportion of a data set is the fraction of the data in a given category For example a class has 18 students There are 2 left handed students and 16 right handed students in the 2 class The proportion of students who are left handed is 20 or 0 1 Proportional relationship In a proportional relationship the values for one quantity are each multiplied by the same number to get the values for the other quantity ZEARN MATH Teacher Edition 33

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Terminology G7 Course Guide For example in this table every value of p is equal to 4 times the value of s on the same row We can write this relationship as p 4s This equation shows that p is proportional to s s p 2 8 3 12 5 20 10 40 Radius A radius is a line segment that goes from the center to the edge of a circle A radius can go in any direction Every radius of the circle is the same length We also use the word radius to mean the length of this segment r O For example r is the radius of this circle with center O Random Outcomes of a chance experiment are random if they are all equally likely to happen Repeating decimal A repeating decimal has digits that keep going in the same pattern over and over The repeating digits are marked with a line above them For example the decimal representation for for 25 is 1 136 which means 1 136363636 22 1 3 is 0 3 which means 0 3333333 The decimal representation Representative A sample is representative of a population if its distribution resembles the population s distribution in center shape and spread For example this dot plot represents a population 34 1 6 1 8 2 2 2 2 4 2 6 Dollars per pound of catfish 2 8 1 6 1 8 2 2 2 2 4 2 6 2 8 ZEARN Dollars per pound ofMATH catfishTeacher Edition

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G7 Course Guide Terminology 1 8 2 2 2the population 2 4 2 6 This dot plot shows a sample 1 6 that is representative of 2 8 Dollars per pound of catfish 1 6 1 8 2 2 2 2 4 2 6 Dollars per pound of catfish 2 8 Right angle A right angle is half of a straight angle It measures 90 degrees right angle Sample A sample is part of a population For example a population could be all the seventh grade students at one school One sample of that population is all the seventh grade students who are in band Sample space The sample space is the list of every possible outcome for a chance experiment For example the sample space for tossing two coins is heads heads tails heads heads tails tails tails Scale A scale tells how the measurements in a scale drawing represent the actual measurements of the object For example the scale on this floor plan tells us that 1 inch on the drawing represents 8 feet in the actual room This means that 2 inches would represent 16 feet and 21 inch would represent 4 feet 1 inch Scale drawing 8 feet A scale drawing represents an actual place or object All the measurements in the drawing correspond to the measurements of the actual object by the same scale ZEARN MATH Teacher Edition 35

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Terminology G7 Course Guide For example this map is a scale drawing The scale shows that 1 cm on the map represents 30 miles on land Map of Texas and Oklahoma by United States Census Bureau via American Fact Finder Public Domain A D 5 7 6 5 F 9 B In this example the scale factor is 1 5 because 4 1 5 6 5 1 5 7 5 and 6 1 5 9 C 6 4 Scale factor To create a scaled copy we multiply all the lengths in the original figure by the same number This number is called the scale factor E Scaled copy A scaled copy is a copy of an figure where every length in the original figure is multiplied by the same number C 6 D F 9 5 7 6 5 4 For example triangle DEF is a scaled copy of triangle ABC Each side length on triangle ABC was multiplied by 1 5 to get the corresponding side length on triangle DEF A B E Straight angle A straight angle is an angle that forms a straight line It measures 180 degrees Supplementary Supplementary angles have measures that add up to 180 degrees straight angle For example a 15 angle and a 165 angle are supplementary 165 165 15 15 Vertical angles Vertical angles are opposite angles that share the same vertex They are formed by a pair of intersecting lines Their angle measures are equal For example angles AEC and DEB are vertical angles If angle AEC measures 120 then angle DEB must also measure 120 C A E Angles AED and BEC are another pair of vertical angles Withdrawal When you take money out of an account it is called a withdrawal D B For example a person removed 25 from their bank account Before the withdrawal they had 350 After the withdrawal they had 325 because 350 25 325 36 ZEARN MATH Teacher Edition

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G7 Course Guide Required Materials Required Materials blank paper coins colored pencils compasses copies of the template cylindrical household items drink mix empty toilet paper roll four function calculators fruits or vegetables geometry toolkits glue or gluesticks graph paper grocery store circulars index cards internet enabled device knife maps or satellite images of the school grounds markers materials assembled from the template metric and customary unit conversion charts mixing containers number cubes paint paper bags paper clips paper plates pattern blocks pre assembled polyhedra pre printed slips cut from copies of the template protractors receipt tape recipes rulers rulers marked with centimeters rulers marked with inches scissors small disposable cups snap cubes sticky notes measuring cup stopwatches measuring spoons straightedges measuring tapes straws measuring tools string metal paper fasteners tape meter sticks tools for creating a visual display ZEARN MATH Teacher Edition trundle wheels water yardsticks 37

