Leadership Pathway: Focus in Grades 6–8 Name

Leadership Pathway: Focus in Grades 6–8 Name
Global Neutral a Global Warm Neutral d3d1c8 Global Accent On Dark ffbf00 Global Accent on Light ff9800 Global Accent Alt 97c410 ELA - Coral ff5147 Math 009f93 Leadership 7872bf Leadership Pathway: Focus in Grades 6–8 211 min. as designed: 112 min before lunch; 99 min after lunch, including a 15 min break Speaker Notes: Participants should sit at grade-level tables. Materials: Index cards - Consider having participants complete as a Do Now so facilitators can reference this information: Name School/District or Organization Role A goal for the week A poster for Shift 1 with the shift written at the top, and split in half for each category: key take-aways and implications for practice. Post-its ® on tables Chart paper Markers Day 1 Handout Packets 1 video in this session—Be sure to load the video prior to participants’ arrival by opening the link and letting it begin to run. This should have the video ready to view without buffering. 11 min. video: Summer 2017

We know from experience the hard work teachers face every day as they strive to help their students meet the challenges set by higher Standards. We are a team of current and former classroom teachers, curriculum writers, school leaders, and education experts who have worked in the public, private, and nonprofit sectors. We are dedicated to empowering teachers by providing free, high-quality, Standards-aligned resources for the classroom, the opportunity for immersive training through our Institutes, and the option of support through our website offerings. Speaker Notes: We are a team of former classroom teachers, curriculum writers, school leaders, and education experts who have worked in the private, public, and non-profit sectors. We are dedicated to teacher learning and teacher growth. We know that teaching is hard work and requires excellent training, high quality materials, and meaningful support for practitioners who are continuously striving to better serve their students. We provide educators with high-quality materials and hands-on professional development to help their students achieve the learning goals set by higher Standards. We empower educators to make strong instructional decisions through immersive training and access to free Standards-aligned resources to adapt for their classrooms, schools, and districts.

FOCUS IN GRADES 6–8 Introduction: Who I Am
Name 1 Name 2 *Facilitators edit slide and notes. Consider using bullets for role and organization or a collage of icons for schools or organizations you have been affiliated with. 2 min. (1 per facilitator) Speaker’s Notes: I am ______ from ______. Include an interesting personal story or background information. My experience has been… If time: Before Common Core / college and career-ready Standards, I was… I was skeptical about Common Core / college and career-ready Standards until ______ happened.

FOCUS IN GRADES 6–8 We Will…
Our overall approach is to blend the CONCEPTUAL with the PRACTICAL Four Strands Focus on the Standards & SHIFTS Go deep with the CONTENT (Do the math; Read and analyze the texts) Analyze instruction and curriculum for ALIGNMENT Understand and use CURRICULUM to best support all learners Practice Standards-based observations, including: How to best prepare before going into classrooms What to look for when in a classroom Questions to ask when following up with a teacher or leader Think about how what we are learning impacts what we will do at home 2 min. Speaker Notes: Our approach is to blend the conceptual with the practical. We work to understand the big ideas and how they look in practice. The three strands that run through all of our work are: Digging deep into math and ELA content by “doing” the math and ela tasks as students to build deeper understanding of the content as well as cognitive empathy Knowing what Standards-aligned instruction looks like – and what it doesn’t Supporting students with gaps in learning We will understand the principles that lie beneath curriculum, how to adapt curriculum, and how to interact with curriculum. This happens best when we understand the “load-bearing walls” of the curriculum – the big ideas that curriculum is based on. The Standards and shifts have been around for a long time, and some of us know them well. That’s awesome! We will go deeper in our study and see how the Standards and shifts look instructionally from the eye of a leader. To do this, we will be asking you to switch hats throughout each day – sometimes engaging purely as a learner of the content, and other times engaging as a leader, thinking about how you will lead others in this work in your role at home. There will also be opportunities to experience activities from the perspectives of both teachers and students.

FOCUS IN GRADES 6–8 The Week at a Glance
Day Ideas Monday 8:30 a.m.– 4:30 p.m. Focus and Coherence Tuesday 8:30 a.m.–4:30 p.m. Rigor Observing the Standards and Shifts Adaptations for Struggling Learners Wednesday The Foundation Text Complexity Thursday Building Knowledge and Vocabulary The Juicy Language of Text Friday 8:30 a.m.–2:30 p.m. Organizational Systems and Structures 1 min. Speaker Notes: Here is what this week will look like.

We Take Data Seriously 3-minute online Daily Survey. Facilitators will address feedback the following day. 2 min. Speaker’s Notes: At the end of each day, we will build in time for you to take 3 minutes to complete an online survey about your experience on that day. Links will be on our website. Facilitators will address feedback the following day. These data are important for us to make each day better for you at SI. At the end of the day on Thursday, we will build in time for you to take 10 minutes to complete Knowledge Survey Post-Test. These data help us see what knowledge you are walking away with after attending SI. We will the survey link shortly before the end of the day. You will be able to compare how you did on the pre-test compared to the post-test. Thursday – 10 minute online Knowledge Survey Post-Test. Answer key will be available.

Norms That Support Our Learning
FOCUS IN GRADES 6–8 Norms That Support Our Learning Take responsibility for yourself as a learner. Honor time frames (start, end, activity). Be an active and hands-on learner. Use technology to enhance learning. Strive for equity of voice. Contribute to a learning environment where it is “safe to not know.” 4 min. Speaker Notes: We have norms for learning together this week. At different points in the week, we may remind you of a norm if we think it has been slipping—or you can remind one another. You can read these for yourselves, but let me expand on a couple: Take responsibility of yourself as a learner: Keep an open mind (esp. about what you don't know or thought you knew); Stay in learning orientation vs. performance orientation—growth mindset; Be an active and hands-on learner: Be active during video observation by capturing evidence in writing Use technology to enhance learning Be present (monitor multitasking, technology, honoring time frames) Equity of voice Share ideas and ask questions. (We each come with unique and diverse perspectives, based on who we are and the roles and contexts we are in. If you have a thought or question, please voice it to maximize our learning.) One person at a time (also monitor airtime); Contribute to a learning environment where it is “safe to not know” Appreciate everyone's perspective and journey Be okay with discomfort and focus on growth Will these work? Are there any others we should add?

Share Your Learning Light bulb moments Why I teach/lead
FOCUS IN GRADES 6–8 Share Your Learning Light bulb moments Why I teach/lead <1 min Speaker Notes: Introduce Teacher2Teacher and ask participants to use the cards on tables and visit the kiosks in the common areas throughout the week to share their learning and thinking with the larger education community.

FOCUS IN GRADES 6–8 Community Builder
Introduce yourself to your table: Share your name, city, role and organization, and one goal for the week. Raise your hand if… You are a school leader You are a district leader You work for a nonprofit You support schools You coach and develop others You consider yourself a “math person” You consider yourself a “literacy person” 10 min. Speaker Notes: 7 min.—Getting to know your table and practicing norms. Give participants a few minutes to introduce themselves at tables using the prompt on the slide. 3 min.— Raise your hand if… As necessary, express that we understand some participants are in roles very close to instruction (as principals, assistant principals, and other school-based leadership roles), and others are in roles (with districts, state agencies, nonprofits or school partners) that can feel removed from the classroom. While some institute activities are designed specifically for those who lead instruction and develop teachers, all participants will have time and space to think about how the ideas and practices we focus on this week apply to your role and context. Transition: Let’s get started by looking at the objectives and agenda for our first session. Image Credit: 9

FOCUS IN GRADES 6–8 Objectives and Agenda
Participants will be able to identify the major work of the grade. Participants will be able to evaluate tasks for alignment to Standards. Participants will be able to observe and coach the focus shift in teacher practice. Agenda: Opening and Community Builder Equity Discussion Framing the Challenge Task Analysis Observing and Coaching for Focus 1 min. Speaker Notes: After a discussion about equity that builds off of this morning’s key note, we’ll look carefully at the shift of focus in math, with an emphasis on why it’s important and what it looks like in grades 6–8.

