Adapting Curriculum Maps & Intro to Module 1 Algebra I June 2017 Speaker’s Notes: This is the beginning of the fourth course of the week here at the Standards Institute. Materials for Days 4 and 5: EngageNY Curriculum maps Module 1 Wiring Diagram (2 per table printed) or Coherence Map (online) IPG (printed) Content Emphases (printed)

ADAPTING CURRICULUM MAPS (ALGEBRA I) Welcome Back! 1 min Speaker’s Notes: Thank you for your time and attention yesterday! We are excited to dig into the EngageNY curriculum modules today.

ADAPTING CURRICULUM MAPS (ALGEBRA I) Introduction: Who I Am Name 1 Name 2 Insert photo Insert photo 3 min Speaker’s Notes: *Facilitators edit slide and notes for this slide. I am ______ from ______. Include an interesting personal story. My experience has been… Before Common Core, I was… I was skeptical about Common Core until ______ happened.

ADAPTING CURRICULUM MAPS (ALGEBRA I) Introduction: Who You Are Raise your hand if… you are a math teacher you are a math teacher coach you hold a different role you teach in a district school you teach in a charter school you teach or work in a different type of school or organization 2 min Speaker’s Notes: Let’s see who is in the room today.

ADAPTING CURRICULUM MAPS (ALGEBRA I) Thank You for Your Feedback! + ∆ 2 min Speaker’s Notes: Thank you for your feedback! I want to talk through some trends for the glows and grows and let you know what I’m doing for the grows within my control.

ADAPTING CURRICULUM MAPS (ALGEBRA I) Norms That Support Our Learning Take responsibility for yourself as a learner Honor timeframes (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 in which it is “safe to not know” 2 min Speaker’s Notes: Here’s a reminder of our norms.

ADAPTING CURRICULUM MAPS (ALGEBRA I) This Week Day Ideas Monday Focus and Within Grade Coherence Tuesday Rigor and the Mathematical Practices Wednesday Across Grade Coherence and Instructional Practice Thursday Adaptation and Curriculum Study Friday Adaptation and Practice “Do the math” Connect to our practice 2 min Speaker's Notes: Here is what this week will look like. Our approach is to blend the conceptual with the practical: We work to understand the big ideas of the Shifts, how they look in practice, and how we can use them to meet the needs of our students. We will apply our understanding of the shifts most rigorously on Days 4 and 5 as we dive into curriculum. The two strands that run through all of our work are: digging deep into math content by “doing” the math connecting all of the ideas and principles we look at to our work back in our districts 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.

ADAPTING CURRICULUM MAPS (ALGEBRA I) Sessions Today and Tomorrow Morning: Adapting the Algebra I Curriculum Map Afternoon: Intro to Module 1 Module Assessments Introductions to Functions Studied This Year—Graphing Stories (Topic A) Tomorrow Morning: Adapting and Teaching Lessons The Structure of Expressions (Topic B) Solving Equations and Inequalities (Topic C) 2 min Speaker’s Notes: Today we are going to look at the Curriculum Map for Algebra I, see how it is well aligned to the standards and shifts and also understand how we should think about adapting it for students that are below grade level. This afternoon we’ll look at the assessment for Module 1 along with the lessons for Topic A. Tomorrow we’ll look at Topics B and C. Materials for Day 4: EngageNY Curriculum maps Module 1 Wiring Diagram (2 per table printed) or Coherence Map (online) Content Emphases (printed)

Participants will be able to ADAPTING CURRICULUM MAPS (ALGEBRA I) Morning: Adapting the Algebra I Curriculum Map Participants will be able to analyze a curriculum map through the lens of the standards and shifts. describe ways of adapting a curriculum map for students below grade level. 2 min Speaker’s Notes: Our approach will involve doing a lot the math in the lessons and working collaboratively to understand as much about the modules as possible. We’ll see how the modules connect back to the big ideas of the instructional shifts; we’ll also think about how the curriculum map can be adapted for students below grade level.

ADAPTING CURRICULUM MAPS (ALGEBRA I) Morning Agenda Curriculum Map Scavenger Hunt Adapting a Curriculum Map 1 min Speaker’s Notes: We’ll start by doing a “scavenger hunt” to get acquainted with the EngageNY curriculum map for Algebra I. Finally I’ll share a way of thinking about adaptations for students below grade level and we’ll take a moment to try doing this for some modules in Algebra I.

ADAPTING CURRICULUM MAPS (ALGEBRA I) I. Curriculum Map Scavenger Hunt! You’ll look at The curriculum map for the year Titles of each module The standards associated with each module (If time) Lessons and assessment items in Module 1 2 min Speaker’s Notes: Let’s see what we can find in the EngageNY curriculum! For this activity you’ll be looking at “A Story of Functions” - the curriculum map for HS ENY curriculum AND the lessons and modules from Algebra I. The first half of questions are tied to the scope and sequence. The second half move beyond.

ADAPTING CURRICULUM MAPS (ALGEBRA I) Scavenger Hunt! 1. Scope and Sequence (Module Titles and Overview Pages): How many modules focus on major work? How many days of instruction is this? What percent of the instructional year is this? 2. Name all modules that include major and supporting content together. 3. Name all modules that emphasize additional content. 20 min Speaker's Notes: …Go! When done, share answers. Answers as are follows: Scope and Sequence Responses: All modules focus on Major Work. Days: approximately 120 days out of 150 Percent of year: 80%  All modules include Major and Supporting content together. No modules emphasize additional content, although Modules 2 and 4 begin with additional content.

ADAPTING CURRICULUM MAPS (ALGEBRA I) II. Adapting a Curriculum Map What should our approach be if we have students who are not ready to access grade-level content? 3 min Speaker’s Notes: Turn and talk to your neighbor. What percentage of your students do you estimate are not at grade level? Share responses with a show of hands (less than 25%, 25% - 50%, more than 50%). We all know, though, that students don’t show up on grade level. What do we do with students who are not ready to access grade-level content?

ADAPTING CURRICULUM MAPS (ALGEBRA I) From the Appendix to Publisher’s Criteria “The natural distribution of prior knowledge in classrooms should not prompt abandoning instruction in grade level content, but should prompt explicit attention to connecting grade level content to content from prior learning. To do this, instruction should reflect the progressions on which the CCSSM are built…. Much unfinished learning from earlier grades can be managed best inside grade level work when the progressions are used to understand student thinking.” 3 min Speaker’s Notes: Unfinished prior learning is best completed in context. That is, we find the places in our curriculum where unfinished earlier learning logically fits. This allows us to preserve focus and coherence.

ADAPTING CURRICULUM MAPS (ALGEBRA I) What We’re Trying to Avoid: “Blanket Review” 2 min Speaker’s Notes: We are trying to avoid the kind of “blanket review” that we grew accustomed to in the past--spending half the year reviewing what we did last year.

