Zearn Math–Teacher Edition: Course Guide, G8 : simplebooklet.com

Table of Contents ABOUT ZEARN MATH Vision 6 Learning principles 6 ABOUT EIGHTH GRADE MATH Approach 7 Scope sequence 7 Pacing 8 A TYPICAL LESSON IN ZEARN MATH Warm Up 10 Concept Exploration 10 Wrap Up 11 IMPLEMENTING ZEARN MATH Planning for a Mission 12 Planning your week 13 Core Days 13 Flex Day 14 Planning for a lesson 15 Preparing students for Independent Digital Lessons 16 SUPPORTING DIVERSE LEARNERS Commitment to accessibility 18 Design features that support all learners 18 Supporting multilingual learners 19 Elements of language 19 Mathematical language routines MLRs 19 Supporting students with disabilities 21 Accessible design features 21 Assistive technology 21 Instructional accommodations 22 ASSESSMENTS AND REPORTS Ongoing formative assessments Daily lesson level assessments The Tower of Power digital and Exit Tickets paper 23 23

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Table of Contents Mission level assessments paper 24 Interim assessments 25 Class and student reports 25 Class reports Progress Pace and Tower Alerts 25 Student Reports 26 Approach to unfinished learning 26 TERMINOLOGY REQUIRED MATERIALS LESSONS BY STANDARDS 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 51

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About Zearn Math G8 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 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 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 6 ZEARN MATH Teacher Edition

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G8 Course Guide About Eighth Grade Math 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 Eighth 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 WEEK K 1 2 3 4 5 6 7 M1 Numbers to 10 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 M2 2D 3D Shapes M3 Comparison of Length Weight Capacity Numbers to 10 M5 M4 Numbers 10 20 Count to 100 by Ones and Tens Number Pairs Addition Subtraction to 10 M6 Analyzing Comparing Composing Shapes 2022 Zearn Licensed Numbers to you pursuant to Activities Zearn s Terms to 5 Digital 50 of Use Numbers to 10 Digital Activities 50 Numbers to 15 Digital Activities 35 Numbers to 20 Digital Activities 35 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 TeacherM1 Edition G1 Add Subtract Small Numbers M2 Meet Place Value M3 Measure Length M4 Add Subtract Big Numbers M5 Work with Shapes M6 Add Subtract to 100 7

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About Eighth Grade Math G8 Course Guide Students begin grade 8 with transformational geometry They study rigid transformations and congruence then dilations and similarity this provides background for understanding the slope of a line in the coordinate plane Next they build on their understanding of proportional relationships from grade 7 to study linear relationships They express linear relationships using equations tables and graphs and make connections across these representations They expand their ability to work with linear equations in one and two variables Building on their understanding of a solution to an equation in one or two variables they understand what is meant by a solution to a system of equations in two variables They learn that linear relationships are an example of a special kind of relationship called a function They apply their understanding of linear relationships and functions to contexts involving data with variability They extend the definition of exponents to include all integers and in the process codify the properties of exponents They learn about orders of magnitude and scientific notation in order to represent and compute with very large and very small quantities They encounter irrational numbers for the first time and informally extend the rational number system to the real number system motivated by their work with the Pythagorean Theorem In the Mission Overview 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 eighth 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 1 ommon Core State Standards Initiative n d Standards for Mathematical Practice Retrieved December 7 2021 from http www corestandards C org Math 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 8 ZEARN MATH Teacher Edition

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G8 Course Guide A Typical Lesson in Zearn Math 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 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 eighth grade curriculum should take about 36 weeks to complete This pace ensures students have sufficient time each week to work through gradelevel 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 Rigid Transformations and Congruence 17 5 2 Dilations Similarity and Introducing Slope 13 4 3 Linear Relationships 15 4 4 Linear Equations and Linear Systems 16 5 5 Functions and Volume 22 6 6 Associations in Data 13 3 7 Exponents and Scientific Notation 16 4 8 Pythagorean Theorem and Irrational Numbers 15 4 9 Putting It All Together 2 1 129 36 Totals 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 including Collaborative Concept Exploration with teacher and peers Independent Digital Lessons to explore concepts further on their own and Wrap Up including Lesson Synthesis led by the teacher and the completion of an individual Exit Ticket 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 9

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A Typical Lesson in Zearn Math G8 Course Guide Every lesson in Zearn Math for Eighth 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 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 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 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 10 ZEARN MATH Teacher Edition

