Professional Development: K-8 Phase I Regional Inservice Center

Professional Development: K-8 Phase I Regional Inservice Center
2010 Alabama Course of Study: Mathematics College- and Career-Ready Standards Welcome to Phase I of Alabama professional development for the implementation of the 2010 Alabama Course of Study: Mathematics. This session is intended only to be an overview of the new mathematics program and we will address some of the challenges that Alabama educators will face during the implementation of this document. Suggestions for successful transitioning into this program will be offered and explored. Together, we can produce the best mathematics curriculum for all Alabama students. (CLICK) Professional Development: K-8 Phase I Regional Inservice Center Summer 2011

Topics for Today Components of the Course of Study
High School Course Progressions/Pathways Standards for Mathematical Practice Literacy Standards for Grades 6-12 History/Social Studies, Science, and Technical Subjects The Big Picture Domains of Study and Conceptual Categories Learning Progressions/Trajectories Vertical Alignment of Content Addressing Content Shifts Early Entry Algebra I Considerations/Consequences Today we will address the following topics: (CLICK) Components of the Course of Study (CLICK) High School Course Progressions/Pathways (CLICK) Standards for Mathematical Practice (CLICK) Literacy Standards for Grades 6-12 History/Social Studies, Science, and Technical Subjects (CLICK) The Big Picture Domains of Study and Conceptual Categories (CLICK) Learning Progressions/Trajectories Vertical Alignment of Content (CLICK) Addressing Content Shifts (CLICK) Early Entry Algebra I Considerations/Consequences Today we will discuss each of these topics. At the end of the session, if there are still questions about any of these topics, please let me know. (CLICK)

Components of the Course of Study
Goal Conceptual Categories Domains of Study Throughout this presentation you will be hearing about the components of the mathematics course of study. Some of the components are addressed in this framework. It is referred to as the Conceptual Framework and it is prominently located on the first page of the document. Also, included in the document is a narrative that explains the Conceptual Framework and its component parts. What is a conceptual framework? Here are a couple of definitions. Theoretical structure of assumptions, principles, and rules that holds together the ideas comprising a broad concept. Business Dictionary.com A group of concepts that are broadly defined and systematically organized to provide a focus, a rationale, and a tool for the integration and interpretation of information. Usually expressed abstractly through word models, a conceptual framework is the conceptual basis for many theories, such as communication theory and general systems theory. Conceptual frameworks also provide a foundation and organization for the educational plan. Dictionary by Farlex ACTIVITY: I will give you a few minutes to examine the Conceptual Framework. Work with someone sitting close by and see if you can describe the mathematics program contained in this COS as depicted in the Conceptual Framework. Let’s look at the components of the Conceptual Framework and their meaning. Compare your description with my description and see if you truly understand the mathematics program. Please let me know at the end of the presentation if there is terminology used in this description that has not been explained or if you have additional questions about any unfamiliar terminology. (CLICK) Across the top of the Conceptual Framework is the goal of the mathematics curriculum, “Building Mathematical Foundations.” The placement of this banner portrays that student achievement of this goal enhances future opportunities and options for the workplace and for everyday life by enabling all students to be college and career ready. Mathematics content contained in this document is both rigorous and aligned throughout the grades, thus providing students with the necessary steps to acquire the knowledge and skills for developing a strong foundation in mathematics. Therefore, the foundation progression is portrayed as steps leading to the result of college and career readiness in mathematics. We will introduce you to these steps today. They include, (CLICK) the Standards for Mathematical Practice, (CLICK) the Position Statements, (CLICK)the K-8 Domains of Study, and (CLICK) the 9-12 Conceptual Categories. The grade-level standards, as well as other components in the course of study will assist you in ensuring that all students (CLICK) graduate high school with the mathematics necessary to be college and career ready. We will elaborate on each step leading to successful graduation as we go through this presentation. (CLICK) Position Statements Standards for Mathematical Practice

Preface Acknowledgments General Introduction Conceptual Framework Position Statements Equity Curriculum Teaching Learning Assessment Technology Standards for Mathematical Practice Let’s look at the individual components of the 2010 mathematics course of study. (CLICK) First you will see the Preface. It gives a little background on the development of the COS. It contains information about the: - Audience (For whom the Course of Study is written), - Objectives (What the writers hope the Course of Study will accomplish), - Stimulus (What prompted the writing of the Course of Study), and - Methodology (How the data and the conclusions were reached). (CLICK) Next are the Acknowledgments pages that recognize the persons involved in the production of the document. These persons include the task force members, state department personnel, and others who assisted with the compilation of the document. Since persons were selected from each state board district and each congressional district, you may recognize the names of some of the persons listed. (CLICK) The General Introduction (p. 1) summarizes the purpose of the document and provides an introduction to the document’s layout. It: - Provides general information about the document, - Includes information about the importance of the subject area, - Describes the scope of the K-12 program in narrative form (program goals, themes, etc.), - Emphasizes new direction(s) for the K-12 program for individual courses, and -Presents a brief explanation of the entire program (CLICK) The Conceptual Framework (p. 3) of the mathematics program consists of two parts. One part is the graphic and the other is the narrative that explains the graphic. We have briefly examined the conceptual framework, but we will examine its parts further in later slides. (CLICK) The Position Statements (p. 4) are narratives concerning issues of mathematics education that the task force provided for all Alabama mathematics educators. It is the place in the document where the task force may express any educational opinions on topics they believe are relevant to all Alabama educators and students. They are beliefs and ideas that are not expressed in standards. In this document they include (CLICK) Equity, Curriculum, Teaching, Learning, Assessment, and Technology. (CLICK) The next section of the document describes the eight Standards for Mathematical Practice (p. 6). They also will be discussed later in this presentation. (CLICK)

Directions for Interpreting the Minimum Required Content GRADE 4 Students will: Domain Cluster Number and Operations in Base Ten Generalize place value understanding for multi-digit whole numbers. 6. Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right [4-NBT1] 7. Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meaning of the digits in each place using >, =, and < symbols to record the results of comparisons. [4-NBT2] 8. Use place value understanding to round multi-digit whole numbers to any place. [4-NBT3] Content Standards Content Standard Identifiers In the document the next two pages are the Directions for Interpreting the Minimum Required Content. These are very important pages in understanding how the standards are presented in the document. The elementary and secondary standards are divided differently and there is an example of each that indicates all of the parts of a standard and how the standards are grouped. Let’s look at how you will see the standards displayed in the document. (CLICK) In the elementary example (p.10), there are numbered and lettered standards that are grouped into domains and clusters. Lettered items, as in Grade 4, standard 14, on page 35 of the document, are just as important as the numbered items and must be mastered. Often, they are specificity of the numbered items. This is a new organizational structure for Alabama mathematics standards and we will expand the discussion of this structure in later slides. At the end of each standard is a (CLICK) content standard identifier that relates it to where that standard may be found in the CCSS document. The coding for these identifiers may be found on the overview pages for Grades K-8 and on the conceptual categories overview pages preceding the high school courses. This reference identifier was provided so that as resources are developed and produced by publishers, or other states using CCSS, you may know which Alabama standard correlates to each CCSS. A summary sheet of what the identifier abbreviations represent will be posted on the state’s Website, along with all of the handouts and slides from this presentation. I will share with you how to access this new resource at the end of this presentation. Each content standard is numbered and some are followed with a-b-c subparts. These subparts are specificity of the content in the numbered item and must also be mastered by the students. Bullets are no longer included in standards. There are still a few examples, and they remain in this document as exemplars that are not required to be taught. Exemplars are models of skills to be taught in a standard. They may show example of the level of rigor or to what extent the skill is to be taught. (CLICK)

ALGEBRA II WITH TRIGONOMETRY Students will: FUNCTIONS Domain Conceptual Category Trigonometric Functions Extend the domain of trigonometric functions using the unit circle. 32. Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle. [F-TF1] 33. Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle. [F-TF2] Define the six trigonometric functions using ratios of the sides of a right triangle, coordinates on the unit circle, and the reciprocal of other functions. Cluster Content Standard Identifiers Content Standards (CLICK) As in the elementary standards, the high school standards are organized with numbered and lettered items that are grouped in domains and clusters (p. 11). (CLICK) The content standard identifier follows each standard just as in the elementary standards. There is an additional identifier in the high school standards, a state of Alabama symbol. This symbol represents content that the Alabama Task Force added to CCSS. The task force had the option of adding up to 15% additional content. After a comparison of the 2009 COS and the CCSS in which 96% of CCSS content was correlated to Alabama’s standards, the task force chose to add very little content to CCSS. Some content was added as complete standards or subparts of standards, so you will see only the Alabama symbol after those; and some content was added in a CCSS, so you will see both the CCSS identifier and the state symbol. There is also another grouping of the high school standards. (CLICK) They are grouped within each course by conceptual category. (CLICK)

Next in the document are the grade-level standards for Grades K-8. (CLICK) Each grade of standards is preceded with an overview of the domains and clusters covered in that grade as well as a narrative about the focus of that grade. (CLICK) A listing of the domains and clusters are also given in outline form. (CLICK) The Standards for Mathematical Practice are repeated for emphasis on each overview page. (CLICK)

After the grade-level narrative, the list of standards is preceded with the statement ‘Students will.’ (CLICK) This is to reiterate that all students must master all standards by the end of that grade. (CLICK) The standards are considered to be the body of the document. Content required to be taught and mastered by the student is contained in standards. Standards include numbered items as well as lettered items. Examples included in the standards are not exhaustive and are for clarification only. (CLICK)

Standards for High School Mathematics Conceptual Categories for High School Mathematics Number and Quantity Algebra Functions Modeling Geometry Statistics and Probability Additional Coding (+) STEM Standards (*) Modeling Standards ( ) Alabama Added Content After the K-8 standards is a section, Standards for High School Mathematics (p. 66), that describes (CLICK) the six conceptual categories and (CLICK) additional coding for high school standards which includes (CLICK) a plus sign (+) for STEM standards and (CLICK) an asterisks (*) for modeling standards, and (CLICK) a symbol of the state of Alabama for content added by the course of study task force. We will expand on the conceptual categories on a later slide. Let’s look at an example of a STEM standard, and Modeling standards, and a standard that was added by the task force. (CLICK)

(+) STEM Standards Geometry Derive the formula A = (1/2)ab sin(C) for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side. [G-SRT9] (+) STEM standards include content that students who want to pursue upper level mathematics, such as calculus; or careers that will involve extensive use of mathematics, such as engineering, will need to be successful. (CLICK) This is an example of a STEM standard found in the Geometry course. A few STEM standards appear in required courses but most are found in elective courses and they are all indicated with a plus sign (+) at the beginning of the standard. (CLICK) (CLICK)

(*) Modeling Standards Algebra I 28. Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. [F-IF5] * Modeling is best interpreted, not as a collection of isolated topics, but rather as having relevance to other standards. Specific modeling standards appear throughout the high school mathematics standards and they are indicated by an asterisk (*) following the standard. (CLICK) This example is found as standard 28 in the Algebra I course. As you can see in this standard, modeling lends itself easily to the process of choosing and using appropriate mathematics and statistics to analyze empirical situations to understand them better, and to improve decisions. Technology is valuable for varying assumptions, exploring consequences, and comparing predictions with data. (CLICK) (CLICK)

Added Content Specific to Alabama Geometry 35. Determine areas and perimeters of regular polygons, including inscribed or circumscribed polygons, given the coordinates of vertices or other characteristics. Another symbol that is new is the additional standards or additional content notation in the high school standards. The task force had the option of adding content to any grade or course in the CCSS that they deemed appropriate. It is content that the task force included from the 2009 document that was not found in the CCSS, but was deemed important for Alabama students to know. This is Alabama specific content and it is indicated with a state symbol of Alabama. (CLICK) This example is standard 35 in the Geometry course. (CLICK) The symbol will be located at the end of the added standard as shown in the example or, if content was added to a CCSS, then the symbol will follow the Content Standard Identifier notation. (CLICK)

Description of Standards Relation to K-8 Content Content Progression in 9-12 Next are the descriptions of the high school Conceptual Categories (p.67). Standards are grouped by domains in elementary grades and by conceptual categories and domains in high school. (CLICK) Each conceptual category has a page describing the standards that are presented in that category. (CLICK) The descriptions also give meaning to the category and how the category relates to the content presented in K-8 standards as well as (CLICK) give insight to how the category is developed in high school standards. All of the conceptual category descriptions precede the high school courses. (CLICK)