ADAPTING CURRICULUM MAPS (ALGEBRA I) Percentage of 8th Grade Math Lessons That Were Entirely Review, by Country (1999) 2 min Speaker’s Notes: In fact, TIMSS data show that in the US, we spend a major chunk of the school year just reviewing. Adapted from FIGURE 3.9. Percentage of eighth-grade mathematics lessons that were entirely review, by country: 1999, http://www.timssvideo.com/sites/default/files/TIMSS%201999%20Math%20Report.pdf

Consider expanding focus on major content where necessary. ADAPTING CURRICULUM MAPS (ALGEBRA I) Adaptation Process: Scope and Sequences Use the progressions to identify prerequisite standards from prior grades for all units. Strategically integrate instruction on prerequisites as needed. + X.1, Y.2 + X.1, Z.5 + Z.2 + X.3 + X.1, Z.5 + X.1, Y.5 + X.4, Y.5, Z.6 X = Grade Below Y = 2 Grades Below Z = 3 Grades Below Consider expanding focus on major content where necessary. 5 min Speaker’s Notes: Let’s review from yesterday. Adapting for students with unfinished learning from prior grades is a multi-step process. When we consider a scope and sequence, we start by thinking about the prerequisites for all units. Imagine, here, that “Grade X” is the year before, “Grade Y” is two years prior,” and “Grade Z” is three years below the grade you teach. Rather than teaching all prerequisite standards at the beginning of the year, plan to strategically integrate instruction on these prerequisites when teaching the relevant content. The need to teach and which prerequisites to teach should be determined by some relevant formative assessment data about your students. When a unit is focused on Major Content—we consider spending more time there. Prioritize units with major content by potentially expanding those units with days for teaching necessary prerequisites and/or spending more time on grade-level standards as determined by needs of your students. Major Content Major Content Major Content

ADAPTING CURRICULUM MAPS (ALGEBRA I) Adaptation Process: Units and Lessons Consider adding additional lessons that address prerequisite content where necessary and appropriate. The prerequisite standards we associate with each unit allow us to adapt lessons and add additional lessons. 1 2 3 4 5 6 7 4 min Speaker’s Notes: Sometimes it is necessary to insert an entire prerequisite lesson or lessons into a unit. This might be at the beginning of a unit or at the beginning of a topic within the unit. In cases where upwards of 50% of students are not at grade level, this strategy may be emphasized more. In other cases, it might be more efficient to adapt lessons to include prerequisite content. This might include adding activities that scaffold the lesson and/or including instruction on prerequisites as part of the lesson. Adapt lessons to include prerequisite content in the context of grade-level objectives.

ADAPTING CURRICULUM MAPS (ALGEBRA I) The 3 C’s Coherent Content in Context 1 min Speaker’s Notes: A handy way to remember! When we adapt resources, we are always looking for coherent content in context. This is not a “blanket review”-- this is choosing important prerequisite content and inserting it where appropriate.

ADAPTING CURRICULUM MAPS (ALGEBRA I) Coherent Content 2 min Speaker’s Notes: Student Achievement Partners has created a couple of resources that help us to locate prerequisite standards. The “Wiring Diagram” is a PDF that shows the connections among the standards in Grades K-8. The “Coherence Map” is an interactive tool that allows you to navigate the standards and see embedded examples from Illustrative Math.

ADAPTING CURRICULUM MAPS (ALGEBRA I) Now You Try: Adaptation At your tables: Look for two modules in Algebra I that you might spend more time on. Why these modules? What, in your experience, will students struggle with related to that content? What are the prerequisite standards you'd use to adapt those modules? 20 min Speaker’s Notes: Now you try. [Note questions for participants.] For #3, participants should use the standards, the “Wiring Diagram,” and the “Coherence Map” to determine the prerequisite standards to add to these two modules.

Share Out 15 min Speaker’s Notes: What are some of the adaptations we made? Highlighted Responses: Participants should note that Modules 1, 3, 4, and 5 most strongly emphasize major content. Any of these are acceptable as the two modules to spend more time on. Accept almost any answer for #2. The intent is draw participant experience into the conversation. For adapting, highlight participants who have located relevant prerequisites going back several grades. Here are some examples for Module 1: Highlight these progressions that support learning in Module 1. Some important prerequisites exist in Grade 8: 8.EE.A.1: Know and apply the properties of integer exponents to generate equivalent numerical expressions. 8.EE.C.7: Solve linear equations in one variable. Additionally, prerequisites involve basic ideas of equation and variable starting in Grade 6 (e.g., 6.EE.B.6) with variables as representations of unknown quantities in expressions and equations and continuing into a sense of the ability of equations to answer real questions about the world in Grade 7 (7.EE.B.4). Work with graphs has roots in Grade 5 (5.G.1: Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate). Graphing continues in Grade 6 (6.NS.C.6c: Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane.) and also in Grade 7 (graphing proportional relationships, 7.RP.A.2) Share Out

SESSION 1 (111M): Rigor– Calibrating Common Core (6 – 8) BREAK Lunch

INTRO TO MODULE 1 (ALGEBRA I) Sessions Today and Tomorrow Morning: Adapting the Algebra I Curriculum Map Afternoon: Intro to Module 1 Module Assessments Introduction to Functions Studied This Year—Graphing Stories (Topic A) Tomorrow Morning: Adapting and Teaching Lessons The Structure of Expressions (Topic B) Solving Equations and Inequalities (Topic C) 1 min Speaker’s Notes: We’re going to continue our exploration of the EngageNY curriculum by taking a closer look at Module 1. This session includes a look at the module assessments and Topic A. Sessions tomorrow will include a look ahead to Topics B and C.

Participants will be able to INTRO TO MODULE 1 (ALGEBRA I) Afternoon: Intro to Module 1 in Algebra I Participants will be able to analyze curriculum through the lens of the standards and shifts. use the lens of the Shifts and increased understanding of focus content to make appropriate curricular adaptations for students who lack prerequisite skills for grade-level work. anticipate student misunderstandings and support them instructionally. 1 min Speaker’s Notes: Our approach will involve doing a lot of the math in the lessons and working collaboratively to understand as much about the modules as possible. We’ll be focused on a couple of aspects: making adaptations for this module by adding lessons and adapting them anticipating student misunderstandings and using these instructionally.

INTRO TO MODULE 1 (ALGEBRA I) Afternoon: Agenda Assessing the Assessments Highlights from Topic A Exploring Lessons and the Sequence of Content for Topic A Implications for Practice 1 min Speaker’s Notes: Our approach today will be to look first at some selected items from the module assessment materials, and then dive into Topic A. We’ll look at a “cool moment” from Topic A, then explore the lessons and sequence of content. Finally we’ll reflect on the big ideas from Topic A and how we can take them back to our classrooms.

INTRO TO MODULE 1 (ALGEBRA I) I. Assessing the Assessments 10 min Speaker’s Notes: The assessment summary is located on the last page of the Module Overview. Participants will likely need to refer to the text of standards to answer these questions. What aspects of rigor are highlighted in these standards? (Highlight responses indicating that the wide variety of standards here highlights all aspects of rigor, with some (e.g., A- APR.A.1, second part) focusing more on procedural fluency, some (e.g., A-SSE.A.x) more on conceptual understanding, and some (A-CED.A.x) mostly on application. Other standards focus on these things in combination. Bonus: What kinds of problems and tasks do you expect to see in the assessment? (There are a variety of reasonable guesses here; highlight ideas about problems that require students to express real relationships using mathematical symbols and/or to perform operations on such equations.) What aspects of rigor are highlighted in these standards? Bonus: What kinds of problems and tasks do you expect to see on the assessment?