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G8 Course Guide A Typical Lesson in Zearn Math 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 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 11

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Implementing Zearn Math G8 Course Guide 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 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 Eighth 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 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 12 ZEARN MATH Teacher Edition

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G8 Course Guide Implementing Zearn Math 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 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 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 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 13

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Implementing Zearn Math G8 Course Guide Wrap Up including lesson synthesis and an Exit Ticket takes about 5 minutes Flex Day In addition to 4 Core Days if you are using the Zearn Math recommended weekly schedule and omitting optional lessons you will have time for a Flex Day each week Consider how you might use this time to continue addressing individual student needs you may have noticed during your Core Day lessons or while reviewing Zearn class and student reports Check Zearn class and student reports to determine what student needs you might address during this time The Pace report indicates which students may need more time to complete Independent Digital Lessons The Tower Alerts report indicates which students are struggling with particular concepts Decide how you will address the needs of different students during Flex Day or Flex time Use the Pace Report to identify any students who have completed fewer than four Independent Digital Lessons that week Some students may need more time to finish these digital lessons If these students are making progress and simply need more time allow these students to spend time during Flex Days finishing their Independent Digital Lessons so they can meet their goals Use the Tower Alerts report to identify groups of students struggling with the same concepts or misconceptions You could teach these groups mini lessons using the Optional 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 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 14 ZEARN MATH Teacher Edition

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G8 Course Guide Implementing Zearn Math When it is time for a Mission level assessment plan to have students complete these assessments during Flex time For more see Assessments and Reports below PLANNING FOR A LESSON You can use your Zearn Math Teacher Edition daily to plan and implement each lesson of the Mission To prepare for teaching each lesson within a Mission we recommend that teachers Read through the lesson 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 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 15

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Implementing Zearn Math G8 Course Guide 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 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 eighth grade these are Fluency available in pilot form beginning in the 22 23 ASY 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 16 ZEARN MATH Teacher Edition

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G8 Course Guide Guided Practice Independent Practice Implementing Zearn Math Model completing paper Student Notes when prompted in the Guided Practice section Discuss strategies for persevering through challenges like working through a Boost within a Tower of Power referencing Student Notes revisiting the Guided Practice and even guessing if needed and letting the digital lesson provide help Remind students that some struggle is both expected and useful and that you will not be helping them to complete these lessons Instead they should try their best to resolve challenges on their own with the support of the software s built in scaffolds and you will frequently check Pace Report and Tower Alerts Report to identify any students who may be struggling unproductively Show students how to work on their Next Up activity Students work through Independent Digital Lessons at their own pace and are always assigned to one of these activities as their Next Up assignment Students can only access the next digital activity in the sequence once they complete their currently assigned activity Show students the accessibility features including Closed captioning Closed captioning for all interactive student videos is available for all Missions for all grades Closed captioning allows students to turn on an English text transcription of all dialogue and other relevant audio information in the Zearn Math video player This accessibility feature is particularly useful for deaf and hard of hearing students as well as multilingual learners Audio support All instructional prompts students see in Independent Digital Lessons have audio support through either recorded audio or Zearn Math s text to speech feature Students can click on the audio button next to text questions or prompts to hear the words spoken aloud All math expressions in Zearn Math software based lessons are read correctly with Zearn Math s text to speech tool Additional audio support if needed can be accessed using supported browser text to speech tools These accessibility features are particularly important for students with cognitive impairments students with learning differences young students and multilingual learners Zoomability Students may resize digital pages up to 200 through browser settings to view images or text closer up without losing any content This accessibility feature is particularly important for students with visual impairments and students using devices with small screens On screen keypad As students work through Independent Digital Lessons they have the option to use an on screen keypad rather than a computer keyboard to type and submit answers This accessibility feature is particularly important for tablet users and young students who may not know how to use a computer keyboard 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 3 https help zearn org 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 17