Narrative Domains and Clusters Standards for Mathematical Practice Each conceptual category has an overview page that follows the description page (p. 68). (CLICK) The focus of the standards contained in the conceptual category is written as a short paragraph at the top of the overview page. (CLICK) The domains and clusters of the category are then listed in outline form below the narrative. (CLICK) Also, the Standards for Mathematical Practice are repeated here as well. (CLICK)

Following the descriptions for the conceptual categories are the course standards for the high school courses. (CLICK) There is also a brief narrative preceding each course that gives important information about that course. For example, before Algebra I (p.81) and Geometry (p.89), this information includes the standards that are to be taught if either of those courses is split into the A and B course progression. (CLICK)

Appendices A-E Appendix A Table 1: Common Addition and Subtraction Situations Table 2: Common Multiplication and Division Situations Table 3: Properties of Operations Table 4: Properties of Equality Table 5: Properties of Inequality Appendix B Possible Course Progressions in Grades 9-12 Possible Course Pathways Appendix C Literacy Standards For Grades 6-12 History/Social Studies, Science, and Technical Subjects Appendix D Alabama High School Graduation Requirements Appendix E Guidelines and Suggestions for Local Time Requirements and Homework Bibliography Glossary In the back of the document are appendices A – E. (CLICK) Appendix A (p. 123) contains five tables that are referenced in the standards. (CLICK) Appendix B (p. 126) contains a graphic of course progressions for high school and a list of some possible course pathways for achievement of the four mathematics graduation requirements. In previous mathematics documents, this section was presented just prior to the high school courses. In order to improve the flow of the document, it is now placed in an appendix. We will discuss Appendix B more on the next slide. (CLICK) Appendix C (p. 128) is new to Alabama’s COS. It is a collection of literacy standards for Grades The document was written for History/Social Studies, Science, and Technical Subjects. Mathematics falls under the ‘Technical Subjects’ section, so that is the section that was included in this document. We will have more information on Appendix C later in this presentation. (CLICK) Appendix D (p. 135) is not new to a mathematics COS and it includes the graduation requirements as defined in the Alabama Administrative Code. (CLICK) Appendix E (p.137) contains the Guidelines and Suggestions for Local Time Requirements and Homework. Appendices D and E are always included in every COS. (CLICK) Next in the document is the bibliography (p.139) citing sources consulted in the creation of the document. This is also not new to a COS document. (CLICK) Last in the document is another new section to Alabama’s mathematics COS, a glossary (p. 140) that was provided by CCSS. This will greatly assist teachers at all grade levels in using the same vocabulary. Students should then learn the correct terminology for mathematical terms. (CLICK)

High School Course Progressions
Required for All Students Algebra I Geometry Algebra II with Trigonometry or Algebra II Courses Must Increase in Rigor New Courses Discrete Mathematics Mathematical Investigations Analytical Mathematics A page that usually precedes the high school courses is now found in Appendix B. This is a diagram showing possible high school course offerings. (CLICK) As you are aware, in the first choice diploma option, Algebra I, Geometry, and Algebra II with Trigonometry are required mathematics courses. (CLICK) The fourth mathematics course may be any other course, as long as the courses taken increase in rigor. LEAs may stipulate the course progressions they require, as long as the state requirements are met. In order for all students to graduate college and career ready, all students must complete Algebra II with Trigonometry or Algebra II. All CCSS could not be included in just Algebra I and Geometry; there are too many standards. Therefore, the Task Force divided the standards contained in CCSS into three courses and all three courses must be taken. (CLICK) New courses are Discrete Mathematics and Mathematical Investigations, which are on the same level of rigor as Algebra II with Trigonometry. Also, another option after Precalculus, and on the same level of rigor as Precalculus, is Analytical Mathematics. These new courses, along with the AP offerings, give Alabama students more course options than the 2003 document. LEAs may also develop additional courses, submit them to the SDE for approval, and offer them to their students. If approved, these courses may count as the fourth math credit. Otherwise, LEAs may offer these courses as electives, which do not require approval but may not count as one of the four mathematics credits for graduation. (CLICK)

High School Course Pathways
Also in Appendix B is a listing of some possible high school course pathways. The pathways listed provide some of the options for a student’s four mathematics credits. The top section will be choices for the majority of Alabama students, although there may be special cases of students needing the list at the bottom of the page. Alabama allows students to begin Algebra I in Grade 8. With these new standards, this creates new considerations and consequences. We will address these later in this presentation. (CLICK)

?? Questions ?? Are there any questions concerning the components of the mathematics course of study? If not, we will continue with the Standards for Mathematical Practice. (CLICK)

The Standards for Mathematical Practice
2010 Alabama Course of Study: Mathematics College- and Career-Ready Standards The 2010 Alabama Course of Study: Mathematics contains two types of standards – practice standards and content standards. The portion of the presentation will focus on the 8 Standards for Mathematical Practice which are common to every grade level. (CLICK) The Standards for Mathematical Practice

Standards for Mathematical Practice
“The Standards for Mathematical Practice describe varieties of expertise that mathematics educators at all levels should seek to develop in their students. These practices rest on important “processes and proficiencies” with longstanding importance in mathematics education.” (CCSS, 2010) Read this quote. (CLICK)

Underlying Frameworks
National Council of Teachers of Mathematics 5 PROCESS Standards Problem Solving Reasoning and Proof Communication Connections Representations Underlying frameworks for the mathematical practice standards are found in documents from two national educational organizations, the National Council of Teachers of Mathematics and the National Research Council. The National Council of Teachers of Mathematics (NCTM) has long held the belief that learning is a process that envelopes the students’ thinking processes through: (CLICK) Problem solving – building new mathematical knowledge through problem solving, solving problems, applying and adapting appropriate strategies to solve problems (CLICK) Reasoning and proof – making and investigating mathematical conjectures, developing mathematical arguments and proofs, selecting and using various types of reasoning (CLICK) Communication – organizing mathematical thinking through communication, communicating coherently to peers, teachers, and others, using the language of mathematics precisely (CLICK) Connections – recognizing and using connections among mathematical ideas, applying mathematics in contexts outside of mathematics (CLICK) Representations – creating and using representations to organize, record, and communicate mathematical ideas, modeling mathematical phenomena, selecting, applying and translating among mathematical representations to solve problems (CLICK) NCTM (2000M). Principles and Standards for School Mathematics. Reston, VA: Author.

Underlying Frameworks
National Research Council Strands of Mathematical Proficiency Conceptual Understanding Procedural Fluency Strategic Competence Adaptive Reasoning Productive Disposition The National Research Council’s report, Adding It Up: Helping Children Learn Mathematics, is a summary of research on mathematics learning from prekindergarten through grade 8. The committee chose the term mathematical proficiency to capture what it means for anyone to learn mathematics successfully. Mathematical proficiency is broken down into five components, or strands: (CLICK) Conceptual understanding – comprehending mathematical concepts (CLICK) Procedural fluency – skill in carrying out procedures accurately and efficiently (CLICK) Strategic competence – ability to formulate, represent and solve mathematical problems (CLICK) Adaptive reasoning – capacity for logical thought, reflection, explanation and justification (CLICK) Productive disposition – habitual inclination to see mathematics as sensible, useful, and worthwhile. “The most important observation the committee makes and stresses is that the five strands are interwoven and interdependent in the development of proficiency in mathematics.” The writers of the Common Core State Standards took all these process standards and developed the 8 Standards for Mathematical Practice. (CLICK) NRC (2001). Adding It Up. Washington, D.C.: National Academies Press.

The Standards for Mathematical Practice
Mathematically proficient students: Standard 1: Make sense of problems and persevere in solving them. Standard 2: Reason abstractly and quantitatively. Standard 3: Construct viable arguments and critique the reasoning of others. Standard 4: Model with mathematics. Standard 5: Use appropriate tools strategically. Standard 6: Attend to precision. Standard 7: Look for and make use of structure. Standard 8: Look for and express regularity in repeated reasoning. Notice that each practice standard begins with the words “Mathematically proficient students:” (CLICK X 8)to bring each standard onto screen. Read each standard. Keep in mind, these standards for mathematical practice are behaviors we want to develop in our students. (CLICK)

Questions to consider…
What does this standard look like in the classroom? What will students need in order to do this? What will teachers need in order to do this? Adapted from Kathy Berry, Monroe County ISD, Michigan Our first activity today is a group activity to get you into the thinking mode about the standards. Some of you might know what these standards are and for others, this may be the first time you have seen them. You will be divided into 8 different groups and each group will be given a practice standard to discuss. Each group will discuss these questions for their standard. You will have approximately five minutes. There aren’t any right or wrong answers at this point. When you consider the standards, you should reflect on these questions. (CLICK) #1 What does this standard look like? (CLICK) #2 What will students need in order to do this? (CLICK) #3 What will teachers need in order to do this? (Presenter distributes handouts: one standard per group) (CLICK)

Standard 1: Make sense of problems and persevere in solving them
Standard 1: Make sense of problems and persevere in solving them. What do mathematically proficient students do? Analyze givens, constraints, relationships Make conjectures Plan solution pathways Make meaning of the solution Monitor and evaluate their progress Change course if necessary Ask themselves if what they are doing makes sense Here’s what Standard 1 looks like. Do you agree with this list of student behaviors? What will students need in order to do this? What will teachers need to do this? (Allow time for discussion) The Mathematical Practice Standards are standards that you can already implement this fall. Now let’s look at the other 7 practice standards. (ADDITIONAL TRAINER NOTES ON STANDARD 1. THESE ARE TO BE USED AS A TRAINER RESOURCE.) Mathematically proficient students: Explain to themselves the meaning of a problem. Look for entry points to its solution. Analyze the givens, constraints, relationships, and goals. Make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. Consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. Monitor and evaluate their progress and change course if necessary. Check their answers to problems using a different method, and they continually ask themselves, “Does this make sense?” Understand the approaches of others to solving complex problems and identify correspondences between different approaches. (CLICK)

Standard 2: Reason abstractly and quantitatively
Standard 2: Reason abstractly and quantitatively. What do mathematically proficient students do? Make sense of quantities and relationships Able to decontextualize Abstract a given situation Represent it symbolically Manipulate the representing symbols Able to contextualize Pause during manipulation process Probe the referents for symbols involved Here’s what Standard 2 looks like. Do you agree with this list of student behaviors? What will students need in order to do this? What will teachers need to do this? (Allow time for discussion) (ADDITIONAL TRAINER NOTES ON STANDARD 2. THESE ARE TO BE USED AS A TRAINER RESOURCE.) Mathematically proficient students: Make sense of quantities and their relationships in problem situations. Bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize – abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents – and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of: Creating a coherent representation of the problem at hand Considering the units involved Attending to the meaning of quantities, not just how to compute them Knowing and flexibly using different properties of operations and objects. (CLICK)

Standard 3: Construct viable arguments and critique the reasoning of others. What do mathematically proficient students do? Construct arguments Analyze situations Justify conclusions Communicate conclusions Reason inductively Distinguish correct logic from flawed logic Listen to/Read/Respond to other’s arguments and ask useful questions to clarify/improve arguments Here’s what Standard 3 looks like. Do you agree with this list of student behaviors? What will students need in order to do this? What will teachers need to do this? (Allow time for discussion) (ADDITIONAL TRAINER NOTES ON STANDARD 3. THESE ARE TO BE USED AS A TRAINER RESOURCE.) Mathematically proficient students: Understand and use stated assumptions, definitions, and previously established results in constructing arguments Make conjectures and build a logical progression of statements to explore the truth of their conjectures Analyze situations by breaking them into cases, and can recognize and use counterexamples Justify their conclusions, communicate them to others, and respond to the arguments of others Reason inductively about data, making plausible arguments that take into account the context from which the data arose. Compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and – if there is a flaw in an argument – explain what it is. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though there are not generalized or made formal until later grades. Later, students learn to determine domains to which an argument applies. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments. (CLICK)