FOCUS IN GRADES 6–8 Equity Equity is engaging in practices that meet students where they are and advances their learning by giving them what they need. It’s about fairness, not sameness. Equity ensures that all children – regardless of circumstances – are receiving high-quality and Standards-aligned instruction with access to high-quality materials and resources. We want to ensure that Standards-aligned instruction is a pathway to the equitable practices needed to close the gaps caused by systemic and systematic racism, bias, and poverty. All week, we will explore our learning through an equity lens, and we will capture those moments visibly here in our room. 1 min. Speaker Notes

Equity – Envision It So You Can See It
FOCUS IN GRADES 6–8 Equity – Envision It So You Can See It For leaders, it is important to have a clear vision of what educationally equitable environments. Gorksi and Salwell provide 5 Principles to guide you. 4 min – jot down concrete examples of what an equitable education environment would look like, sound like, and feel like to students, families, and staff. 6 min – share in pairs at your tables, looking for commonalities and new ideas to expand your thinking 5 min – whole group sharing of ideas you heard that will help all of us Looks Like Sounds Like Feels Like 15 min. Speaker Notes: As we work through the literacy Standards and other exercises, we will do so with a lens of equity. This exercise is designed to help inform the way we think about equity and literacy, and to give space for leaders to engage in the very important visioning work that guides change and strategy. Explain to the participants that they will be involved in virtual observations and analysis of curriculum, lesson, tasks and instruction Ask them to use the Gorski-Salwell principles as well as their own ideas to think concretely about what equitable instruction looks like. How will they know equitable instruction when they see it? 4 min - Participants should work independently at first to think through their own understandings of equity and how it should “play out” in their buildings before they share with others. 6 min – Sharing in pairs - tell them no larger since we have just 6 min; also suggest they share with someone they don’t yet know well 5 min – Whole group capture. Add ideas to whatever physical representation of equity you have created to build over the course of the week, e.g. equity wall or equity ladder Note - re: the Gorski-Salwell Equity Literacy article that was part of their pre-work and is in the front of their handout packets. Note: Gorski-Salwell article focuses on students experiencing poverty and it is important to state that you know every student in their building is not experiencing poverty; however, the principles outlined by Gorski offer a place around which they, as leaders, can structure equitable thinking and equitable practice.

Classroom Video Observations
2 min. Speaker Notes: Throughout the week we will be using classroom observation videos to analyze Standards-aligned instruction. (As necessary based on the group) We can agree that classroom instruction is at the heart of our work, and a necessary and extremely useful platform for understanding what the shifts and Standards look like in practice. A few notes abut the videos we use, their purposes and their limitations. We find them on the internet. Many of them are teacher-submitted videos. They’re not perfect – no lesson is, no teacher is. Everyone of these teachers is well-intentioned and has taken the risk of sharing their teaching with the world – and we respect them for that. They’re not necessarily representative of a diverse teacher force, although we have made a serious effort to find videos with more diversity, there just are not too many out there We have had more success finding videos that show students with similar demographics to the students you teach. When faced with a choice, we have chosen videos that will support our learning goals for you, even if the people in them are not reflective of your school reality. We have examples and non-examples. They are not intended to vilify a teacher. Our intent is to give you practice analyzing instruction and to tune your eye to Standards-aligned practices. Some of the teachers are here at this institute as facilitators! They will all tell you how much they have learned since the videos were made.

Time for a Classroom Visit
FOCUS IN GRADES 6–8 Time for a Classroom Visit Think about how you normally prepare to observe a math lesson. What do you check in advance? What are the go-to tools you use? Watch the video. Treat the video as instruction in one of your classrooms. Capture the evidence that you observe in writing so you can provide low-inference feedback later. Consider feedback. What points of feedback would help this teacher grow in terms of instruction of mathematics? 1 min. Speaker notes: As an introduction for this session on Focus, you will watch a video. Principals and other school-based leaders should pretend the teacher is a teacher in your building (or for those who are not school-based, a teacher in a school or district you work with). Write down your evidence for feedback. (Please do not sit and watch as if it is a TV show!) “Low inference feedback” is feedback that is primarily a sharing of observable evidence, with a minimal sharing of inference, interpretation or judgment As you think about “feedback for growth,” consider both what you will praise and what you will help the teacher polish. If you do not give direct feedback to teachers in your current role, use this opportunity to either (1) plan a conversation with a school or district leader you work with after observing this teacher as if it were one of their classrooms, or (2) engaging in the activity as if you were a principal or coach to further develop observation skills and build cognitive empathy for this work.

Informal Classroom Observation
FOCUS IN GRADES 6–8 Informal Classroom Observation Watch 11 min. of 14 min. video Stop after student says “Oh, 4 times t plus 2” Speaker Notes: Be sure to embed the video on this slide or have the video loaded prior to participants’ arrival by opening the link and letting it begin to run. This should then have the video ready to view without buffering.

FOCUS IN GRADES 6–8 Turn & Talk With a partner, discuss what you observed, the evidence you captured, and the questions you have for Ms. Smith. 10 min. Speaker Notes: NOTE to FACILITATOR: Don't give everything away here; just see what participants come up with; they are meant to arrive to the big take-aways on 2nd viewing. 5 min.—Turn & Talk w/ partner 4 min.—Whole group share: 1 min.—ask for 1 piece of positive feedback with supporting evidence and 1 min.—1 piece of improvement supporting evidence (don’t ask for feedback for improvement since a coach should gather more information about the teacher’s thinking before providing feedback). 1 min.—If it doesn’t come up, ask: Did anyone check to see if this Standard is part of the major work of 6th grade? Standard: 6.EE.C.9 1 min.—TRANSITION: There is a lot of strong instruction going on in this classroom, and we will come back to this video again to discuss further. First, let’s learn a little about the Focus Shift so we can deepen our understanding before assessing Ms. Smith’s instruction any further. 1 min. – What evidence of equitable practices are evident?

Framing the Challenge FOCUS IN GRADES 6–8 NAEP Grade 12 – 2013 1 min.
Speaker Notes: Some of us mentioned a passion for student achievement—we want to see our students succeed. However, it’s no secret that U.S. students are struggling. In grade 12, only 26% of students are proficient in the National Assessment of Educational Progress mathematics as of 2013. This is our call to action. While these numbers raise a call to action, what questions do they present regarding equity and access? How do these number reinforce group stereotypes? What instructional questions do these numbers present?

FOCUS IN GRADES 6–8 National Mathematics Advisory Panel
“A focused, coherent progression of mathematics learning, with an emphasis on proficiency with key topics, should become the norm in elementary and middle school mathematics curricula. Any approach that continually revisits topics year after year without closure is to be avoided. By the term focused, the Panel means that curriculum must include (and engage with adequate depth) the most important topics underlying success in school algebra. Improvements like those suggested in this report promise immediate positive results with minimal additional cost.” 1 min. Speaker Notes: Do not read it, but point out the highlighted text. So how do we get more students ready for college and career? The National Mathematics Advisory Panel studied all the relevant research and came up with this recommendation: curricula must focus on the key elements of algebra. (page xvi)

FOCUS IN GRADES 6–8 Look at the Standards for Your Grade
What do you notice about the major content for your table’s grade level? How do the Standards at your grade level lead to student success in algebra later? 10 min. Speaker Notes: Hand out the SAP Focus document. Assign each table a grade level. As necessary based on the group, note that we are using the Common Core State Standards and codes, which are likely similar but possibly not an exact match to their state’s college and career-ready Standards. 7 min.—Ask participants to notice how the Standards lead to success in algebra. 3 min.—Then ask participants to share. Responses should emphasize Standards within the NS, RP, and EE domains. Broad issue of why algebra is … in the first place … success with algebra means students are far more likely to be successful in credit-bearing courses in college.

Before We Start: Orienting to the Organization of the Math Standards
FOCUS IN GRADES 6–8 Before We Start: Orienting to the Organization of the Math Standards 6.RP.A.1 6: grade level RP: domain: Domains are larger groups of related Standards. Standards from different domains may sometimes be closely related. Domains generally go across multiple grade levels. A: cluster: Clusters summarize groups of related Standards. Note that Standards from different clusters may sometimes be closely related because mathematics is a connected subject. 1: Standard number: Standards define what students should understand and be able to do. 2 min. Speaker Notes: Let’s start by talking about the way the math Standards are organized. We know some of you are familiar with this already. We will briefly look at the structure together to make sure everyone moves forward with this knowledge. NOTE to FACILITATOR: Emphasize importance of cluster as a frame to the Standard. Point out within-grade coherence.

Quick Review FOCUS IN GRADES 6–8 Domain Grade Level Cluster Standard
2 min. Speaker Notes: Quickly review the structure of the Standards.