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Supporting Diverse Learners G8 Course Guide that will help students learn how to use Zearn Math and how to build the mindsets habits and confidence in math Supporting Diverse Learners COMMITMENT TO ACCESSIBILITY Zearn believes that with proper structures accommodations and support all children can learn mathematics As such we designed Zearn Math to be accessible for all students using the Universal Design for Learning UDL principles to maximize access and engagement for all students We have also added supports and structures throughout to help teachers accommodate the needs of diverse learners For more see above sections on Planning for a lesson as well as Preparing students for Independent Digital Lessons under Implementing Zearn Math DESIGN FEATURES THAT SUPPORT ALL LEARNERS To support a diverse range of learners including students with unfinished learning multilingual learners and students with disabilities Zearn Math design features include Consistent lesson structures The structure of every lesson is the same Warm Up Concept Exploration Wrap Up By keeping the components of each lesson similar from day to day the flow of work in class becomes predictable for students This reduces cognitive demand and enables students to focus on the mathematics at hand rather than the mechanics of the lesson Concepts developing over time from concrete to abstract Mathematical concepts are introduced simply concretely and repeatedly with complexity and abstraction developing over time Students begin with concrete examples and transition to diagrams and tables before relying on symbols to represent the mathematics they encounter Moreover this CPA approach is repeated throughout lessons Missions and across the grade to continually give students access to new ideas 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 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 18 ZEARN MATH Teacher Edition

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G8 Course Guide Supporting Diverse Learners 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 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 19

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Supporting Diverse Learners G8 Course Guide 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 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 20 ZEARN MATH Teacher Edition

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G8 Course Guide Supporting Diverse Learners 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 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 21

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Supporting Diverse Learners G8 Course Guide 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 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 22 ZEARN MATH Teacher Edition

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G8 Course Guide Assessments and Reports 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 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 23

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Assessments and Reports G8 Course Guide 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 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 24 ZEARN MATH Teacher Edition

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G8 Course Guide Assessments and Reports 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 on demand 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 below By checking the Pace Report teachers can identify groups of students who need more time to meet weekly learning goals with 4 5 The Zearn partnership page of the ANet website can be found at https www achievementnetwork org anet zearn partnership learn more To learn about the Zearn Class Reports and Student Reports you may access visit https help zearn org hc en us articles 4403432402071Teacher Reports 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 25

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Assessments and Reports G8 Course Guide 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 by anchoring to ideas they already know or intuitively make sense to them This approach emphasizes the big 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 26 ZEARN MATH Teacher Edition

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G8 Course Guide Assessments and Reports 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 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 27

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Terminology G8 Course Guide Terminology Alternate interior angles Alternate interior angles are created when two parallel lines are crossed by another line called a transversal Transversal Alternate interior angles are inside the parallel lines and on opposite sides of the transversal This diagram shows two pairs of alternate interior angles Angles a and d are one pair and angles b and c are another pair a c b d Center of a dilation The center of a dilation is a fixed point on a plane It is the starting point from which we measure distances in a dilation P In this diagram point P is the center of the dilation A B C Clockwise Clockwise means to turn in the same direction as the hands of a clock It is a turn to the right This diagram shows Figure A turned clockwise to make Figure B B A Congruent One figure is congruent to another if it can be moved with translations rotations and reflections to fit exactly over the other C A D B In the figure Triangle A is congruent to Triangles B C and D A translation takes Triangle A to Triangle B a rotation takes Triangle B to Triangle C and a reflection takes Triangle C to Triangle D Constant term In an expression like 5x 2 the number 2 is called the constant term because it doesn t change when x changes In the expression 7x 9 9 is the constant term In the expression 5x 8 8 is the constant term In the expression 12 4x 12 is the constant term 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 B E For example point B in the first triangle corresponds to point E in the second triangle Segment AC corresponds to segment DF 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 28 ZEARN MATH Teacher Edition

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G8 Course Guide Terminology Counterclockwise Counterclockwise means to turn opposite of the way the hands of a clock turn It is a turn to the left This diagram shows Figure A turned counterclockwise to make Figure B A B Cube root The cube root of a number n is the number whose cube is n It is also the edge length of a cube with a volume 3 __ of n We write the cube root of n as n 3 ___ 3 ___ For example the cube root of 64 written as 64 is 4 because 43 is 64 64 is also the edge length of a cube that has a volume of 64 Dependent variable A dependent variable represents the output of a function We need to buy 20 pieces of fruit and decide to buy apples and bananas If we select the number of apples first the equation b 20 a shows the number of bananas we can buy The number of bananas is the dependent variable because it depends on the number of apples Dilation A dilation is a transformation in which each point on a figure moves along a line and changes its distance from a fixed point The fixed point is the center of the dilation All of the original distances are multiplied by the same scale factor For example triangle DEF is a dilation of triangle ABC The fixed center point is O and the scale factor is 3 E F D B C A O This means that every point of triangle DEF is 3 times as far from O as every corresponding point of triangle ABC Function A function is a rule that assigns exactly one output to each possible input The function y 6x 4 assigns one value of the output y to each value of the input x For example when x 5 then y 6 5 4 or 34 se us Leg e Leg nu ote Hyp Here are some right triangles Each hypotenuse is labeled po ten Hypotenuse The hypotenuse is the side of a right triangle that is opposite the right angle It is the longest side of a right triangle Leg Hy Leg Leg Leg Hypotenuse Hypotenuse Leg Leg 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 29