Standard 4: Model with mathematics
Standard 4: Model with mathematics. What do mathematically proficient students do? Apply mathematics to solve problems from everyday life situations Apply what they know Simplify a complicated situation Identify important quantities Map math relationships using tools Analyze mathematical relationships to draw conclusions Reflect on improving the model Here’s what Standard 4 looks like. Do you agree with this list of student behaviors? What will students need in order to do this? What will teachers need to do this? (Allow time for discussion) (ADDITIONAL TRAINER NOTES ON STANDARD 4. THESE ARE TO BE USED AS A TRAINER RESOURCE.) Mathematically proficient students: Apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. Identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts, and formulas. They can analyze those relationships mathematically to draw conclusions. Routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose. (CLICK)

Standard 5: Use appropriate tools strategically
Standard 5: Use appropriate tools strategically. What do mathematically proficient students do? Consider and use available tools Make sound decisions about when different tools might be helpful Identify relevant external mathematical resources Use technological tools to explore and deepen conceptual understandings Here’s what Standard 5 looks like. Do you agree with this list of student behaviors? What will students need in order to do this? What will teachers need to do this? (Allow time for discussion) (ADDITIONAL TRAINER NOTES ON STANDARD 5. THESE ARE TO BE USED AS A TRAINER RESOURCE.) Mathematically proficient students: Consider the available tools when solving a mathematical problem. These tools might include pencil and paper, concrete models, a ruler, a protractor, a calculator, a spreadsheet, a computer algebra system, a statistical package, or dynamic geometry software. Are sufficiently familiar with tools appropriate for their grade or course to make sound decisions about when each of these tools might be helpful, recognizing both the insight to be gained and their limitations. For example, mathematically proficient high school students analyze graphs of functions and solutions generated using a graphing calculator. Detect possible errors by strategically using estimation and other mathematical knowledge. When making mathematical models, they know that technology can enable them to visualize the results of varying assumptions, explore consequences, and compare predictions with data. Identify relevant external mathematical resources, such as digital content located on a website, and use them to pose or solve problems. Use technological tools to explore and deepen their understanding of concepts. (CLICK)

Standard 6: Attend to precision
Standard 6: Attend to precision. What do mathematically proficient students do? Communicate precisely to others Use clear definitions in discussions State meaning of symbols consistently and appropriately Specify units of measurements Calculate accurately & efficiently Here’s what Standard 6 looks like. Do you agree with this list of student behaviors? What will students need in order to do this? What will teachers need to do this? (Allow time for discussion) (ADDITIONAL TRAINER NOTES ON STANDARD 6. THESE ARE TO BE USED AS A TRAINER RESOURCE.) Mathematically proficient students: Communicate precisely to others. Use clear definitions in discussion with others and in their own reasoning. State the meaning of the symbols they choose, including using the equal sign consistently and appropriately. They are careful about specifying units of measure, and labeling axes to clarify the correspondence with quantities in a problem. Calculate accurately and efficiently Express numerical answers with a degree of precision appropriate for the problem context. In the elementary grades, students give carefully formulated explanations to each other. By the time they reach high school they have learned to examine claims and make explicit use of definitions. (CLICK)

Standard 7: Look for and make use of structure
Standard 7: Look for and make use of structure. What do mathematically proficient students do? Discern patterns and structures Use strategies to solve problems Step back for an overview and can shift perspective Here’s what Standard 7 looks like. Do you agree with this list of student behaviors? What will students need in order to do this? What will teachers need to do this? (Allow time for discussion) (ADDITIONAL TRAINER NOTES ON STANDARD 7. THESE ARE TO BE USED AS A TRAINER RESOURCE.) Mathematically proficient students: Look closely to discern a pattern or structure. Young students, for example, might notice that three and seven more is the same amount as seven and three more, or they may sort a collection of shapes according to how many sides the shapes have. Later, students will see 7 x 8 equals the well remembered 7 x X 3, in preparation for learning about the distributive property. In the expression X^2 + 9X +14, older students can see the 14 as 2 X 7 and the 9 as Recognize the significance of an existing line in a geometric figure and can use the strategy of drawing an auxiliary line for solving problems. Can step back for an overview and shift perspective. They can see complicated things, such as some algebraic expressions, as single objects or as being composed of several objects. For example, they can see 5 – 3(x – y)^2 as 5 minus a positive number times a square and use that to realize that its value cannot be more than 5 for any real numbers x and y. (CLICK)

Standard 8: Look for and express regularity in repeated reasoning
Standard 8: Look for and express regularity in repeated reasoning. What do mathematically proficient students do? Notice if calculations are repeated Look for general methods and shortcuts Maintain oversight of the processes Attend to details Continually evaluates the reasonableness of their results Here’s what Standard 8 looks like. Do you agree with this list of student behaviors? What will students need in order to do this? What will teachers need to do this? (Allow time for discussion) (ADDITIONAL TRAINER NOTES ON STANDARD 8. THESE ARE TO BE USED AS A TRAINER RESOURCE.) Mathematically proficient students: Notice if calculations are repeated, and look both for general methods and for shortcuts. Upper elementary students might notice when dividing 25 by 11 that they are repeating the same calculations over and over again, and conclude they have a repeating decimal. By paying attention to the calculation of slope as they repeatedly check whether points are on the line through (1,2) with slope 3, middle school students might abstract the equation (y-2) / (x-1) = 3. Noticing the regularity in the way terms cancel when expanding (x-1) (x+1), (x-1) (x2 + x +1), and (x-1)(x3 + x2 +x +1) might lead them to the general formula for the sum of a geometric series. As they work to solve a problem, mathematically proficient students maintain oversight of the process, when attending to the details. They continually evaluate the reasonableness of their intermediate results. (CLICK)

The Standards for [Student] Mathematical Practice
SMP1: Explain and make conjectures… SMP2: Make sense of… SMP3: Understand and use… SMP4: Apply and interpret… SMP5: Consider and detect… SMP6: Communicate precisely to others… SMP7: Discern and recognize… SMP8: Note and pay attention to… Remember, the Mathematical Practice Standards describe behaviors we want to develop in our students. It is up to the teacher to provide tasks that give students an opportunity to develop and display these behaviors. This slide provides a quick overview of the behaviors we want to see in our students. Now, that we’ve had a chance to discuss the mathematical practice standards, what do they remind you of? Aren’t the Practice Standards just Best Practices that we’ve all been using for years? It’s just good teaching. These practice standards are not just ‘something else’ to be taught. They are Best Practices that we pass on to our students through meaningful mathematical tasks. (CLICK)

CONNECTION and BALANCE
Mathematical Practice Mathematical Content Our ultimate goal is to make sure the students make a connection between the Standards for Mathematical Practice and the Standards for Mathematical Content. Let’s look at a Task to see how the Standards can be implemented. (CLICK)

The Buttons Task is intended for upper elementary or early middle school grades. As you work through this task, think about the mathematical practice standards that your students might use. (Trainer distributes one handout per person.) (CLICK)

Each of you has received a Buttons Task handout
Each of you has received a Buttons Task handout. You are asked to complete parts 1-3 individually. Then find a partner to compare your work with. Complete part 4 with your partner looking for as many ways as possible to solve the problem. You will have 5 minutes to solve the BUTTON TASK. Begin now. Give 5 minutes. (CLICK)

Draw Pattern 4 next to Pattern 3. See answer above.
How many white buttons does Gita need for Pattern 5 and Pattern 6? Explain how you figured this out. 15 buttons and 18 buttons How many buttons in all does Gita need to make Pattern 11? Explain how you figured this out. 34 buttons Gita thinks she needs 69 buttons in all to make Pattern 24. How do you know that she is NOT correct? How many buttons does she need to make Pattern 24? 73 buttons Here is a slide with the answers that could be the solutions. #1 - Pattern 4 has 12 white buttons and 1 black button. Any questions? #2 - Pattern 5 has 15 white buttons and pattern 6 has 18 white buttons. Would someone share how they discovered this? (Could have used the pattern, pattern 2 has 6 white, pattern 3 has 9 white, etc., or they could have drawn the picture.) #3 – Pattern 11 would need 33 white buttons plus the one black button. Some students would forget to add the 1 black button to the total. (Ask for a volunteer to share their thinking on this problem.) Notice that is questions 1-3, we start with the pattern and are looking for the total number of buttons. Question #4 asks us to think differently. Here we are given the total number and asked to work backward to determine if the total number is correct. #4 – Is there just one correct way to work #4? No. The important element in all these problems is the explanation that the students provide. When you answered the questions, did you use any particular mathematical processes? Pause. CLICK

Let’s quickly look at question #3
Let’s quickly look at question #3. Here we see two different methods of determining an answer. Let’s look at student responses to this question. (CLICK)

Here are two samples of students’ answers which can illustrate how differently students can think about finding the solution to a problem. (Give time for participants to read through). Do you allow your students to demonstrate how they think? These instructions for this task ask you to allow students to evaluate the responses from Learner A and Learner B. They are asked to make sense of Learner A’s and Learner B’s reasoning. (CLICK)

Which of the Mathematical Practices were needed to complete the task?
(Discussion) Possible answers: Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Look for and make use of structure Look for and express regularity in repeated reasoning You might not have used all these practice standards during this task. Do you see how this task taught ‘thinking skills’ in addition to some mathematics’ skills? (CLICK)

Analyzing the Button Task
The Button Task was: Scaffolded Foreshadows linear relationships Requires critical thinking skills Did not suggest specific strategy Let’s look at the button task: (CLICK) The task was scaffolded. Early questions were tied to diagram. The later questions required more abstract thinking. However, if the student had trouble thinking abstractly, he/she could still work the problem using either concrete examples or drawing. (CLICK) This task used black and white buttons. This foreshadows linear relationships which include two quantities and a relationship between the quantities. (CLICK) The tasks required two methods of thinking. We began with a pattern that asked for a total number of buttons. By the time we reached question 4, we were given a total number and asked to determine if they were correct for a certain pattern number. (CLICK) The tasks did not suggest a specific strategy. Each student was free to develop their own strategy and then explain their reasoning. This task was taken from the Website insidemathematics.org. This is a good resource for additional practice standards exercises. (CLICK)

The Standards for [Student] Mathematical Practice
“Not all tasks are created equal, and different tasks will provoke different levels and kinds of student thinking.” Stein, Smith, Henningtsen & Silver, 2000 “The level and kind of thinking in which students engage determines what they will learn.” As you can read on the slide, all tasks are NOT created equal. Engaging the students in higher order thinking determines what they will learn and will inspire them to think “outside the box”. And, it’s not just about having the student ‘do’ a task, it’s the nature of the task and the relationship between the task and the opportunities the tasks provides for the student to learn. (CLICK) Herbert, Carpenter, Fennema, Fuson, Wearne, Murray, Oliver, & Human, 1997

But, WHAT TEACHERS DO with the tasks matters too!
The Mathematical Tasks Framework Tasks are enacted by teachers and students Tasks as they appear in curricular materials Tasks are set up by teachers It is important to recognize that what teachers do with the tasks matters. The tasks that appear in curricular materials, along with tasks that are set up and enacted by teachers, all impact student learning. Do you delve into higher order thinking skills? Do you allow open ended questioning? Do you encourage discovery? (CLICK) Student Learning Stein, Grover, & Henningsen (1996) Smith & Stein (1998) Stein, Smith, Henningsen, & Silver (2000)

Standards for [Student] Mathematical Practice
The Standards for Mathematical Practice place an emphasis on student demonstrations of learning… Equity begins with an understanding of how the selection of tasks, the assessment of tasks, and how the student learning environment create inequity in our schools… Equity in our classrooms is essential and we must provide opportunities for all students to demonstrate these mathematical practices. To ensure equity, select tasks that can be differentiated. Some will need to be enhanced to meet the needs of students with a greater understanding of the content. While other tasks will have to be broken down into smaller parts for other students to work. Help students reason strategically. Encourage them to ‘think outside of the box’. Choose the best assessments that provide an accurate picture of the student’s understanding and development. (CLICK)

Mathematical Practice Standards
Leading with the Mathematical Practice Standards You can begin by implementing the 8 Standards for Mathematical Practice now Think about the relationships among the practices and how you can move forward to implement BEST PRACTICES Analyze instructional tasks so students engage in these practices repeatedly You can begin the process of implementing the Standards for Mathematical Practice now. Become familiar with the practice standards and the behaviors that you want to develop in your students. Select tasks that provide opportunities for your students to demonstrate desired behaviors. Where can you find mathematical tasks? Some are embedded in your instructional materials (textbooks, additional resources)..As you begin the process of selecting new curricular materials, be aware of the tasks that are provided in the resources. Tasks can be found on several websites. Insidemathematics.org contains many tasks categorized by grade level and course. (CLICK)