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Lessons by Standard G7 Course Guide Lessons by Standard Standard Lesson 7 EE 1 7 6 18 7 6 19 7 6 20 7 6 21 7 6 22 7 9 7 7 EE 2 7 6 12 7 EE 3 7 3 11 7 5 12 7 5 17 7 6 2 7 6 3 7 6 4 7 6 5 7 6 6 7 6 11 7 6 12 7 EE 4 7 5 15 7 6 5 7 6 9 7 6 11 7 6 12 7 6 13 7 6 15 7 7 5 7 9 3 7 EE 4 a 7 EE 4 b 7 G 1 38 Lesson Standard Lesson 7 RP 2 b 7 2 2 7 2 3 7 2 5 7 G 6 7 1 6 7 2 8 7 3 6 7 7 12 7 7 13 7 7 14 7 7 15 7 7 16 7 7 17 7 9 4 7 9 5 7 9 9 7 RP 2 c 7 2 4 7 2 5 7 2 6 7 3 5 7 RP 2 d 7 2 11 7 RP 3 7 3 5 7 4 6 7 4 7 7 4 8 7 4 9 7 4 10 7 4 11 7 4 12 7 4 13 7 4 14 7 4 15 7 4 16 7 9 1 7 9 2 7 9 3 7 9 4 7 9 6 7 9 8 7 9 13 7 SP 1 7 8 12 7 8 13 7 8 14 7 8 15 7 8 20 7 SP 2 7 8 13 7 8 14 7 8 15 7 8 16 7 8 17 7 8 20 7 SP 7 8 11 7 8 12 7 SP 3 7 8 11 7 8 18 7 SP 4 7 8 15 7 8 16 7 8 18 7 8 19 7 8 20 7 9 3 7 SP 5 7 8 2 7 8 3 7 8 4 7 8 5 7 8 6 7 SP 6 7 8 1 7 8 3 7 8 4 7 8 5 7 8 6 7 SP 7 7 8 3 7 8 4 7 8 5 7 8 14 7 SP 7 a 7 8 3 7 8 20 7 SP 7 b 7 8 4 7 8 5 7 8 6 7 SP 8 a 7 8 9 7 SP 8 b 7 8 8 7 8 9 7 SP 8 c 7 8 6 7 8 7 7 8 10 7 NS 1 7 5 1 7 5 4 7 5 6 7 6 18 7 7 6 7 NS 1 a 7 5 2 7 5 3 7 NS 1 b 7 5 1 7 5 2 7 5 3 7 NS 1 c 7 5 1 7 5 3 7 5 5 7 5 6 7 5 7 7 6 18 7 NS 1 d 7 5 3 7 NS 2 7 5 9 7 5 11 7 NS 2 a 7 5 8 7 5 9 7 NS 2 b 7 5 11 7 6 14 7 6 16 7 6 17 7 NS 2 c 7 5 9 7 5 10 7 1 1 7 1 2 7 1 3 7 1 4 7 1 5 7 1 6 7 1 7 7 1 8 7 1 9 7 1 10 7 1 11 7 1 12 7 1 13 7 2 1 7 3 6 7 3 11 7 9 4 7 9 13 7 NS 2 d 7 4 5 7 5 1 7 8 16 7 9 4 7 NS 3 7 5 7 7 5 12 7 5 13 7 5 14 7 5 15 7 5 16 7 5 17 7 9 3 7 9 6 7 RP 1 7 2 8 7 4 2 7 4 3 7 9 5 7 RP 2 7 2 2 7 2 3 7 2 4 7 2 5 7 2 6 7 2 7 7 2 8 7 2 9 7 2 10 7 2 11 7 2 12 7 2 13 7 2 14 7 2 15 7 3 3 7 4 3 7 4 4 7 4 5 7 5 9 7 5 12 7 5 14 7 9 3 7 9 5 7 5 15 7 5 16 7 6 4 7 6 5 7 6 7 7 6 8 7 6 9 7 6 10 7 6 11 7 6 12 7 9 7 7 G 2 7 3 2 7 7 6 7 7 7 7 7 8 7 7 9 7 7 10 7 7 17 7 G 3 7 7 11 7 7 13 7 G 4 7 3 3 7 3 4 7 3 5 7 3 7 7 3 8 7 3 9 7 3 10 7 3 11 7 9 4 7 9 11 7 9 12 7 G 5 Standard 7 7 2 7 7 3 7 7 4 7 7 5 7 RP 2 a 7 2 2 7 2 3 7 2 10 7 3 1 7 3 3 7 3 5 7 3 7 ZEARN MATH Teacher Edition

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G7 Course Guide Standards by Lesson Standards by Lesson Mission 1 Mission 2 Mission 3 Lesson Standard Lesson Standard Lesson Standard Lesson 1 7 G 1 Lesson 1 7 G 1 Lesson 1 7 RP 2 a Lesson 2 7 G 1 Lesson 2 Lesson 2 7 G 2 Lesson 3 7 G 1 7 RP 2 7 RP 2 a and 7 RP 2 b 7 G 1 Lesson 3 Lesson 3 Lesson 4 7 RP 2 7 RP 2 a and 7 RP 2 b 7 G 4 7 RP 2 and 7 RP 2 a Lesson 4 7 RP 2 and 7 RP 2 c Lesson 4 7 G 4 Lesson 5 7 RP 2 7 RP 2 b and 7 RP 2 c Lesson 5 7 G 4 7 RP 2 a 7 RP 2 c and 7 RP 3 Lesson 6 7 RP 2 and 7 RP 2 c Lesson 6 7 G 1 and 7 G 6 Lesson 7 7 RP 2 Lesson 7 7 G 4 and 7 RP 2 a Lesson 8 7 G 6 7 RP 1 and 7 RP 2 Lesson 8 7 G 4 Lesson 9 7 G 4 Lesson 10 7 G 4 Lesson 11 7 EE 3 7 G 1 and 7 G 4 Lesson 5 7 G 1 Lesson 6 7 G 1 and 7 G 6 Lesson 7 7 G 1 Lesson 8 7 G 1 Lesson 9 7 G 1 Lesson 10 7 G 1 Lesson 11 7 G 1 Lesson 9 7 RP 2 Lesson 12 7 G 1 Lesson 10 7 RP 2 and 7 RP 2 a Lesson 13 7 G 1 Lesson 11 7 RP 2 and 7 RP 2 d Lesson 12 7 RP 2 Lesson 13 7 RP 2 Lesson 14 7 RP 2 Lesson 15 7 RP 2 ZEARN MATH Teacher Edition 39