Before We Start … Using the App in Math
FOCUS IN GRADES 6–8 Before We Start … Using the App in Math 3 min. (quicker if everyone has it; if not, have them do it as you proceed…) Speaker Notes: We will be referencing the Standards frequently. Let’s take a moment to make sure everyone has the Mastery Connect Common Core app. There are versions of the app for different states. However, for our work this week we will reference the CCSS as a universal set, so it’s best we are all looking at those Standards together. Confirm everyone has the app on their phone OR is using the CCSS website on their computer. Apple: Android: Windows: Amazon:

FOCUS IN GRADES 6–8 Before We Start … Using the App in Math 1 min. Speaker Notes: To find Standards: Choose “Standards.” Choose “Math-Traditional.” (Traditional refers to the high school course organization of “Algebra 1”, “Geometry”, and “Algebra 2”; this is prevalent in the United States) Choose a grade.

FOCUS IN GRADES 6–8 Before We Start … Using the App in Math Scroll down to preview Standards by cluster Within a Standard, swipe left or right to view other Standards 6.RP.A.2 What does RP stand for? What is the cluster title for this Standard? 2 min. Speaker Notes: Scroll to find a Standard within a domain & cluster. (Language is included after the code to give some indication of what the Standard is about.) Once a Standard is chosen: Swipe left and right to see the Standards before and after the one you chose. What does RP stand for? (The domain in large print at top: Ratios and Proportional Relationships) What is the cluster for this Standard? (“A.” The text is in bold italics: Understand ratio concepts and use ratio reasoning to solve problems.) NOTE: Call out that Standards in curriculum and other resources don't always include cluster letter but they are in this app. You can also type key words into the search bar. If you type them at the main menu before selecting a grade, you can search across all grades. If you use the search bar within a grade, your search will only produce Standards from that grade level. Search Bar: Type code or key words to search

Quick Task: Using the App
FOCUS IN GRADES 6–8 Quick Task: Using the App You are in a 7th grade classroom, and students are writing an expression for the sequence of operations in each of the following: Add 3 to x, subtract the result from 1, then double what you have. b. Add 3 to x, double what you have, then subtract 1 from the result. Navigate the app to find the Standard students are likely addressing. 4 min. Speaker Notes: Possible answers: 7.EE.A.1 Share these ideas for getting to the Standard: Possibility 1: Select grade 7. Select domain “Expressions and Equations.” Select the first Standard in the domain and swipe until you read the Standard about applying properties of operations to add, subtract, factor and expand liner expressions … Possibility 2: Type “expressions” in the search bar. Scroll until you see 7th grade Standards. Select the first Standard in the domain and swipe until you read the Standard about applying properties of operations to add, subtract, factor, and expand liner expressions … If time: Ask participants if they had any other ways of finding the Standard.

1 min. Speaker Notes: The first shift is indeed called focus and requires a deep focus on a smaller number of topics. Read or give participants time to read the slide. IMAGE CREDIT: Shift #1: “The Common Core calls for greater focus in mathematics. Rather than racing to cover many topics in a mile-wide, inch-deep curriculum, the Standards ask math teachers to significantly narrow and deepen the way time and energy are spent in the classroom.”

What’s in? What’s out? FOCUS IN GRADES 6–8 Grade
Which two of the following represent areas of major focus for the indicated grade? 6 Understand ratio concepts and use ratio reasoning to solve problems Identify and utilize rules of divisibility Apply and extend previous understandings of arithmetic to algebraic expressions 7 Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers Use properties of operations to generate equivalent expressions Generate the prime factorization of numbers to solve problems 8 Standard form of a linear equation Define, evaluate, and compare functions Understand and apply the Pythagorean Theorem 1 min. Speaker Notes: Without looking at the Standards, please work with an elbow partner to look at the row for your table’s grade level and determine what two topics in each row ARE a focus of instruction for that grade level and which one topic is NOT a focus of instruction. For those of you with limited experience with the math Standards, make a guess based on what you know!

What’s in? What’s out? FOCUS IN GRADES 6–8 Grade
Which two of the following represent areas of major focus for the indicated grade? 6 Understand ratio concepts and use ratio reasoning to solve problems Identify and utilize rules of divisibility Apply and extend previous understandings of arithmetic to algebraic expressions 7 Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers Use properties of operations to generate equivalent expressions Generate the prime factorization of numbers to solve problems 8 Standard form of a linear equation Define, evaluate, and compare functions Understand and apply the Pythagorean Theorem 2 min Speaker Notes: Share: 6: Rules of divisibility are not specifically named in the Standards; they may come up in instruction related to other content but they are not specific outcomes 7: Prime factorization is not specifically named in the Standards; it may come up in instruction related to other content, but is not a specific outcome 8: Linear equations are a focus of grade 8, however, Standard form is not specifically named as an outcome Algebra 1: Quadratic functions are studied in algebra 1, but not quadratic inequalities Transition: So we see that whole topics are out or moved to other grades and sub-topics that traditionally have been a focus of instruction are not explicitly named. Within the topics that are included, there are assigned levels of priority.

FOCUS IN GRADES 6–8 Content Emphases Guidance from SAP organizes content in terms of major, supporting, and additional content: Major clusters are the highest priority. Supporting clusters are designed to support and strengthen areas of major emphasis. Additional clusters may not connect tightly or explicitly to the major work. 4 min.—handout: SAP Focus Math Speaker Notes: Who is familiar with the AchieveTheCore.org website? The resources available there are created by Student Achievement Partners (SAP), a nonprofit founded by lead writers of the Common Core that works to support implementation of college and career-ready Standards. Major content is the most essential for future work in mathematics. Major content indicates what the majority of time should be spent teaching this content. The materials should devote at least 65% and up to approximately 85% of the class time to the major work of the grade (with grades K–2 nearer the upper end of that range [i.e., 85%]). These are guiding principles of the PARCC and Smarter Balanced assessments. Note that CLUSTERS, not individual Standards, are organized into categories. Suggest importance of familiarity with the clusters for a grade level and the types of Standards that would be in each cluster. 1 min.—WHOLE GROUP Ask: I know this is a kindergarten example, but it is perfect for us to ensure you understand how to read these documents. What is the emphasis in kindergarten? Transition: Now you will do it for your grade at your table groups. POSSIBLE QUESTIONS FROM PARTICIPANTS: Are you saying that teachers can cut out the supporting and additional Standards? No, we are saying that that work should be done, and it should be done in connection with context/linking to major Standards. But this organization can be used to prioritize when making tough curricular decisions. From the PARCC Model Content Frameworks for Mathematics: “To say that some things have greater emphasis is not to say that anything in the Standards can safely be neglected in instruction. Neglecting material will leave gaps in student skill and understanding and may leave students unprepared for the challenges of a later grade. All Standards figure in a mathematical education and will therefore be eligible for inclusion on the PARCC Assessment. However, the assessments will strongly focus where the Standards strongly focus.” What if my curriculum tells me to...? Also, I think we need to somehow emphasize the challenge of non-aligned/aligned curriculum and the impact that can have on teacher focus.

FOCUS IN GRADES 6–8 Your Turn—5 minutes In table groups, look at your assigned grade level. Identify the major work of the grade. Be prepared to report your decisions. 8 min (1 min for directions; 7 min for work time) Speaker Notes: Each table will have 7 minutes to look at a grade level in the SAP Focus handout (Assign grades 6, 7 or 8 to each table) and prepare to confirm the major work of the grade. As you do, please also notice what is NOT there. NOTE: Make sure that session participants can go back and forth between this document and the common core app. Can suggest download full PDF with all grade levels and perhaps use iBook. 7 min – GROUP Work time…. Transition: Let’s confirm what you found Click through each slide for share of that group/grade level…

FOCUS IN GRADES 6–8 Focus in Grade 6 1 min. Speaker’s Notes:
Ask the tables who looked at 6th grade: What is the emphasis in 6th grade? Operations with fractions, ratios and proportions, and beginning work with expressions and equations As necessary based on your group, ask about terms that need to be defined and consider adding 1 or 2 of them to chart paper for reference as a glossary (e.g., the difference between an expression and an equation).