Mid-Module Assessment: End-of-Module Assessment: INTRO TO MODULE 1 (ALGEBRA I) Let’s “Do the Math” for Some Assessment Items Mid-Module Assessment: #1a–c and #2a–c End-of-Module Assessment: #1 and #2 20 min Speaker’s Notes: Note for participants that the Mid-Module Assessment begins on page 106 and the End-of-Module Assessment begins on page 312 of the Teacher Materials. Have participants “do” these assessment items: From the Mid-Module Assessment: #1 (all parts) and #2 (all parts) From the End-of-Module Assessment: #1 and #2 (also ask participants to look at #3)

INTRO TO MODULE 1 (ALGEBRA I) At Your Table: Assessing the Assessments For each assessment item: What standards are evident in this item and how do you know? What aspects of rigor are highlighted in this item and how do you know? Also consider: Compare the mid-module assessment to the end-of-module assessment. How does learning progress across the module? 12 min Speaker’s Notes: Have participants score their own responses using the rubric and sample responses provided after the assessment, and then discuss the questions. Mid-Module Item #1: N.Q.A.1 is highlighted in all parts, as this problem focuses on students’ understanding of units and how units relate to the situation described. Additionally, part a) also addresses N.Q.A.2, as students are required to define quantities to create their graphs. This problem requires conceptual understanding (determining the relationships described and how to represent them), procedural fluency (correctly using representations to find information) and application. Mid-Module Item #2: Part a: N.Q.A.1 – students draw on their knowledge of units to estimate the quantity in question. Part b: N.Q.A.3 – students must make accuracy claims given the limitations stated in the problem. Part c: N.Q.A.2 – students must use the context of this problem to identify the appropriate units to be used when modeling this situation with a graph. End-of-Module Item #1: 1(a-d) highlight A-REI.A.1, as students simply need to known the steps to correctly solve equations, while (e) highlights A-SSE.A.1b (students are considering the properties of expressions on each side of the equal sign as a whole) and A-REI.B.3 (the focus is now on what ‘solution set’ means). Parts (a-d) focus pretty straightforwardly on procedural fluency, although part (e) also requires conceptual fluency in order to answer the second part of the question. End-of-Module Item #2: Both parts highlight A-CED.A.3, as students are focusing on the meaning of ‘greater’ and ‘less’ within a particular set of constraints. This problem highlights conceptual understanding of ideas of variable and expression. Note on #3: Participants should note that the Mid-Module Assessment focuses mostly on fundamental ideas about representing relationships with mathematical symbols and determining information from what is produced, while the End-of-Module Assessment expands greatly upon the use and comparison of equations and expressions and asks students to perform far more sophisticated actions with and on them.

II. Highlights from Topic A 1 min Speaker’s Notes: Let’s take a look at the big picture for Topic A.

INTRO TO MODULE 1 (ALGEBRA I) Topic A Overview 5 min Speaker’s Notes: Have participants read through the Topic Overview for this topic. What do you notice? What is this topic about? Highlighted responses: This topic is about using a variety of equations and their graphs to understand, interpret, and analyze real-world situations and real-world data. Bonus: Why begin the year with this topic? (Sample: Algebra I can in many ways be thought of as the study of the ways in which different kinds of equations can be used to analyze and interpret the world around us. It covers a series of function families in relative depth and, when taught well, focuses on the different uses each function family can have in helping us to understand and think about the things we see and the questions and problems we encounter. For that reason, it is fitting that the year begins with an overview of functions, their structure, and their application to real-world data and constraints.) If raised by participants, briefly address the different structures noted after each lesson. We may see that some lessons look different from others; some issues to consider are how these structures all contribute to student understanding of the key concepts in this topic, and how we might adapt these structures to work best in our own classrooms.

INTRO TO MODULE 1 (ALGEBRA I) Topic Highlight: Lesson 4 15 min Speaker’s Notes: Lead participants through a “cool” activity from Algebra I, Lesson 4 (the first “problem set” problem in the teacher materials). As participants go through the activity, they should think about a few key questions. Ask: What content standards are students engaging in? Reasonable answers include: N-Q.A.1: students are using units and scale to interpret the graph. N-Q.A.2: students are interpreting this model given particular quantities. The task draws on middle school understanding of the basics of a graph of nonlinear relationship (8.F.5). What practice standards are students engaging in? (MP.2, MP.3, MP.4, MP.5, and MP.8 are all reasonable to argue for – students are reasoning and making arguments about the graph, using the data as a tool for understanding the situation being modeled, and searching for something approaching a regular pattern in the curve.) What aspects of the activity make it rigorous? (Students need to be fluent in reading the graph, to be able to understand what, conceptually, the graph shows and why, and to apply that knowledge to the situation the graph is modeling.)

III. Exploring Lessons and the Sequence of Content for Topic A 1 min Speaker’s Notes: Let’s dive in and take a look at the sequence of content for Topic A.

INTRO TO MODULE 1 (ALGEBRA I) Sequence of Content Do the exit tickets for Topic A. Describe the sequence of content to your neighbor. Cite examples of rigor. What are the expectations for prior knowledge/skills? Where would you add supplementary lessons? On which standards? 12 min Speaker’s Notes: Have participants “do the math” on the exit tickets for this topic. Afterward, discuss the questions above. The point is for participants to understand the progression of content, understand the rigor, and be able to adapt based on the principles already discussed (coherent content in context). Describe the sequence of content to your neighbor. Cite examples of rigor. The sequence emphasizes application, specifically modeling situations using graphs. The tasks start simply (i.e., identifying time intervals in Lesson 1) and grow more complex (creating a full model for a complex situation in Lesson 5). The examples start with linear cases and eventually include an exponential one. What are the expectations for prior knowledge/skills? (Highlight responses including basic ability to read and understand graphs, understanding of units and what they mean, and foundational knowledge of expressions, functions, and relations, specifically linear equations (see for example, 8.F.5, 8.EE.5, 7.EE.1.) Where would you add supplementary lessons? On which standards? Two examples: a lesson might be added prior to lesson 1 concerning functions and their properties, or a lesson might be added before lesson 4 that focuses on reading and interpreting graphs. These lessons might focus on N-Q.A.1, N-Q.A.2, and N-Q.A.3. Additionally some strategic lessons on middle school content (8.F.5, 8.EE.5) could be helpful at the start of the topic.

INTRO TO MODULE 1 (ALGEBRA I) Digging Deep, Lesson by Lesson Content and connections Implications for practice Key moments Other parts 1 min Speaker’s Notes: As a group, we are going to dig into each lesson to discover the “nuts and bolts” of the lessons. Our focus is going to be on content (understanding the ideas presented in each lesson, and how ideas connect across lessons) and implications for practice (the teacher moves that contribute to student understanding, and possible adaptations to meet student needs). For each lesson, we will look at two features: Key Moments (lesson summary, opening example, and discussion) Supporting components (other parts and problem set).