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Terminology G8 Course Guide Image An image is the result of translations rotations and reflections on an object Every part of the original object moves in the same way to match up with a part of the image F E B In this diagram triangle ABC has been translated up and to the right to make triangle DEF Triangle DEF is the image of the original triangle ABC D C A Independent variable An independent variable is an amount that is used to calculate another amount An independent variable represents the input of a function We need to buy 20 pieces of fruit and decide to buy some apples and bananas If we select the number of apples first the equation b 20 a shows the number of bananas we can buy The number of apples is the independent variable because we can choose any number for it Irrational number An irrational number is a number that is not a fraction or the opposite of a fraction Pi and 2 are examples of irrational numbers e Leg se us Legs The legs of a right triangle are the sides that make the right angle nu ote Hyp Here are some right triangles Each leg is labeled po ten Leg Leg Hy Leg Leg Leg Hypotenuse Linear relationship A linear relationship between two quantities means they are related like this When one quantity changes by a certain amount the other quantity always changes by a set amount In a linear relationship one quantity has a constant rate of change with respect to the other The relationship is called linear because its graph is a line The graph shows a relationship between number of days and number of pages read y 160 140 Number of pages read The scatter plot shows that there is a negative association between the price of the book in dollars and the number of books sold at that price 100 80 60 20 1 2 3 4 Number of days 5 x 160 Number sold Negative association A negative association is a relationship between two quantities where one tends to decrease as the other increases In a scatter plot the data points tend to cluster around a line with negative slope Different stores across the country sell a book for different prices 120 40 When the number of days increases by 2 the number of pages read always increases by 60 The rate of change is constant 30 pages per day so the relationship is linear Leg Leg Hypotenuse 120 80 40 6 8 10 12 Price in dollars 14 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 30 ZEARN MATH Teacher Edition

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G8 Course Guide Here is a scatter plot that shows lengths and widths of 20 different left feet The foot whose length is 24 2 cm and width is 7 4 cm is an outlier Positive association A positive association is a relationship between two quantities where one tends to increase as the other increases In a scatter plot the data points tend to cluster around a line with positive slope The relationship between height and weight for 25 dogs is shown in the scatter plot There is a positive association between dog height and dog weight 12 11 Foot width cm Outlier An outlier is a data value that is far from the other values in the data set 10 9 8 7 20 22 24 26 Foot length cm 30 32 96 80 64 48 32 16 0 6 9 12 15 18 Pythagorean Theorem The Pythagorean Theorem describes the relationship between the side lengths of right triangles 27 30 b2 9 a2 16 160 140 Amount earned dollars In this graph y increases by 15 dollars when x increases by 1 hour The rate of change is 15 dollars per hour 24 c2 25 The square of the hypotenuse is equal to the sum of the squares of the legs This is written as a2 b2 c2 Rate of change The rate of change in a linear relationship is the amount y changes when x increases by 1 The rate of change in a linear relationship is also the slope of its graph 21 Dog height inches The diagram shows a right triangle with squares built on each side If we add the areas of the two small squares we get the area of the larger square 28 112 Dog weight pounds Terminology 120 100 80 60 40 20 1 2 3 4 5 6 Time hours 7 8 9 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 31