Ask the tables who looked at 7th grade: What is the emphasis in 7th grade? Expressions and equations, ratios and proportions, and rational number arithmetic As necessary based on your group, ask about terms that need to be defined and consider adding 1 or 2 of them to chart paper for reference as a glossary (e.g., rational vs. irrational numbers).

Ask the tables who looked at 8th grade: What is the emphasis in 8th grade? Expressions and equations, functions, and congruence/similarity As necessary based on your group, ask about terms that need to be defined and consider adding 1 or 2 of them to chart paper for reference as a glossary (e.g., function).

FOCUS IN GRADES 6–8 Summary What are the common threads in the Major Work content for grades 6–8? In a middle school, what content topics would you anticipate to observe teachers spending the most time on? How would you ensure EVERY student has the opportunity to engage in the major work of this grade band? 2 min. Speaker Notes: Whole Group Share Ratio and proportions, expressions and equations, functions Transition: To see what the major work looks like (and does not look like) at each grade level, let’s dive in and do some math. IMAGE CREDITS:

Task Analysis (Whole Group)
FOCUS IN GRADES 6–8 Task Analysis (Whole Group) 1 min. Speaker Notes: To see what the major work looks like (and does not look like) at each grade level, let’s dive in and do some math. One purpose for this section is to understand what it means for tasks to align to content Standards and to understand better what constitutes the major work at each grade level. A second purpose is to experience a questioning protocol for you to use to develop teachers and/or leaders as they deepen their understanding of the demands of the Standards. Illustrative Mathematics is an important resource we will use.

Protocol Do the Math Discussion Questions:
FOCUS IN GRADES 6–8 Protocol Do the Math Discussion Questions: To what grade and Standard is the task aligned? Is this part of the major work of that grade? What are the knowledge and skills required to be successful on this task? How does this task connect to the major work in the grades above and below? 1 min. Speaker Notes: Here is the protocol we’ll use. (go through slide). This protocol is an excellent way to drive planning and learning with teachers. Use these questions in planning sessions to help unpack what is required by the Standards, to help ensure Focus, to help understand across-grade Coherence. Use these questions to debrief a lesson that you observed. Remember framing around varying levels of comfort with doing math. Connect to growth mindset, points in Kate’s keynote. Principals will need to deal w/ math to supervise it from a content place. This training will require us to do some math, but more importantly, will give you some look-fors and some questions to ask when you’re completing instructional observations—even if you don’t have a math background. Likewise, leaders in roles across contexts benefit from having a stronger grasp of the content. Understanding the Standards and shifts themselves, and what they look like in practice, informs school and district support as well as decisions about curriculum, professional development, and policy.

Task #1 Do the Math Pairs Discuss
FOCUS IN GRADES 6–8 Task #1 Do the Math Molly runs 1/3 of a mile in 4 minutes. If Molly continues at the same speed, how long will it take her to run one mile? Draw and label a picture showing why your answer to part (a) makes sense. Pairs Discuss To what grade and Standard is the task aligned? Is this part of the major work of that grade? What are the knowledge and skills required to be successful on this task? How does this task connect to the major work in the grades above and below? 10 min. Speaker Notes: 1 min. Take a look at this example task and do the math individually 7 min. Partners discuss What grade and Standard is this aligned to? Is it part of the major work? What are the knowledge and skills required to be successful on this task? How does this connect to major work in the grades above and below? 2 min. Share out Look for or provide the following responses: The task requires students to solve a ratio problem. The task is aligned to 7.RP.1. (It would be a more challenging 6th grade problem because of the work with fractions.) This is part of the major work and connects to multiplication of fractions in grade 5, ratio work in grade 6, and functions in grade 8. Source:

Task #2 Do the Math Pairs Discuss
FOCUS IN GRADES 6–8 Task #2 Do the Math The number of siblings for a group of 6th grade students is shown below: 1, 0, 2, 1, 6, 0, 2, 0, 1, 10 Make a dot plot of the data. Find the mean and the median of the data. What does the mean tell you about the data? Which measure of average (mean or median) do you think best describes the data? Why? Pairs Discuss To what grade and Standard is the task aligned? Is this part of the major work of that grade? What are the knowledge and skills required to be successful on this task? How does this task connect to the major work in the grades above and below? 10 min. Speaker Notes: 2 min. Take a look at this example task and do the math individually 7 min. Partner then quick share out What grade and Standard is this aligned to? Is it part of the major work? What are the knowledge and skills required to be successful on this task? How does this connect to major work in the grades above and below? 2 min. Share out Look for or provide the following responses: The task requires students to make a dot plot and answer questions about the mean and median, including interpreting them The task signals 6.SP.A.2, 6.SP.B.4, and 6.SP.B.5.c. These are NOT part of the major work in grade 6. It is the beginning of statistical work that is continued in grade 7, where students compare populations using statistics. Which students get the opportunity to DO the MATH? How is DOING the MATH an equitable practice?*** How do teachers’ perceptions about students impact and influence which students get to DO the MATH?

Lunch 60 min. Speaker Notes:
Transition—After lunch, we will apply what we have learned to the classroom setting by going back and observing Ms. Smith’s lesson again—this time for Focus.

Observing and Coaching for Focus
1 min. Speaker Notes: Transition: We will now apply what we have learned to the classroom setting. We want to be proficient at identifying the grade-level Standards, determining whether the Standards being taught are the major work of the grade, and knowing the questions to ask that will deepen teachers’ understanding of the math. Let’s go back and observe Ms. Smith’s lesson again.

Observing for Focus Watch the video again. Standard: 6.EE.C.9 Prepare:
FOCUS IN GRADES 6–8 Observing for Focus Watch the video again. Standard: 6.EE.C.9 Prepare: Standards app Content emphasis Capture Evidence: What Standards are being taught? Is the instruction addressing the intended Standard? Is this part of the major work of that grade? Is there evidence of equitable practice? 6 min. Speaker Notes: 1 min. Directions—Let’s go back and watch the 6th grade video with this lens. Let’s start by preparing—get your Standards queued up for the Standard and pull up the content emphases for 6th grade. 5 min.—At tables, discuss the Standard being taught. We’ll start at 3:23 and cut some at the end, stopping at the 12:00 mark Video:

Observing for Focus FOCUS IN GRADES 6–8 9 min. video
Start at 3:23 and cut some at the end, stopping at the 12:00 mark Speaker Notes: Be sure to embed the video in this slide or load the video prior to participants’ arrival by opening the link and letting it begin to run. This should have the video ready to view without buffering. Video:

After the Observation To what grade and Standard is the task aligned?
FOCUS IN GRADES 6–8 After the Observation To what grade and Standard is the task aligned? Is this part of the major work of that grade? What are the knowledge and skills required to be successful on this task? How does this task connect to the major work in the grades above and below? Is there evidence of equitable practices? 15 min. Speaker Notes: 5 min.—First, you will deconstruct what you just saw in terms of Focus. Turn & Talk w/ partner. 10 min.—Whole group discussion of each question. (Standard language is on next slide for reference during discussion.) MAIN POINTS: QUESTIONS PARTICIPANTS MAY ASK: But the teacher's (pedagogy) was solid ... how can I expect more than this in my building? If what's being taught doesn't align to the depth of the Standards and focus where it's supposed to, it doesn't matter how well the lesson is taught. Students won't get where we need them to to be (short term, proficient this year; long term, college and career ready). But shouldn't we break down the Standard and teach and assess its individual parts? Breaking down Standards into discrete concepts, skills and vocab is a powerful tool for teachers when planning instruction and anticipating student errors or misconceptions—before instruction and when analyzing student work. But getting students to true mastery of the Standards requires they be able to do the entire Standard, not just a portion of it, or multiple portions of it in isolation of each other. If students aren't ready, teachers must figure out how to slow down and/or scaffold, but the Standard should be taught and assessed as a whole.

Observing for Focus Standard: 6.EE.C.9
FOCUS IN GRADES 6–8 Observing for Focus Standard: 6.EE.C.9 Represent and analyze quantitative relationships between dependent and independent variables. Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time.

FOCUS IN GRADES 6–8 After the Observation What questions would you now want to ask Ms. Smith? 2 min. Speaker Notes: Solicit 1-3 answers (don’t spend much time here). We have a couple to suggest that can help unpack her thinking and provide opportunities for her development.