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Standards by Lesson G7 Course Guide Mission 4 Mission 5 Lesson Standard Lesson 1 7 RP A1 Lesson 2 7 RP 1 Lesson 3 7 RP 1 and 7 RP 2 Lesson 4 7 RP 2 Lesson 5 7 NS 2 d and 7 RP 2 Lesson 6 7 RP 3 Lesson 7 7 RP 3 Lesson 8 7 RP 3 Lesson 9 7 RP 3 Mission 6 Lesson Standard Lesson Standard Lesson 1 7 NS 1 7 NS 1 b 7 NS 1 c and 7 NS 2 d Lesson 1 7 EE B2 Lesson 2 7 EE 3 Lesson 2 7 NS 1 a and 7 NS 1 b Lesson 3 7 EE 3 Lesson 4 Lesson 3 7 NS 1 a 7 NS 1 b 7 NS 1 c and 7 NS 1 d 7 EE 3 and 7 EE 4 a Lesson 5 7 EE 3 7 EE 4 and 7 EE 4 a Lesson 4 7 NS 1 Lesson 6 7 EE 3 Lesson 5 7 NS 1 c Lesson 7 7 EE 4 a Lesson 6 7 NS 1 and 7 NS 1 c Lesson 8 7 EE 4 a Lesson 9 7 EE 4 and 7 EE 4 a Lesson 10 7 EE 4 a Lesson 11 7 EE 3 7 EE 4 and 7 EE 4 a Lesson 12 7 EE 2 7 EE 3 7 EE 4 and 7 EE 4 a Lesson 13 7 EE 4 Lesson 14 7 EE 4 b Lesson 15 7 EE 4 Lesson 10 7 RP 3 Lesson 7 7 NS 1 c and 7 NS 3 Lesson 11 7 RP 3 Lesson 8 7 NS 2 a Lesson 12 7 RP 3 Lesson 13 7 RP 3 Lesson 9 7 NS 2 7 NS 2 a 7 NS 2 c and 7 RP 2 Lesson 14 7 RP 3 Lesson 10 7 NS 2 c Lesson 15 7 RP 3 Lesson 11 Lesson 16 7 RP 3 7 NS 2 and 7 NS 2 b Lesson 12 7 EE 3 7 NS 3 and 7 RP 2 Lesson 13 7 NS 3 Lesson 16 7 EE 4 b Lesson 14 7 NS 3 and 7 RP 2 Lesson 17 7 EE 4 b Lesson 15 7 EE 4 7 EE 4 a and 7 NS 3 Lesson 18 Lesson 16 7 EE 4 a and 7 NS 3 7 EE 1 7 NS 1 and 7 NS 1 c Lesson 19 7 EE 1 Lesson 17 7 EE 3 and 7 NS 3 Lesson 20 7 EE 1 Lesson 21 7 EE 1 Lesson 22 7 EE 1 1 While not representative of the full scope of the standard this lesson is building towards full understanding of 7 RP A 1 2 While not representative of the full scope of the standard this lesson is building towards full understanding of 7 EE B 4 40 ZEARN MATH Teacher Edition

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G7 Course Guide Standards by Lesson Mission 7 Mission 9 Lesson Standard Lesson Standard Lesson Standard Lesson 1 7 G B3 Lesson 1 7 SP 6 Lesson 1 7 RP 3 Lesson 2 7 G 5 Lesson 2 7 SP 5 Lesson 2 7 RP 3 Lesson 3 7 G 5 Lesson 4 7 G 5 Lesson 3 7 SP 5 7 SP 6 7 SP 7 and 7 SP 7 a Lesson 3 7 EE 4 7 NS 3 7 RP 2 7 RP 3 and 7 SP 4 Lesson 5 7 EE 4 and 7 G 5 Lesson 6 Lesson 4 Lesson 4 7 G 2 and 7 NS 1 7 SP 5 7 SP 6 7 SP 7 and 7 SP 7 b 7 G 1 7 G 4 7 G 6 7 NS 2 d and 7 RP 3 Lesson 7 7 G 2 Lesson 5 Lesson 5 7 G 6 7 RP 1 and 7 RP 2 Lesson 8 7 G 2 7 SP 5 7 SP 6 7 SP 7 and 7 SP 7 b Lesson 6 7 NS 3 and 7 RP 3 Lesson 6 7 SP 5 7 SP 6 7 SP 7 b and 7 SP 8 c Lesson 7 7 EE 1 and 7 EE 4 a Lesson 7 7 SP 8 c Lesson 8 7 RP 3 Lesson 8 7 SP 8 b Lesson 9 7 G 6 Lesson 10 7 RP 3 Lesson 9 3 Mission 8 7 G 2 Lesson 10 7 G 2 Lesson 11 7 G 3 Lesson 12 7 G 6 Lesson 13 7 G 3 and 7 G 6 Lesson 9 7 SP 8 a and 7 SP 8 b Lesson 14 7 G 6 Lesson 10 7 SP 8 c Lesson 11 7 G 4 Lesson 15 7 G 6 Lesson 11 7 SP 3 Lesson 12 7 G 4 Lesson 16 7 G 6 Lesson 12 7 SP 1 Lesson 13 7 G 1 and 7 RP 3 Lesson 17 7 G 2 and 7 G 6 Lesson 13 7 SP 1 and 7 SP 2 Lesson 14 7 SP 1 7 SP 2 and 7 SP 7 Lesson 15 7 SP 1 7 SP 2 and 7 SP 4 Lesson 16 7 NS 2 d 7 SP 2 and 7 SP 4 Lesson 17 7 SP 2 Lesson 18 7 SP 3 and 7 SP 4 Lesson 19 7 SP 4 Lesson 20 7 SP 1 7 SP 2 7 SP 4 and 7 SP 7 a While not representative of the full scope of the standard this lesson is building towards full understanding of 7 G 5 ZEARN MATH Teacher Edition 41

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Appendix I Instructional Routines G6 Course Guide Appendix I Instructional Routines The kind of instruction appropriate in any particular lesson depends on the learning goals of that lesson Some lessons may be devoted to developing a concept others to mastering a procedural skill yet others to applying mathematics to a real world problem These aspects of mathematical proficiency are interwoven into Zearn Math The Zearn Math Teacher Edition includes a small set of activity structures and references a small high leverage set of teacher moves that become more and more familiar to teachers and students as the year progresses ALGEBRA TALK What One expression is displayed at a time Students are given a few minutes to quietly think and give a signal when they have an answer and a strategy The teacher selects students to share different strategies for each one Who thought about it a different way Their explanations are recorded for all to see Students might be pressed to provide more details about why they decided to approach a problem a certain way It may not be possible to share every possible strategy for the given limited time the teacher may only gather two or three distinctive strategies per problem Problems are purposefully chosen to elicit different approaches Where Warm Up Why Algebra Talks build algebraic thinking by encouraging students to think about the numbers and variables in an expression and rely on what they know about structure patterns and properties of operations to mentally solve a problem Algebra Talks promote seeing structure in expressions and thinking about how changing one number affects others in an equation While participating in these activities students need to be precise in their word choice and use of language ANTICIPATE MONITOR SELECT SEQUENCE CONNECT What Fans of 5 Practices for Orchestrating Productive Mathematical Discussions Smith and Stein 2011 will recognize these as the 5 Practices In this curriculum much of the work of anticipating sequencing and connecting is handled by the materials in the activity narrative launch and synthesis sections Teachers will need to develop their capacity to prepare for and conduct whole class discussions Where Warm Up Concept Exploration Wrap Up Why In Zearn Math many activities can be described as do math and talk about it but the 5 Practices lend more structure to these activities so that they more reliably result in students making connections and learning new mathematics 2022 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license 42 ZEARN MATH Teacher Edition