INTRO TO MODULE 1 (ALGEBRA I) Content in the Key Moment: Lesson 1 What key concept(s) are being developed? How does the opening example and discussion lead students to those concepts? What about the task makes it rigorous? 15 min Speaker’s Notes: Have participants read the lesson summary, the first example, and the discussion and questions that follow. Then discuss the questions with the whole group What key concept(s) are being developed? Sample response: A key concept of this lesson is that information can be understood from graphs and that graphs can be used to model information – the relationship goes in both directions. Students will work both to graph data and to intuit data from graphs. How does the opening example and discussion lead students to those concepts? In this example, students think about the different ways that graphs can represent a situation, with a particular focus on choosing what aspect of the situation to represent and thinking about what units make sense when doing so. What about the task makes it rigorous? This task emphasizes application, as the student must understand the relationship between what the man is doing and the mathematics that can be used to model this.

INTRO TO MODULE 1 (ALGEBRA I) Implications for Practice: Lesson 1 What are students doing? Are they engaging in mathematical practices? What is the teacher doing to facilitate and engage them with the content? How would you adapt this lesson to meet student needs? 12 min Speaker’s Notes: Discuss with the whole group. What are students doing? Are they engaging in mathematical practices? Highlight responses indicating that students are engaging in a variety of practices, with particular emphasis on the first four: students are making sense of the situation mathematically and considering what about it is appropriate to graph reasoning abstractly about what they see in the video arguing for their own interpretation of the situation [and possibly for what they find to be incorrect in the video] certainly modeling a situation mathematically. What is the teacher doing to facilitate and engage them with the content? Rather than simply demonstrating how to do the work or telling students what their models should do, the teacher is pushing students to think deeply about the situation and then to make an argument either for how to model the data or for what data can be understood from the model. How would you adapt this lesson to meet student needs? It is important to note here that student difficulty or a seeming lack of familiarity with modeling or interpreting models is not a good reason to just tell students what to do during this lesson. That should be avoided at all costs. Instead, if students require additional support in this work, that support should come as additional focus on what a graph really is, how to read one, and how to use one to model a known situation (see work at the MS level with 6.EE.9, 8.EE.5, 8.F.4; in this case, since it is likely that some students, if not all, will already be familiar with these ideas, teachers might have students work on these or other related problems in small groups before moving on to a larger class-based/individual approach. In this way, the teacher can help students to develop their own math reasoning and precision while working with their peers. Teachers might also incorporate some pre-lesson work around graphs and their interpretations in order to further support students for this lesson.)

INTRO TO MODULE 1 (ALGEBRA I) Other Parts: Lesson 1 What additional ideas or skills do further examples elicit from students? Which problems link most directly to those on the mid-module assessment? How would you adapt these problems to meet student needs? 20 min Speaker’s Notes: Have participants read through the other parts and the problem set. Then discuss the questions with the whole group. What additional ideas or skills do further examples elicit from students? Highlight responses that indicate that students will draw on their knowledge of linear functions and that they will also work on the ability to verbally describe and explain data to one another. Which problems link most directly to those on the end-of-module assessment? These problems are relatively focused, so all of them relate pretty strongly to the problems in the mid-module assessment. Problem 1 is perhaps the most direct link of all, as the first problem on the mid-module assessment asks students to draw a graph to model a situation (which they then also interpret, but only if they have correctly drawn and labeled it). How would you adapt these problems to meet student needs? As with before, one option is to ask students who feel comfortable graphing and interpreting data to share their understandings of the work that is being done. Adding in additional problems that are similar, but not identical, can allow these students to share their expertise, while still leaving available practice problems for students to work with. A second option is to break the beginnings of the problems up into smaller steps if large groups of students seem to be struggling to model and interpret. Finally, adding some problems that are more accessible, in addition to these (see 6.EE.9, 8.F.4, 8.F.5), helps to differentiate as well.

INTRO TO MODULE 1 (ALGEBRA I) Content in the Key Moment: Lesson 2 What key concept(s) are being developed? How does the opening example and discussion lead students to those concepts? What about the task makes it rigorous? 15 min Speaker’s Notes: Have participants skim the lesson and read the opening example and discussion/questions. Then have partners discuss at tables. Share responses with the whole group. What key concept(s) are being developed? Highlight responses that suggest that the mathematical work in this lesson involves the introduction of concepts of non-linear relationships, specifically quadratics and the ability to graph them and to recognize such graphs. How does the opening example and discussion lead students to those concepts? The opening example pushes students to model a seemingly simple event, a ball rolling down a ramp, only to discover that when time is considered there is something more happening than a simply linear occurrence. By sharing their work with others, students can sharpen the ideas they are developing about what this relationship might look like. What about the task makes it rigorous? As with the previous lesson, students are working on the application of a real-world event to a mathematical model, and are drawing on their conceptual understanding of the relationship between the occurrence and the mathematics in order to model appropriately.

INTRO TO MODULE 1 (ALGEBRA I) Implications for Practice: Lesson 2 What are students doing? Are they engaging in mathematical practices? What is the teacher doing to facilitate and engage them with the content? How would you adapt this lesson to meet student needs? 12 min Speaker’s Notes: Discuss with partners and share responses to the whole group. What are students doing? Are they engaging in mathematical practices? Highlighted Responses: Students are drawing conclusions about the nature of functions (and of predictions) from examples of relations. They are making sense (MP.1) and reasoning and constructing arguments about the nature of functions (MP.3), which can be said to be using other mathematical practices as well. What is the teacher doing to facilitate and engage them with the content? Highlighted response: Teachers are supporting student thinking by pushing them to think carefully about the numerical relationships they see and then to reason through their implications. While teachers should not be providing students with answers, they should certainly be guiding them through the questions and helping them to think mathematically. How would you adapt this lesson to meet student needs? Highlighted response: There are only two tables, and while their meaning may be clear to some students, it may be less clear to others. Including additional function and non-function tables and spending additional time reasoning with students about outputs and their meaning might be helpful here.

INTRO TO MODULE 1 (ALGEBRA I) Other Parts: Lesson 2 What additional ideas or skills do further examples elicit from students? Which problems link most directly to those on the mid-module assessment? How would you adapt these problems to meet student needs? 20 min Speaker’s Notes: Have participants read through the other parts and the problem set. As before, discuss with partners and share answers with the whole group. What additional ideas or skills do further examples elicit from students? Highlighted response: Substantial conceptual work occurs in the remaining parts of this lesson. Students consider the ways in which equations can represent functional relationships, they address the issue of real-world constraints on functions, and they make explicit the definition of ‘function’ that they began to develop in the introductory exercise. Which problems link most directly to those on the end-of-module assessment? Highlighted response: This lesson focuses on recognizing functions based on the definition of ‘function,’ which is not directly addressed on the end- of-module assessment. However, without this key understanding, the problems on the end-of-module assessment that relate to functions cannot be completed. How would you adapt these problems to meet student needs? Highlighted response: Methods of adapting these problems might be similar to suggestions for the initial exercise, including spending additional time on the conceptual work students are doing in these problems or providing additional examples.

