Presentation on theme: "OELCS 2005 Math Module 3 Speaker Notes Focus, Coherence, and Rigor"— Presentation transcript:
1OELCS 2005 Math Module 3 Speaker Notes Focus, Coherence, and Rigor Mathematical Shifts of theCommon Core State StandardsFocus, Coherence, and RigorMay 2013Common Core Training for AdministratorsMiddle Grades MathematicsDivision of Academics, Accountability, and School Improvement
2OELCS 2005 Math Module 3 Speaker Notes Mathematical Shifts of the Common Core State Standards:Focus, Coherence and RigorAGENDAPurpose and Vision of CCSSMImplementation TimelineSix Shifts in MathematicsDesign and OrganizationInstructional Implications: Classroom Look-forsExpectations of Student PerformanceCCSSM Resources: WebsitesReflections / Questions and Answers2 minutes
3OELCS 2005 Math Module 3 Speaker Notes Community NormsWe are all learners todayWe are respectful of each otherWe welcome questionsWe share discussion timeWe turn off all electronic devices__________________1 minuteReview the norms – helps the group be mre thoughtful and productive.Ask the participants if there is any norm they would like to include
4OELCS 2005 Math Module 3 Speaker Notes Purpose and Vision of the CCSSM
5Why Common Standards? Consistency Equity Opportunity Clarity Previously, every state had its own set of academic standards and different expectations of student performance.ConsistencyCommon standards can help create more equal access to an excellent education.EquityStudents need the knowledge and skills that will prepare them for college and career in our global economy.Opportunity3 minutes4 reasons for common standards:Consistency among statesEquity for all children to have access to an excellent educationOpportunity to compete in a global economyClarity of standards for all stakeholders. Clarity is critical so that the expectations are attained at every grade level so that students are prepared for the upcoming grade level given the hierarchal nature of mathematics.These new standards are clear and coherent in order to help students, parents, and teachers understand what is expected.Clarity
6College and Career Readiness: Anchor for the Common Core The Common Core State Standards were back-mapped from the anchor of college and career readiness because governors and state school chiefs realized there was a significant gap between high school expectations for students and what students are expected to do in college/career.Among high school graduates, about only half are academically prepared for postsecondary education.2 minutes- Misalignment between our expectations (high school diploma) and what college demands—David Coleman/Pres of College BoardRESEARCH BASE (Greene & Winters, 2005)Among high school juniors and seniors taking the ACT college entrance exam, half of the students were ready for college-level reading assignments in core subjects like math, history, science, and English (ACT, 2006).MathStudents are expected to have deep knowledge of core mathematical concepts (such as ratio and proportion) that are gatekeepers for success in advanced mathematics courses in college or advanced technical training in a career.Students are expected to apply their mathematical knowledge to new and novel situations.ELAStudents are expected to read more non-fiction (periodicals, technical manuals, etc.) and more complex textsStudents are expected to read with greater independenceQuality of students’ writing in college isn’t meeting professors’ expectations
7College Remediation and Graduation Rates Remediation rates and costs are staggeringAs much as 40% of all students entering 4-year colleges need remediation in one or more coursesAs much as 63% in 2-year collegesDegree attainment rates are disappointingFewer than 42% of adults aged hold college degrees1 minute-Misalignment between our expectations (high school diploma) and what college demands—David Coleman/Pres of College BoardAs much as 40% of all students entering 4-year colleges need remediation in one or more courses. There is a gap in the expectations of colleges and careers and student preparation upon graduation from high school. The “architect” of Common Core, also president if the College Board, speaks to this gapSource: The College Completion Agenda 2010 Progress Report, The College Board
8Are We Mathematically Ready for College and Careers? OELCS 2005 Math Module 3 Speaker NotesAre We Mathematically Ready for College and Careers?Video: 3:22/ with discussion 6 minutes Verizon video-click in outer blue area-Do we have a sense of urgency for change?-Ask administrators to self-reflect: Is the instruction occurring in your classrooms going to lead to this level of mathematical understanding for the next generation?-Can someone volunteer to explain the mathematical misconception?1:38:00 College remediation;David Coleman’s Testimony to the Florida Legislature’s K-12 Subcommittee
9OELCS 2005 Math Module 3 Speaker Notes Common Core State Standards MissionThe Common Core State Standards provide a consistent, clear understanding of what students are expected to learn, so teachers and parents know what they need to do to help them. The standards are designed to be robust and relevant to the real world, reflecting the knowledge and skills that our young people need for success in college and careers. With American students fully prepared for the future, our communities will be best positioned to compete successfully in the global economy.1 minuteThe CCSS provides consistent and clear understanding of what students are expected to learn. They are designed to be robust and applicable to the real world and reflect the skills needed for career and college success and to effectively compete in the global economy.NAEP and TIMMS (Trends in International Mathematics and Science Study) have always shown a need for change toward how math instruction is delivered.
10Florida’s Common Core State Standards Implementation Timeline M-DCPSYear / Grade levelK123 – 89 – 12F LLCCSS fully implementedB LCCSS fully implemented and assessedF LF L2 minutesSlide has fly-in.Show first and mention that this timeline is the state of FL implementation timeline.Hit enter for a MDCPS implementation. Miami-Dade County is ahead of the game.Unlike the State timeline, next year’s ( ) 3rd graders will not be seeing CCSSM for the first time. They have been learning it the last two years. We were able to give them a running start since grades 1 and 2 do not take FCAT 2.0.The current first graders are our common core babies. These students will be taking the PARCC assessment in grade 3. They should be better prepared because they have only been instructed using CCSSM.FOR ELEM ONLY – Are all K-2 teachers fully implementing CCSS?Next year, other grades will be using a blended model; the Mathematics pacing guide will guide teachers in this blended model.F – Full Implementation of CCSSML – Full implementation of content area literacy standards including: text complexity, quality and range in all grades (K-12)B – Blended instruction of CCSS with NGSSS; last year of NGSSS assessed on FCAT 2.0 (Grades 3-8); 4th quarter will focus on NGSSS/CCSSM grade level content gaps1010
11(4th 9 weeks Common Core Lockdown) FCAT 2.0PARCCK1234567(4th 9 weeks Common Core Lockdown)89101112NGSSSCCSSM3 minutesWill be a blended year (NGSSS /CCSSM) however the NGSSS standards will be assessed, therefore it is essential for schools to ensure the Common Core Standards referenced in the pacing guides are covered fully. The 4th nine weeks for grades 3-8 should be on Common Core Lockdown.