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G6 Course Guide Appendix I Instructional Routines NOTICE AND WONDER What Students are shown some media or a mathematical representation The prompt to students is What do you notice What do you wonder Students are given a few minutes to write down things they notice and things they wonder After students have had a chance to write down their responses the teacher asks several students to share things they noticed and things they wondered these are recorded by the teacher for all to see Usually the teacher steers the conversation to wondering about something mathematical that the class is about to focus on Where Warm Up Concept Exploration Why The purpose is to make a mathematical task accessible for all students with these two low stakes questions by thinking about them and responding students gain entry into the context and might get their curiosity piqued Taking steps to become familiar with a context and the mathematics that might be involved is making sense of problems Note Notice and Wonder and I Notice I Wonder are trademarks of NCTM and the Math Forum and used in these materials with permission NUMBER TALK What One problem is displayed at a time Students are given a few minutes to quietly think and give a signal when they have an answer and a strategy The teacher selects students to share different strategies for each problem Who thought about it a different way Their explanations are recorded for all to see Students might be pressed to provide more details about why they decided to approach a problem a certain way It may not be possible to share every possible strategy for the given limited time the teacher may only gather two or three distinctive strategies per problem Problems are purposefully chosen to elicit different approaches often in a way that builds from one problem to the next Where Warm Up Why Number talks build computational fluency by encouraging students to think about the numbers in a computation problem and rely on what they know about structure patterns and properties of operations to mentally solve a problem Dot images are similar to number talks except the image used is an arrangement of dots that students might count in different ways While participating in these activities students need to be precise in their word choice and use of language POLL THE CLASS What Used to register an initial response or an estimate most often in activity launches or to kick off a discussion every student in class reports a response to a prompt This can also be used when data needs to be collected from 2022 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license ZEARN MATH Teacher Edition 43

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Appendix I Instructional Routines G6 Course Guide each student in class for example What is the length of your ear in centimeters Teachers need to develop a mechanism by which poll results are collected and displayed so that this frequent form of classroom interaction is seamless Smaller classes might be able to conduct a roll call by voice For larger classes students might be given mini whiteboards or a set of colored index cards to hold up Free and paid commercial tools are also readily available Where Concept Exploration Why Going on record with an estimate or a gut reaction makes people want to know if they were right and increases investment in the outcome If coming up with an estimate is too daunting ask students for a guess that they are sure is too low or too high Putting some boundaries on possible outcomes of a problem is an important skill for mathematical modeling Collecting data from the class to use in an activity makes the outcome of the activity more interesting TAKE TURNS What Students work with a partner or small group They take turns in the work of the activity whether it be spotting matches explaining justifying agreeing or disagreeing or asking clarifying questions If they disagree they are expected to support their case and listen to their partner s arguments The first few times students engage in these activities the teacher should demonstrate with a partner how the discussion is expected to go Once students are familiar with these structures less set up will be necessary While students are working the teacher can ask students to restate their question more clearly or paraphrase what their partner said Where Concept Exploration Why Building in an expectation through the routine that students explain the rationale for their choices and listen to another s rationale deepens the understanding that can be achieved through these activities Specifying that students take turns deciding explaining and listening limits the phenomenon where one student takes over and the other does not participate Taking turns can also give students more opportunities to construct logical arguments and critique others reasoning THINK PAIR SHARE What Students have quiet time to think about a problem and work on it individually and then time to share their response or their progress with a partner Once these partner conversations have taken place some partnerships are selected to share their thoughts with the class Where Concept Exploration 2022 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license 44 ZEARN MATH Teacher Edition

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G6 Course Guide Appendix I Instructional Routines Why This is a teaching routine useful in many contexts whose purpose is to give all students enough time to think about a prompt and form a response before they are expected to try to verbalize their thinking First they have an opportunity to share their thinking in a low stakes way with one partner so that when they share with the class they can feel calm and confident as well as say something meaningful that might advance everyone s understanding Additionally the teacher has an opportunity to eavesdrop on the partner conversations so that she can purposefully select students to share with the class TRUE OR FALSE What One statement is displayed at a time Students are given a few minutes to quietly think and give a signal when they have an answer The teacher selects students to share different ways of reasoning for each statement Who thought about it a different way While students may evaluate each side of the equation to determine if it is true or false encourage students to think about ways to reason that do not require complete computations It may not be possible to share every possible reasoning approach for the given limited time the teacher may only gather two or three distinctive strategies per problem Statements are purposefully chosen to elicit different approaches often in a way that builds from one statement to the next Where Warm Up Why Depending on the purpose of the task the true or false structure encourages students to reason about numeric and algebraic expressions using base ten structure the meaning of fractions meaning and properties of operations and the meaning of comparison symbols While the structure of a true or false is similar to that of a number talk number talks are often focused on computational strategies while true or false tasks are more likely to focus on more structural aspects of the expressions Often students can determine whether an equation an inequality or a statement is true or false without doing any direct computation While participating in these activities students need to be precise in their word choice and use of language WHICH ONE DOESN T BELONG What Students are presented with four figures diagrams graphs or expressions with the prompt Which one doesn t belong Typically each of the four options doesn t belong for a different reason and the similarities and differences are mathematically significant Students are prompted to explain their rationale for deciding that one option doesn t belong and given opportunities to make their rationale more precise Where Warm Up Why Which One Doesn t Belong fosters a need to define terms carefully and use words precisely in order to compare and contrast a group of geometric figures or other mathematical representations 2022 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license ZEARN MATH Teacher Edition 45