INTRO TO MODULE 1 (ALGEBRA I) At Your Table: Lessons 3–5 Other Parts: What additional ideas or skills do further examples elicit from students? Which problems link most directly to those on the mid-module assessment? How would you adapt or supplement these problems to meet student needs? Content in the Key Moments: What key concept(s) are being developed? How does the opening example and discussion lead students to those concepts? What about the task makes it rigorous? Implications for Practice: What are students doing? Are they engaging in mathematical practices? What is the teacher doing to facilitate and engage them with the content? How would you adapt this lesson to meet student needs? 25 min Speaker’s Notes: Have participants read through lessons 3-5. Then discuss questions with table groups. Share answers with the whole group. Content in the Key Moments: Although these three lessons do fairly different things, the opening examples are notably related in their focus on interpreting situations and graphs of situations, whether in the service of an increased understanding of exponential functions (although, notably, that initial example does not relate to exponents), of the interpretation of functions, or of the modeling of given situations. The introductory work students do draws most strongly on conceptual understanding and application as they work to relate world phenomena and graphs of those phenomena. Implications for Practice: Not surprisingly, MP.4 is strongly highlighted here due to the modeling work that students are doing, and they will also need to persevere in analyzing relationships between quantities (MP.1) and to think carefully about the structures of functions as well as those that are present in the world around them (MP.7). In order to support students in doing this, the teacher can help them to make and continually clarify connections between what they see on the page and the stories they are discussing. These lessons all draw on understandings students have begun to develop in the past, and supplementation thus may likely be aided by a pre-assessment or pre-discussion in which the teacher can ascertain students’ level of comfort and familiarity with concepts like exponentiation, mathematical modeling, and interpretation of graphs. Other Parts: In some activities, there is a lot of text that students need to read. Therefore, close reading strategies like 3 Reads to support making sense of content with annotation. Alternatively, take out the text and let the language emerge naturally and name it for the students, identifying the key words/notations they are going to use moving forward.

IV. Implications for Practice 1 min Speaker’s Notes: We will finish today by discussing some implications your practice. IV. Implications for Practice

INTRO TO MODULE 1 (ALGEBRA I) IV. Implications for Practice Reflect on Topic A. What is the focus content, and how does instruction support student understanding of that content? What are the essential student learning experiences that support the focus content? How will you adapt or supplement this sequence of lessons to meet student needs? 10 min Speaker’s Notes: Discuss with the whole group and record key takeaways in the room for ongoing reference. What is the focus content, and how does instruction support student understanding of that content? Highlight responses that indicate that the focus of this topic is on creating and interpreting graphs representing a number of different (functional or not) relationships and on understanding the relationships between graphs of data and situations that occur in the world (N-Q.A.1, N-Q.A.2, A-CED.A.3, A-REI.D.10). Instruction supports this understanding through supports given to students in doing this work on their own and with one another, allowing students to practice the interpretation of data and the analysis of graphs that they will need to be able to engage in on their own. What are the essential student learning experiences that support the focus content? This topic is rather focused, containing a number of exercises and activities in which students create graphs based on situations and read graphs to draw conclusions. Any responses naming such activities are on the right track. Note also that the emphasis is on real world situations. How will you adapt or supplement this sequence of lessons to meet student needs? Highlight responses that indicate that pre-assessments can determine if there are particular types of functional relationships that students are unfamiliar with, as well as their level of familiarity with graphing and the interpretation of graphs. Using this data as well as informal assessment during class, lessons and activities can be added in to offer additional supports for particular areas of concern, and particular investigations or problems can be lengthened to ensure that students have adequate time to investigate, really think about the relationship, and then understand the results and the conclusions that can be drawn. See also earlier comments on prerequisite MS content (6.EE.9, 7.RP.2, 8.F.4, 8.F.5, 8.EE.5)--incorporating lessons and/or activities on these standards will serve to support all students.

Knowledge Survey Post-Test 12 minutes Speaker’s Notes: Today, we are going to ask you to take a slightly longer survey. Like the last 3 days, you will again be asked to give us feedback on the session and facilitation. In addition, you will take the knowledge survey post-test, which measures how much you know about the learning objectives from this week. You will see the same quiz-like questions as the pre-test, which you took before you came to Institute. Please take this post-test very seriously. It is very important for us to know whether the intended learning outcomes were met, how much you have learned, and how we can improve on the sessions. You can and are encouraged to use the resources and materials from this week to answer the questions. You will get to see the correct answer to each question. You will find the link to the survey in your email inbox (the same email address you used to register for Standards Institute). The email came from “research@standardsinstitutes.org”. Please complete this survey before you leave today. [If asked], yes, they can continue to take the survey after the end of the session. It will stay open until we have a desirable response rate.

ADAPTING AND TEACHING LESSONS IN MODULE 1 (ALGEBRA I) Welcome Back! 1 min Speaker’s Notes: Thank you for your time and attention yesterday! We are excited to continue digging into the EngageNY curriculum modules today.

ADAPTING AND TEACHING LESSONS IN MODULE 1 (ALGEBRA I) Thank You for Your Feedback! + ∆ 2 min Speaker’s Notes: Thank you for your feedback! I want to talk through some trends for the glows and grows and let you know what I’m doing for the grows within my control.

Take responsibility for yourself as a learner ADAPTING AND TEACHING LESSONS IN MODULE 1 (ALGEBRA I) Norms That Support Our Learning Take responsibility for yourself as a learner Honor timeframes (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 in which it is “safe to not know” 2 min Speaker’s Notes: Here’s a reminder of our norms.

ADAPTING AND TEACHING LESSONS IN MODULE 1 (ALGEBRA I) This Week Day Ideas Monday Focus and Within Grade Coherence Tuesday Rigor and the Mathematical Practices Wednesday Across Grade Coherence and Instructional Practice Thursday Adaptation and Curriculum Study Friday Adaptation and Practice “Do the math” Connect to our practice 2 min Speaker's Notes: Here is what this week will look like. Our approach is to blend the conceptual with the practical: We work to understand the big ideas of the Shifts, how they look in practice, and how we can use them to meet the needs of our students. We will apply our understanding of the shifts most rigorously on Days 4 and 5 as we dive into curriculum. The two strands that run through all of our work are: digging deep into math content by “doing” the math connecting all of the ideas and principles we look at to our work back in our districts 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.

Morning: Adapting the Algebra I Curriculum Map ADAPTING AND TEACHING LESSONS IN MODULE 1 (ALGEBRA I) Sessions Yesterday and Today Yesterday Morning: Adapting the Algebra I Curriculum Map Afternoon: Intro to Module 1 Module Assessments Introductions to Functions Studied This Year—Graphing Stories (Topic A) Today Morning: Adapting and Teaching Lessons The Structure of Expressions (Topic B) Solving Equations and Inequalities (Topic C) 2 min Speaker’s Notes: Yesterday we looked at the scope and sequence for this grade and started to look at a module. Today we’ll continue in our journey through the module. Materials for Day 5: Module 1 Wiring Diagram (2 per table printed) or Coherence Map (online) IPG (printed)

ADAPTING AND TEACHING LESSONS IN MODULE 1 (ALGEBRA I) Objectives Participants will be able to analyze curriculum through the lens of the standards and shifts. use the lens of the shifts and increased understanding of focus content to make appropriate curricular adaptations for students who lack prerequisite skills for grade-level work. prepare and deliver lessons using the core actions in the IPG. 2 min Speaker’s Notes: Our approach will involve doing a lot of the math in the lessons and working collaboratively to understand as much about the modules as possible. We’ll see how the modules connect back to the big ideas of the instructional shifts; we’ll also see how the lessons can be adapted and can come alive using the Instructional Practice Guide. We will even teach some lessons to each other!