12OELCS 2005 Math Module 3 Speaker Notes Six Shifts in MathematicsActivity begins once shifts are introduced
13OELCS 2005 Math Module 3 Speaker Notes Mathematical ShiftsFOCUS deeply on what is emphasized in the StandardsCOHERENCE: Think across grades, and link to major topics within gradesRIGOR: Require-FluencyDeep Understanding1 minuteThere a six major mathematical shifts of the common core state standards. The last four (Fluency, Deep Understanding, Modeling and Dual Intensity) are components of Rigor.These shifts are not independent of each other.In order for one to occur, it is dependent on another.– for example, in order to ensure students have DEEP UNDERSTANDING of the content, there must be a narrower and more specific FOCUS on the priority concepts (not mile wide and inch deep) and the teacher must understand the COHERENCE of the math concepts and how topics progress from year to year in order to design lessons where their students can connect math concepts to each other (fragmented knowledge vs connected knowledge)– a point emphasized by The Structure is the Standards- Essay by CCSSM writers Jason Zimba, Phil Daro, and Bill McCallum.Model/ApplyDual Intensity
15OELCS 2005 Math Module 3 Speaker Notes Name that Shift…At your tables, use the provided cards to place under the appropriate shift listed on the handout: focus, coherence, fluency, deep understanding, application, and dual intensity.After this is complete, your table will receive one large card identifying what the student does and the teacher does for a particular shift. Discuss with your table the shift that the card describes and tape it to the corresponding chart paper. Be ready to explain your reasoning.15 minutesSlides following are solutions to the activity.
16OELCS 2005 Math Module 3 Speaker Notes Shift 1: FocusTeachers use the power of the eraser and significantly narrow and deepen the scope of how time and energy is spent in the math classroom. They do so in order to focus deeply on only the concepts that are prioritized in the standards so that students reach strong foundational knowledge and deep conceptual understanding and are able to transfer mathematical skills and understanding across concepts and grades.1 minuteIt is important to recognize that “fewer standards” are no substitute for focused standards. Achieving “fewer standards” would be easy to do by resorting to broad, general statements. Instead, these Standards aim for clarity and specificity->focus. Concepts are prioritized to narrow focus, be specific and delve deeper.Common Core State Standards document (p. 3)Teachers focus on big concepts throughout the school year.Example:In middle grades, there is a major emphasis on the concept of ratio and proportion.Students are able to transfer mathematical skills and understanding across concepts and grades.–Spend more time on Fewer ConceptsAchievethecore.org
17Mathematics Shift 1: Focus OELCS 2005 Math Module 3 Speaker NotesMathematics Shift 1: FocusWhat the Student Does…What the Teacher Does…Spend more time on fewer conceptsExtract content from the curriculumFocus instructional time on priority conceptsGive students the gift of time3 minutes to go over all solution slides (30 seconds per solution slide)SOLUTION TO ACTIVITY SLIDEConcepts are prioritized to narrow focus, be specific and delve deeper.Spend more time on Fewer Concepts
18OELCS 2005 Math Module 3 Speaker Notes “Teach Less,Learn More…”- Ministry of Education, SingaporeQuote by David Coleman, who quoted THE MINISTRY OF EDUCATION from The Singapore Teaching and Learning website
19OELCS 2005 Math Module 3 Speaker Notes K-8 Priorities in MathPriorities in Support of Rich Instruction and Expectations of Fluency and Conceptual UnderstandingK–2Addition and subtraction, measurement using whole number quantities3–5Multiplication and division of whole numbers and fractions6Ratios and proportional reasoning; early expressions and equations7Ratios and proportional reasoning; arithmetic of rational numbers1 minuteThe foundation for students’ success in Algebra 1 is the progression from numbers & fractions ratios and proportional reasoning linear relationships. Note the priorities above.8Linear algebraAchievethecore.org
20OELCS 2005 Math Module 3 Speaker Notes Shift 2: CoherencePrincipals and teachers carefully connect the learning within and across grades so that students can build new understanding onto foundations built in previous years.Teachers can begin to count on deep conceptual understanding of core content and build on it. Each standard is not a new event, but an extension of previous learning.A student’s understanding of learning progressions can help them recognize if they are on track.2 minutesEach standard is not a new event, but an extension of previous learning.The CCSS Math standards are built on a progression of knowledge from one year to the next. Standards build on previous knowledge, all standards are extensions of what was learning in the past. We need to know our grade-level standards, and at least one grade below and above the classes we teach, keeping in mind what students have learned, what we will teach them, and how will they build on this next year!Common Core provides a three dimensional spiral approach to the curriculum. Teachers build concepts on prior knowledge.Mid: In 7th grade students solve real‐world and mathematical problems involving area, volume and surface area of two‐ and three‐dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms and in 8th grade students solve real‐world and mathematical problems involving volume of cylinders, cones, and spheres.Keep Building on learning year after yearAchievethecore.org
21Mathematics Shift 2: Coherence OELCS 2005 Math Module 3 Speaker NotesMathematics Shift 2: CoherenceWhat the Student Does…What the Teacher Does…Build on knowledge from year to year, in a coherent learning progressionConnect the threads of critical areas across grade levelsConnect to the way content was taught the year before and will be taught the following yearsFocus on priority progressionsSOLUTION TO ACTIVITY SLIDEStudent – Build on Knowledge, Teachers Connect focus areas across grades and focus on grade level priority progressionsKeep Building on learning year after year