?? Questions ?? Are there any questions concerning the Standards for Mathematical Practice? If not, we will continue with the Literacy Standards in the 2010 Alabama Mathematics Course of Study. (Collect Practice Standards Cards) (CLICK)

Literacy Standards for Grades 6 – 12
2010 Alabama Course of Study: Mathematics College- and Career-Ready Standards This section focuses on understanding the Literacy Standards in the 2010 Alabama Course of Study: Mathematics which includes reading and writing in the mathematics classroom. Literacy will now be included in all courses of study for all subject areas. (CLICK) Literacy Standards for Grades 6 – 12

APPENDIX C Literacy Standards for Grades 6 – 12 History/Social Studies, Science and Technical Subjects “These standards are designed to supplement students’ learning of the mathematical standards by helping them meet the challenges of reading, writing, speaking, listening, and language in the field of mathematics.” The 2010 Mathematics Course of Study contains Literacy Standards for grades 6 – 12. They are found in Appendix C but can also be viewed in the English Language Arts Course of Study in Appendix B. The Literacy standards are designed to be a supplement to other Course of Study Standards including mathematics, listed as a ‘Technical Subject’ within the document. Within the Position Statements on p. 4 of the Mathematics Course of Study we see the Literacy Standards specifically mentioned under the section on Curriculum. (READ THE STATEMENT ON SCREEN) (CLICK)

It is essential for educators to:
select and develop resources that ensure students can connect their curriculum with the real world. help students recognize and apply math concepts in areas outside of the mathematics classroom. provide students with opportunities to participate in mathematical investigations. Through the Literacy Standards, educators are to facilitate instruction so students make connections between mathematics and other subject areas. It is essential for Educator to: (CLICK AND READ x 4) help students develop problem-solving techniques and skills which enable them to interconnect ideas and build on existing content.

Basis of Literacy Standards
The Literacy Standards for Reading and Writing are based on the College and Career Readiness (CCR) anchor standards as outlined in the English Language Arts (ELA) common core. Both of which are outlined in Appendix C. The Literacy Standards are based on the English Language Arts (ELA) ‘College and Career Readiness (CCR)’ Anchor Standards, for both Reading and Writing. They are broken down into two parts: Reading in Technical Subjects Writing in Technical subjects As mentioned earlier ‘Technical Subjects’ includes mathematics. (CLICK)

Layout of the Literacy Standards
Appendix C p College and Career Readiness Anchor Standards for Reading p Reading Standards for Literacy in History/Social Studies 6-12 p Reading Standards for Science and Technical Subjects 6-12 p College and Career Readiness Anchor Standards for Writing p Writing Standards for Literacy in History/Social Studies, Science and Technical Subjects grades (through p. 134) In the appendices, here is how the Standards are presented: (CLICK) First, on page 128, there is an outline of the College and Career Readiness Anchor Standards. These are the standards we mentioned in the previous slide; the basis of the Literacy Standards. Next are the Reading Standards for History and Social Studies (p. 129). Read the first sentence on page We will look at an example of a K-5 Reading standard in just a moment. On Page 130, you will see the specific requirements for mathematics grades 6-12: The Reading Standards for Technical Subjects which includes Mathematics. Then, just like the outline for reading, the Course of Study gives us the ‘Outline of the College and Career Anchor Standards for Writing’. Again, these are taken from the ELA (English Language Arts Common Core) and are the basis of the writing portion of the Literacy Standards. Finally, on page 132, begins the 3 pages that outline the standards for ‘Writing in Technical Subjects’ – mathematics. Also, the first sentence on this page states that writing literacy standards for K-5 are integrated into the ELA writing standards. We will look at how mathematics reinforces the K-5 ELA standards in a minute. (CLICK FOR EMPHASIS x 2) Mathematics teachers in grades 6-12 will look directly to both: The Reading and Writing Standards for Technical Subjects for their objectives. (CLICK)

1st Grade Mathematics / Standard 2
Course Standard: 2. Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem. ELA Reading Standard: Grade 1, Standard 10: Ask and answer questions about key details in a text. Problem: I was cleaning the classroom. I found 5 pencils on the floor. I found 6 pencils under the window. I found 2 pencils on the desk. How many pencils did I find? Here is an 1st Grade problem where an ELA reading standard can be implemented. We are using Grade 1, Standard #2. (READ) (CLICK) It uses an ELA standard from grade 1. Here is the problem (READ) Aside from solving the equation, what must the student demonstrate to show mastery of this ELA standard? (Wait for responses) Possible responses: Answer questions about this problem. Perhaps write an extension to this problem. Now, let’s see how a writing standard can be implemented. (CLICK) Teacher/Instructional Leader Notes: Assess for student understanding by asking questions regarding details of the problem. Reading problems provide the teacher with tremendous insight into students understanding.

4th Grade Mathematics / Standard 11
Course Standard: 11. Find whole-number quotients and remainders with up to four-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. ELA Writing Standard: Grade 4, Standard 23d: Write informative or explanatory texts to examine a topic and convey ideas and information clearly. d. Use precise language and domain-specific vocabulary to inform about or explain the topic. Problem: Solve the division problem 56 ÷ 4. You may use cubes, grid paper, drawings, or other math tools to help you. Explain how you solved the problem. Here is an 4th Grade example where an ELA reading standard can be implemented. We are using Grade 4, Standard #11. (READ) (CLICK) It uses an ELA standard from grade 4. Here is the problem (READ) Aside from solving the problem, what must the student demonstrate to show mastery of this ELA standard? (Wait for responses) Possible responses: Write an explanation of the steps used in solving this problem. Use mathematical vocabulary in their explanation. (CLICK) Teacher/Instructional Leader Notes: After students have computed the answer to the problem, ask them to write a story problem for the mathematical problem. Requiring students to write an explanation of their answers provides insight for the teacher into student understanding.

Snapshot View Notice that the ten reading standards are in grade spans
Snapshot View Notice that the ten reading standards are in grade spans A great layout to assist teachers in differentiating instruction! We will take a close-up look in a moment. But first, here is an overall ‘snapshot view’ of what the READING Standards look like in the appendices. (If attendees have a copy of the standards, say: ) Please turn to page 130 in your standards to view this more closely. Notice how the Standards are in Grade Spans: (Point to the columns) 6-8 9-10 11-12 This is a very useful layout for teachers as they differentiate instruction to meet the needs of various learners and to show progression in the instruction. Let’s take a closer look at the first standard. (CLICK)

A closer look: 1.Cite specific textual evidence to support analysis of science and technical texts. 1. Cite specific textual evidence to support analysis of science and technical texts, attending to the precise details of explanations or descriptions. 1. Cite specific textual evidence to support analysis of science and technical texts, attending to important distinctions the author makes and to any gaps or inconsistencies in the account. Here we isolated the first Reading Standard from page 130. This is the first of the ten reading standards. Notice how the standard is common throughout all grade spans, with the level of difficulty increasing as the student progresses. (Allow time for participants to read and note differences between grade bands – point out as needed.) The next slide gives a fun example of this standard at all levels. (CLICK)

Famous Mathematician Cards (aka: ‘The Baseball Card Project’)
This project is just a fun way to have students write a report on a famous mathematician. It is also a great project when you are not wanting to introduce a new math concept, for example, during testing week. Students can format their report just like a baseball card. (CLICK) The front has the name, a picture, and the date the mathematician lived. The back of the card has any factual information: Birthplace Famous quotes Education Field of mathematics Why the mathematician was famous Interesting stories If you notice, this student has simple references listed on the back: The Internet and an Encyclopedia. This is a young student. As the age span progresses, you would expect more specific information. In 9th and 10th grade, I would expect to see the specific website and the date the information was found, or the specific Encyclopedia. An 11th or 12th grade student should cite each entry on the project in proper APA or MLA format. Check with your English Department on which format the students are taught. Lets take a look at another reading standard. FRONT BACK

Another Reading Standard:
Grades 6 – 8: Students should be able to read a word problem and create an image of some sort (diagrams, graphs, etc…) Grades 9 – 10: Students should ALSO be able to reverse this skill: translate diagrams and charts into meaningful problems or equations. Grades 11 – 12: Finally, they should expand this skill to other sources (video, data) and use it to address questions and solve problems. This is Reading Standard #7, just as it appears in the Appendices on page 130. Notice again, that the standard progresses by grade. Essentially, it says: (CLICK) In Grade 6-8 (Read) In Grade 9-10 (Read) In Grade (Read) As stated earlier, this is a great layout for differentiating instruction as teachers strive to meet the needs of Tier II students in the classroom, under the guidelines of RtI (Response to Instruction). For example: A teacher teaching Algebra I to 9th graders would expect them to meet the standards in the middle column. But, if they had a student who struggled in reading, they could possibly look to the column for grade span 6-8 for Tier II instruction. Similarly, if a teacher has students who are excelling, the student could be pushed toward the Grade span. Let’s look at a sample problem for this same standard.

Grade 8 Mathematics / Standard 22
Course Standard: 22. Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions. ELA Standard: Reading Standard 7: Integrate quantitative or technical information expressed in words in a text with a version of that information expressed visually. Problem: Settlers in the Old West would often fashion tents out of a piece of cloth thrown over tent poles. They would secure it to the to the ground with stakes forming an isosceles triangle for the opening. How long would the cloth have to be so that the opening of the tent was 4 meters high and 6 meters wide? Here is an 8th Grade Geometry problem on Pythagorean Theorem. We are using Course Standard #22. (READ) (CLICK) It uses Reading Standard #7 which we recently reviewed. Here is the problem (READ) Aside from solving the equation, what must the student demonstrate to show mastery of Reading Standard #7? (Wait for responses) Yes, the student must draw and label the diagram correctly. Let’s look at the solution.

Teacher/Instructional Leader Notes:
Solution: Original Problem: Settlers in the Old West would often fashion tents out of a piece of cloth thrown over tent poles. They would secure it to the to the ground with stakes forming an isosceles triangle for the opening. How long would the cloth have to be so that the opening of the tent was 4 meters high and 6 meters wide? The vertical pole forms 2 right triangles, so I am using the Pythagorean Theorem. a2 + b2 = c2 = c2 = c2 25 = c2 5 = c But, there are two sides to the tent, so the material needs to be 10 meters long. Answer: The cloth needs to be 10 meters long. 4 6 The 8th grade student is to ‘create an image’ from the word problem. The teacher should continuously challenge the student to include detailed information such as the congruent sides and the right angle notation. And then, (CLICK) the teacher should challenge the student to show all work and (CLICK) explain necessary details through the incorporation of writing. This is an example of how literacy is incorporated into mathematics. Notice that this problem is not only about settlers in the old west, it brings in mathematics through the use of the Pythagorean theorem, translation of verbal expressions into algebraic expressions, and construction of drawings based on written descriptions . Notice the student has their final answer in a complete sentence and offers explanation as needed. It is important that students be able to defend their problem set-up and process toward solving the problem. We’ve been talking about how students write their responses but we haven’t looked at our writing standards. Let’s look at the first one now. (CLICK) 3 (1/2 of 6) Teacher/Instructional Leader Notes: Expressing answers as a complete sentence incorporates routine writing. Continually express the importance of accuracy and clarity in diagrams. Assess student ability to translate the word problem into a diagram separately from the ability to solve a problem. It is vital to include word problems in mathematics instruction. It is equally important students be given an opportunity to share idea’s or concerns about their work and to receive timely feedback.