ADAPTING AND TEACHING LESSONS IN MODULE 1 (ALGEBRA I) Agenda Highlights from Topic B Exploring Lessons and the Sequence of Content for Topic B Buddy Teaching with the IPG Implications for Practice Highlights from Topic C Exploring Lessons and the Sequence of Content for Topic C Buddy Teaching an Adapted Lesson 1 min Speaker’s Notes: Our approach today will be to dive into Topics B and C. We’ll look at a “cool moment” from each topic, then explore the lessons and sequence of content. Finally we’ll reflect on the big ideas from each topic and how we can take them back to our classrooms.

I. Highlights from Topic B 1 min Speaker’s Notes: Let’s take a look at the big picture for Topic B.

ADAPTING AND TEACHING LESSONS IN MODULE 1 (ALGEBRA I) Topic B Overview 5 min Speaker’s Notes: Have participants read through the Topic Overview for this topic. What do you notice? What is this Topic about? Sample response: This topic focuses on two related ideas: equivalence of expressions and polynomial expressions in particular, including operations on polynomials. An understanding of polynomial functions will require a solid foundation in what equivalence means for expressions, as will an understanding of the implications of performing operations on polynomials. An understanding of the concept of expressions is key for this topic. Later work with quadratic and exponential functions will depend on deep understanding of expressions.

Topic Highlight: Lesson 6 ADAPTING AND TEACHING LESSONS IN MODULE 1 (ALGEBRA I) Topic Highlight: Lesson 6 8 min Speaker’s Notes: Lead participants through a “cool” activity from Algebra I, Lesson 6 (Exercise 6 and suggested discussion). As participants go through the activity, they should think about a few key questions. What content standards are students engaging in? Students are working with A-APR.A.1 as they approach ideas of multiplication of polynomials. One can also argue that they are working on A-SSE.A.2, as the structure of the polynomials listed will influence the way they draw their picture and what pieces it contains. What practice standards are students engaging in? Arguments can be made for a number of standards, with the following being most apparent: MP.2: students are contextualizing a polynomial expression as a geometric representation through reasoning about the meaning behind the expression MP.4: students are modeling this product with a visual representation of its parts MP.6: students are accurately and precisely constructing their rectangle to carefully and correctly represent the quantities in the two polynomials MP.7: it is the structure of the polynomials that supports student ability to create this representation. What aspects of the activity make it rigorous? Sample response(s): Successful completion of this problem requires the procedural fluency to determine the parts making up the structure of this expression and the conceptual understanding necessary to translate that into a geometric form.

II. Exploring Lessons and the Sequence of Content for Topic B 1 min Speaker's Notes: Let’s take a look at the sequence of content for Topic B.

Do the exit tickets for Topic B. ADAPTING AND TEACHING LESSONS IN MODULE 1 (ALGEBRA I) Sequence of Content Do the exit tickets for Topic B. Describe the sequence of content to your neighbor. Cite examples of rigor. What are the expectations for prior knowledge/skills? Where would you add supplementary lessons? On which standards? 12 min Speaker’s Notes: Have participants “do the math” on the exit tickets for this topic. Afterward, discuss the questions above. The point is for participants to understand the progression of content, understand the rigor, and be able to adapt based on the principles already discussed (coherent content in context). Describe the sequence of content to your neighbor. Cite examples of rigor. Highlight responses: The topic starts from conceptual underpinnings of work with multiplication (i.e., “Draw a picture to represent the expression,” in the exit ticket for Lesson 6. Examples get more complex and some focus on procedures (i.e., example 2 from Lesson 8’s exit ticket: Find (𝑤2 − 𝑤 + 1) + (𝑤3 − 2𝑤2 + 99).”) What are the expectations for prior knowledge/skills? Highlight responses mentioning some familiarity with the arithmetic properties, a knowledge of variables and expressions and a (very basic) concept of what proof means in mathematics. Some interesting notes, in considering the standards, are that study of the arithmetic properties begins very early: [1.OA.3 – Commutative property of addition]: Apply properties of operations as strategies to add and subtract. Examples: If 8 + 3 = 11 is known, then 3 + 8 = 11 is also known. [Associative property of addition]: To add 2 + 6 + 4, the second two numbers can be added to make a ten, so 2 + 6 + 4 = 2 + 10 = 12. [3.MD.7c]: Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b + c is the sum of a × b and a × c. Use area models to represent the distributive property in mathematical reasoning. The relevant middle school standards are the study of expressions in Grade 6 (6.EE.1-4) and Grade 7 (7.EE.1-2) Where would you add supplementary lessons? On which standards? Possible responses might indicate that supplementary lessons could be included on the arithmetic properties (or on applying the arithmetic properties to things like proof, since they are often learned only as a “can-you-recognize-this-property” property), which would focus on standard A-APR.A.1, or on mathematical understandings of proof, or that given student needs the lessons on polynomials might be split into more lessons to ensure that students have a solid conceptual understanding of what polynomials actually are, what they mean, and how they act, supporting standard A-SSE.A.2. Additionally, participants should name study of the middle and elementary prerequisite standards at the start of the topic, or in other appropriate places.

As you prepare, think about: ADAPTING AND TEACHING LESSONS IN MODULE 1 (ALGEBRA I) III. Buddy Teaching with the IPG As you prepare, think about: Framing your objective in the context of Topic B. What content came before? What are students doing during the lesson? As the teacher, what will you be doing? 5 min Speaker’s Notes: Prepare participants to engage in a sample teaching activity at their tables. Have table groups count off by fours, so that there are 1-2 people on each team. Each team will prepare one lesson in Topic B to teach to the rest of the table. (Note: they will not be teaching the entire lesson--just the opening example and accompanying discussion/questions.)

ADAPTING AND TEACHING LESSONS IN MODULE 1 (ALGEBRA I) Summary of Core Actions 5 min Speaker’s Notes: Ask participants to summarize each Core Action at their tables. Then summarize for the group: Core Action 1 is about meeting the demands of the standards and shifts. Core Action 2 is about long-standing best practices (i.e., establishing clear learning goals, checking for understanding). Core Action 3 is about engaging students in the mathematical practices (i.e., attending to precision, constructing arguments). Remind yourself about the IPG and annotate the plan to ensure it shows at least one indicator for each Core Action.

Teach the lesson through to the end of the discussion portion. ADAPTING AND TEACHING LESSONS IN MODULE 1 (ALGEBRA I) Table Teaching Ground Rules Teachers go “all in” for their roles. Stay in character through any trouble spots. Students are “middle of the class.” Follow directions, practice, don’t “know it all.” Teach the lesson through to the end of the discussion portion. Stick to the time limits so everyone has a chance to teach. 25 min Speaker’s Notes: Set a reasonable time limit on each sample teach (6-7 minutes should be adequate in most cases). Give participants the ground rules and elaborate as needed to prepare them for the activity.