22OELCS 2005 Math Module 3 Speaker Notes Shift 3: FluencyTeachers help students to study algorithms as “general procedures” so they can gain insights to the structure of mathematics (e.g. organization, patterns, predictability).Students are expected to have speed and accuracy with simple calculations and procedures so that they are more able to understand and manipulate more complex concepts.Students are able to apply a variety of appropriate procedures flexibly as they solve problems.2 minutes1st component of rigor---Fluent in the Standards means “fast and accurate.” It might also help to think of fluency as meaning the same thing as when we say that somebody is fluent in a foreign language: when you’re fluent, you flow. Fluent isn’t halting, stumbling, or reversing oneself. Assessing fluency requires attending to issues of time (and even perhaps rhythm, which could be achieved with technology). The word fluency was used judiciously in the Standards to mark the endpoints of progressions of learning that begin with solid underpinnings and then pass upward through stages of growing maturity. In fact, the rarity of the word itself might easily lead to fluency becoming invisible in the Standards—one more among 25 things in a grade, easily overlooked. Assessing fluency could remedy this, and at the same time allow data collection that could eventually shed light on whether the progressions toward fluency in the Standards are realistic and appropriate. Common Core requires specific sets of fluencies per grade levels in order to achieve a deep conceptual understanding of related concepts.Mid: For example in third grade, students need to multiply/divide fluently within 100. This fluency is an essential prerequisite to completing the calculations for surface area and volume in the middle grades.Spend time Practicing(First Component of Rigor)Achievethecore.org
23Mathematics Shift 3: Fluency OELCS 2005 Math Module 3 Speaker NotesMathematics Shift 3: FluencyWhat the Student Does…What the Teacher Does…Spend time practicing, with intensity, skills (in high volume)Push students to know basic skills at a greater level of fluencyFocus on the listed fluencies by grade levelUses high quality problem sets, in high volumeSOLUTION TO ACTIVITY SLIDEStudent – Practice time, Teachers- focus on grade level fluencies utilizing high quality problem sets which provides opportunities for ample practiceSpend time Practicing
24OELCS 2005 Math Module 3 Speaker Notes K-8 Key FluenciesGradeRequired FluencyKAdd/subtract within 51Add/subtract within 102Add/subtract within 20Add/subtract within 100 (pencil and paper)3Multiply/divide within 100Add/subtract within 10004Add/subtract within 1,000,0005Multi-digit multiplication6Multi-digit divisionMulti-digit decimal operations7Solve px + q = r, p(x + q) = r8Solve simple 22 systems by inspection2 minutesPlease note that there are algorithmic fluencies in middle grades. Associated with particular standards.Procedural fluency (skill in carrying out procedures flexibly, accurately, efficiently and appropriately),Grade 5 does include division with 2 digit divisor and 4 digit dividend. Grade 6 it becomes multi-digit division.Grade 5 has +,-,x,/ with decimals up to the hundredths. Grade 6 it becomes multi-digit decimals.MACC.6.NS.2.2 Multi-digit divisionMACC.6.NS.2.3 Multi-digit decimal operationsMACC.7.EE.2.4a Solve px + q = r, p(x + q) = rMACC.8.EE.3.8b Solve simple 22 systems by inspectionAchievethecore.org
25OELCS 2005 Math Module 3 Speaker Notes Shift 4: Deep Conceptual UnderstandingTeachers teach more than “how to get the answer;” they support students’ ability to access concepts from a number of perspectives so that students are able to see math as more than a set of mnemonics or discrete procedures.Students demonstrate deep conceptual understanding of core math concepts by applying them to new situations as well as writing and speaking about their understanding.1 minuteThe instructional approach emphasizes conceptual understanding rather than memorization of procedures. Students articulate mathematical reasoning and understand why the algorithms work.Mid: For example, students in 6th grade find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes. Students are able to transfer prior knowledge to derive the formulas.Understand Math, Do Math, and Prove it(Second Component of Rigor)Achievethecore.org
26Mathematics Shift 4: Deep Understanding OELCS 2005 Math Module 3 Speaker NotesMathematics Shift 4: Deep UnderstandingWhat the Student Does…What the Teacher Does…Show mastery of material at a meaningful levelArticulate mathematical reasoningDemonstrate deep conceptual understanding of priority conceptsExplain and justify their thinkingCreate opportunities for students to understand the “answer” from a variety of access pointsEnsure that students understand WHY they are doing what they’re doing-ASK PROBING QUESTIONSGuide student thinking instead of telling the next stepContinuously self reflect and build knowledge of concepts being taughtSOLUTION TO ACTIVITY SLIDELast bullet- teachers should continue to build their own knowledge of the mathematical content and connections in a collaborative settingStudent – demonstrate mastery of material and articulates mathematical reasoning, Teachers-create opportunities for students to understand the answers at varying access points, ask probing questions and guide students thinking opposed to telling and continuously self-reflect to build capacity.Understand Math, Do Math, and Prove it
27OELCS 2005 Math Module 3 Speaker Notes Shift 5: Applications (Modeling)Teachers provide opportunities to apply math concepts in “real world” situations. Teachers in content areas outside of math ensure that students are using math to make meaning of and access content.Students are expected to use math and choose the appropriate concept for application even when they are not prompted to do so.1 minuteStudents are able to choose and apply various concepts when solving real-world problems.Mid: For example, students in 6th grade solve real‐world and mathematical problems involving area, surface area, and volume.It is critical that students understand the meaning of the concepts to be able to apply in real world situations. For example, if students are presented with a scenario where they must determine the amount of paint needed to paint the walls of a room, there may not be the word “area” used in the word problem to clue the students as to which formula to apply. They must know the meaning of the term to know when to apply the formula.Apply math in Real World situations(Third Component of Rigor)
28Mathematics Shift 5: Application (Modeling) OELCS 2005 Math Module 3 Speaker NotesMathematics Shift 5: Application (Modeling)What the Student Does…What the Teacher Does…Utilize math in other content areas and situations, as relevantChoose the right math concept to solve a problem when not necessarily prompted to do soApply math including areas/ courses where it is not directly required (i.e. in science)Provide students with real world experiences and opportunities to apply what they have learnedSOLUTION TO ACTIVITY SLIDEStudent will have the ability to apply math in other content areas, and make appropriate decisions about which strategies can be used to solve problems without being prompted. Teachers incorporate cross content references when applicable and provides real world experiences to allow students the opportunity to apply what they learned.Apply math in Real World situations