Questions that Develop
FOCUS IN GRADES 6–8 Questions that Develop Leading the Conversation: To what grade and Standard is the task aligned? Is this part of the major work of that grade? What are the knowledge and skills required to be successful on this task? How does this task connect to the major work in the grades above and below? If not grade-level Standards: Why was instruction not addressing grade-level Standards? What data or other work supports the decision to teach non-grade- level Standards? If not major work of the grade: How will this chosen Standard authentically lead students back to working with math content that is emphasized in this grade? 4 min. Speaker notes: We’ve already spent a good deal of time deepening our own learning using the first set of questions (in gray). Use them first to get a strong understanding of the teacher’s understanding of the math and the Standards. This second set of questions will provide a window into the planning and decision-making that drove the teacher’s lesson. It also leads the discussion into the “what’s next” for these students. How are these questions the same or different than the way you usually debrief classroom observations? How would these questions help develop your teachers? For non school-based roles, how do the ideas raised in these questions connect to your work toward ensuring students are college and career-ready? Transition: Let’s practice coaching Ms. Smith on the Focus shift.

Coaching Role Play: Purpose and Process
FOCUS IN GRADES 6–8 Coaching Role Play: Purpose and Process The objective of this activity is to give leaders practice coaching a teacher on the Focus shift in the context of an authentic classroom situation. Get Ready (4 min.) Pair Up (2 min.) Role Play & Feedback #1 (11 min.) Role Play & Feedback #2 (11 min.) 2 min Speaker Notes: State the purpose of this role play: leaders have to practice talking about the changes they want to see. Leaders have to practice talking about content as well – especially if you don’t consider yourself a “math person.” Again, for those of you who do not regularly provide feedback directly to teachers, consider either (1) engaging in this process as a principal or teacher coach to build cognitive empathy, or (2) preparing a coaching conversation with a school or district partner based on having observed the classroom. For example, you may be a school partner co-observing with a principal who did not see the misalignment in the Standards or shifts in the classroom and needs support developing the teacher in this area. If choosing this option, it’s helpful but not necessary to partner with someone in a similar role. Provide an overview of the process: You will have 4 minutes to prepare to coach Ms. Smith. If it would be a better fit for your role, you may prepare to coach a principal with whom you have just observed this teacher. This will be quiet, preparation time. You will pair up, choose who goes first. First role play, coach shares goals for the coaching sessions and sets the “heat” level. 5 min role play 1 min to gather your reflections and evidence for feedback 5 min reflection and feedback This will be intentionally quick – most leaders do not have a ton of time to debrief a quick observation, so we are practicing doing this quickly and efficiently. I will manage time and signal when you move to a different part of the protocol.

Coaching Role Play 4 minutes—Everybody Gets Ready 2 minutes—Pair Up
FOCUS IN GRADES 6–8 Coaching Role Play The objective of this activity is to give leaders a chance to practice coaching a teacher about the Focus shift in the context of an authentic classroom situation. 4 minutes—Everybody Gets Ready Identify your goals for this coaching session. What do you want the teacher to know and be able to try as a result of this interaction? Draft entry question(s), clarifying questions and probing questions. Draft key learning and next steps you want the teacher to walk away ready to try. 2 minutes—Pair Up Choose a partner. Identify who will go first. Role Play #1 shares goals and the level of “heat” you’d like to practice coaching. 11 min. Speaker Notes: Click though each part as the time stated. <Click> and give them 4 min. to Get Ready <Click> and give them 2 min. to partner, choose who goes first. Next slide <Click> and give them 5 min. for the role play

Role Play #1: 5 Minutes FOCUS IN GRADES 6–8 5 min.
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Role Play #1: Reflect and Feedback
FOCUS IN GRADES 6–8 Role Play #1: Reflect and Feedback 1 minute—Each role writes reflections of effectiveness of coaching conversation from their point of view 2 minutes—Identify what worked. Coach first Start with stating your goal(s) for the discussion and 1–2 moves you made that supported that goal. Share 1–2 other pluses that you can identify Teacher 1–2 moves that the coach made that deepened your understanding of Focus. 2 minutes—Iidentify suggestions for improvement. 1–2 things you’d like to do differently or improve. 1–2 things the coach should consider to strengthen practice. 5 min.

Transition to Role Play #2
FOCUS IN GRADES 6–8 Transition to Role Play #2 Review preparation notes. Share coaching goals and the level of “heat” you’d like to practice coaching. 1 min. Speaker Notes: Time to switch roles. #2, share your goals and level of heat Be ready on my signal. IMAGE CREDITS:

Role Play #2: 5 Minutes FOCUS IN GRADES 6–8 5 min. IMAGE CREDITS:

Role Play #2: Reflect and Feedback
FOCUS IN GRADES 6–8 Role Play #2: Reflect and Feedback 1 minute—Each role writes reflections of effectiveness of coaching conversation from their point of view. 2 minutes—Identify what worked. Coach first Start with stating your goal(s) for the discussion and 1–2 moves you made that supported that goal. Share 1–2 other pluses that you can identify. Teacher 1–2 moves that the coach made that deepened your understanding of Focus. 2 minutes—Identify suggestions for improvement. 1–2 things you’d like to do differently or improve. 1–2 things the coach should consider to strengthen practice. 5 min.

FOCUS IN GRADES 6–8 Thumb Rating: Did we meet our objectives?
Participants will be able to identify the major work of the middle school grades. Participants will be able to evaluate tasks for alignment to Standards. Participants will be able to observe and coach the focus shift in teacher practice. <1 min. Speaker’s Notes: Before we wrap up this first Math session and take a break, let’s do a thumb rating for how well we individually feel the session’s objectives were met and then we will take a moment for individual processing time. Have participants give a thumb rating for how well each objective was met. If necessary, remind them that this is a helpful check in for them, feedback for you as facilitators, and information to relay to the session content developers.

FOCUS IN GRADES 6–8 Processing & Application
STOP AND JOT What important understanding do you want to take away from our discussion about Shift 1? What implications does the importance of focus have for your work? Consider: Professional development Planning Curriculum Equity Systems/Structures Policy & Programming 3 min Speaker Notes: In whatever format you are using to track your reflections and action steps, take a few minutes to individually reflect on key learning for this session and implications for practice in your role. How is focus currently going in your context and what next steps for improvement could you take. As an exit ticket, have participants respond to each question on separate Post-it ® notes. Have them place each note on a posted piece of chart paper for Shift 1, split in half for each category: key take-aways and implications for practice (in schools in general and/or their specific role). This is also a good place to remind participants to think about equitable practices and add comments/questions to the equity wall. If necessary based on how well the points were received over the course of the afternoon, ask, “How does a deep understanding of Shift 1 influence educators’ ability to create equitable classrooms?” Check the poster for participant take-aways and implications during the break and note any points that need to be further addressed. Sum up: This is really about having Standards front and center for teachers, observation and planning supports around lesson planning and delivery. And a culture of intentionality around the selection of or implementation of curriculum. Transition: We’ll take a break now. When we return, we’ll work with Shift 2, Coherence.

Take a break… 15 min. IMAGE CREDITS:

Leadership Pathway: Coherence in Grades 6–8 Summer 2017
Global Neutral a Global Warm Neutral d3d1c8 Global Accent On Dark ffbf00 Global Accent on Light ff9800 Global Accent Alt 97c410 ELA - Coral ff5147 Math 009f93 Leadership 7872bf Leadership Pathway: Coherence in Grades 6–8 113 min. as designed Materials: A poster for Shift 2 with the shift written at the top, and split in half for each category: key take-aways and implications for practice. Vertical Articulation Challenge slips Post-its ® on tables Chart paper Markers Day 1 Handout Packets 1 video—Be sure to load the video prior to participants’ arrival by opening the link and letting it begin to run. This should have the video ready to view without buffering. 11 min video: Summer 2017

Coherence Session COHERENCE IN GRADES 6–8 Objectives
Participants will be able to describe the coherence shift both as a logical sequencing of content across grades and as important connections between Standards, clusters, and domains within the grade. Participants will be able to identify prerequisite Standards for grade- level Standards. Participants will be able to observe and coach the coherence shift in teacher practice. Agenda Opening and Activator Coherence: What and Why? Across-Grade Coherence Within–Grade Coherence Observing for Coherence Role Teams Apply an Equity Lens to Coherence 1 min. Speaker Notes: We’ll start by looking carefully at the shift of coherence in math, with an emphasis on why it’s important and what it looks like in grades 6–8.