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Terminology G8 Course Guide Rational number A rational number is a fraction or the opposite of a fraction Some examples of rational numbers are 74 0 63 0 2 13 5 9 Reflection A reflection across a line moves every point on a figure to a point directly on the opposite side of the line The new point is the same distance from the line as it was in the original figure B This diagram shows a reflection of A over line that makes the mirror image B A Relative frequency The relative frequency of a category tells us the proportion at which the category occurs in the data set It is displayed as a fraction or a percentage of the total number There were 21 dogs in the park some white some brown some black and some multi color The table shows the frequency and the relative frequency of each color The relative frequency can also be expressed as a decimal or a percentage Color Frequency Relative frequency White 5 5 21 24 Brown 7 7 21 33 Black 3 3 21 14 Multi color 6 6 21 29 Rigid transformation A rigid transformation is a move that does not change any measurements of a figure Translations rotations and reflections are rigid transformations as is any sequence of these Rotation A rotation moves every point on a figure around a center by a given angle in a specific direction This diagram shows Triangle A rotated around center O by 55 degrees clockwise to get Triangle B B A 55 O 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 32 ZEARN MATH Teacher Edition

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G8 Course Guide Scatter plot A scatter plot is a graph that shows the values of two variables on a coordinate plane It allows us to investigate connections between the two variables 112 Dog weight pounds Terminology Each plotted point corresponds to one of 25 dogs The coordinates of each point tell us the height and weight of that dog 96 80 64 48 32 16 0 6 9 12 15 18 21 24 Dog height inches 27 30 Scientific notation Scientific notation is a way to write very large or very small numbers We write these numbers by multiplying a number between 1 and 10 by a power of 10 For example the number 425 000 000 in scientific notation is 4 25 108 The number 0 0000000000783 in scientific notation is 7 83 10 11 Segmented bar graph A segmented bar graph compares two categories within a data set The whole bar represents all the data within one category Then each bar is separated into parts segments that show the percentage of each part in the second category 100 Has cell phone 75 No cell phone 50 25 0 10 12 years old 13 15 years old 16 18 years old This segmented bar graph shows the percentage of people in different age groups that do and do not have a cell phone For example among people ages 10 to 12 about 40 have a cell phone and 60 do not have a cell phone Sequence of transformations A sequence of transformations is a set of translations rotations reflections and dilations on a figure The transformations are performed in a given order P Q A B This diagram shows a sequence of transformations to move Figure A to Figure C Similar Two figures are similar if one can fit exactly over the other after rigid transformations and dilations E F C In this figure triangle ABC is similar to triangle DEF If ABC is rotated around point B and then dilated with center point O then it will fit exactly over DEF This means that they are similar C R First A is translated to the right to make B Next B is reflected across line to make C B A D O 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 33

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Terminology Slope The slope of a line is a number we can calculate using any two points on the line To find the slope divide the vertical distance between the points by the horizontal distance The slope of this line is 2 divided by 3 or 32 G8 Course Guide y 4 3 Vertical distance 2 1 Horizontal distance 1 2 3 4 Solution to an equation with two variables A solution to an equation with two variables is a pair of values of the variables that make the equation true x For example one possible solution to the equation 4x 3y 24 is 6 0 Substituting 6 for x and 0 for y makes this equation true because 4 6 3 0 24 Square root The square root of a positive number n is the positive number whose square is n It is also the side length of a square whose area is n We write the square root of n as n For example the square root of 16 written as 16 is 4 because 42 is 16 16 is also the side length of a square that has an area of 16 Straight angle A straight angle is an angle that forms a straight line It measures 180 degrees System of equations A system of equations is a set of two or more equations Each equation contains two or more variables We want to find values for the variables that make all the equations true Straight angle These equations make up a system of equations x y 2 x y 12 The solution to this system is x 5 and y 7 because when these values are substituted for x and y each equation is true 5 7 2 and 5 7 12 Tessellation A tessellation is a repeating pattern of one or more shapes The sides of the shapes fit together perfectly and do not overlap The pattern goes on forever in all directions This diagram shows part of a tessellation Transformation A transformation is a translation rotation reflection or dilation or a combination of these Translation A translation moves every point in a figure a given distance in a given direction B This diagram shows a translation of Figure A to Figure B using the direction and distance given by the arrow A 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 34 ZEARN MATH Teacher Edition