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Appendix II Access for Multilingual Learners G6 Course Guide GROUP PRESENTATIONS Some activities instruct students to work in small groups to solve a problem with mathematical modeling invent a new problem design something or organize and display data and then create a visual display of their work Teachers need to help groups organize their work so that others can follow it and then facilitate different groups presentation of work to the class Teachers can develop specific questioning skills to help more students make connections and walk away from these experiences with desired mathematical learning For example instead of asking if anyone has any questions for the group it is often more productive to ask a member of the class to restate their understanding of the group s findings in their own words Appendix II Access for Multilingual Learners INTRODUCTION Zearn Math for Seventh Grade builds on foundational principles for supporting language development for all students This appendix aims to provide guidance to help teachers recognize and support students language development in the context of mathematical sense making Embedded within the Zearn Math Teacher Edition are instructional supports and practices to help teachers address the specialized academic language demands in math when planning and delivering lessons including the demands of reading writing speaking listening conversing and representing in math Aguirre Bunch 2012 Therefore while these instructional supports and practices can and should be used to support all students learning mathematics they are particularly wellsuited to meet the needs of linguistically and culturally diverse students who are learning mathematics while simultaneously acquiring English This table reflects the attention and support for language development at each level of the Zearn Math curriculum Course f oundation of curriculum theory of action and design principles that drive a continuous focus on language development student terminology Mission Mission specific progression of language development included in each Mission Overview Lesson language goals embedded in learning goals describe the language demands of the lesson definitions of new terminology additional supports for multilingual learners based on language demands of the activity Activity additional supports for multilingual learners based on language demands of the activity mathematical language routines 2022 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license 46 ZEARN MATH Teacher Edition

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G6 Course Guide Appendix II Access for Multilingual Learners THEORY OF ACTION Zearn believes that language development can be built into teachers instructional practice and students classroom experience through intentional design of materials teacher commitments administrative support and professional development Our theory of action is grounded in the interdependence of language learning and content learning the importance of scaffolding routines that foster students independent participation the value of instructional responsiveness in the teaching process and the central role of student agency in the learning process Mathematical understandings and language competence develop interdependently Deep conceptual learning is gained through language Ideas take shape through words texts illustrations conversations debates examples etc Teachers peers and texts serve as language resources for learning Instructional attention to academic language development historically limited to vocabulary instruction has now shifted to also include instruction around the demands of argumentation explanation generalization analyzing the purpose and structure of text and other mathematical discourse Scaffolding provides temporary supports that foster student autonomy Learners with emerging language at any level can engage deeply with central mathematical ideas under specific instructional conditions Mathematical language development occurs when students use their developing language to make meaning and engage with challenging problems that are beyond students mathematical ability to solve independently and therefore require interaction with peers However these interactions should be structured with temporary supports that students can use to make sense of what is being asked of them to help organize their own thinking and to give and receive feedback Instruction supports learning when teachers respond to students verbal and written work Eliciting student thinking through language allows teachers and students to respond formatively to the language students generate Formative peer and teacher feedback creates opportunities for revision and refinement of both content understandings and language Students are agents in their own mathematical and linguistic sense making Mathematical language proficiency is developed through the process of actively exploring and learning mathematics Language is action in the very doing of math 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 Lesson and activity level supports for multilingual learners stem from the design principles below and are aligned to the language domains of reading writing speaking listening conversing and representing in math Aguirre Bunch 2012 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 2022 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license ZEARN MATH Teacher Edition 47

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Appendix II Access for Multilingual Learners G6 Course Guide Based on their observations of student language teachers can make adjustments to their teaching and provide additional language support where necessary Teachers can select from the Supports for multilingual learners provided in the Zearn Math Teacher Edition as appropriate When selecting from these supports teachers should take into account the language demands of the specific activity and the language needed to engage the content more broadly in relation to their students current ways of using language to communicate ideas as well as their students English language proficiency DESIGN PRINCIPLES FOR PROMOTING MATHEMATICAL LANGUAGE USE AND DEVELOPMENT The framework for supporting multilingual learners in Zearn Math includes four design principles for promoting mathematical language use and development in curriculum and instruction The design principles and related routines work to make language development an integral part of planning and delivering instruction while guiding teachers to amplify the most important language that students are expected to bring to bear on the central mathematical ideas of each Mission Principle 1 Support Sense Making Scaffold tasks and amplify language so students can make their own meaning Students do not need to understand a language completely before they can engage with academic content in that language Language learners of all levels can and should engage with grade level content that is appropriately scaffolded Students need multiple opportunities to talk about their mathematical thinking negotiate meaning with others and collaboratively solve problems with targeted guidance from the teacher Teachers can make language more accessible for students by amplifying rather than simplifying speech or text Simplifying includes avoiding the use of challenging words or phrases Amplifying means anticipating where students might need support in understanding concepts or mathematical terms and providing multiple ways to access them Providing visuals or manipulatives demonstrating problem solving engaging in think alouds and creating analogies synonyms or context are all ways to amplify language so that students are supported in taking an active role in their own sense making of mathematical relationships processes concepts and terms Principle 2 Optimize Output Strengthen opportunities and supports for students to describe their mathematical thinking to others orally visually and in writing Linguistic output is the language that students use to communicate their ideas to others oral written visual etc and refers to all forms of student linguistic expressions except those that include significant back and forth negotiation of ideas That type of conversational language is addressed in the third principle All students benefit from repeated strategically optimized and supported opportunities to articulate mathematical ideas into linguistic expression Opportunities for students to produce output should be strategically optimized for both a important concepts of the Mission or grade level and b important disciplinary language functions for example making conjectures and claims justifying claims with evidence explaining reasoning critiquing the reasoning of others making generalizations and comparing approaches and representations The focus for optimization must be determined in part by how students are currently using language to engage with important disciplinary concepts When opportunities to produce output are optimized in these ways students will get spiraled practice 2022 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license 48 ZEARN MATH Teacher Edition