Snapshot View : Writing Standards (page 1 of 3)
Just like the reading standards, we will look at the writing standards more closely in a moment. First, note that the Writing Standards stretch over 3 pages. This is page 132 in your Course of Study. The Writing Standards are also divided by Grade Spans: 6-8, 9-10, and (Point at columns) Unlike the Reading Standards, which are written differently for Social Studies than they are for Science and Mathematics, the Writing Standards are the same for History/Social Studies, Science and Technical Subjects. The teacher needs to consider the specific discipline when applying the standards. This first standard goes into great detail on how a student should construct a formal written argument in regards to discipline specific texts. Take a moment to glance over this first standard and its subparts. (PAUSE) Students need to be taught to do this, step by step. A good place to start might be back at the sample problem we just viewed. (CLICK)

REVISITING: Grade 8 Standard 22
Course Standard: 22. Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions. Original Problem: Settlers in the Old West would often fashion tents out of a piece of cloth thrown over tent poles. They would secure it to the to the ground with stakes forming an isosceles triangle for the opening. How long would the cloth have to be so that the opening of the tent was 4 meters high and 6 meters wide? NEXT Standard: Writing Standard #1: Write arguments focused on discipline-specific content. Recall in our previous example the teacher had the students solve a word problem using the Pythagorean Theorem and incorporating English language arts #7 reading standard. (CLICK) We are now going to add a Writing Standard to the same problem. (READ) In this scenario, the teacher presents the solutions solved incorrectly. The students write an argument, using applicable mathematics vocabulary, that disputes or defends the logic used in a sequential manner. NEW ASSIGNMENT: The teacher presents solutions from the original assignment which were labeled incorrectly, had faulty logic and/or an incorrect solution. Randomly distribute and direct students to write a brief argument for each solution to either defend or dispute the logic used.

Snapshot View : Writing Standards p. 2
Close-up: 2. Write informative/explanatory texts, including the narration of historical events, scientific procedures/ experiments, or technical processes: Introduction Development of ideas Transitions Vocabulary Style Conclusion Here is a snap-shot view of the Second Writing Standard. Which is also written with subparts. (CLICK) In short, it guides the student through writing informative text (read square). This could be as simple as a two-column proof.

Writing Standard #3 In science and technical subjects, students must be able to write precise enough descriptions of the step-by-step procedures they use in their investigations or technical work so others can replicate them and (possibly) reach the same results. Writing standard #3 does not stand alone as a requirement, but rather is part of all the other objectives. (READ SCREEN) (CLICK)

Snapshot View : Writing Standards p. 3
This is a snapshot view of the remaining 7 (of 10) writing standards. They cover: The Production and Distribution of Writing Research to build and present knowledge Range of writing (CLICK)

*The same for all three levels
A closer look: *The same for all three levels 10. Write routinely over extended time frames (time for reflection and revision) and shorter time frames (a single sitting or a day or two) for range of discipline-specific tasks, purposes, and audiences. Here we isolated the final writing standard. One that makes a very important statement. And, is the same for all three grade spans. (READ) If your school is an AMSTI school, especially at the High School level, this is incorporated in your texts. The AMSTI workbook “Cookies”, for example, takes the students through multiple reading and writing activities as they learn to read and write Linear Inequalities. Students revisit their logic throughout the text, extending it with each activity. If your school is not an AMSTI school, there are numerous ways to incorporate writing into the mathematics classroom and many teachers are already doing this on a daily basis throughout the state. Let’s look at some questioning that encourages thought towards writing in the mathematics classroom. (CLICK)

Questioning that Encourages Thought
Does the rule I am using work for all cases? Why, why not? How can I describe what is happening without using specific numbers? How can I predict what’s going to happen without doing all the calculations? Was my prediction correct; how was my logic faulty? What process reverses the one I am using and when is it appropriate? How did two different students reach two different answers? Defend logic. Are there multiple ways to work the same problem? If so, how did you decide which process to use? Can you write a scenario (word problem) for the diagram? Describe your frustrations with the process learned today. Outline everything you understand about the process you used today. (CLICK AND READ x 10) The teacher needs to learn to present prompts that help express their understanding of the content. Some activities that encourage this process are: -Journaling -Exit Slips -Portfolios -Foldables and more. (CLICK) Driscoll, M. Fostering Algebraic Thinking

Grade 8 / Geometry Standard 18
Course Standard: 18. Describe the effect of dilations, translations, rotations and reflections on two-dimensional figures using coordinates. [G3] ELA Standard(s): Reading Standard 7: Integrate quantitative or technical information expressed in words in a text with a version of that information expressed visually. Writing Standard 2f: Provide a concluding statement that follows from and supports the information presented. Problem: Mr. Smith asked his students to plot the following points in order, connecting them to form a triangle: (3,0) (7, 1) (4, 5) (3,0). Here are the student responses. Which is correct? Describe the errors in logic made on the remaining three and the result of those errors. A B C D. Here is a final sample problem using both a reading and writing standard. Review the course standard. (CLICK) Note we are using both a reading and writing standard. (READ) Lets review the problem (READ) And the solution.

Possible Solution: Triangle A is plotted correctly
A B C D Triangle A is plotted correctly In triangle B, the student switched the (x,y) coordinates. Instead of plotting (3,0) they plotted (0, 3). The student might be confused about which axis is the x and which axis is the y. In Triangle C, the student went in the negative direction for the x coordinate but plotted the y correctly, this caused a reflection around the y-axis. In triangle D the student plotted the x coordinate correctly but went in the negative direction for the y, this caused a rotation and a shift in the graph. Here is the student solution. I’m going to pause to give you time to read through their responses. (PAUSE) As teachers and teacher leaders, what should we be looking for in the response? (CLICK to answer on next slide)

Teacher/Teacher Leader Notes
Is the student’s mathematical logic correct? Can they describe errors found in others’ mathematical thinking? Activities like this may be used as a bell ringer (sparking discussion prior to a lesson) or as an exit slip to assess understanding. It is important that the responses are assessed by the teacher through grading or discussion. (CLICK AND READ x 4) After viewing the Reading and Writing Standards, and looking at some simple examples; there is one overall thought we want to leave you with as teachers and administrators in regards to the Literacy Standards. (CLICK)

Final Thought: The Literacy Standards Allow Flexibility in Reading and Writing
Predictions Proofs Compare/Contrast methods Reflection Journals Word Problems Summarize One thing the inclusion of technical standards in the ELA documents allows for is flexibility. Nowhere is the mathematics teacher told HOW to incorporate these standards into their mathematics curriculum, just that they are to do it often and with rigor. If one method doesn’t work well with one class, try another – try several! The sky is the limit! (CLICK) Writing directions for replication by others Descriptions of Process or change

?? Questions ?? Are there any questions concerning the Literacy Standards in the 2010 Alabama Mathematics Course of Study? If not, we will continue with the Domains of Study/Conceptual Categories and Learning Progressions/Trajectories. (CLICK)

2010 Alabama Course of Study: Mathematics College- and Career-Ready Standards
We will now discuss and explore the domains of study, conceptual categories, and learning progressions/trajectories in this section of the presentation. (CLICK) Domains of Study/Conceptual Categories Learning Progressions/Trajectories

CHARACTERISTICS Aligned with college and work expectations
Written in a clear, understandable, and consistent format Designed to include rigorous content and application of knowledge through high-order skills Formulated upon strengths and lessons of current state standards Informed by high-performing mathematics curricula in other countries to ensure all students are prepared to succeed in our global economy and society Grounded on sound evidence-based research All standards contained in this document are: (CLICK) Aligned with college and work expectations; (CLICK) Written in a clear, understandable, and consistent format; (CLICK) Designed to include rigorous content and application of knowledge through high-order skills; (CLICK) Formulated upon strengths and lessons of current state standards; (CLICK) Informed by high-performing mathematics curricula in other countries to ensure all students are prepared to succeed in our global economy and society; and (CLICK) Grounded on sound evidence-based research. (CLICK)

2010 Alabama Course of Study: Mathematics
Coherent Rigorous Well-Articulated Enables Students to Make Connections All content contained in this document is (CLICK) coherent, (CLICK) rigorous, (CLICK) well-articulated across the grades, (CLICK) and focuses on enabling students to make connections between important mathematical ideas. (CLICK) ACOS, p. 4

Coherence Articulated progressions of topics and performances that are developmental and connected to other progressions. Conceptual understanding and procedural skills stressed equally. Real-world/Situational application expected. (CLICK) The mathematics curriculum has been sorted into topics articulated as progressions that are developmental and connected. (CLICK) Both conceptual understandings and procedural skills have equal importance. (CLICK) Application of learning is expected at all levels. (CLICK)

FOCUS Key ideas, understandings, and skills are identified.
Deep learning stressed. Key ideas, understandings, and skills are identified in each grade or course, while stressing deep learning. (CLICK)

Mathematical Content Format
Grade Domain Cluster Standard Course Conceptual Category Domain Cluster Standard The organizational structure of the 2010 Alabama Course of Study was discussed briefly during the Components of the Course of Study section. Let’s look in more detail at the format. The format is consistent throughout K-8, with an additional dimension in high school. The high school standards are organized into conceptual categories which have been grouped into courses. (CLICK) K-8 9-12

What is the difference? Domain Cluster Standards
Definitions of domains, clusters, and standards are on the top of page 10 in the COS. Read through these and discuss the definitions with your shoulder partner. (Allow a few partners to report to whole group. Click to continue definitions on next slide.) (CLICK)

What is the difference? Domain: Overarching “big ideas” that connect content across the grade levels. Cluster: Group of related standards below a domain. Standards: Define what a student should know (understand) and do at the conclusion of a course or grade. (CLICK) Domains are large groups of related standards. (CLICK) Clusters are groups of related standards and appear below domains. (CLICK) Standards are numbered/lettered beneath each cluster. (CLICK)

K-8 Domains Illustrate progression of increasing complexity from grade to grade. Organize standards within each grade. Note: Domains typically span a few grades. Domains: (CLICK) Are progressions of increasing complexity from grade to grade. (CLICK) Organize standards within each grade. (CLICK) Are overarching big ideas that connect topics across the grades. (CLICK)

Mathematics Domains of Study by Grade
The standards in Grades K – 8 are focused around eleven domains of study. They are listed in the first column. The predominate grades each domain is studied is noted with a check. The progression of domains demonstrates the mathematical progression through grade K- 8. All domains are not present in each grade, however a domain that stops or changes names is foundational and serves in the learning of new ideas or applications. An example is Number and Operations in Base Ten which spans Kindergarten through grade 5 and Fractions which spans Grades 3 – 5. These two domains merge into The Number System in 6-8. Geometry spans K-8 (as well as High School). (CLICK)

K-8 Clusters May appear in multiple grades.
Illustrate progression of increasing complexity from grade to grade. Standards that are related are identified by a cluster. The same cluster may appear in multiple grade levels with their respective standards growing developmentally. An example is in grades 1 and 2. (CLICK)

K – 8 Cluster Add and subtract within 20.
Grade 1 Grade 2 Add and subtract within 20. Relate counting to addition and subtraction (e.g., by counting on 2 to add 2). [1-OA5] Add and subtract within 20, demonstrating fluency for addition and subtraction within Use strategies such as counting on; making ten (e.g., = = = 14); decomposing a number leading to a ten (e.g., 13 – 4 = 13 – 3 – 1 = 10 – 1 = 9); using the relationship between addition and subtraction (e.g., knowing that = 12, one knows 12 – 8 = 4); and creating equivalent but easier or known sums (e.g., adding by creating the known equivalent = = 13). [1-OA6] Fluently add and subtract within 20 using mental strategies. (See standard 6, Grade 1, for a list of mental strategies.) By end of Grade 2, know from memory all sums of two one-digit numbers. [2-OA2] An example of a cluster appearing in multiple grade levels is in Grades 1 and 2. In 1st grade the students are depending on the strategies to add and subtract. However, in 2nd grade, students have progressed in their ability to reason numerically by understanding generalizations. (CLICK)

Content Standards Content standards in this document contain minimum required content. Each content standard completes the phrase “Students will.” Reflect both mathematical understandings and skills, which are equally important. (Read the slide (CLICK) Minimum in quantity, not quality. (CLICK) (CLICK) ) The order in which standards are listed within a course or grade is not intended to convey a sequence for instruction. (CLICK)

Activity: A Closer Look
Turn to the Mathematics standards for your grade. Domain by Domain, read the cluster headings and count the number of standards within each cluster. Write the number of standards that corresponds to each cluster heading in the boxes provided. Let’s break into three groups: K-2, 3-5, and 6- 8 grade-level groups to complete this activity. Directions: (CLICK) (CLICK) (CLICK) Discuss the number you identified and reach a consensus with your grade level group. Decide how do the number of standards compare to the number of skills? Are they the same? Explain your answers. Have a spokesperson from the grade level group share out. Possible answers: See answer key document. (CLICK)