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G8 Course Guide Terminology Transversal A transversal to two parallel lines is a line that cuts across them intersecting each one m This diagram shows a transversal line k intersecting parallel lines m and k Two way table A two way table provides a way to compare two categorical variables It shows one of the variables across the top and the other down one side Each entry in the table is the frequency or relative frequency of the category shown by the column and row headings A study investigates the connection between meditation and the state of mind of athletes before a track meet This two way table shows the results of the study Meditated Did not meditate Total Calm 45 8 53 Agitated 23 21 44 Total 68 29 97 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 A For example angles AEC and DEB are vertical angles If angle AEC measures 120 then angle DEB must also measure 120 D E Angles AED and BEC are another pair of vertical angles C B y 10 Vertical intercept The vertical intercept is the point where the graph of a line crosses the vertical axis 8 6 4 2 The vertical intercept of this line is 0 6 or just 6 10 8 6 4 2 2 2 4 6 8 10 x 4 6 8 10 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 35

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Required Materials G8 Course Guide Required Materials Blank paper Colored pencils Compasses Copies of templates Dried linguine pasta Four function calculators Geometry toolkits Tracing paper graph paper colored pencils scissors and an index card to use as a straightedge or to mark right angles Graduated cylinders Graph paper Isometric graph paper Long straightedge Measuring tapes Pre printed cards cut from copies of the templates Pre printed slips cut from copies of the templates Protractors Rulers Rulers marked with centimeters Rulers marked with inches Scissors Spherical objects Stopwatches Straightedges String Tape Tools for creating a visual display Toothpicks pencils straws or other objects 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 36 ZEARN MATH Teacher Edition

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Lessons by Standards G8 Course Guide Lessons by Standards Standard Lesson Standard Lesson 8 NS 1 8 8 14 8 8 15 8 EE 6 8 2 10 8 2 11 8 2 12 8 3 7 8 3 10 8 3 11 8 3 14 8 NS 2 8 8 1 8 8 4 8 8 5 8 8 12 8 8 13 8 EE 7 8 G 1 8 1 2 8 1 3 8 1 4 8 1 6 8 1 7 8 1 8 8 1 9 8 1 10 8 1 11 8 1 13 8 1 14 8 3 8 8 4 3 8 4 4 8 4 5 8 4 6 8 4 7 8 4 8 8 4 9 8 G 2 8 1 11 8 1 12 8 1 13 8 1 15 8 2 6 8 2 7 8 EE 8 8 3 13 8 3 14 8 4 9 8 4 10 8 4 11 8 4 12 8 4 13 8 4 14 8 4 15 8 4 16 8 G 3 8 1 5 8 1 6 8 2 4 8 2 5 8 2 12 8 SP 1 8 G 4 8 2 6 8 2 7 8 2 9 8 6 1 8 6 2 8 6 3 8 6 4 8 6 5 8 6 6 8 6 7 8 6 8 8 SP 2 8 6 4 8 6 5 8 6 6 8 6 8 8 G 5 8 1 14 8 1 15 8 1 16 8 2 8 8 2 13 8 9 2 8 SP 3 8 6 6 8 6 8 8 G 6 8 8 7 8 8 9 8 SP 4 8 6 9 8 6 10 8 G 7 8 8 6 8 8 7 8 8 8 8 8 10 8 F 1 8 G 8 8 8 11 8 5 1 8 5 2 8 5 3 8 5 4 8 5 5 8 5 17 8 9 1 8 F 2 8 5 7 8 5 8 8 G 9 8 5 13 8 5 14 8 5 15 8 5 16 8 5 17 8 5 18 8 5 19 8 5 20 8 5 21 8 5 22 8 F 3 8 5 4 8 5 7 8 5 8 8 5 18 8 F 4 8 5 8 8 5 9 8 5 10 8 5 11 8 F 5 8 5 5 8 5 6 8 5 10 8 EE 1 8 7 2 8 7 3 8 7 4 8 7 5 8 7 6 8 7 7 8 7 8 8 7 11 8 7 14 8 EE 2 8 8 2 8 8 3 8 8 4 8 8 5 8 8 10 8 8 12 8 8 13 8 EE 3 8 7 9 8 7 10 8 7 11 8 7 12 8 7 14 8 7 16 8 EE 4 8 7 10 8 7 11 8 7 12 8 7 13 8 7 14 8 7 15 8 7 16 8 EE 5 8 3 2 8 3 3 8 3 4 8 3 6 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 38 ZEARN MATH Teacher Edition