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G6 Course Guide Appendix II Access for Multilingual Learners in making their thinking about important mathematical concepts stronger with more robust reasoning and examples and making their thinking clearer with more precise language and visuals Principle 3 Cultivate Conversation Strengthen opportunities and supports for constructive mathematical conversations pairs groups and whole class Conversations are back and forth interactions with multiple turns that build up ideas about math Conversations act as scaffolds for students developing mathematical language because they provide opportunities to simultaneously make meaning communicate that meaning and refine the way content understandings are communicated When students have a purpose for talking and listening to each other communication is more authentic During effective discussions students pose and answer questions clarify what is being asked and what is happening in a problem build common understandings and share experiences relevant to the topic As mentioned in Principle 2 learners must be supported in their use of language including when having conversations making claims justifying claims with evidence making conjectures communicating reasoning critiquing the reasoning of others engaging in other mathematical practices and above all when making mistakes Meaningful conversations depend on the teacher using lessons and activities as opportunities to build a classroom culture that motivates and values efforts to communicate Principle 4 Maximize Meta awareness Strengthen the meta connections and distinctions between mathematical ideas reasoning and language Language is a tool that not only allows students to communicate their math understanding to others but also to organize their own experiences ideas and learning for themselves Meta awareness is consciously thinking about one s own thought processes or language use Meta awareness develops when students and teachers engage in classroom activities or discussions that bring explicit attention to what students need to do to improve communication and reasoning about mathematical concepts When students are using language in ways that are purposeful and meaningful for themselves in their efforts to understand and be understood by each other they are motivated to think of ways in which language can be both clarified and clarifying Meta awareness in students can be strengthened when for example teachers ask students to explain to each other the strategies they brought to bear to solve a challenging problem They might be asked How does yesterday s method connect with the method we are learning today or What ideas are still confusing to you These questions are metacognitive because they help students to reflect on their own and others learning Students can also reflect on their expanding use of language for example by comparing the language they used to clarify a mathematical concept with the language used by their peers in a similar situation This is called metalinguistic awareness because students reflect on English as a language their own growing use of that language and the particular ways ideas are communicated in mathematics Students learning English benefit from being aware of how language choices are related to the purpose of the task and the intended audience especially if oral or written work is required Both metacognitive and metalinguistic awareness are powerful tools to help students self regulate their academic learning and language acquisition These four principles are guides for curriculum development as well as for planning and execution of instruction including the structure and organization of interactive opportunities for students They also serve as guides for and observation analysis and reflection on student language and learning 2022 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license ZEARN MATH Teacher Edition 49

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Appendix II Access for Multilingual Learners G6 Course Guide MATHEMATICAL LANGUAGE ROUTINES For instances where students need even more support than what s in the curriculum Zearn recommends that teachers read and consider using the mathematical language routines MLRs listed below MLR 1 Stronger and Clearer Each Time MLR 2 Collect and Display MLR 3 Clarify Critique Correct MLR 4 Information Gap MLR 5 Co Craft Questions MLR 6 Three Reads MLR 7 Compare and Connect MLR 8 Discussion Supports The mathematical language routines MLRs were selected because they are effective and practical for simultaneously learning mathematical practices content and language A mathematical language routine is a structured but adaptable format for amplifying assessing and developing students language The routines emphasize uses of language that is meaningful and purposeful rather than about just getting answers These routines can be adapted and incorporated across lessons in each Mission to fit the mathematical work wherever there are productive opportunities to support students in using and improving their English and disciplinary language use Each MLR facilitates attention to student language in ways that support in the moment teacher peer and selfassessment for all learners The feedback enabled by these routines will help students revise and refine not only the way they organize and communicate their own ideas but also ask questions to clarify their understanding of others ideas Mathematical Language Routine 1 Stronger and Clearer Each Time Purpose To provide a structured and interactive opportunity for students to revise and refine both their ideas and their verbal and written output Zwiers 2014 This routine also provides a purpose for student conversation through the use of a discussion worthy and iteration worthy prompt The main idea is to have students think and write individually about a question use a structured pairing strategy to have multiple opportunities to refine and clarify their response through conversation and then finally revise their original written response Subsequent conversations and second drafts should naturally show evidence of incorporating or addressing new ideas and language They should also show evidence of refinement in precision communication expression examples and reasoning about mathematical concepts How it happens PROMPT This routine begins by providing a thought provoking question or prompt The prompt should guide students to think about a concept or big idea connected to the content goal of the lesson and should be answerable in a format that is connected with the activity s primary disciplinary language function 2022 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license 50 ZEARN MATH Teacher Edition

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G6 Course Guide Appendix II Access for Multilingual Learners 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 RESPONSE SECOND DRAFT Finally after meeting with 2 3 different partners students write a second draft This draft should naturally reflect borrowed ideas from partners as well as refinement of initial ideas through repeated communication with partners This second draft will be stronger with more or better evidence of mathematical content understanding and clearer more precision organization and features of disciplinary language function After students are finished their first and second drafts can be compared 2 3 min Mathematical Language Routine 2 Collect and Display Purpose To capture a variety of students oral words and phrases into a stable collective reference The intent of this routine is to stabilize the varied and fleeting language in use during mathematical work in order for students own output to become a reference in developing mathematical language The teacher listens for and scribes the language students use during partner small group or whole class discussions using written words diagrams and pictures This collected output can be organized revoiced or explicitly connected to other language in a display that all students can refer to build on or make connections with during future discussion or writing Throughout the course of a Mission and beyond teachers can reference the displayed language as a model update and revise the display as student language changes and make bridges between prior student language and new disciplinary language Zwiers et al 2017 This routine provides feedback for students in a way that supports sense making while simultaneously increasing meta awareness of language How it happens COLLECT During this routine circulate and listen to student talk during paired group or as a whole class discussion Jot down the words phrases drawings or writing students use Capture a variety of uses of language that can be connected to the lesson content goals as well as the relevant disciplinary language function s Collection can happen digitally or 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 2022 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license ZEARN MATH Teacher Edition 51

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Appendix II Access for Multilingual Learners G6 Course Guide Mathematical Language Routine 3 Clarify Critique Correct Purpose To give students a piece of mathematical writing that is not their own to analyze reflect on and develop The intent is to prompt student reflection with an incorrect incomplete or ambiguous written mathematical statement and for students to improve upon the written work by correcting errors and clarifying meaning Teachers can demonstrate how to effectively and respectfully critique the work of others with meta think alouds and pressing for details when necessary This routine fortifies output and engages students in meta awareness More than just error analysis this routine purposefully engages students in considering both the author s mathematical thinking as well as the features of their communication How it happens ORIGINAL STATEMENT Create or curate a written mathematical statement that intentionally includes conceptual or common errors in mathematical thinking as well as ambiguities in language The mathematical errors should be driven by the content goals of the lesson and the language ambiguities should be driven by common or typical challenges with the relevant disciplinary language function This mathematical text is read by the students and used as the draft or original statement that students improve 1 2 min DISCUSSION WITH PARTNER Next students discuss the original statement in pairs The teacher provides guiding questions for this discussion such as What do you think the author means Is anything unclear or Are there any reasoning errors In addition to these general guiding questions 1 2 questions can be added that specifically address the content goals and disciplinary language function relevant to the activity 2 3 min IMPROVED STATEMENT Students individually revise the original statement drawing on the conversations with their partners to create an improved statement In addition to resolving any mathematical errors or misconceptions clarifying ambiguous language other requirements can be added as parameters for the improved response These specific requirements should be aligned with the content goals and disciplinary language function of the activity 3 5 min Mathematical Language Routine 4 Information Gap Purpose To create a need for students to communicate Gibbons 2002 This routine allows teachers to facilitate meaningful interactions by positioning some students as holders of information that is needed by other students The information is needed to accomplish a goal such as solving a problem or winning a game An information gap creates a need for students to orally or visually share ideas and information in order to bridge a gap and accomplish something that they could not have done alone Teachers should demonstrate how to ask for and share information how to justify a request for information and how to clarify and elaborate on 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 partners 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 2022 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license 52 ZEARN MATH Teacher Edition