29OELCS 2005 Math Module 3 Speaker Notes Shift 6: Dual IntensityThere is a balance between practice and understanding; both are occurring with intensity. Teachers create opportunities for students to participate in “drills” and make use of those skills through extended application of math concepts.1 minuteThere is a balance between fluency and problem solving applications. Mathematical understanding and procedural skill are equally important.For example, teachers provide time to practice while giving opportunities for students to apply learned concepts and model real life situations with mathematics.Mid: For example in 8th grade, students not only need to understand conceptually the derivation of the formula for the volume of a cylinder, but they must also get sufficient practice to achieve a combination of procedural fluency and conceptual understanding.Think fast and Solve problems(Fourth Component of Rigor)Achievethecore.org
30Mathematics Shift 6: Dual Intensity What the Student Does…What the Teacher Does…Practice math skills with an intensity that results in fluencyPractice math concepts with an intensity that forces application in novel situationsFind the balance between conceptual understanding and practice within different periods or different unitsBe ambitious in demands for fluency and practice, as well as the range of applicationSOLUTION TO ACTIVITY SLIDEStudents and Teachers understand the importance of both Fluency and Application.Think fast and Solve problems
31OELCS 2005 Math Module 3 Speaker Notes Designand Organization
32Design and Organization Standards for Mathematical ContentK-8 standards presented by grade levelOrganized into domains that progress over several gradesGrade introductions give 2–4 focal points at each grade levelStandards for Mathematical PracticeCarry across all grade levelsDescribe habits of mind of a mathematically expert student4 minutesStress that in math, there are TWO components. What will drive the transformation in mathematics instruction are the MATH PRACTICES. This will become the focus of the Look-fors later in the presentation.The Common Core Mathematics Standards are composed of the 8 Mathematical Practices that carries across all grade levels and focuses on the habits of mind that students must develop to demonstrate mastery of common core standards. The second component of the CCSSM are the Mathematical Content Standards which are grade level standards that are organized by domains which progress over several grades fork-8 and organized by conceptual categories for grades 9-12.3232
33OELCS 2005 Math Module 3 Speaker Notes Mathematical PracticesMake sense of problems and persevere in solving themReason abstractly and quantitativelyConstruct viable arguments and critique the reasoning of othersModel with mathematicsUse appropriate tools strategicallyAttend to precisionLook for and make use of structureLook for and express regularity in repeated reasoningFar fewer things done well– go deeper
34OELCS 2005 Math Module 3 Speaker Notes Standards for Mathematical PracticeHow we teach is just as importantas what we teach….2 minutesThe 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. The first of these are the NCTM process standards of problem solving, reasoning and proof, communication, representation, and connections. The second are the strands of mathematical proficiency specified in the National Research Council’s report Adding It Up: adaptive reasoning, strategic competence, conceptual understanding (comprehension of mathematical concepts, operations and relations), procedural fluency (skill in carrying out procedures flexibly, accurately, efficiently and appropriately), and productive disposition (habitual inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence and one’s own efficacy). Common Core State Standards document (p. 9)“The Standards for Mathematical Practice are unique in that they describe how teachers need to teach to ensure their students become mathematically proficient. We were purposeful in calling them standards because then they won’t be ignored.” Quote by Bill McCallum- CCSSM writer
35OELCS 2005 Math Module 3 Speaker Notes Learning ExperiencesIt matters how students learnLearning mathematics is more than just learning concepts and skills. Equally important are the cognitive and metacognitive process skills. These processes are learned through carefully constructed learning experiences.For example, to encourage students to be inquisitive and have a deeper understanding of mathematics, the learning experiences must include carefully structured opportunities where students discover mathematical relationships and principles on their own.2 minutesIt matters how the students are learning the math content, not just that they can get an answer to a procedure. From:Ministry of Education, Singapore (quoted as a key resource for Common Core writers such as Jason Zimba, Bill McCallum, & the “architect” David Coleman)■2013 O & N(A)-Level Mathematics Teaching and Learning SyllabusSee link above---NOTE how the Singapore syllabi made for teachers (from which this slide is developed) emphasizes metacognition and cognitive processes just as much, if not more, than the math content. Students need to be taught to be intelligent thinkers-analytical, inquisitive, in-depth thinkers.
36OELCS 2005 Math Module 3 Speaker Notes What doesmathematical understanding look like?4 minutesLeading into HABITS OF MIND slideOne hallmark of mathematical understanding is the ability to justify, in a way appropriate to the student’s mathematical maturity, why a particular mathematical statement is true or where a mathematical rule comes from.There is a world of difference between a student who can summon a mnemonic device to expand a product such as (a + b)(x + y) and a student who can explain where the mnemonic comes from. The student who can explain where the rule comes from understands the mathematics, and may have a better chance to succeed at a less familiar task such as expanding (a + b + c)(x + y).-Common Core State Standards document (p. 4)
37OELCS 2005 Math Module 3 Speaker Notes Overarching Habits of Mind of aProductive Mathematical Thinker1. Make sense of problems and persevere in solving them6. Attend to precisionReasoning and ExplainingModelingandUsing ToolsSeeing Structure and Generalizing2. Reason abstractly and quantitatively3. Construct viable arguments and critique the reasoning of others4. Model with mathematics5. Use appropriate tools strategically7. Look for and make use of structure8. Look for and express regularity in repeated reasoning2 minutesThe practices can be further organized into 4 Categories (Habits of Mind, Reasoning and Explaining, Modeling and Using Tools, and Seeing Structure and generalizing.
