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The PARCC Institute – High School Math: Preparing for PARCC! NJ’s Next Generation Standardized Assessment System FEA/PSA - Judith T. Brendel - Spring 2014

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2 Welcome…

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3 Desired outcomes… understand the overall substance, design and technical aspects of next generation PARCC assessments gain access and practice with PARCC tasks and related resources better enable educators to effectively lead the transition to CCSS and PARCC assessments.

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4 4 “…revolutionary transformation rather than evolutionary tinkering.” US DOE, NETP 2010 What should teaching and learning in the 21 st century look like?”

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6 6 Education for a Contemporary Age Preparing a Globally Competent and Innovative Workforce

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7 7 A Changing World… A growing need for a paradigm shift in the way we teach and learn… A Nation at Risk (1983) http://www2.ed.gov/pubs/NatAtRisk/findings.html http://www.ed.gov/pubs/NatAtRisk/index.html http://www.ed.gov/pubs/NatAtRisk/index.html SCANS Report and America 2000 http://wdr.doleta.gov/SCANS/whatwork/whatwork.pdf http://wdr.doleta.gov/SCANS/whatwork/whatwork.pdf (What Work Requires of Schools) “The best time to plant a tree is twenty years ago; the second best time is today.” (Ancient Chinese Proverb)

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8 8 A Changing Student… (recommended resources) Digital Natives, Digital Immigrants – Parts I and II – Do They Really Think Differently? (Prensky, 2001) http://www.marcprensky.com/writing/default.asp http://www.marcprensky.com/writing/default.asp Marc Prensky’s Essential 21st Century Skills http://www.marcprensky.com/writing/Prensky- Essential_21stCenturySkills.pdf http://www.marcprensky.com/writing/Prensky- Essential_21stCenturySkills.pdf “Different kinds of experiences lead to different brain structures.” Dr. Bruce D. Perry, Baylor College of Medicine

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9 9 A Changing Student… (recommended resources) Authentic Intellectual Work and Standardized Tests: Conflict or Coexistence (2001) http://ccsr.uchicago.edu/content/publications.php?pub_id=38# http://ccsr.uchicago.edu/content/publications.php?pub_id=38# How People Learn: Brain, Mind, Experience and School (1999, 2003) http://www.nap.edu/openbook.php?record_id=6160 http://www.nap.edu/openbook.php?record_id=6160

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10 Listen to our students! “I am a 21 st Century Learner!”

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11 How? Fostering essential skills … Communication Collaborative problem solving Critical thinking Creativity Innovation … through innovative pedagogy and ubiquitous technology. Global competence Content knowledge Entrepreneurship Adaptability Interpersonal

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12 “I do not teach my students; I simply create the conditions for their learning.” (Albert Einstein) 2006 Innovative Teachers Forum. Retrieved May 10, 2010 on : http://www.edlabgroup.org/tl/resources/InnovativeTeachers2006.pdf http://www.edlabgroup.org/tl/resources/InnovativeTeachers2006.pdf What conditions will foster these skills?

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13 21 st learning… …what should it look like?what should it look like?

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14 21 st learning… http://www.pascack.k12.nj.us/cms/lib5/NJ01000238/Centricity/Domain/87 /Writing%20Equations%202.swf

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15 Common standards,… …common (online) assessments, and common instruction that promote the essential skills.

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16 Reflection… What trends will continue to shape the world in which our students will live and work? What skills will our students need to succeed in their future? What type of learning environments would best support to development of these skills? …what are your thoughts?

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17 Let’s take a (quick) break!

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18 Let’s get to work…

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19 Let’s take our… (page-3) PARCC Pre-Assessment! Item 9: grade-7 level math w/new CCSS (What’s different?) ADD H.S. EXAMPLE

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20 A (Quick) Walk through the PARCC!

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21 Race to the Top Assessment Grants: $350 million of Race-to-the-Top Fund to consortia of states to design and develop common K-12 assessment systems aligned to CCSS In September 2010, the U.S. Department of Education awarded grants to: Partnership for Assessment of Readiness for College and Careers (PARCC) – 18 States, & DC Smarter Balanced Assessment Consortium (SBAC) Winning consortia - four years - to develop assessments systems, States participating will administer new assessments statewide by 2014-2015 ACHIEVE was selected through a competitive bid process, by PARCC to be the Project Manager.