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G6 Course Guide Appendix II Access for Multilingual Learners 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 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 Questions Purpose To allow students to get inside of a context before feeling pressure to produce answers to create space for students to produce the language of mathematical questions themselves and to provide opportunities for students to analyze how different mathematical forms and symbols can represent different situations Through this routine students are able to 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 about assumptions that they think are important 1 2 minutes STUDENTS COMPARE QUESTIONS Students compare the questions they generated with a partner 1 2 minutes before sharing questions with the whole class Demonstrate or ask students to demonstrate identifying specific questions that are aligned to the content goals of the lesson as well as the disciplinary language function If there are no clear examples teachers can demonstrate adapting a question or ask students to adapt questions to align with specific content or function goals 2 3 minutes ACTUAL QUESTION S REVEALED IDENTIFIED Finally the actual questions students are expected to work on are revealed or selected from the list that students generated Mathematical Language Routine 6 Three Reads Purpose To ensure that students know what they are being asked to do create opportunities for students to reflect on the ways mathematical questions are presented and equip students with tools used to actively make sense of mathematical situations and information Kelemanik Lucenta Creighton 2016 This routine supports reading comprehension sense making and meta awareness of mathematical language It also supports negotiating information in a text with a partner through mathematical conversation 2022 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license ZEARN MATH Teacher Edition 53

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Appendix II Access for Multilingual Learners G6 Course Guide 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 number of markers after instead of markers Some of the quantities will be explicit example 32 apples while others are implicit example the time it takes to brush one tooth Record the quantities as a reference to use when solving the problem after the third read 3 5 minutes READ 3 INDIVIDUAL PAIRS OR SHARED READING During the third read the final question or prompt is revealed Students discuss possible solution strategies referencing the relevant quantities recorded after the second read It may be helpful for students to create diagrams to represent the relationships among quantities identified in the second read or to represent the situation with a picture Asturias 2015 1 2 minutes Mathematical Language Routine 7 Compare and Connect Purpose To foster students meta awareness as they identify compare and contrast different mathematical approaches and representations This routine leverages the powerful mix of disciplinary representations available in mathematics as a resource for language development In this routine students make sense of mathematical strategies other than their own by relating and connecting other approaches to their own Students should be prompted to reflect on and linguistically respond to these comparisons for example exploring why or when one might do or say something a certain way identifying and explaining correspondences between different mathematical representations or methods or wondering how a certain concept compares or connects to other concepts Be sure to demonstrate asking questions that students can ask each other rather than asking questions to test understanding Use think alouds to demonstrate the trial and error or fits and starts of sensemaking similar to the way teachers think aloud to demonstrate reading comprehension This routine supports metacognition and metalinguistic awareness and also supports constructive conversations How it happens STUDENTS PREPARE DISPLAYS OF THEIR WORK Students are given a problem that can be approached and solved using multiple strategies or a situation that can be modeled using multiple representations Students are assigned the job of preparing a visual display of how they made sense of the problem and why their solution makes sense Variation is encouraged and supported among the representations that different students use to show what makes sense COMPARE Students investigate each others work by taking a tour of the visual displays Tours can be self guided a travellers and tellers format or the teacher can act as docent by providing questions for 2022 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license 54 ZEARN MATH Teacher Edition

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G6 Course Guide Appendix II Access for Multilingual Learners 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 language students use to communicate about mathematical features that are important for solving the problem or modeling the situation Call attention to the similarities and differences between the ways those features appear Mathematical Language Routine 8 Discussion Supports Purpose To support rich and inclusive discussions about mathematical ideas representations contexts and strategies Chapin O Connor Anderson 2009 Rather than another structured format the examples provided in this routine are instructional moves that can be combined and used together with any of the other routines They include multimodal strategies for helping students make sense of complex language ideas and classroom communication The examples can be used to invite and incentivize more student participation conversation and meta awareness of language Eventually as teachers continue to demonstrate students should begin using these strategies themselves to prompt each other to engage more deeply in discussions How it happens Unlike the other routines this support is a collection of strategies and moves that can be combined and used to support discussion during almost any activity Examples of possible strategies Revoice student ideas to demonstrate mathematical language use by restating a statement as a question in order to clarify apply appropriate language and involve more students Press for details in students explanations by requesting for students to challenge an idea elaborate on an idea or give an example Show central concepts multi modally by using different types of sensory inputs acting out scenarios or inviting students to do so showing videos or images using gesture 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 2022 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license ZEARN MATH Teacher Edition 55

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Appendix II Access for Multilingual Learners G6 Course Guide 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 FRAMES Sentence frames can support student language production by providing a structure to communicate about a topic Helpful sentence frames are open ended so as to amplify language production not constrain it The table shows examples of generic sentence frames that can support common disciplinary language functions across a variety of content topics Some of the lessons in these materials include suggestions of additional sentence frames that could support the specific content and language functions of that lesson language function sample sentence frames describe It looks like I notice that I wonder if Let s try A quantity that varies is ___________ What do you notice What other details are important explain First I ___________ because Then Next I I noticed ___________ so I I tried ___________ and what happened was How did you get What else could we do justify I know ___________ because I predict ___________ because If ___________ then ___________ because Why did you How do you know Can you give an example generalize ___________ reminds me of ___________ because ___________ will always ___________ because ___________ will never ___________ because Is it always true that Is ___________ a special case critique That could couldn t be true because This method works doesn t work because We can agree that ___________ s idea reminds me of Another strategy would be ___________ because Is there another way to say do 2022 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license 56 ZEARN MATH Teacher Edition