38OELCS 2005 Math Module 3 Speaker Notes Overarching Habits of Mind of a Productive Mathematical ThinkerMP 1: Make sense of problems and persevere in solving them.MP 6: Attend to precisionMathematically proficient students can…Mathematically proficient students can…use mathematical vocabulary to communicate reasoning and formulate precise explanationscalculate accurately and efficiently and specify units of measure and labels within the context of the situationexplain the meaning of the problem and look for entry points to its solutionmonitor and evaluate their progress and change course if necessaryuse a variety of strategies to solve problems3 minutesMP 1A worthwhile mathematical taks is one thatis open-endeddoes not have a solution path that is immediately obvious (or implied)requires students to think and not just rely on memorized proceduresrequires students to connect mathematical skill, understanding, and reasonrequires students to interpret and communicate results.Provide students with problems that require planning (before solving) and evaluation (after solving).Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution.They analyze givens, constraints, relationships, and goals.They make conjectures about the form and meaning of the solution andThey plan a solution pathway rather than simply jumping into a solution attempt.They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution.They monitor and evaluate their progress and change course if necessary.Elementary:Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, “Does this make sense?”They can understand the approaches of others to solving complex problems and identify correspondences between different approaches.Secondary:Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends.MP 6Mathematically proficient students:try to communicate precisely to others.try to 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.carefully specify units of measure and label 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.Students give carefully formulated explanations to each other.Students have learned to examine claims and make explicit use of definitions.Gather InformationMake aplanAnticipate possible solutionsContinuously evaluate progressCheck resultsQuestion sense of solutions
39OELCS 2005 Math Module 3 Speaker Notes Reasoning and ExplainingMP 2: Reason abstractly and quantitatively.MP 3: Construct viable arguments and critique the reasoning of othersMathematically proficient students can…Mathematically proficient students can…have the ability to contextualize and decontextualize problems involving quantitative relationships:decontextualize - to abstract a given situation and represent it symbolically and manipulate the representing symbolscontextualize - to pause as needed during the manipulation process in order to probe into the referents for the symbols involved.make a mathematical statement (conjecture) and justify itlisten, compare, and critique conjectures and statements4 minutesMP 2:Mathematically proficient students make sense of quantities and their relationships in problem situations.They bring two complementary abilities to bear on problems involving quantitative relationships:the ability to decontextualize—to 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 referentsability 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; and knowing and flexibly using different properties of operations and objects.Elementary:This particular Standard for Mathematical Practice incorporates an elementary student’s ability to translate a word problem into an equivalent number sentence.Additionally, students recognize that all relevant information within the problem has a quantitative value that is expressed with a numeric symbol.After successfully solving the problem, students are able to explain how the numeric representations are related to the original word problem.Secondary:Teachers who are developing students’ capacity to "reason abstractly and quantitatively" help their learners understand the relationships between problem scenarios and mathematical representation, as well as how the symbols represent strategies for solution.A middle childhood teacher might ask her students to reflect on what each number in a fraction represents as parts of a whole.A different middle childhood teacher might ask his students to discuss different sample operational strategies for a patterning problem, evaluating which is the most efficient and accurate means of finding a solution.MP 3:Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments.They make conjectures and build a logical progression of statements to explore the truth of their conjectures.They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples.They justify their conclusions, communicate them to others, and respond to the arguments of others.They reason inductively about data, making plausible arguments that take into account the context from which the data arose.Mathematically proficient students are also able to 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.Children begin to reason from their own experiences and create arguments, even mathematical ones, before they enter the classroom as students.As students begin a more formal of study of mathematics, teachers should seek to build on the understandings that students bring to the classroom and move students toward commonly employed techniques for mathematical arguments and more formal language.Students’ early mathematical reasoning often relies on pattern recognition, generalization from examples, and classification; therefore, teachers should provide students with ample opportunities for students to use these skills as they make conjectures, search for evidence, and explain and justify ideas.For example, the teacher may ask, “If we skip count by twos, will we ever get a number that ends in 5?” Students can offer conjectures about the answer and study the pattern of numbers created when skip counting by twos. When they reach conclusions, the teacher can ask them to explain their thinking and critique the explanations of their classmates.Students need such opportunities on a regular basis in order to develop the ability to create and examine mathematical arguments.Students learn to determine areas to which an argument applies.listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve arguments.For example, a teacher can ask students to relate the domain of the function to its graph and, where applicable, to the quantitative relationship it describes. Students should be able to explain why a domain is appropriate for a given situation.
40OELCS 2005 Math Module 3 Speaker Notes Modeling and Using ToolsMP 4: Model with Mathematics.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 a school event or analyze a problem in the community.MP 5: Use appropriate tools strategicallyMathematically proficient students can…Mathematically proficient students can…apply mathematics to solve problems that arise in everyday lifereflect and make revisions to improve their model as necessarymap mathematical relationships using tools such as diagrams, two-way tables, graphs, flowcharts and formulas.consider the available tools when solving a problem (i.e. ruler, calculator, protractor, manipulatives, software)use technological tools to explore and deepen their understanding of concepts5 minutesMP 4:Mathematically proficient students:• apply the mathematics they know to solve problems arising in everyday life, society, and the workplace.• apply what they know to make assumptions and approximations to simplify a complicated situation, realizing that these may need revision later.• identify important quantities in a practical situation.• map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas.• analyze those relationships mathematically to draw conclusions.• routinely interpret their mathematical results in the context of the situation.• reflect on whether the results make sense, possibly improving the model if it has not served its purpose.Elementary:In early grades, this might be as simple as writing an addition equation to describe a situation.Secondary:In middle grades, a student might apply proportional reasoning to plan a 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.MP 5:Mathematically proficient studentsare 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. Being able to choose the appropriate tool for a real world situation when the tool is not identified.Mathematically proficient students at various grade levels are able to identify relevant external mathematical resources, such as digital content located on a website, and use them to pose or solve problems. They are able to use technological tools to explore and deepen their understanding of concepts.For example, middle school students consider available tools (including estimation and technology) when solving a mathematical problem and decide when certain tools might be helpful. For instance, students in grade 6 might use physical objects or applets to construct nets and calculate the surface area of three-dimensional figures.High school students analyze graphs of functions and solutions generated using a graphing calculator.They 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.They are able to use technological tools to explore and deepen their understanding of concepts.