How Many Skills? Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. [4-NBT2] Read multi-digit whole numbers using base-ten numerals. Read multi-digit whole numbers using number names. Read multi-digit whole numbers using expanded form. Write multi-digit whole numbers using base-ten numerals. Write multi-digit whole numbers using number names. Write multi-digit whole numbers using expanded form Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. Now let’s look at Grade 4, standard 7 on page 34 in the COS to see how many skills may be embedded in one standard. (CLICK X 7) (1. Ask participants to discuss how many skills they think are in standard #7. 2. Allow a minute for them to discuss at their tables. 3. Have a few participants respond and then click to show how this standard breaks down into skills. 4. Tell participants they will analyze the standards and determine the number of skills in each grade level standard in future professional development.) Notice the coding of the standard. The first number represents the grade level, or course for high school. The second number represents the standard and the third is the number of the identified skill(s) contained in the standard. Do not worry if you do not fully understand how to analyze standards; we will be looking at skills and subskills more closely in Phase II. (CLICK)

Grade Level Overview Grade Level Narrative Grade Level Focus
Earlier, we briefly discussed the overviews and narratives of each grade and high school conceptual category. Each grade in K-8 begins with an overview of the domains and clusters, as well as, a narrative about the focus of that grade. (CLICK) These narratives identify the critical areas, which cut across topics, in the grade and specifies the content for that grade level by describing 2 – 4 critical areas. (CLICK) The description of each critical area illustrates the focus for the learning. (CLICK) Critical Area

CRITICAL AREAS BRING FOCUS TO THE NEW STANDARDS
Next we will engage in a hands-on activity. (CLICK)

CRITICAL AREAS Identify Two to Four Areas of Concentrated Study.
Bring Focus to the Standards. Provide the Big Ideas for Building Curriculum and Guiding Instruction. Critical Areas provide a sense of … sophistication for mathematical understanding at the grade level. the learning progressions for the grade. extensions from prior standards. what’s important at the grade level. (CLICK) There are two to four critical areas in the grade level narrative for each grade level. (CLICK) They bring focus to the standards at each grade by providing the big ideas that educators can use to build their curriculum and to guide instruction. The NCTM Focal Points were used as a model for the creation of the critical areas. (Note as an FYI:) Grade # of critical areas K 2 1 4 2 4 3 4 4 3 5 3 6 4 7 4 8 3 (CLICK)

INVESTIGATING FOCUS In groups of 2-4, select one of the critical areas for your grade. Read your critical area and underline the key words that help summarize this area. Discuss with your table partners the key words you underlined for your grade and how they will help guide the focus of your instruction. (Refer to the slide for specific directions. Allow a few minutes for discussion in groups. Allow someone to share a key word and how it will help guide their instruction.) (CLICK)

INVESTIGATING CRITICAL AREAS
In grade-level groups, analyze the critical areas for your grade. Underline the key words and phrases that help summarize this area. Design a poster that describes the focus of your grade level. Divide participants by grade levels – kindergarten through 8. Ask each group to read through the critical areas for their grade level, underlining important words and phrases as they read. Then, each group will develop a graphic (on chart paper) that will explain to the other participants the focus of their grade level. This activity will demonstrate to participants how the learning progresses across the grade levels. Groups will share out when done with this activity.

The Big Picture High School Functions, Statistics, Modeling and Proof
K-2 Number and number sense. 3-5 Operations and Properties (Number and Geometry) Fractions 6-8 Algebraic and Geometric Thinking Data Analysis and using Properties Broad topics can be used to organize instruction for the entire year. Let’s look at The Big Picture of the focus of study by grade bands. (CLICK)

Mathematics Domains of Study by Grade
Remember we have looked at these domains earlier. As you can see, the grade bands overlap and connect as the focus of the standards is expanded and applied across the grade bands. Even though it appears that these domains end at grade 5, they do not because they are foundational in the learning progression for higher grades. (CLICK)

What Are Learning Trajectories. And What Are They Good For
What Are Learning Trajectories? And What Are They Good For? —Save the Last Word for Me!!! Read the excerpt from Learning Trajectories in Mathematics: A Foundation for Standards, Curriculum, Assessment, and Instruction Identify 3 ideas that you are willing to talk about with colleagues. Highlight the location in the text where these ideas appear. This activity is: “Save the Last Word for Me.” You will begin reading at the first full paragraph of the article. (Read the directions on the slide. Continued on next slide.) (CLICK) 96

Learning Progressions/Trajectories
Confrey (2007) “Developing sequenced obstacles and challenges for students…absent the insights about meaning that derive from careful study of learning, would be unfortunate and unwise.” CCSS, p. 4 “… the development of these Standards began with research-based learning progressions detailing what is known today about how students’ mathematical knowledge, skill, and understanding develop over time.” In addition the sequence of topics and performances that is outlined in a body of mathematics standards must also respect what is known about how students learn. As Confrey (2007) points out, “developing sequenced obstacles and challenges for students…absent the insights about meaning that derive from careful study of learning, would be unfortunate and unwise.” (CLICK) “… the development of these Standards began with research-based learning progressions detailing what is known today about how students’ mathematical knowledge, skill, and understanding develop over time.” CCSS 2010, p. 4 Just exactly what are learning progressions/trajectories? Think about this question as you participate in the next activity. (CLICK)

Directions for Save the Last Word for Me
Designate a facilitator and timekeeper. A volunteer begins by reading the sentence(s) from the text that embody one of his/her selected ideas. The speaker does not comment on the text at this point. The individual to right of first speaker takes up to one minute to comment on the selected text. The next two individuals also take up to one minute to comment on the initial speaker’s idea. The individual selecting the idea has up to 1 minutes to react to colleagues’ ideas and to talk about why she or he thought this was important. Another group member introduces one idea, and the group follows the same protocol. Continue until all members have shared or until time is called. (Read slide and explain to participants the directions for the activity.) How was this a useful way to explore the ideas in the text and to explore your own thinking? What questions were raised during this protocol? (CLICK)

Learning Trajectories – sometimes called learning progressions – are sequences of learning experiences hypothesized and designed to build a deep and increasingly sophisticated understanding of core concepts and practices within various disciplines. The trajectories are based on empirical evidence of how students’ understanding actually develops in response to instruction and where it might break down. Daro, Mosher, & Corcoran, 2011 To better grasp the mathematical understandings, it is important to have a common reference for the meaning of a learning progression.(Read what is on the slide first, then read the next two sentences.) The K- 8 Common Core Math Standards which are incorporated into Alabama’s Mathematics Course of Study are formatted into learning progressions based on the domains. (CLICK)

Learning Progression Framework
Ending Point Ending Point Starting Point Starting Point K 1 2 3 4 5 6 7 8 HS Counting and Cardinality Number and Operations in Base Ten Ratios and Proportional Relationships Number and Quantity Number and Operations – Fractions The Number System Operations and Algebraic Thinking Expressions and Equations Algebra Functions Geometry Measurement and Data Statistics and Probability The domains are the learning progressions. Guiding Question (Discussion for Table Groups) What do you notice when looking at the K-8 domains? (Allow participants to talk at their tables as facilitator rotates around the room. Bring participants back together whole group and allow table groups to report out. Before charting responses to show the starting and ending point arrows. (CLICK X 2) Chart the rest of the responses.) (Possible responses are: Starting and ending points – students need to have understanding of standards in the domains to be able to move on to the next domain. Counting and Cardinality only in Kindergarten. If a child does not attend Kindergarten, he is already behind. So how will you help the child learn these missed concepts? Fractions are not taught until Grade 3 Ratio and Proportion taught in 6th and 7th only Functions are not taught until Grade 8 Operations and Algebraic Thinking in K-5 is the foundation for both Expressions and Equations, and Functions in Grades 6-8. K-5 Measurement and Data, which splits into Statistics and Probability and Geometry in Grade 6) What is not easily seen, is how a learning progression may indirectly impact multiple progressions that start later in school years. Math educators are use to thinking about strands in standards (there are 5 broad strands in state standards in Alabama’s current COS) – you can think about the progressions (domains) as small strands – slightly more finely divided with one important difference which is that the progressions have a starting point and an ending point. In particular there is a transition from K-5 to 6-8 which brings in a new set of progressions - the implication is that the O&A, NBT, and Fractions work is meant to be finished at the end of grade 5 so we are meant to use that as foundation to move on to a higher level of understanding –domains have a beginning and an ending point. (CLICK)

Investigating the Domains/Conceptual Categories
Domains provide common learning progressions. Curriculum and teaching methods are not dictated. Standards are not presented in a specific instructional order. Standards should be presented in a manner that is consistent with local collaboration. (CLICK) Domains are common learning progressions that can progress across grade levels. (CLICK) Domains do not dictate instructional curriculum or teaching methods. (CLICK) Topics within domains are not meant to be taught in the order presented. (CLICK) Teachers should present the standards in a manner that is consistent with decisions that are made in collaboration with their K-12 mathematics team. (CLICK) 101 101

Table Team Work Beginning at the lowest grade examine the domain and conceptual category, cluster and standards at your grade level - identify how the use of numbers and number systems change from K- 12. Counting & Cardinality (CC) – K only Number and Operations in Base Ten (NBT) – K-5 Number and Operations – Fractions (NF)– 3-5 The Number System (NS)– 6-8 Look at the grade level above and grade level below (to see the context). Make notes that reflect a logical progression, increasing complexity. As a table group share a vertical progression (bottom–up or top-down) on chart paper. (Group participants in gradebands K-2, 3-5, and 6-8.) To help you with this activity you might want to look for the Content Standard Identifiers ( CC, NBT, NF, NS, and N(9-12)). (Go over directions on slide.) (Possible information for presenter: Numbers and Number Systems. During the years from kindergarten to eighth grade, students must repeatedly extend their conception of number. At first, “number” means “counting number”: 1, 2, 3... Soon after that, 0 is used to represent “none” and the whole numbers are formed by the counting numbers together with zero. The next extension is fractions. At first, fractions are barely numbers and tied strongly to pictorial representations. Yet by the time students understand division of fractions, they have a strong concept of fractions as numbers and have connected them, via their decimal representations, with the base-ten system used to represent the whole numbers. During middle school, fractions are augmented by negative fractions to form the rational numbers. In Grade 8, students extend this system once more, augmenting the rational numbers with the irrational numbers to form the real numbers. In high school, students will be exposed to yet another extension of number, when the real numbers are augmented by the imaginary numbers to form the complex numbers. With each extension of number, the meanings of addition, subtraction, multiplication, and division are extended. In each new number system—integers, rational numbers, real numbers, and complex numbers—the four operations stay the same in two important ways: They have the commutative, associative, and distributive properties and their new meanings are consistent with their previous meanings.) (CLICK)

What Goes On The Chart Paper?
Summary and/or representation of how the concept of the use of numbers grows throughout your grade band. Easy for others to interpret or understand. Visual large enough for all to see. More than just the letters and numbers of the standards – include key words or phrases. Summary and/or representation of how the concept of the use of numbers grows throughout your grade band. Easy for others to interpret or understand Visual large enough for all to see More than just the letters and numbers of the standards – include key words or phrases (CLICK)

Banding Together for a Common Message
Display posters side-by-side and in order on the wall. Begin at the grade band you studied. Read the posters for your grade band. Discuss similarities and differences between the posters. Establish a clear vision for your grade band. Notice not only what students need to know before they enter your course, but what they need to know for the next course as well. (CLICK)

Let’s Talk About It! As a table group, consider your journey through the 2010 ACOS as you studied the concept of the use of numbers K-12. What did you learn? What surprised you? What questions do you still have? Read slide. (CLICK)

Learning Progressions
K 1 2 3 4 5 6 7 8 HS Counting and Cardinality Number and Operations in Base Ten Ratios and Proportional Relationships Number and Quantity Number and Operations – Fractions The Number System This diagram illustrates how the learning progressions are distributed across the Alabama Course of Study Standards (coherence). Let’s look at the Number Domains as they build across K-12. (CLICK)

Value of Learning Progressions/Trajectories to Teachers
Know what to expect about students’ preparation. More readily manage the range of preparation of students in your class. Know what teachers in the next grade expect of your students. Identify clusters of related concepts at grade level. Clarity about the student thinking and discourse to focus on conceptual development. Engage in rich uses of classroom assessment. Here are some ways learning progressions/trajectories can be valuable to teachers. Reflect on the following two questions and then turn and talk to your table partner: How do the progressions apply to your work? Which of the statements on the screen would be most beneficial to you? (CLICK)