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G8 Course Guide Standards by Lesson Standards by Lesson Mission 1 Mission 2 Mission 3 Lesson Standard Lesson Standard Lesson Standard Lesson 1 8 G 11 Lesson 1 8 G 32 Lesson 1 8 EE 53 Lesson 2 8 G 1 Lesson 2 8 G 32 Lesson 2 8 EE 5 Lesson 3 8 G 1 Lesson 3 8 G 32 Lesson 3 8 EE 5 Lesson 4 8 G 1 Lesson 4 8 G 3 Lesson 4 8 EE 5 Lesson 5 8 G 3 Lesson 5 8 G 3 Lesson 5 8 EE 53 Lesson 6 8 G 1 and 8 G 3 Lesson 6 8 G 2 and 8 G 4 Lesson 6 8 EE 5 Lesson 7 8 G 1 a and 8 G 1 b Lesson 7 8 G 2 and 8 G 4 Lesson 7 8 EE 6 Lesson 8 8 G 1 a and 8 G 1 b Lesson 8 8 G 5 Lesson 8 8 EE 5 and 8 G 1 Lesson 9 8 G 4 Lesson 9 8 EE 64 Lesson 9 8 G 1 a 8 G 1 b and 8 G 1 c Lesson 10 8 EE 6 Lesson 10 8 EE 6 Lesson 10 8 G 1 a and 8 G 1 b Lesson 11 8 EE 6 and 8 G 3 Lesson 11 8 EE 6 Lesson 11 8 G 1 and 8 G 2 Lesson 12 8 EE 6 and 8 G 3 Lesson 12 8 EE 8 a5 Lesson 12 8 G 2 Lesson 13 8 G 5 Lesson 13 8 EE 8 a Lesson 13 8 G 1 a and 8 G 2 Lesson 14 8 EE 8 a Lesson 14 8 G 1 and 8 G 5 Lesson 15 8 G 2 and 8 G 5 Lesson 16 8 G 5 Lesson 17 8 G 1 Lesson 156 While not representative of the full scope of the standard this lesson is building towards full understanding of 8 G 1 While not representative of the full scope of the standard this lesson is building towards full understanding of 8 G 3 3 While not representative of the full scope of the standard this lesson is building towards full understanding of 8 EE 5 4 While not representative of the full scope of the standard this lesson is building towards full understanding of 8 EE 6 5 While not representative of the full scope of the standard this lesson is building towards full understanding of 8 EE 8 a 6 This lesson extends the learning from Lesson 14 to introduce students to linear inequalities in one and two variables preparing students for success in future math courses 1 2 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 39

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Lessons by Standards G8 Course Guide Mission 4 Mission 5 Mission 6 Lesson Standard Lesson Standard Lesson Standard Lesson 1 8 EE 77 Lesson 1 8 F 1 Lesson 1 8 SP 1 Lesson 2 8 EE 77 Lesson 2 8 F 1 Lesson 2 8 SP 1 Lesson 3 8 EE 7 Lesson 3 8 F 1 Lesson 3 8 SP 1 Lesson 4 8 EE 7 Lesson 4 8 F 1 and 8 F 3 Lesson 4 8 SP 1 and 8 SP 2 Lesson 5 8 EE 7 Lesson 5 8 F 1 and 8 F 5 Lesson 5 8 SP 1 and 8 SP 2 Lesson 6 8 EE 7 and 8 EE 7 b Lesson 6 8 F 5 Lesson 6 Lesson 7 8 EE 7 a Lesson 7 8 F 2 and 8 F 3 8 SP 1 8 SP 2 and 8 SP 3 Lesson 7 8 SP 1 Lesson 8 8 EE 7 a Lesson 8 8 F 2 8 F 3 and 8 F 4 Lesson 8 Lesson 9 8 EE 7 and 8 EE 8 Lesson 9 8 F 4 8 SP 1 8 SP 2 and 8 SP 3 Lesson 9 8 SP 4 Lesson 10 8 EE 8 Lesson 10 8 F 4 and 8 F 5 Lesson 10 8 SP 4 Lesson 11 8 EE 8 Lesson 11 8 F 4 Lesson 11 8 SP 1 and 8 SP 4 Lesson 12 8 EE 8 8 EE 8 a and 8 EE 8 b Lesson 12 8 G 6 Lesson 13 8 EE 8 and 8 EE 8 a Lesson 13 8 G 9 Lesson 14 8 G 9 Lesson 14 8 EE 8 Lesson 15 8 G 9 Lesson 15 8 EE 8 and 8 EE 8 b Lesson 16 8 G 9 Lesson 16 8 EE 8 Lesson 17 8 F 1 8 F 4 and 8 G 9 Lesson 18 8 F 3 and 8 G 9 Lesson 19 8 G 9 Lesson 20 8 G 9 Lesson 21 8 G 9 Lesson 22 8 F 2 and 8 G 9 8 Lesson 129 Lesson 139 While not representative of the full scope of the standard this lesson is building towards full understanding of 8 EE 7 While not representative of the full scope of the standard this lesson is building towards full understanding of 8 G 6 9 These lessons allow students to engage with compound probability connected to the thinking they built in the Mission around bivariate data preparing students for success in future math courses 7 8 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 40 ZEARN MATH Teacher Edition