Coherence: What and Why?
COHERENCE IN GRADES 6–8 Coherence: What and Why? How would you teach students to graph the proportional relationship between the number of pounds of coffee and the total cost? Lena paid $18.96 for 3 pounds of coffee. 5 min. Speaker Notes: First, reflect on how you would explain this to an 8th grader who is just beginning to relate proportional reasoning to graphing. (1 min independent reflection) Share responses include: teaching unit rate, teaching slope, teaching how to construct an appropriately scaled graph (2 min). Ask which one would be appropriate to teach first. Explain: unit rate comes in 6th grade, must be a secure foundation before moving on; lines cannot be graphed before students know how to construct an appropriate scale (2 min) Let’s look at some Standards.

COHERENCE IN GRADES 6–8 What’s the Right Order? Use ratio and rate reasoning to solve real-world and mathematical problems … by making tables of equivalent ratios, finding missing values in tables, and plotting the pairs of values on the coordinate plane. Graph proportional relationships, interpreting the unit rate as the slope of the graph; compare different proportional relationships in different ways. Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate. Grade 6 Grade 8 5 min. Speaker Notes: Luckily, this logical progression is baked into the Standards. What is the correct order of these Standards? Give participants some time to try to order these, then display the answers. The Standards are organized to develop ideas gradually over time. Ask participants to try to order these Standards sequentially—work individually <Click> to share correct answer.: A = Grade 6 B = Grade 8 C = Grade 7 TAKE AWAY—The study of mathematics rests on the idea of developing ideas from existing ones. Similarly, this is how students learn; they learn mathematics based on what they already understand, developing ideas from existing ones. Emphasize logical progression. Grade 7

Coherence is Key “A focused, coherent progression of mathematics learning, with an emphasis on proficiency with key topics, should become the norm in elementary and middle school mathematics curricula. Any approach that continually revisits topics year after year without closure is to be avoided. By the term focused, the Panel means that curriculum must include (and engage with adequate depth) the most important topics underlying success in school algebra. By the term coherent, the Panel means that the curriculum is marked by effective, logical progressions from earlier, less sophisticated topics into later, more sophisticated ones. Improvements like those suggested in this report promise immediate positive results with minimal additional cost.” 1 min. Speaker Notes: Let them read it on their own first. Highlight the KEY POINT: The idea of logical progressions of learning is an important one. This is what mathematics is: developing new ideas from existing ones. In the Final Report of the National Mathematics Advisory Panel, this idea was highlighted. Anticipated Questions: How do we know this is important? Can connect to what lead writers of state Standards heard in testimony, noticed in college students: seeing math as branching out of isolated skills and procedures that get more complicated without seeing underlying principles and how all math is unified by them (McCallum video on coherence). IMAGE CREDITS:

Coherence ACROSS Grades
LEADERSHIP PATHWAY: COHERENCE IN HIGH SCHOOL Coherence ACROSS Grades Learning is carefully connected across grades so that students can build new understanding onto foundations built in previous years. Across-Grade Coherence Learning is carefully connected across grades so students can build new understanding onto foundations built in previous years. 1 min. Speaker Notes: One of our objectives for you today is to be able to describe BOTH aspects of coherence. Coherence will have a couple of meanings for us, but one important one is about the progression of content ACROSS grades. This connectedness is what helps us make sense of math. The previous approach to teaching math, mile wide, inch deep, led to instruction that was repetitive and disconnected across grades. With both FOCUS and COHERENCE, there is less review of the same topics and more building toward the next logical step. Each year, students are building on previous knowledge to develop a coherent sequence of understanding from K to 12. IMAGE CREDITS:

Vertical Coherence Challenge
COHERENCE IN GRADES 6–8 Vertical Coherence Challenge In your groups, you have 13 Standards on pieces of paper; most come from the Ratio and Proportions domain in grades 6–8. They are not labeled! Determine which Standards are prerequisites for other Standards. First 10 minutes—work without resources. Note: There is more than one vertical strand. Bonus: Can you determine which Standards belong in which grade? 25 min Speaker Notes: 2 min set-up So let’s see what this looks like. We just talked the fact there are fundamental truths in mathematics that connect across grade levels. Now you are going to have time to explore the how the Standards span across grades. Many of you have done a similar vertical mapping activity. NOT A TEST, idea is to engage in conversation about the connections between and within grades that is built into the Standards, NOT COMPETE. Read each card aloud and closely. We are going to “see” the vertical coherence of the Standards. Work in pairs (not as a table). Let participants know that there is more than one branch. Include some 4th or 5th grade Standards, and at least 1 HS Standard Tell them they should not use resources for the first 10 minutes, just what they know about skills progression. Focus on reading the words in the Standards and discuss the grades and the transitions and the way the verbs change. String together Standards coherently. 8 min – work without resources 15 min - Now we are going to let you use resources and to continue this challenge. They can use their Standards app or the SAP Focus document from the Focus session earlier. Vertical Coherence Challenge Answer Key (accompanies diagram on next slide) A. 8.EE.6 B. 5.NF.3 C. 8.F.2 D. 7.RP.1 E. F-BF.1 (High School, Algebra I) F. 6.RP.2 G. 5.G.2 H. 7.G.1 I. 8.EE.8 J. 4.MD.2 K. 7.RP.2 L. 6.RP.3a M/Q. 7.RP.3 Link to Standards doc participants will use:

COHERENCE IN GRADES 6–8 1 min. Speaker Notes:
Who has used SAP’s Coherence Map tool? How many of you are familiar with Jason Zimba’s Wiring Diagram? The diagram is awesome but complex, so our friends at Student Achievement Partners have created an interactive coherence map (based on the Writing Diagram) to help us determine Coherence (both across and within grades). In addition to coherence, this tool identifies whether the Standards are major, additional or supporting clusters, and It also includes sample tasks for many of the Standards. Transition: We’re going to show you how to use the tool now, and then you will check your Vertical Progressions Challenge accuracy using the tool.

Coherence Map Go to http://achievethecore.org/coherence-map/ Click on
COHERENCE IN GRADES 6–8 Coherence Map Go to Click on Choose a grade level to map out the Ratio and Proportions (RP) Domain. Use the map to check the accuracy of your Vertical Progression Challenge. Revise as needed. Note which Standards belong in which grade. 10 min. Speaker Notes: Do this with your partner. Go to Click on GET STARTED Choose a grade level to map out the Ratio and Proportions (RP) Domain. Use the map to check the accuracy of your Vertical Progression Challenge. Revise as needed. Note which Standards belong in which grade. Tutorial/Demo: Navigation Bar at top: Grade, Domain, Standard Domain/Standards page shows MAJOR, SUPPORTING, ADDITIONAL at top Click on MAP Standard to see connections Arrow (A->B) represents link such that if student hasn’t mastered A yet not likely to master B, but does not REQUIRE mastery in order or suggest as immediate next step. Dash (- - -) indicates related Standards within same grade level See sample Task & Solution, which is a powerful way to build content knowledge by seeing what the language of the Standard actually means. (Standards are meaningless until you know how they will be assessed – Paul Bambrick Santoyo, Driven by Data)

A Picture of Coherence E D C F B K J A H L I G M
COHERENCE IN GRADES 6–8 A Picture of Coherence Grades 4 and 5 Grade 6 Grade 7 Grade 8 High School E F-BF.1 D 7.RP.1 C 8.F.2 F 6.RP.2 B 5.NF.3 J 4.MD.2 K 7.RP.2 A 8.EE.6 H 7.G.1 L 6.RP.3a 5 min. Speaker’s Notes: Here is a picture of how these Standards are organized by grade, as well as some logical connections between them. What is something you noticed about the coherence across grades? Ideas to highlight: While this exercise was centered in the RP domain, it’s impossible to stay there without tapping into other domains. This is the richness of the Standards, and also the difficulty of teaching the Standards. Standards F, K, H, A, C, and E illustrate how proportional reasoning (in grades 6 and 7) opens the door to geometry, expressions/equations, and functions in grades 8 and 9. Standards G, L, and K show the progression of how work with coordinates develops in grade 5 and becomes a part of understanding ratios in grades 6 and 7. I 8.EE.8 G 5.G.2 M 7.RP.3