. Review the Format 2003 ACOS 2010 ACOS Contains bullets
Does not contain bullets Does not contain a glossary Contains a glossary . Let’s wrap up this section of the PD by looking briefly at some of the similarities and especially the differences between the current and new documents. Take a few minutes to discuss and review the similarities and differences between the current Alabama Standards and the 2010 ACOS format. (Allow about 2-3 minutes for participants to compare the current ACOS to the 2010 format for a couple of more statements to add to the chart. ) (Possible Responses: Bullets are no longer included in standards Lettered and numbered items (just as important – both must be mastered). Modeling standards STEM standards Glossary in 2010 but not in 2003 The grade clusters are different; K-8, and 9-12. The Domains progress across grade levels – not all domains are addressed in every grade; The number of standards are different for each grade and course. They range from 22 in Grade K to 28 in Grade 8. ) (CLICK)

?? Questions ?? Are there any questions concerning the Domains of Study, Conceptual Categories, or Learning Progressions/Trajectories? If not, we will continue with identifying content shifts in the 2010 Alabama Mathematics Course of Study. (CLICK)

2010 Alabama Course of Study: Mathematics College- and Career-Ready Standards
Each new course of study provides an opportunity to study the standards and adjust teaching plans accordingly. Because several standards have changed grade levels or moved to a different course, there will be some content from the 2010 standards that will have to be taught (along with the 2003 standards) during the school year to prepare students for full implementation of the 2010 ACOS during the school year. However, by studying these new standards with an eye toward developing plans to address this content, teachers and curriculum coordinators can insure that students are prepared for the new standards. Some may choose to develop modules specifically to address this content, while others may simply opt to add this additional content to their classes this year. (CLICK) Content Shifts

Content Correlation… KINDERGARTEN - GEOMETRY
Analyze, compare, create, and compose shapes. 20. Analyze and compare two- and three-dimensional shapes, in different sizes and orientations, using informal language to describe their similarities, differences, parts (e.g., number of sides and vertices/’corners’) and other attributes (e.g., having sides of equal length.) [K-G4] 21. Model shapes in the world by building shapes from components (e.g., sticks and clay balls) and drawing shapes. [K-G5] 22. Compose simple shapes to form larger shapes. [K-G6] First, let’s see what is meant by a content shift by working with kindergarten standards from the geometry domain. We’ll look at a cluster of standards and see what content, if any, has changed grade levels. The cluster is Analyze, compare, create, and compose shapes and contains standards These standards are found in your ACOS on page 15. 20. Analyze and compare two- and three-dimensional shapes, in different sizes and orientations, using informal language to describe their similarities, differences, parts (e.g., number of sides and vertices/’corners’) and other attributes (e.g., having sides of equal length.) [K-G4] 21. Model shapes in the world by building shapes from components (e.g., sticks and clay balls) and drawing shapes. [K-G5] 22. Compose simple shapes to form larger shapes. [K-G6] Ask if you have any Kindergarten teachers in your session. Are these standards currently taught in kindergarten in the 2003 document? (Allow time for reflection.) Let’s look and see. (CLICK)

CORRELATES WITH 2010 ACOS Kindergarten
21. Model shapes in the world by building shapes from components (e.g., sticks and clay balls) and drawing shapes. [K-G5] 22. Compose simple shapes to form larger shapes. [K-G6] CORRELATES WITH 2003 ACOS Kindergarten 6. Create combinations of rectangles, squares, circles, and triangles using shapes or drawings. After searching the Kindergarten standards, we find that standards #21 and #22 correlate with standard #6 from the ‘03 kindergarten course of study. (Read aloud Standard #6 that the 2010 content correlates to.) (CLICK)

KINDERGARTEN - GEOMETRY Analyze, compare, create, and compose shapes.
20. Analyze and compare two- and three-dimensional shapes, in different sizes and orientations, using informal language to describe their similarities, differences, parts (e.g., number of sides and vertices/’corners’) and other attributes (e.g., having sides of equal length.) [K-G4] 21. Model shapes in the world by building shapes from components (e.g., sticks and clay balls) and drawing shapes. [K-G5] 22. Compose simple shapes to form larger shapes. [K-G6] (CLICK) Now for standard 20, do you think this content is currently addressed in kindergarten in the 2003 standards? (CLICK)

CORRELATES WITH 2010 ACOS Kindergarten
20. Analyze and compare two- and three-dimensional shapes, in different sizes and orientations, using informal language to describe their similarities, differences, parts (e.g., number of sides and vertices/’corners’) and other attributes (e.g., having sides of equal length.) [K-G4] CORRELATES WITH After consulting the 2003 standards, we find that this content is found in Grade 1, Standard 8, bullet 1. The first grade standard is Describing similarities and differences between plane and solid shapes. That means the content from 2010 standard #20 constitutes a content shift. This content was previously taught in first grade but has now been moved back to kindergarten and is at a higher level of rigor. Notice the verb used in the 2003 (describe) and compare it to the verb from the 2010 COS (analyze). So, in the school year, the kindergarten teacher needs to address this content that has been moved down from first grade into kindergarten in order to prepare her students for first grade in the school year This content will not be covered in Grade 1 of the 2010 ACOS. So, if the kindergarten teacher (in the SY ) does not cover this, the student will have a ‘gap’ in their understanding. Any questions on what constitutes a content shift? Does everyone understand the procedure for determining content shifts? We have completed content correlation on each grade level, specifically looking for content that has either moved from one grade to another, is new to the Alabama standards, or is no longer taught in the ACOS. From those efforts, we developed a Content Correlation Document to assist you with planning for the 2011 school year. Let’s take a look at the document. (CLICK) 2003 ACOS First Grade 1.8.B.1 Describing similarities and differences between plane and solid shapes

Content Correlation Document
2003 ACOS 2010 ACOS CURRENT ALABAMA CONTENT PLACEMENT 2010 GRADE 1 CONTENT 1.1 Demonstrate concepts of number sense by counting forward and backward by ones, twos, fives, and tens up to 100; counting forward and backward from an initial number other than 1; and using multiple representations for a given number. 1.9. Count to 120, starting at any number less than 120. In this range, read and write numerals and represent a number of objects with a written numeral. [1-NBT1] 1.1.B.1 Identifying position using the ordinal numbers 1st through 10th CONTENT NO LONGER ADDRESSED IN GRADE 1 1.1.B.2 Using vocabulary, including the terms equal, all, and none, to identify sets of objects 1.7. Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false. [1-OA7] 1.1.B.3 Recognizing that the quantity remains the same when the spatial arrangement changes CONTENT NOW ADDRESSED IN KINDERGARTEN: 1.4.b. Understand that the last number name said tells the number of objects counted. The number of objects is the same regardless of their arrangement or the order in which they were counted. [K-CC4b] First, we’ll discuss the different sections of the content correlation document. This document is a content correlation for Grade 1. The first section is a correlation of the 2003 ACOS with the 2010 ACOS. In the left column, (CLICK) you will find all 2003 course of study standards and bullets for the Grade 1. (CLICK) In the right column you find the 2010 standard(s) that have been correlated with the current standard. Any content that is highlighted, indicates additional content that must be introduced along with the 2003 standard. For example, Count to 120 is highlighted in the 2010 content standard that has been correlated with standard 1 of the 2003 document. When you read the 2010 standard and compare it with the 2003 standard, you notice that the 2003 standards required students to count up to 100. The 2010 standard requires that they count to 120. This represents additional content that must be addressed in the upcoming school year. (CLICK) Notice that the 2003 standard. 1.1.B.1 Identifying position using the ordinal numbers 1st through 10th is no longer addressed in Grade 1 in the 2010 standards. In fact, this bullet is not addressed at all in the 2010 ACOS. (CLICK) Now, look at standard. 1.1.B.3, Recognizing that the quantity remains the same when the spatial arrangement changes. This content is now addressed in Kindergarten, Standard. 4b, which states: Understand that the last number name said tells the number of objects counted. The number of objects is the same regardless of their arrangement or the order in which they were counted. [K-CC4b] (CLICK)

2003 ACOS 2010 ACOS CONTENT MOVED TO GRADE 1 IN 2010 ACOS 2.6 Solve problems using the associative property of addition. 1.3. Apply properties of operations as strategies to add and subtract. (Students need not use formal terms for these properties.) [1-OA3] (Associative property of addition) 3.1.B.1 Comparing numbers using the symbols >, <, =, and 1.11. Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <. [1-NBT3] 4.10 Complete addition and subtraction number sentences with a missing addend or subtrahend. 1.8. Determine the unknown whole number in an addition or subtraction equation relating three whole numbers. [1-OA8] The next section in the Content Correlation document reflects content that has moved from another grade level to Grade 1. Notice in the left column, once again you find 2003 standards, in the right column the 2010 standards. In this example, notice that what is currently taught in second grade, (CLICK) Solve problems using the associative property of addition, is now found in the Grade 1 Standard #3 (CLICK), Apply properties of operations as strategies to add and subtract. (Students need not use formal terms for these properties.) [1-OA3] (Associative property of addition). Note the code at the end of the standard from the 2010 ACOS. (CLICK)- [1-OA3] – The number in brackets is the content standard identifier and indicates where this standard can be found in the CCSS document. This number will help you correlate resources that are available from other organizations, such as NCTM or other national organizations. Also, some standards from grades 3 and 4 have been moved to grade 1. First grade students are now expected to compare two-digit numbers and record their results of the comparisons with the symbols >, = and <. This was previously a third grade standard. Another example, what was previously a fourth grade standard, Complete addition and subtraction number sentences with a missing addend or subtrahend, is now a requirement of first grade, standard #8, Determine the unknown whole number in an addition or subtraction equation relating three whole numbers. [1-OA8]. Once again, the highlighted portion indicates additional content that must be addressed in the school year. In order to assist teachers who will be teaching new content from another grade-level, this would be a perfect opportunity to have the teachers collaborate in designing lessons. For example, if a first-grade teacher now must teach content that was taught in Grade 3 in the 2003 document, the third-grade teacher could collaborate with the first-grade teacher. (CLICK)

NEW GRADE 1 CONTENT IN 2010 ACOS None The final section of the document (CLICK) contains content that is entirely new to the Alabama Course of Study. In Grade 1, you can see there is no new content. (CLICK)

Grade 1 Content Correlation
Which 2010 standard(s) correlates to standard 13 from the 2003 ACOS? Is there any additional content related to standard 13 that should be addressed in the upcoming school year? What content has been moved from Grade 3 to Grade 1? Is there any content that is no longer addressed in Grade 1? How many standards? Is there any content that is new to Alabama in Grade 1 in the 2010 ACOS? (The participants will have an opportunity to answer questions from the Content Correlation Document. Ask everyone to turn to the Grade 1 document and discuss the following questions with their table partners. Allow 5 minutes for them to work on this.) Answers: Which 2010 standard(s) correlates to Standard. 13 from the 2003 ACOS? #18 Is there any additional content related to standard 13 that should be addressed in the upcoming school year? Yes. The students must organize, represent, and interpret data with up to three categories. What content has been moved from Grade 3 to Grade 1? Comparing numbers using <, >, =. Is there any content that is no longer addressed in Grade 1? How many standards? Yes, 7 standards Is there any content that is new to Alabama in Grade 1 of the 2010 ACOS? No (Briefly go over answers to these questions. Ask participants if there are any questions interpreting the content correlation document.) (CLICK)

How can I be sure my students are prepared for the implementation of the ACOS in the school year? (Read slide.) First of all, you must be aware of these content changes and begin to make plans to address any standards that may constitute a content shift for your students. Schools cannot wait until the year of implementation ( ) to make these plans. Teachers will need to address these content shifts during the school year to insure that students are prepared for the full implementation the next year. Let’s see how this Content Correlation document can be used to assist with these plans. (CLICK)