41OELCS 2005 Math Module 3 Speaker Notes Seeing Structure and GeneralizingMP 7: Look for and make use of structureMP 8: Look for and express regularity in repeated reasoningMathematically proficient students can…Mathematically proficient students can…look closely to determine possible patterns and structure (properties) within a problemanalyze a complex problem by breaking it down into smaller partsnotice repeating calculations and look for efficient methods/ representations to solve a problemgeneralize the process to create a shortcut which may lead to developing rules or creating a formula3 minutesMP 7:Mathematically proficient students:look closely to discern a pattern or structure.Elementary:Young students might notice that three and seven more is the same amount as seven and three more. They may sort a collection of shapes according to how many sides the shapes have.Students can recognize the pattern that exists in the teen numbers; every teen number is written with a 1 (representing one ten) and ends with the digit that is first stated.Intermediate students will see 7 x 8 equals the well-remembered 7 x x 3, in preparation for the distributive property.Secondary:Mathematically proficient students, in the expression x2 + 9x + 14, can see 14 as 2 x 7 and the 9 asThey recognize the significance of an existing line in a geometric figure and can use the strategy of drawing an auxiliary line for solving problems.The can see complicated things, such as some algebraic expressions, as single objects or as being composed of several objects. (e.g., They 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.)MP 8:notice if calculations are repeated.look both for general methods and for shortcutsUpper 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.i.e. 2/11= ….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.Students can write the ratio of the circumference of a circle to the diameter of the circle; discuss, develop and justify this ratio for several circles; and determine that this ratio is constant for all circles.As high school students work to solve a problem, derive formulas or make generalizations, they maintain oversight of the process, while attending to the details. They continually evaluate the reasonableness of their intermediate results.
42GROUP ACTIVITY Each group will receive: An envelope containing 8 small cards and a handout of the listed mathematical practices.Instructions:Match each of the 8 small cards with its mathematical practice (using the handout of the listed mathematical practices).20 minutes2 minutes to explain and distribute materials10 minutes for participants to do activity8 minutes to review solutionsHere are the standards of mathematical practice laid out in a way that classifies them as much as possible.Each group has 8 cards. Each card matches one of the standards of mathematical practice as it appears in the classroom.Try to match the card with the standard. Each group will also get a set of 8 large cards – one for each practice. When we review each one, hold upthe correct card for the practice!
43OELCS 2005 Math Module 3 Speaker Notes SOLUTIONS TO ACTIVITY
44OELCS 2005 Math Module 3 Speaker Notes SOLUTIONS TO ACTIVITY
45OELCS 2005 Math Module 3 Speaker Notes SOLUTIONS TO ACTIVITY
46OELCS 2005 Math Module 3 Speaker Notes SOLUTIONS TO ACTIVITY
47OELCS 2005 Math Module 3 Speaker Notes SOLUTIONS TO ACTIVITY
48OELCS 2005 Math Module 3 Speaker Notes SOLUTIONS TO ACTIVITY
49OELCS 2005 Math Module 3 Speaker Notes SOLUTIONS TO ACTIVITY
50OELCS 2005 Math Module 3 Speaker Notes SOLUTIONS TO ACTIVITY
51OELCS 2005 Math Module 3 Speaker Notes Connecting the Math Practices to Look-ForsActivity begins once shifts are introduced
52OELCS 2005 Math Module 3 Speaker Notes 4 minutesProvide this look-fors document for administrators to use as they watch the video of classroom instruction on the following slide.NOTE:First Priority- OBSERVE THE LEARNING in the next video– Use the “Students:” column of the look-fors 1st. When we note that students i.e. communicated and defended their reasoning, then we can check what the teacher did to accomplish this with the students.There are many more check boxes that can exist—an infinite number- so do not assume that because a part of the video is not exact to a checkbox that it is not indicating the practice. There are many more ways to demonstrate each of these practices, so much so that they cannot all be listed. Use this as a GUIDE.
53OELCS 2005 Math Module 3 Speaker Notes Observe the learning, not the teaching…Focal point is the student learning…
54OELCS 2005 Math Module 3 Speaker Notes Overarching Habits of Mind of aProductive Mathematical Thinker1. Make sense of problems and persevere in solving them6. Attend to precisionReasoning and ExplainingModelingandUsing ToolsSeeing Structure and Generalizing2. Reason abstractly and quantitatively3. Construct viable arguments and critique the reasoning of others4. Model with mathematics5. Use appropriate tools strategically7. Look for and make use of structure8. Look for and express regularity in repeated reasoning30 secondsIn most cases, when look-fors can be grouped as above. If I see students modeling and using tools, it is likely they are engaged in both practices 4 and 5. If students are reasoning and explaining, it is likely they are engaged in practices 2 and 3. And so forth…
55OELCS 2005 Math Module 3 Speaker Notes Video Clip:Classroom Instruction
56OELCS 2005 Math Module 3 Speaker Notes 15 minutesDon’t click on picture!! Click on the black to play!!I DO and WE DO slide– use this video to pause intermittently and review the demonstration of practices.Side note: Notice her classroom environment—it is obvious she is not a traditional teacher with the rich activities postedVery beginning 1st question asked- MP# 6 Attend to Precision -Notice how from the very beginning, the teacher probes the thinking of the student to be more precise with his definition of a variable. This is important to ensure there are no misconceptions or false generalizations in the minds of ALL the students in the class. It also ensures a deeper understanding of the term. Asks WHY would you use a variable?—purpose of the symbol not just what it is-Goes Deeper (Math Shift)1:26 minutes MP#4 Model with Mathematics- multiple representations2:03 minutes MP#7 Look for and Make Use of Structure- analyze patterns and apply them in context2:13 min MP#8 Look for and express regularity in repeated reasoning – write a rule to show the relationship (generalize the process to develop a rule)2:13 min MP#4 Model with Mathematics & MP#5 Use appropriate tools strategically- use the tool pattern blocks to model growth patterns3:40 min MP#3 Construct Viable Arguments -#3 Diego justified his reasoning- uses the meaning of indep and dep variables to justify his answerNote: He was not prompted to justify yet he did so regardless-habit of mind. If he had not, the teacher should ask for the rationale.Can stop at 3:50 minIncrease in rigor discussed at 6:25-7:05~ Focus, Deeper Understanding, Application
57OELCS 2005 Math Module 3 Speaker Notes Content Standards andProgressions
58Clusters are groups of related standards Domains are larger groups/categories of standards that progress across gradesClusters are groups of related standardsContent standards define what students should understand and be able to doDomain1 minuteDomains are large groups of related standards. Clusters are groups of related standards. Standards define what students should be able to understand and be able to do- part of a cluster- Have the participants locate Grade 7 Expressions and Equations Domain on page 49ClusterStandard5858
592 minutesExplain the different components of the document. Have participants follow along in their common core binder.1st page of each grade level provides the “critical areas” of that grade level. (grade 6 on page 39-40)2nd page is an overview (or snapshot) of the domains and clusters of that grade level. Also includes the 8 Mathematical Practices. (grade 6 right after page 40-should be numbered page 41 but is not numbered in the document)3rd and following pages are the standards. (grade 6 starts on page 42)
60OELCS 2005 Math Module 3 Speaker Notes New Florida Coding for CCSSMNote: In the state of Florida, clusters will be numbered.MACC.7.EE.1.2MACC.2.OA.1.1DomainCommonCore1 minuteMA-stands for mathCC stands for Common Core7 is the grade levelEE is the domain- Expressions and Equations1 is the cluster #2 is the standard #MathStandardClusterGrade Level
61Florida Coding Scheme for Common Core State Standards MACC.8.EE.3.7Identify the clusterIdentify the grade levelIdentify the standardIdentify the domainFind the standard in your CCSSM binder2 minutes- p.54ANS:Cluster 3Grade 8Standard 7Domain EE- Expressions and EquationsLocated on page 54 of the Common Core State Standards- call on someone to read aloud to ensure the participants understand how to navigate through the document.