COHERENCE IN GRADES 6–8 Implications What are the implications of coherence for students who are working harder to grasp the mathematical concepts in your schools? How might the across-grade principle and/or the use of the Coherence Map create an equitable learning culture? In what ways could you apply the principle of across grade coherence, or use the Coherence Map, in your role? 2 min. Speaker Notes: Ask whole group. KEY TAKEAWAYS—Stress usefulness as resource for thinking through scaffolding for students struggling with grade level Standards—can trace connections backwards to previous grades. Also, talk about the importance of professional development/conversations with teachers across grade levels. This part is the leadership development: helping leaders think about how they create systems/routines that are rooted in growing and improving the implementation of the shifts. Speak to the importance of vertical mapping and teachers to engage in this work together across grade levels. IMAGE CREDITS:

Within-Grade Coherence
Coherence is also built into the Standards in how they reinforce a major topic in a grade by utilizing supporting, complementary topics. 1 min. Speaker Notes: You may have seen examples of this in the Coherence Map, and we want to focus on it a bit. Coherence has another meaning—coherence within the grade. Instead of a list of unrelated Standards, content is connected across domains. Let’s see what it looks like in a student task. IMAGE CREDITS:

Do the Math—Grade 7 7.EE.B.3 7.EE.B.4 7.RP.A.3 COHERENCE IN GRADES 6–8
9 min. Speaker Notes: 6 min. Take a look at the following task. (a) do the math and (b) explain which two domains are evident in the task. What Standards and/or clusters are evident in the task? 3 min. This problem can be solved with a ratio table or by finding a unit rate, or by using expressions and /or equations. This problem fosters proportional thinking and lends itself to a discussion of algebraic reasoning, especially if the numbers are substituted for “less clean” ones. The problem highlights using expressions and equations (7.EE.B.3 and 7.EE.B.4) as well as proportional reasoning (7.RP.A.3). KEY POINT—[Discussion of Standard/cluster alignment.] There can be more than one domain/cluster within a grade level for any give tasks. During our first session, we discussed major work of the grade. This is an example of how supporting work connects to the major work and helps build links. 7.EE.B.3 7.EE.B.4 7.RP.A.3

Coherence in the Standards
COHERENCE IN GRADES 6–8 Coherence in the Standards 8.SP.A.3 Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. For example, in a linear model for a biology experiment, interpret a slope of 1.5 cm per hour as meaning that an additional hour of sunlight each day is associated with an additional 1.5 cm in mature plant height. 2 min Speaker Notes: Within grade coherence is often written into the Standards themselves. Let’s look at this example: 8.SP.A.3 Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. For example, in a linear model for a biology experiment, interpret a slope of 1.5cm/hr as meaning that an additional hour of sunlight each day is associated with an additional 1.5 cm in mature plant height. In 8th grade SP is supporting work, while linearity is major work. The Statistics and Probability Standard is written in reference to the major work of linear algebra and functions. Supporting Standards are meant to be in service of the major work of the grade; they are intended to enhance and reinforce major work, not detract from it. Instead of statistics being “yet another thing to cover,” detracting from focus, this 8th grade Standard tells you how to link working with bivariate data to the major work of the grade, linear algebra and functions. 8.SP.A.3 connects to 8.EE.B – Understand the connections between proportional relationships, lines and linear equations. Many major and supporting Standards in a grade level have references to each other that illustrate how they can work together.

Observing for Coherence
1 min. Speaker Notes: Transition—We will now apply what we have learned to the classroom setting. We want to be proficient at identifying the grade-level Standards, determining whether the Standards being taught are the major work of the grade, and knowing the questions to ask that will deepen teachers’ understanding of math coherence.

Key Supervision Questions for Coherence
COHERENCE IN GRADES 6–8 Key Supervision Questions for Coherence Across-Grade Coherence Does the instruction carefully connect learning across grades so students can build new understanding onto foundations built in previous years? Within-Grade Coherence Is the instruction leveraging how the Standards within a grade were built to reinforce a major topic by utilizing supporting, complementary topics? 1 min. Speaker Notes: These are the key questions leaders and coaches ask when engaging classroom observations from a Coherence lens. These questions will help you collect the right evidence while in the classroom; they are terrific guiding questions around teacher development as well. If appropriate, offer: For those of you who do not regularly observe instruction, jot a note down about how the principles behind these questions are relevant to your work. How could you apply this check for alignment to Shift 2?

COHERENCE IN GRADES 6–8 Observing for Coherence Leader Tasks Across-Grade Coherence Within-Grade Coherence Preparation Determine domain of focus. Review Standards, progressions document. Use Standards app and Coherence Map tools. Look-for Are the students who get it making connections to previous learning? For students who are not getting it, is the teacher leading students to make connections to previous learning? Are the non-major work Standard(s) being taught supporting priority content? Post-observation Ask: What prerequisite knowledge is a student lacking to be able to make those connections? Consider: Share time studying the wiring diagram and linking Standards, with next steps digging into curriculum for additional lessons on knowledge gaps. If supporting Standards are not linking to major work of the grade: What do the Standards say? Same question as before: How can this chosen Standard authentically lead students back to working with math content to be emphasized in this grade? 4 min Speaker Notes: Here is a process for leaders to use when observing math instruction. Before you observe for Coherence, prepare by knowing what you are walking in to see. If you can, get the information ahead of time. If you cannot, figure out the the domain of focus and the intended Standard(s). Use your app! During your time in the classroom, keep looking for student learning, the teacher’s role in providing connections to prior learning, the teacher’s response to struggling learners, etc. Post-observation: If you haven’t done it before the observation, use the progressions documents and/or the Coherence Map to prepare for the discussion with the teacher. Even better if you use them during the discussion. Use these questions to discuss what you saw, develop the teacher’s knowledge and skill around coherence and math. Transition: Let’s practice with another classroom visit, this time a 7th grade classroom.

COHERENCE IN GRADES 6–8 Observing for Coherence 7th Grade, Ms. Doden Standard: 7.RP.A.2 Prepare Determine the domain of focus for the unit or module Look up the Standard Preview the corresponding progressions document or Coherence Map to find linked prerequisite Standards and any within grade connections. 5 min Speaker Notes: Let’s start by looking up the intended Standard. Then use the Coherence Map to check out the prerequisites for this Standard and any within grade connections. Share (Standards on next two slides for reference during discussion.) Note: If they map the Standard in the Coherence Map, they find that prerequisite Standards include: 6.RP.A.2 - Understand the concept of a unit rate a/b associated with a ratio a:b with b /= 0, and use rate language in the context of a ratio relationship. For example, “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar.” “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.” 6.RP.A.3 - Use ratio and rate reasoning to solve real-world and mathematical problems (e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations). 7.RP.A.1 - Compute unit rates associated with ratios of including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction 1/2/1/4 miles per hour, equivalently 2 miles per hour. Note: this last Standard is a related Standard, and if students cannot meet 7.RP.A.1 they are unlikely to meet 7.RP.A.2 (from SAP Coherence Map).

COHERENCE IN GRADES 6–8 Observing for Coherence 7.RP.A.2 Analyze proportional relationships and use them to solve real-world and mathematical problems. Recognize and represent proportional relationships between quantities. 7.RP.A.2.A - Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin. 7.RP.A.2.B - Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. 7.RP.A.2.C - Represent proportional relationships by equations. For example, if total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn. 7.RP.A.2.D - Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate.

COHERENCE IN GRADES 6–8 Observing for Coherence Linked Prerequisite Standards: 6.RP.A.2 - Understand the concept of a unit rate a/b associated with a ratio a:b with b /= 0, and use rate language in the context of a ratio relationship. For example, “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar.” “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.” 6.RP.A.3 - Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. 7.RP.A.1 - Compute unit rates associated with ratios of including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction 1/2/1/4 miles per hour, equivalently 2 miles per hour.

COHERENCE IN GRADES 6–8 Observing for Coherence Standard: 7.RP.A.2 Prepare Determine the domain of focus for the unit or module Look up the Standard Preview linked Standards using the corresponding progressions document or Coherence Map Capture Evidence Are the students who “get it” making connections to previous learning? For students who are “not getting it”, how is the teacher supporting them to make connections to previous learning? Are the non-major work Standard(s) being taught supporting priority content? <1 min Speaker Notes: As we watch this lesson, capture evidence for questions we discussed: Are the students who get it making connections to previous learning? For students who are not getting it, is the teacher leading students to make connections to previous learning? Are the non-major work Standard(s) being taught supporting priority content? Pay close attention to the students who “get it” and those who may “not get it”? Pay close attention to the teacher’s response to both sets of students.