ADAPTING AND TEACHING LESSONS IN MODULE 1 (ALGEBRA I) After Teaching The team to the left of the teachers gives one “glow” (something successful) and one “grow” (a question or comment) for the lesson. Teachers briefly describe their planning processes for the lesson: How did the problem and discussion advance the key concept of the lesson? How would you adapt these problems to meet student needs? 10 min Speaker’s Notes: Suggest that participants ground their feedback in the language of the IPG. As teaching gets underway, supervise and keep time to make sure the exercise is running smoothly at each table.

ADAPTING AND TEACHING LESSONS IN MODULE 1 (ALGEBRA I) IV ADAPTING AND TEACHING LESSONS IN MODULE 1 (ALGEBRA I) IV. Implications for Practice Reflect on Topic B. What is the focus content, and how does instruction support student understanding of that content? What are the essential student learning experiences that support the focus content? How will you adapt or supplement this sequence of lessons to meet student needs? 10 min Speaker’s Notes: Discuss with the whole group and record key takeaways in the room for ongoing reference. Reflect on Topic B. What is the focus content, and how does instruction support student understanding of that content? Highlight responses that indicate that this topic focuses on algebraically equivalent expressions and polynomials (A-SSE.A.2, A-APR.A.1), and that instruction supports understanding of the content by enabling students to think about these concepts in multiple ways – geometrically/visually, by using ideas of logic and proof, by starting with small numerical examples and building to more theoretical and general ideas, etc. What are the essential student learning experiences that support the focus content? Highlight responses mentioning students’ drawing out of sums and products geometrically (particularly when these involve polynomials) and any problems or activities in which students are asked to “prove” something to be true. How will you adapt or supplement this sequence of lessons to meet student needs? Sample response: This topic is fairly introductory, so it is likely to need less adaptation than the previous topic. One possibility for adaptation is to break this topic up into two sets of two lessons, one focusing on algebraic equivalence and one focusing on polynomials, with a review (and/or quiz) in-between. Additionally, it is possible that students who have not done as much with variables might benefit from additional days spent translating ideas using numbers into general statements and properties about variables (much of this can be found in ENY lessons related to 6.EE.1-4). For example, the second lesson in this topic presupposes that students will quickly produce counterexamples to the claim that a+b+c=a x b x c, but this can only be the case when students have an understanding of what that claim actually implies, which may not be true. See also earlier comments about prerequisite content, going back as far as elementary school (1.OA.3, using properties to add/subtract and 3.MD.7c, understanding the distributive property through tiling/area).

V. Highlights from Topic C 1 min Speaker’s Notes: Let’s take a look at the big picture for Topic C.

ADAPTING AND TEACHING LESSONS IN MODULE 1 (ALGEBRA I) Topic C Overview 5 min Speaker’s Notes: Take a moment to read through the Topic Overview for this topic. What do you notice? What is this Topic about? This topic is succinctly summarized by its title – it is about solving equations and inequalities and all of the understandings that come with this hugely important concept covering many major clusters (A-CED.A, A-REI.B). Participants may note that the topic blends equation-solving procedures (i.e., A-REI.3, A-REI.6) with application and modeling (A-CED). The conceptual emphasis of A-REI.1 is an important aspect as well that may be new for teachers. Note that, as this topic is quite long (15 lessons), this session will cover the first ten lessons on solving equations and inequalities and the next session will cover the following five lessons, which focus specifically on multivariate equations and systems of equations.

ADAPTING AND TEACHING LESSONS IN MODULE 1 (ALGEBRA I) Topic Highlight: Lesson 18 10 min Speaker’s Notes: Lead participants through a “cool” activity from Algebra I, Lesson 18 (the introductory example and accompanying discussion in the teacher materials). As participants go through the activity, they should think about a few key questions. What content standards are students engaging in? The focus on equivalence supports standard A.REI.A.1. While this problem does not directly address other content standards for this module specifically (although it does refer back to previous standards relating to expressions), it sets up understandings that will be key in supporting standards like A-CED.A.3, A-CED.A.4, and A-REI.B.3.) What practice standards are students engaging in? Arguments can be made for most of the practices; some of the most apparent include: MP.2: students are reasoning abstractly given the structure of rational expressions involving variables MP.3: students are critiquing the reasoning presented in the problem and are making their own arguments for the correctness of their answers MP.6: students are ensuring that, rather than accepting generalizations or only checking a couple of examples, they are thinking and arguing precisely about the expressions in the problem. What aspects of the activity make it rigorous? Sample response: Students need procedural fluency with operations (particularly involving ratios) in order to think through this problem, but perhaps even more importantly they need a solid conceptual understanding of the relationship between the expressions they see and the possible meanings of the quantities they are considering.

ADAPTING AND TEACHING LESSONS IN MODULE 1 (ALGEBRA I) VI ADAPTING AND TEACHING LESSONS IN MODULE 1 (ALGEBRA I) VI. Exploring Lessons and the Sequence of Content for Topic C 1 min Speaker's Notes: Let’s look at the sequence of content for Topic C.

Do the exit tickets for Topic C Lessons 10–19. ADAPTING AND TEACHING LESSONS IN MODULE 1 (ALGEBRA I) Sequence of Content Do the exit tickets for Topic C Lessons 10–19. Describe the sequence of content to your neighbor. Cite examples of rigor. What are the expectations for prior knowledge/skills? Where would you add supplementary lessons? On which standards? 20 min Speaker’s Notes: Have participants “do the math” on the exit tickets for lessons 10-19 of this topic. Afterward, discuss the questions above. The point is for participants to understand the progression of content, understand the rigor, and be able to adapt based on the principles already discussed (coherent content in context). Describe the sequence of content to your neighbor. Cite examples of rigor. Participants may note that the lessons progress from a basic understanding of finding the values that make an equation true or false to solving increasingly complex equations and inequalities. Examples of rigor include the conceptual focus on explanations of true/false equations in Lesson 10 and some real-world applications (Lesson 20). Procedural skill with equation-solving shows up in almost all examples. What are the expectations for prior knowledge/skills? This topic does not presuppose much knowledge of solving equations, but does presuppose a fairly solid familiarity with inequalities. Additionally, students should have a fair amount of fluency around arithmetic operations, including those on variables, and arithmetic properties. Equation-solving has its roots in elementary school when students find missing numbers in equations involving the four operations. It is formalized in Grade 6 (6.EE.5-8) where students understand solving an equation as finding an unknown number that makes it true and solve one-step equations. Students solve two-step equations in Grade 7 (7.EE.4) and more complicated equations and systems of two linear equations in Grade 8 (8.EE.7, 8.EE.8). Where would you add supplementary lessons? On which standards? Highlight responses indicating that supplementary lessons would begin at the start of the topic with the sixth grade standards 6.EE.5-8, on the foundations of equation solving (conceptually, what it means, and procedurally, how to solve one-step equations), and could follow the progression through Grade 7 (7.EE.4) and Grade 8 (8.EE.7). They may also focus on inequalities; if students are less familiar with inequalities than is presupposed by the topic, anywhere from one to perhaps three additional lessons might be incorporated toward the middle of this set of ten lessons to support students’ conceptual understanding of inequalities and how to work with and interpret them. This would focus on standards A-CED.A.3 and A-REI.B.3 or middle school standards (7.EE.4). Additionally, results from the mid-module assessment might suggest that additional supplementation is necessary, which might include further focus on the idea of variables, for example.