62Note that the Common Core Standards can be found in CPALMS
632 minutesAsk participants:Which domain is K-8? GeometryWhich domain is solely in grade 8? FunctionsNote the different naming conventions in K-5 vs middle grades, with the exception of Geometry.Note that it is not a 1 to 1 horizontal progression across the domains.
64OELCS 2005 Math Module 3 Speaker Notes Common CoreProgressionsCommon CoreProgressions
65OELCS 2005 Math Module 3 Speaker Notes Think across grades and link to major topics within gradesThe Standards are designed around coherent progressions from grade to grade.Teachers carefully connect the learning across grades so that students can build new understanding onto foundations built in previous years.Each standard is not a new event, but an extension to previous learning.1 minuteDefinition: Describes a topic across a number of grade levels based on conceptual development and the logical structure of mathematics.The Standards are designed around coherent progressions from grade to grade. Teachers need to be knowledgeable of developmental pathways and key learning trajectories, so that all students at all levels have the opportunity to learn the mathematics they need to progress. Each standard is not a new event, but an extension to previous learning.Siemon, Breed & Virgona 2006
66OELCS 2005 Math Module 3 Speaker Notes Geometry3Understand that shapes in different categories may share attributes.6Find the area of right triangles, other triangles, special quadrilaterals, and polygons.63 minutesParticipants will be provided samples of grade 3 and grade 6 Geometry progressions standards. Provide participants with copies of the Geometry Progression handout and explain that key components of the standards have been extracted to focus on the main point of the standard.Use this slide to provide participants with Third and Sixth grades Geometry standards in preparation for the progression activity.
67Progression- Activity OELCS 2005 Math Module 3 Speaker NotesProgression- ActivityIn your groups, use the geometry progression handout to identify the grade level corresponding to each bullet.10 minutesProvide geometry progression handout to participantsIn groups, participants will match each bullet to the corresponding grade levelParticipants will continue with the remaining grade levels (K, 1, 2, 4, 5, 7, 8, HS)Summarize findings as a whole group with next slide
68OELCS 2005 Math Module 3 Speaker Notes Correctly name shapes regardless of their orientations and overall size.Geometry1Distinguish between defining attributes versus non‐defining attributes .2Recognize and draw shapes having special attributes.3Understand that shapes in different categories may share attributes.4Classify two-dimensional figures based on the presence or absence of parallel and perpendicular lines.5Understand that attributes belonging to a category of two‐dimensional figures also belong to all subcategories of that category.6Find the area of right triangles, other triangles, special quadrilaterals, and polygons.67Solve real‐world and mathematical problems involving area, volume and surface area.4 minutesUse this slide to conduct a whole class discussion of Geometry progression activity findings.8Know the formulas for the volumes of cones, cylinders, and spheres.HSProve theorems about parallelograms.
69OELCS 2005 Math Module 3 Speaker Notes The Key Progression of Middle Grades MathCommon CoreProgressions1 minuteThere is one progression that is KEY to students’ readiness to high school Algebra- “the cornerstone”– as David Coleman explains:Elem: FractionsMiddle Grades: Ratios and Proportional ReasoningThese are the predictors of a child’s readiness and success in Algebra.THE MATH THAT MATTERS MOST
70OELCS 2005 Math Module 3 Speaker Notes Elementary grades work with part to whole relationships in fraction form.In 6th grade, the concept of ratio is introduced, and students look at tables of equivalent ratios and their representations on a graph.In 7th grade, students focus more on the use of multiple representations to solve proportion problems, including ratio tables, graphs, and equations, with a special focus on the constant of proportionality or unit rate.Finally in 8th grade, students extend the proportional reasoning developed in 6th and 7th grade to examine linear relationships with multiple representations.Grades 3-5Grade 62 minutesExplain how the content of each grade level is dependent on the understanding of the prior content. Teachers also need to be aware of how the concept will be developed in the upcoming grade levels.The foundation for students’ success in Algebra 1 (the cornerstone) is the progression from numbers & fractions ratios and proportional reasoning linear relationships.Grade 7Grade 8Ratio and Proportionality Grade Level Progression
71OELCS 2005 Math Module 3 Speaker Notes Expectations ofStudent PerformancePARCC Sample Items vs. FCAT 2.0 Sample ItemsNow we will compare and contract the expectations of student performance from PARCC versus FCAT 2.0 utilizing PARCC prototypes and FCAT 2.0 Sample Items.