COHERENCE IN GRADES 6–8 Observing for Coherence 11 min video Speaker Notes: Be sure to embed the video in this slide or load the video prior to participants’ arrival by opening the link and letting it begin to run. This should have the video ready to view without buffering. Video:

After the Observation Is this part of the major work of that grade?
COHERENCE IN GRADES 6–8 After the Observation Is this part of the major work of that grade? Are the students who get it making connections to previous learning? For students who are not getting it, is the teacher leading students to make connections to previous learning? Are the non-major work Standard(s) being taught supporting priority content? 10 min Speaker Notes: 5 min—First, you will deconstruct what you just saw in terms of COHERENCE. Turn & Talk w/ partner 5 min—Whole group share: MAIN POINT: This is major work. Setting up the ratio of brown color cars to green cars … what’s the ratio? This part of the lesson has the students back in 6.RP.A.3 as they “Use ratio and rate reasoning to solve real-world and mathematical problems (e.g., by reasoning about tables of equivalent ratios)”

COHERENCE IN GRADES 6–8 After the Observation What questions would you now want to ask Ms. Doden? 2 min Speaker Notes: Solicit 1-3 answers (don’t spend much time here). We have a couple of ideas to suggest that can help unpack her thinking and provide opportunities for her development.

Questions that Develop
COHERENCE IN GRADES 6–8 Questions that Develop Leading the Conversation Are the students who “get it” making connections to previous learning? For students who are “not getting it”, how is the teacher supporting students to make connections to previous learning? Are the non-major work Standard(s) being taught supporting priority content? If students are still not making connections: Ask: What prerequisite knowledge might the student still need to make those connections? Consider: Share time studying the coherence map and linking Standards, with next steps being digging into curriculum for additional lessons on knowledge gaps. If supporting Standards are not linking to major work of the grade: What do the Standards say? Same question as before: How can this chosen Standard authentically lead students back to working with math content that is to emphasized in this grade? 2 min Speaker Notes: As we did with the video observation for Focus, we’d like to offer these additional post-observation questions that can help develop a teacher’s knowledge and skill around Coherence. We’ve already spent time with this first set of questions in gray. This second set of questions will provide a window into the teacher’s knowledge and skill with what students need to learn about the mathematics and to demonstrate this Standard. It also leads the discussion into the “what’s next” for these students. How are these questions the same or different than the way you usually debrief classroom observations? How would these questions help develop your teachers? For non school-based roles, how do the ideas raised in these questions connect to your work toward ensuring students are college and career-ready? Transition: We will not do a coaching role play for this lesson but will have the opportunity to practice coaching conversations when we reconvene tomorrow. Let’s take some time to reflect on the session’s learning.

Reflection: Coherence
COHERENCE IN GRADES 6–8 Reflection: Coherence What is the state of Coherence in curriculum, planning, and professional development in your school or context? Curriculum Does your curriculum identify the prerequisite skills needed for a unit or lesson? Is across-grade Coherence evident, helping students deepen understanding by making links between domains and clusters? Planning Is Coherence a regular consideration in teacher and team lesson planning? How and when are prerequisite skills addressed when students are below grade level? Professional Development What professional development has occurred for teachers? Do they know Coherence well enough to effectively include it in planning and instruction? 4 min Speaker Notes: In whatever format you are using to track your reflections and action steps, take a few minutes to individually, reflect on how COHERENCE is currently going in our context and what next steps for improvement you could take. These questions can serve as a guide for your thinking. Silent write; no share. Transition: Now we will have the opportunity to share and re-shape our planning with people in similar roles. Anticipated Questions: A leader or two might suggest that the district has aligned the curriculum to the Standards. And it has a scope and sequence in place. Might want to highlight the work that the teachers are doing around aligning teaching to curriculum. Emphasize Engage as an aligned curriculum that takes some of this pressure off teachers to ensure that the curriculum is both focused and coherent. Allow teachers and leaders to focus on implementation during instruction. Charter vs. district—less control over curriculum. How is coherence relevant to me? If you're stuck with something it's still your responsibility. Work with what you have but ensure shifts and Standards are being taught. Moral obligation to speak to decision-makers about curriculum and show why not aligned?

COHERENCE IN GRADES 6–8 Role Team Time
Meet your role team! 1. Download your key learning with one another and share how it is relevant to your role. 2. Share how coherence is going in your context and one step for improvement you are planning to take. 10 min. Speaker’s Notes: If necessary and appropriate for the group, allow time for processing in role teams. Have participants get into groups by similar role: principals, assistant principals, coaches, district leaders, state leaders, supporting partner organizations, etc. Encourage them to bring their notes, take a few seconds for introductions, and then quickly get to discussing the prompts on the slide. They should each take responsibility for tracking what they discuss. Facilitator: If necessary for time consider allotting fewer minutes. IMAGE CREDITS

COHERENCE IN GRADES 6–8 Thumb Rating: Did we meet our objectives?
Participants will be able to describe the coherence shift both as a logical sequencing of content across grades and as important connections between Standards, clusters, and domains within the grade. Participants will be able to identify prerequisite Standards for grade-level Standards. Participants will be able to observe and coach the coherence shift in teacher practice. <1 min. Speaker’s Notes: Before we wrap up this first Math session and take a break, let’s do a thumb rating for how well we individually feel the session’s objectives were met and then we will take a moment for individual processing time. Have participants give a thumb rating for how well each objective was met. If necessary, remind them that this is a helpful check in for them, feedback for you as facilitators, and information to relay to the session content developers.

COHERENCE IN GRADES 6–8 Processing & Application
STOP AND JOT What important understanding do you want to take away from our discussion about Shift 2? What implications does the importance of coherence have for your work? Consider: Professional development Planning Curriculum Equity Systems/Structures Policy & Programming 3 min Speaker Notes: As an exit ticket, have participants respond to each question on separate Post-it ® notes. Have them place each note on a posted piece of chart paper for Shift 2, split in half for each category: key take-aways and implications for practice (in schools in general and/or their specific role). This is also a good place to remind participants to think about equitable practices and add comments/questions to the equity wall. If necessary based on how well the points were received over the course of the afternoon, ask, “How does a deep understanding of Shift 3 influence educators’ ability to create equitable classrooms?” Check the poster for participant take-aways and implications during the break and note any points that need to be further addressed. Transition: Before leaving for the day, we have two final items: an expression of gratitude and the daily feedback survey.

1 min Speaker Notes: Before we adjourn for the day, let’s take one moment to appreciate the teachers we have observed today. All week, we will watch video of teachers who took risks and submitted their instructional videos to various open education resource sites. We are able to learn because of them and from them. IMAGE CREDITS:

References FOCUS AND COHERENCE IN GRADES 6–8 Slide Source 5 min
18, 61 (page xvi) 65, 66 29–33, 69 74, 77–80 15, 16; 41–43, 45 17 29–33 22–25 Apple: Android: Windows: Amazon: 37 5 min Speaker Notes: 1 min set-up; 4 min silent write Restate session objectives: this session was designed for you to be able to describe the coherence shift both as a logical sequencing of content across grades and as important connections between Standards, clusters, and domains within the grade. We also want you to be able to observe and coach the coherence shift in teacher practice. In whatever format you are using to track your reflections and action steps, take a few minutes to individually, or in district/school teams, reflect on how COHERENCE is currently going in our context and what next steps for improvement you could take. Anticipated Questions A leader or two might suggest that the district has aligned the curriculum to the Standards. And it has a scope and sequence in place. Might want to highlight the work that the teachers are doing around aligning teaching to curriculum. Emphasize Engage as an aligned curriculum that takes some of this pressure off teachers to ensure that the curriculum is both focused and coherent. Allow teachers and leaders to focus on implementation during instruction. Charter vs district - less control over curriculum. How is coherence relevant to me? If you're stuck with something it's still your responsibility. Work with what you have but ensure shifts and Standards are being taught. Moral obligation to speak to decision-makers about curriculum and show why not aligned?

Image Credits FOCUS AND COHERENCE IN GRADES 6–8
Slide 9: Slides 26, 34: Slides 49, 51, 52: Slide 56: Slide 61: Slides 62, 67: Slide 68: Slide 86: Slide 86:

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Leadership Pathway: Focus in Grades 6–8 Name

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