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G8 Course Guide Lessons by Standards Mission 7 10 Mission 8 Mission 9 Lesson Standard Lesson Standard Lesson 1 8 EE 110 Lesson 1 8 NS 2 Lesson 2 8 EE 1 Lesson 2 8 EE 2 Lesson 3 8 EE 1 Lesson 3 8 EE 2 and 8 NS 2 Lesson 4 8 EE 1 Lesson 4 8 EE 2 and 8 NS 2 Lesson 5 8 EE 1 Lesson 5 8 EE 2 and 8 NS 2 Lesson 6 8 EE 1 Lesson 6 8 G 7 Lesson 7 8 EE 1 Lesson 7 8 G 6 and 8 G 7 Lesson 8 8 EE 1 Lesson 8 8 G 7 Lesson 9 8 EE 3 Lesson 9 8 G 6 Lesson 10 8 EE 3 and 8 EE 4 Lesson 10 Lesson 11 8 EE 1 8 EE 3 and 8 EE 4 8 EE 2 8 G 7 and 8 NS 2 Lesson 11 8 G 8 Lesson 12 8 EE 3 and 8 EE 4 Lesson 12 8 EE 2 and 8 NS 2 Lesson 13 8 EE 4 Lesson 13 8 EE 2 and 8 NS 2 Lesson 14 8 EE 1 8 EE 3 and 8 EE 4 Lesson 14 8 EE 2 and 8 NS 1 Lesson 15 8 EE 4 Lesson 15 8 NS 1 Lesson 16 8 EE 3 and 8 EE 4 Lesson Standard Lesson 1 8 F 1 8 F 5 8 SP 1 8 SP 2 and 8 SP 3 Lesson 2 8 G 5 While not representative of the full scope of the standard this lesson is building towards full understanding of 8 EE 1 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 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 Eighth 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 l anguage 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 sense making similar to the way teachers think aloud to demonstrate reading comprehension This routine supports metacognition and metalinguistic awareness and also supports constructive conversations How it happens STUDENTS PREPARE DISPLAYS OF THEIR WORK Students are given a problem that can be approached and solved using multiple strategies or a situation that can be modeled using multiple representations Students are assigned the job of preparing a visual display of how they made sense of the problem and why their solution makes sense Variation is encouraged and supported among the representations that different students use to show what makes sense COMPARE Students investigate each others work by taking a tour of the visual displays Tours can be self guided a travellers and tellers format or the teacher can act as docent by providing questions for students to ask of each other pointing out important mathematical features and facilitating comparisons Comparisons focus on the typical structures purposes and affordances of the different approaches or representations what worked well in this or that approach or what is especially clear in this or that representation During this discussion listen for and amplify any comments about what might make this or that approach or representation more complete or easy to understand CONNECT The discussion then turns to identifying correspondences between different representations Students are prompted to find correspondences in how specific mathematical relationships operations quantities or values appear in each approach or representation Guide students to refer to each other s thinking by asking them to make connections between specific features of expressions tables graphs diagrams words and other representations of the same mathematical situation During the discussion 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 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 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 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 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 will always will never 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 Both compare and contrast and and One thing that is the same is One thing that is different is How are and What do and because because because are alike because are different because different have in common 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 represent represents stands for corresponds to Another way to show 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 is Appendix III Access for Students with Disabilities INTRODUCTION All students are individuals who can know use and enjoy mathematics Zearn Math for Eighth 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 Eighth Grade includes in each lesson supplemental instructional strategies labeled Support for Students with Disabilities that are designed to increase access and eliminate barriers These lesson specific supports can be used as needed to help students succeed with a specific activity without reducing the mathematical demand of the task and can be faded out as students gain understanding and fluency 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 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 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 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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