First Grade Mathematics Curriculum
First Nine Weeks 2003 COS # DESCRIPTION CONTENT TO BE ADDED 1.5.B B B.3 Create repeating patterns. Describing characteristics of patterns Extending patterns including number patterns Identifying patterns in the environment B.1 Locate days, dates, and months on a calendar. Using vocabulary associated with a calendar 1.1 1.1.B.2 Demonstrate concepts of number sense by counting forward and backward by ones, twos, fives, and tens up to 100; counting forward and backward from an initial number other than 1; and using multiple representations for a given number. Using vocabulary, including the terms equal, all, and none, to identify sets of objects 1.1.B.3 1.1.B.4 1.1.B.5 Demonstrate concepts of number sense by counting forward and backward by ones, twos, fives, and tens up to 100; counting forward and backward from an initial number other than 1; and using multiple representations for a given number. Recognizing that the quantity remains the same when the spatial arrangement changes Determining the value of the digit in the ones place and the value of the digit in the tens place in a numeral Determining the value of a number given the number of tens and ones NO NEW CONTENT NO NEW CONTENT 1.9. Count to 120, starting at any no. less than 120; Read & write numerals. Represent a number of objects with a numeral [1-NBT1] 1.7. Understand meaning of equal sign (=); Determine if addition & subtraction equation are true or false. [1-OA7] Here is an example of a curriculum plan for the first nine weeks in a first grade classroom. Let’s look at the Grade 1 Content Correlation Document and see if any changes should be made in our plans for next year. First find standard 5 in the document. Look for standards 5.1, 5.2, and 5.3. Is there any new content required to prepare our students? (CLICK) NO. Is this content addressed in the new 2010 COS? No, this standard will not be taught in Grade 1 in the 2010 ACOS. What about for standard 12? Look for standards 12 and Any new content required there? (CLICK) NO. What about standard 1 and 1.2? Any new content required there? (CLICK) Yes. When you look at the highlighted portion of the 2010 standard, you find additional content that must be addressed in the upcoming school year. The new content is: Count to 120, starting at any no. less than 120 Read & write numerals Represent a number of objects with a numeral Understand meaning of equal sign (=) Determine if addition & subtraction equation are true or false After studying standards 1, 1.3, 1.4 and 1.5, is there any new content that should be addressed next year? (CLICK) Yes. The 2010 ACOS provides special cases that must be addressed. Notice that the new content is found in grade 1 standards in the 2010 ACOS. Evaluating your curriculum in this way will provide a resource that teachers can use in planning their curriculum units for the upcoming school year. (CLICK)) 1.10. a.10 can be thought of as a bundle of ten ones. [1-NBT2a] 1.10.c.The numbers 10, 20, 30, 40, 50, 60,70, 80, 90 refer to one, two, three, four, five, six, seven, eight, or nine tens (and 0 ones) [1-NBT2c]

Fourth Grade Pacing Guide
Third Nine Weeks 2003COS # DESCRIPTION CONTENT TO BE ADDED FROM 2010 4.3 Rename improper fractions as mixed numbers and mixed numbers as improper fractions. 4.4 Demonstrate addition and subtraction of fractions with common denominators. 4.8 Recognize equivalent forms of commonly used fractions and decimals. 4.16 Determine if outcomes of simple events are likely, unlikely, certain, equally likely, or impossible. 4.11 Identify triangles, quadrilaterals, pentagons, hexagons, or octagons based on the number of sides, angles, and vertices. 4.12 Find locations on a map or grid using ordered pairs. 4.15 4.17 Represent categorical and numerical data using tables and graphs, including bar graphs, and line plots. 4.14 Measure length, width, weight, and capacity using metric and customary units, and temperature in degrees Fahrenheit and degrees Celsius. 4.14.c. Add and subtract mixed numbers with like denominators [4-NF3c] 4.13. Compare two fractions with different numerators and different denominators [4-NF2] NO NEW CONTENT NO NEW CONTENT 4.26. Draw points, lines, line segments, rays, angles (right, acute, obtuse) and perpendicular and parallel lines. Identify these in two dimensional figures. [4-G1] 4.27. Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines or angles of a specified size. [4-G2] NO NEW CONTENT Now, it’s your turn to determine if any content should be added to the fourth grade curriculum. You will use your Grade 4 Content Correlation Document. (Participants will have copy of this handout in their packet) (Each participant will analyze the Fourth Grade Pacing Guide to determine what content, if any, should be added to adequately prepare their students.) Allow minutes for their analysis. Then, ask for volunteers to share out. As they share out, you may (CLICK) and the answers will appear on the screen. This process will be assist you in planning your curriculum units for the upcoming school year. You can use you local curriculum guide and identify content that will be shifting to another grade level. This will ensure that your students will be prepared to implement the new mathematics standards in the school year. (CLICK) 4.22. Solve problems inv. addition & subtraction of fractions using information presented in line plots [4-MD4] 4.19. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. [4-MD1]

What about the assessments?
Just a little background on the assessments. The ARMT is based on standards from the 2003 ACOS. In 2008 and 2009, when the 2009 course of study for mathematics was being developed, the course of study committee used a draft of the common core state standards for mathematics as a reference document. So, standards in the 2009 ACOS correlated quite well with the common core standards. After the 2009 ACOS was adopted by the state board, assessment went to work on items based on the 2009 standards. Then, the decision was made not to implement the 2009 document but to wait for the official release of the Common Core State Standards for Mathematics and see if Alabama would decide to adopt these standards. By this time, the contract for the assessment on the 2003 standards had expired and assessment moved to develop items correlated to the 2009 ACOS. These items are more rigorous. The ARMT+ was developed based on the 2009 ACOS. Once the decision was made not to implement the 2009 ACOS, assessment removed any items that correlated with the 2009 ACOS and not the So, on the ARMT+, the items DO correlate with the 2003 document but they are written at a more rigorous level than the previous versions. Further information on the assessments will be provided in the fall by the SDE. (CLICK)

2011-2012 2012-2013 2003 ACOS + Identified Content from 2010 ACOS
So, you can see, it’s essential that you continue to teach the 2003 standards, but at a more rigorous level. Expect more from your students. Also, to insure that all necessary content has been covered and that students are prepared for full implementation of the 2010 ACOS during the school year, teachers must teach the 2003 course of study along with identified content from the 2010 ACOS. This is where the Content Correlation Document will help you with planning your school year. Then, during school year, when full implementation of the 2010 ACOS takes place and teachers must teach the standards from the 2010 COS, you must continue to address some of the standards from the 2003 course of study because the ARMT+ will still be used and it is based on the 2003 course of study standards. There will be an additional correlation document provided during a later phase of the implementation PD to assist with this transition. (CLICK)

?? Questions ?? Are there any questions concerning content shifts? If not, we will continue with Algebra I in Grade 8, Considerations/Consequences in the 2010 Alabama Mathematics Course of Study. (CLICK)

Algebra I in the 8th Grade: Considerations and Consequences
2010 Alabama Course of Study: Mathematics College- and Career-Ready Standards Taking Algebra I in the 9th Grade as a “first choice,” and following up with Geometry, Algebra II with Trigonometry, and another mathematics course, will ensure that at the end of high school a student will be college and career ready. The State Department of Education does not advocate for the Algebra I course in Grade 8, but allows for system level decisions to determine whether offering coursework that includes a Grade 8 experience of Algebra I. This session of the Phase I professional development on the 2010 Alabama Course of Study: Mathematics will explore the considerations and consequences of offering an Algebra I course in the Grade 8. (CLICK) Algebra I in the 8th Grade: Considerations and Consequences

Algebra I in Grade 8: Considerations and Consequences
Do you have middle school students who should have the option of taking Advanced Placement (AP) Mathematics, or two advanced mathematics courses as part of their high school experience? Some Pathways for Students Who Complete Algebra I in Grade 8 Geometry Geometry Geometry Algebra II W/Trig Algebra II W/Trig Algebra II W/Trig Precalculus Discrete Mathematics Precalculus Analytical Mathematics Precalculus Advanced Placement (AP) Mathematics Course (ACOS: Mathematics, 2010, p. 127) How you answer this question will be one of the considerations in deciding whether to offer Algebra I in Grade 8. If a successful Algebra I experience at Grade 9 is the goal for all students, then an early experience of Algebra I in the Grade 8 is not for all students. And if the purpose is to give a child the opportunity to take college-level AP Mathematics in high school, then the early experience of Algebra I in the Grade 8 may not be the path that needs to be taken by the majority of students or even the average student. (CLICK)

“Systems offering Algebra I in the eighth grade have the responsibility of ensuring that all Algebra I course content standards and Grade 8 course content standards be included in instruction.” (ACOS: Mathematics, 2010, p. 81) The State Department of Education will provide further guidance and training (Phase II) in the fall of relative to issues local education agencies may encounter in providing an Algebra I course in Grade 8. First Bullet – COS guidance for systems that want to offer Algebra I in the Grade 8 is summed up in the first bullet. Providing a Grade 8 Algebra I course requires some serious decision-making. One of the first issues to face is the rigor and the sheer number of skills that must be mastered by students contained in the 2010 Alabama Course of Study: Mathematics for the content in the Grade 8 course and in the Algebra I course. (CLICK) Second Bullet – While Phase I training introduces considerations and consequences, the Phase II training will be able to look in greater depth at the arrangement of standards for course sequences, and discuss other key parts of the 2010 COS like the critical areas of focus, overview of possible teaching units, clusters of standards with instructional notes, and maintaining alignment of learning progressions as it relates to accelerating students through middle school content into an Algebra I experience. (CLICK)

Decisions to accelerate students into a high school Algebra I course before Grade 9 should not be rushed. Placing students into an Algebra I course too early should be avoided at all costs. Local education agency’s decision should: Be Advertised Be Equitable Provide Written Policy Decisions to accelerate students into a high school Algebra I course before Grade 9 should be based on solid evidence of student learning. First and Second Bullets – One of the main goals of the new 2010 COS is to prepare students to successfully complete an Algebra I course in the Grade 9. If there is any question about a student’s ability to master all of the content in Grades 7, 8, and Algebra I courses in middle school, then the student should not be accelerated into Algebra I coursework ahead of time. (CLICK) Third Bullet - If a LEA allows students to take Algebra I in Grade 8, then there should be three items addressed in writing: 1. Registration for this accelerated course should be advertised for all to see. 2. The admission to the early course should be equitable for all students who meet the enrollment requirements. 3. The policy for early admission into the course should be a part of LEA written policy. (CLICK) Fourth Bullet - According to the Brookings Institute's 2009 Brown Center Report on American Education, the NAEP scores of students taking Algebra I in the Grade 8 varied widely. The data showed that of the students who took Algebra I early (in Grade 8), the bottom 10 percent scored far below grade level. This is a reminder that, rather than skipping or rushing through content, students should have appropriate progressions through foundational content to maximize their likelihoods of success in high school mathematics. This also indicates that some students would likely have greater success in mathematics by following the normal progression through Grades 7 and 8 courses and take Algebra I in Grade 9. (CLICK)

Not all students are ready for Algebra I in Grade 8. The 2010 COS Algebra I content is not the same as the Algebra I content in earlier Alabama Courses of Study. Much of what was previously included in Algebra I will now be taught in Grades 6-8 in the COS. First Bullet – Only two states have mandated that all students take Algebra I in the 8th Grade (Minnesota and California). Currently, California’s policy that all students take Algebra I in the 8th Grade has gone to court and is still pending. (CLICK) Second Bullet –Given the shifts of content that have occurred through the progression of courses, it would be wise to closely examine who is ready for Algebra I in Grade 8. The mathematics courses for all grades in the 2010 COS are more rigorous than the same grade level courses in previous years. The middle school mathematics courses are more rigorous in order to prepare students for a more rigorous high school Algebra I experience. If there is any doubt concerning whether a child will be able to successfully accelerate through Grades 7, 8, and Algebra I content before the 9th Grade, then the child should take the regular Grade 7 and Grade 8 course sequence in order to have a successful experience of Algebra I in Grade 9.

?? Questions ?? Are there any questions concerning Algebra I in Grade 8: Considerations and Consequences? (CLICK)

Contact Information ALSDE Office of Student Learning Curriculum and Instruction Section Cindy Freeman, Mathematics Specialist Phone: This concludes the presentation of Phase I of the 2010 college- and career-ready mathematics standards. Are there any other questions? Would you please take a minute and complete the evaluation form? Please include any further questions you have and be sure to put your contact information if you would like a personal response. Common questions will be posted on our Website along with answers and comments from state personnel. You may access this information at the address listed on the screen. This Website will be an excellent source of information concerning the college- and career-ready standards for mathematics and English language arts. It will include presentations, handouts, lessons and lesson ideas, links, and other valuable resources. If you have additional questions concerning the standards, please contact either Dr. Davis or Ms. Freeman at the addresses listed on the screen. Thank you for your attention and have a safe trip home.

Professional Development: K-8 Phase I Regional Inservice Center

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Professional Development: K-8 Phase I Regional Inservice Center

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