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G6 Course Guide Appendix III Access for Students with Disabilities language function sample sentence frames compare and contrast Both ___________ and ___________ are alike because ___________ and ___________ are different because One thing that is the same is One thing that is different is How are ___________ and ___________ different What do ___________ and ___________ have in common represent ___________ represents ___________ ___________ stands for ___________ ___________ corresponds to ___________ Another way to show ___________ is How else could we show this interpret We are trying to We will need to know We already know It looks like ___________ represents Another way to look at it is What does this part of ___________ mean Where does ___________ show Appendix III Access for Students with Disabilities INTRODUCTION All students are individuals who can know use and enjoy mathematics Zearn Math for Seventh Grade empowers students with activities that capitalize on their existing strengths and abilities to ensure that all learners can participate meaningfully in rigorous mathematical content The Zearn Math lessons support a flexible approach to instruction and provide teachers with options for additional support to address the needs of a diverse group of students Zearn Math for Seventh Grade includes in each lesson supplemental instructional strategies labeled Support for Students with Disabilities that are designed to increase access and eliminate barriers These lessonspecific 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 DESIGN PRINCIPLES These materials reflect three key design principles that support and engage all students in today s diverse mathematics classrooms The design principles and related supports work together to make each activity in each lesson accessible to all students 2022 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license ZEARN MATH Teacher Edition 57

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Appendix III Access for Students with Disabilities G6 Course Guide Principle 1 Access for All This foundational design principle draws from the Universal Design for Learning UDL framework and shapes the instructional goals recommended practices lesson plans and assessments to support a flexible approach to instruction ensuring all students have an equitable opportunity to learn Principle 2 Presume Competence All students are individuals who can learn apply and enjoy mathematics The activities in these materials position students to capitalize on their existing abilities and provide supports that eliminate potential barriers to learning when they arise Each lesson is designed for a wide range of abilities and all students are given access to grade level problems Student competence to engage with mathematical tasks should be assumed with additional supports provided only when needed Principle 3 Strengths based approach All students including students with disabilities are resourceful and resilient members of the mathematics community When the unique strengths and interests of students with disabilities are highlighted during class discussions their contributions enhance the learning of all students in the classroom AREAS OF COGNITIVE FUNCTIONING The lesson and activity level supports for students with disabilities are aligned to an area of cognitive functioning and are paired with a suggested strategy aimed to increase access and eliminate barriers All of the supports can be used discreetly and are designed to be used as needed Many of these supports can be implemented throughout the academic year for example peer tutors can help build classroom culture provide opportunities for teamwork and build collaboration skills while also supporting those who struggle Other supports should be faded out as students gain understanding and fluency with key ideas and procedures Additional supports for students with disabilities are designed to address students strengths and needs in the following areas of cognitive functioning which are integral to learning mathematics Brodesky et al 2002 Conceptual processing which includes perceptual reasoning problem solving and metacognition Expressive receptive language which includes auditory and visual language processing and expression Visual spatial processing which includes processing visual information and understanding relation in space e g visual mathematical representations and geometric concepts Executive functioning which includes organizational skills attention and focus Memory which includes working memory and short term memory Social emotional functioning which includes interpersonal skills and the cognitive comfort and safety required in order to take risks and make mistakes Fine motor skills which includes tasks that require small muscle movement and coordination such as manipulating objects graphing cutting writing 2022 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license 58 ZEARN MATH Teacher Edition

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G6 Course Guide References References Aguirre J M Bunch G C 2012 What s language got to do with it Identifying language demands in mathematics instruction for English language learners In S Celed n Pattichis N Ramirez Eds Beyond good teaching Advancing mathematics education for ELLs pp 183 194 Reston VA National Council of Teachers of Mathematics Asturias Mendez Luis Harold 2015 Feb Access for All Linked Learning and Language Three Reads and Problem Stem Strategies Presentation at the English Learner Leadership Conference Sonoma CA Brodesky A Parker C Murray E Katzman L 2002 Accessibility strategies toolkit for mathematics CAST n d About Universal Design for Learning Retrieved December 7 2021 from https www cast org impact universal design for learning udl Chapin S O Connor C Anderson N 2009 Classroom discussions Using math talk to help students learn grades K 6 second edition Sausalito CA Math Solutions Publications Common Core State Standards Initiative n d Standards for Mathematical Practice Retrieved December 7 2021 from http www corestandards org Math Practice Gibbons P 2002 Scaffolding language scaffolding learning Teaching second language learners in the mainstream classroom Portsmouth NH Heinemann Kelemanik G Lucenta A Creighton S J 2016 Routines for reasoning Fostering the mathematical practices in all students Portsmouth NH Heinemann Leong Y H Ho W K Cheng L P 2015 Concrete Pictorial Abstract Surveying its origins and charting its future https repository nie edu sg bitstream 10497 18889 1 TME 16 1 1 pdf Paunesku D Walton GM Romero C Smith EN Yeager DS Dweck CS Mind Set Interventions Are a Scalable Treatment for Academic Underachievement Psychological Science 2015 26 6 784 793 https doi org 10 1177 0956797615571017 Schmidt W H Wang H C McKnight C C 2005 Curriculum coherence An examination of US mathematics and science content standards from an international perspective J Curriculum Studies 37 5 525 559 https doi org 10 1080 0022027042000294682 Smith M S Stein M K 2011 5 practices for orchestrating productive mathematics discussions Reston VA National Council of Teachers of Mathematics Stacey K Burton L Mason J 1982 Thinking mathematically Addison Wesley Walton G M Cohen G L 2007 A question of belonging race social fit and achievement J Pers Soc Psychol 92 1 82 https doi org 10 1037 0022 3514 92 1 82 Zwiers J 2014 Building academic language Meeting Common Core Standards across disciplines grades 5 12 2nd ed San Francisco CA Jossey Bass Zwiers J Dieckmann J Rutherford Quach S Daro V Skarin R Weiss S Malamut J 2017 Principles for the Design of Mathematics Curricula Promoting Language and Content Development Retrieved from Stanford University UL SCALE website http ell stanford edu content mathematics resources additionalresources ZEARN MATH Teacher Edition 59

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