72The Standards & The Assessment OELCS 2005 Math Module 3 Speaker NotesThe Standards & The AssessmentDefine what students should understand and be able to do in their study of mathematicsThese standards are “focused” and “coherent” (i.e., conceptually DEEP)1 minuteThe CCSSM define what students should understand and be able to do –focused, coherent—must teach for deeper understanding.PARCC assesses at a deeper level (i.e. performance assessment). Will determine whether students are on track to be college and career ready.Next generation assessment systemTechnology-basedAssesses at a conceptually DEEP level
73OELCS 2005 Math Module 3 Speaker Notes PARCC AssessmentsWHATHOWTransformative FormatsPROBLEMS WORTH DOINGMulti-step problems, conceptual questions, applications, and substantial procedures will be common, as in an excellent classroom.BETTER STANDARDS DEMAND BETTER QUESTIONSInstead of reusing existing items, PARCC will develop custom items to the Standards.FOCUSPARCC assessments will focus strongly on where the Standards focus. Students will have more time to master concepts at a deeper level.DRAG & DROPFILL-IN RESPONSESCOMPARISONSRADIO BUTTONS / MCCHECK BOXESWRITTEN RESPONSESFOCUSPARCC assessments will focus strongly on where the Standards focus. Students will have more time to master concepts at a deeper level.PROBLEMS WORTH DOINGMulti-step problems, conceptual questions, applications, and substantial procedures will be common, as in an excellent classroom.BETTER STANDARDS DEMAND BETTER QUESTIONSInstead of reusing existing items, PARCC will develop custom items to the Standards.3 minutesTransformative formats making possible what can not be done with traditional paper-pencil assessments (e.g., simulations to improve a model, game-like environments, drawing/constructing diagrams or visual models, etc.)Review each of the transformative formats:Radio Buttons/Multiple Choice (one possible answer)Drag & DropCheck Boxes (many possible answers)Comparisons (pull down menu to select choice- i.e.: <,>, etc)Fill-in Responses (type in the response)Written Responses (infuses writing to explain)
74Overview of PARCC Mathematics Task Types Description of Task TypeI. Tasks assessing concepts, skills and proceduresBalance of conceptual understanding, fluency, and applicationCan involve any or all mathematical practice standardsMachine scorable including innovative, computer-based formatsWill appear on the End of Year and Performance Based Assessment componentsII. Tasks assessing expressing mathematical reasoningEach task calls for written arguments / justifications, critique of reasoning, or precision in mathematical statements (MP.3, 6).Can involve other mathematical practice standardsMay include a mix of machine scored and hand scored responsesIncluded on the Performance Based Assessment componentIII. Tasks assessing modeling / applicationsEach task calls for modeling/application in a real-world context or scenario (MP.4)
75Design of PARCC Math Summative Assessments Performance Based Assessment (PBA)Type I items (Machine-scorable)Type II items (Mathematical Reasoning/Hand-Scored – scoring rubrics are drafted)Type III items (Mathematical Modeling/Hand-Scored and/or Machine-scored - scoring rubrics are drafted)End-of-Year Assessment (EOY)Type I items only (All Machine-scorable)
76Grade 6 Example Numbering / Ordering Numbers / Absolute Value OELCS 2005 Math Module 3 Speaker NotesGrade 6 Example Numbering / Ordering Numbers / Absolute Value
77OELCS 2005 Math Module 3 Speaker Notes FCAT 2.0 – Grade 630 secondsHere, students are asked to find the least value.MA.6.A.5.1 Use equivalent forms of fractions, decimals, and percents to solve problems - Moderate DOK
78OELCS 2005 Math Module 3 Speaker Notes PARCC – Grade 6Part a4 minutes Note-they must read the entire word problem to proceed with the following slides.Use pointer to show locations on number lineDiscuss:In terms of what the item requires of students, compare/contrast:-Format-Depth and RigorNote: Drag & Drop Format. Students do not calculate here; they must understand number sense to appropriately place the negative decimals on the number line.
79OELCS 2005 Math Module 3 Speaker Notes PARCC – Grade 6Part b1 minute1st answer is correct: Cake F weighs less than Cake G because -5 < -3.Discuss:In terms of what the item requires of students, compare/contrast:-Format-Depth and RigorNote: Students do not just select the inequality but the choice with the appropriate rationale.
80OELCS 2005 Math Module 3 Speaker Notes PARCC – Grade 6Part c2 minutesLast answer is correct: The cake that is furthest from the target weight.Discuss:In terms of what the item requires of students, compare/contrast:-Format-Depth and RigorNote that the ability to answer this question revolves on students’ conceptual understanding of absolute value. There is no calculation/procedure with this problem.
81OELCS 2005 Math Module 3 Speaker Notes PARCC – Grade 6Part d2 minutesSelect all that apply. There are two solutions that should be check marked. The two on the right:A cake with a reading of -5.3 oz.A cake with a reading of 3.1 oz.Discuss:In terms of what the item requires of students, compare/contrast:-Format-Depth and RigorNote: Students must select all that apply; therefore, simply guessing will not have the same probability of being correct as with FCAT’s multiple choice.Note: CPALMs- states that Florida will use all 4 levels of DOK with PARCC. The 4th level is Extended Thinking & Complex Reasoning. Since PARCC has performance assessment/tasks, this level which requires extended time can be utilized, whereas, it was not for FCAT (information as of 4/5/13)
82OELCS 2005 Math Module 3 Speaker Notes CCSSM Resources:Websites
83OELCS 2005 Math Module 3 Speaker Notes 1 minuteThe following sites will be uploaded on the commoncore.dadeschools.net website. There are CCSSM powerpoints already there from presentations with department leaders.Council of the Great City Schools: Common Core Works The Partnership for Assessment of Readiness for College and Careers (PARCC) Florida Department of Education: COUNTDOWN TO COMMON CORE Implementing the Common Core State Standards The Teaching Channel Videos Illustrative Mathematics Achieve Tools for the Common Core Standards commoncoretools.me Sense Making in Mathematics math.serpmedia.org/tools_specialized.html Inside Mathematics
84OELCS 2005 Math Module 3 Speaker Notes ReflectionsHow will the implementation of the Common Core Mathematical Practices shape future classroom instruction?Provide opportunities for reflections
85OELCS 2005 Math Module 3 Speaker Notes Handout to take with them: take home reading.Principals from multiple states share how they met the challenges of shifting to Common Core. Some of these states are in full implementation already so they can provide valuable reflection for where we are headed in terms of best practices as an administrator.
86OELCS 2005 Math Module 3 Speaker Notes Office of Academics and TransformationDivision of Academics, Accountability, & School ImprovementQuestions/Concerns:Department of Mathematics and ScienceMiddle Grades Mathematics1501 N.E. 2nd Avenue, Suite 326Miami, FLOffice:Fax:Thank the participants for their time and efforts.