With your group, consider: ADAPTING AND TEACHING LESSONS IN MODULE 1 (ALGEBRA I) Digging Deep: Jigsaw With your group, consider: The content in the key moment (opening example and discussion) of your lesson. Implications for teaching practice in the key moment. The significance of the other parts (further examples, problem set). 5 min Speaker's Notes: Prepare participants to engage in an activity with members of other tables. Have table groups count off by fives, and then send all “ones” to one area of the room, “twos” to another area, etc. Each team will study and report back to the whole group on one lesson in Topic C. (Ideally, groups prepare their findings on a poster for the entire group.) The questions for examination are the same as in Session 1, so participants will be familiar with examining lessons in this way.

ADAPTING AND TEACHING LESSONS IN MODULE 1 (ALGEBRA I) Jigsaw: Things to Consider Other Parts: What additional ideas or skills do further examples elicit from students? Which problems link most directly to those on the mid-module assessment? How would you adapt or supplement these problems to meet student needs? Content in the Key Moments: What key concept(s) are being developed? How does the opening example and discussion lead students to those concepts? What about the task makes it rigorous? Implications for Practice: What are students doing? Are they engaging in mathematical practices? What is the teacher doing to facilitate and engage them with the content? How would you adapt this lesson to meet student needs? 25 min Speaker’s Notes: Give groups 5-7 minutes to read over the lesson, 7-10 minutes to discuss and prepare their presentation, and a maximum of five minutes each to present. Given the challenging nature of the math content in this topic, participants should think carefully about how to adapt or supplement each lesson to meet student needs without sacrificing the rigor of the tasks involved. Content in the Key Moments: Students are developing fundamentally important ideas of solution in these lessons, including a consideration of what solution sets for mathematical relationships look like and what the manipulation of equations and formulas in the service of finding a solution actually means. The opening examples generally ask students to break a motivating example down into a number of aspects or components that can be considered in the service of developing a stronger sense of aspects of solving and solution. While such work is often taught as a simple series of procedures, these lessons lean heavily toward conceptual understanding of the meaning of solving rather than simply discussing useful procedures for the act of solving. Implications for Practice: Most of the mathematical practices are present here as students run through a gamut of activities and experiences in which they model and interpret situations, reason from data and from structure, and focus their thinking in precise ways with a focus on regularity of reasoning. In many ways, the teacher’s job in this set of lessons is to ensure that students are doing the heavy lifting that these activities require of their thinking rather than simply learning shortcuts or procedures divorced from the meaning of what they are doing. If this is something students struggle with (or, perhaps more likely, if they have been taught about solving equations in a way that does not lend itself to this conceptual understanding, adaptations might revolve around providing students with additional opportunities to make explicit connection between what they are doing and what this work means as they expand their ability to solve and understand various equations. Other Parts: The further examples here are less focused on additional skills than they are on supporting deeper understanding, and students are developing a fuller sense of what each aspect of solving means as they continue on in a given lesson. Much of this work is closely aligned with the end-of-module assessment, which also asks students to think carefully through aspects of the solution of equations. Due to the wide range of problems in these lessons and the range of thinking students will do on the assessment, supplementation might revolve around taking some of these problems as a starting point and expanding them or slowing them down in order to make sure that students have a solid understanding of the meaning behind all aspects of all problems.

Adapt a lesson in Topic C using coherent content in context. ADAPTING AND TEACHING LESSONS IN MODULE 1 (ALGEBRA I) VII. Buddy Teaching an Adapted Lesson Protocol: Adapt a lesson in Topic C using coherent content in context. Explain the adaptation to your partner. Teach the adapted section to your partner. 20 min Speaker’s Notes: Prepare participants to engage in a sample teaching activity at their tables. Have table groups count off by fours, so that there are 1-2 people on each team. Each team will adapt one a part of a lesson in Topic c to teach to the rest of the table. Adaptations should come from those generated on previous slide.

ADAPTING AND TEACHING LESSONS IN MODULE 1 (ALGEBRA I) VIII ADAPTING AND TEACHING LESSONS IN MODULE 1 (ALGEBRA I) VIII. Implications for Practice Reflect on Topic C. What is the focus content, and how does instruction support student understanding of that content? What are the essential student learning experiences that support the focus content? How will you adapt or supplement this sequence of lessons to meet student needs? 12 min Speaker’s Notes: Discuss with the whole group and record key takeaways in the room for ongoing reference. Optional: Facilitators may also choose to ask participants to reflect on the week as a whole, including major takeaways and next steps in their schools and districts. Focus Content Topic C focuses on solving equations, and instruction is focused on ensuring that students are actually considering the solutions to a variety of equations and not simply going through an established procedure without accompanying understanding. Essential Student Learning Experiences In this topic, essential student learning experiences are not disguised – the focus is on solving equations, and students learn about this by considering, discussing, and solving a variety of equations in a variety of ways. Each new problem offers a particular perspective and a particular relationship that students can incorporate into their sense of ‘solution’. Adaptation/Supplementation Although the purpose of this topic can be summarized in just two words, solving equations involves quite a large number of practices, habits of mind, and understandings, and minor issues with any of these can trick students into thinking that they are unable to do this work. Thus, useful adaptations to these lessons might be focused around the results of a series of formal and informal assessments of students’ faculty with the ideas this topic presents and, while likely not major or extremely time-intensive, will be instrumental in fixing the minor confusions and disconnects that may arise from each problem in order to ensure that students are comfortable and confident in their work.

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References Slide # Source 14 http://achievethecore.org/page/266/k-8-publishers-criteria-for-the-common-core-state-standards-for-mathematics-detail-pg 16 Adapted from FIGURE 3.9. Percentage of eighth-grade mathematics lessons that were entirely review, by country: 1999, http://www.timssvideo.com/sites/default/files/TIMSS%201999%20Math%20Report.pdf 20 http://achievethecore.org/page/844/ccssm-wiring-diagram 59 http://achievethecore.org/content/upload/IPG_Coaching_Print%20Guide_Math_HS_04.2015.pdf 11, 27-28, 31-32, 35-36, 38-39, 41-42, 54-55, 64-65, 69 https://www.engageny.org

Image References Slide # Name and Photographer 2 “Welcome” by Prayitno (Flickr) 13 “Mind the Gap” by CGP Grey (Flickr) 22 “Sharing” by ryancr (Flickr) 23 “Coffee Break” by Sam Carpenter (Flickr) 30 “highlights” by Bruce Aldridge (Flickr) 33 “I am the river {explored #1}” by M Reza Faisal (Flickrriver) 37 “IMG_1246” by Jaine (Flickr) 40 “Olympic Week – Teacher for a Day” by Chicago 2016 (Flickr) 43 “Math” by Akash Kataruka (Flickr) 46 “Welcome” by Bob Duan (Flickr) 53 “the highlight of my day!” by Kate Ter Haar (Flickr) 56 “NOAA Ocean Explorer: NOAA Ship Okeanos Explorer: INDEX 2012 ‘Gulf of Mexico’” (Flickr) 63 “Hellsgeriatric” by Vit C Rainbow (Flickr) 66 “Eclipse Sequence” by Robert Adams (Flickr) 68 “jigsaw puzzle pieces” by Electric-Eye (Flickr)