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22 Race to the Top Assessment Grants: New Jersey is PARCC Governing Board State: Will administer the assessment system statewide 2014-15 school year. Will field test assessment items spring 2014. Governing Board meets quarterly. The chief state school officer for each of the governing states sits on the PARCC Governing Board. This to make major policy, operational, design and financial decisions regarding PARCC. Executive Committee meets weekly. (Governing Board Members from 6 states) ACHIEVE won competitive bid, selected by PARCC to be the Project Manager.

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23 Why New Common Assessments? Current Assessment Systems… Too many tests, often with disconnected purposes (e.g., instructional improvement vs. accountability vs. college admissions) Not challenging enough to measure CCR Do not measure the full range of college- and career- ready knowledge and skills (such as research, analysis, critical thinking, and collaboration)

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24 Why New Common Assessments? Current Assessment Systems… Fail to generate information for educators and students quickly enough or at all Are widely inconsistent across states making results impossible to compare

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25 Why New Common Assessments? Next-Generation Common Assessment Systems will… Measure students’ mastery of Common Core State Standards Provide a common measure of college and career readiness Include a range of item types that allow for the assessment of higher-order skills

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26 Why New Common Assessments? Next-Generation Common Assessment Systems will… Leverage new technologies in assessment and reporting to get actionable student data to educators and parents in real time Mitigate challenges associated with student mobility by ensuring students will have the same expectations wherever they live

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27 PARCC Assessment Consortium

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28 K-2 3-8 High School K-2 formative assessment being developed, aligned to the PARCC system Timely student achievement data showing students, parents and educators whether ALL students are on-track to college and career readiness ONGOING STUDENT SUPPORTS/INTERVENTIONS College readiness score to identify who is ready for college-level coursework SUCCESS IN FIRST-YEAR, CREDIT- BEARING, POSTSECONDARY COURSEWORK Targeted interventions & supports: 12 th -grade bridge courses PD for educators

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29 Solve problems involving the major content for their grade level with connections to practices Solve problems involving the additional and supporting content for their grade level with connections to practices Express mathematical reasoning by constructing mathematical arguments and critiques Use the modeling practice to solve real world problems Demonstrate fluency in areas set forth in the Standards for Content in grades 3-6 What does it mean? “Students are on-track or ready for college and careers” (Math)

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30 Assessment Transition Timeline 30 Assessment Transition Timeline Spring 2012 NJ ASK Aligned to NJCCCS Spring 2013 NJ ASK Aligned to the CCSS and NJCCCS (Except Gr. 6-8 Math) Spring 2014 NJ ASK Aligned to the CCSS SY 2014-15 Full administration of PARCC assessments “Transitional Assessments”

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31 The PARCC Commitment… PARCC is designed to promote quality instruction aligned to the CC Standards, so the assessment is worthy of preparation rather than a distraction from good work. TEACHING to the TEST may be a GOOD THING!

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32PVRSD Math TF – Work Session 1 | November 18, 2010 Understanding the Common Core State Standards …is to understand PARCC

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33 Why Common Core State Standards? 33 "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," which will place American students in a position in which they can compete in a global economy.

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34 Why Common Core State Standards? Before Common Core State Standards we had standards, but rarely did we have standards-based instruction. Long lists of broad, vague statements Mysterious assessments Coverage mentality Focused on teacher behaviors – “the inputs”

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35 Principles of the CCSS… FEWER - CLEARER - HIGHER Aligned to requirements for College and Career Readiness Based on evidence Honest about time

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36 The CCSS Difference: Grade 8 Mathematics Before: NJCCCS (2004) 1. Understand and apply the Pythagorean Theorem. After: CCSS (2010) 1. Explain a proof of the Pythagorean Theorem and its converse. 1. Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions. 1. Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.

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37 a 2 + b 2 = c 2 a b c 3 3 9 416 4 5 5 25 a = 4 b = 3 c = ?

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38 Implications of the CCSS on WHAT and HOW to teach… What are the Critical Shifts to Consider?

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39 COMMON CORE SHIFTS in ASSESSMENTS Shift 1: Focus Priority standards = focus of the assessments. Other standards deemphasized. Shift 2: Coherence Assessments will reflect the progression of content and concepts as depicted in the standards across grade levels. Shift 3: Fluency It will be assumed students possess required fluencies through grade 8; as such, students will not be allowed to use calculators in grades 3-5. Students will be allowed to use four-function calculators with a square root key or scientific calculators in grade 6 and scientific calculators in grades 7-8.

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40 CC SHIFTS in ASSESSMENTS continued ….. Shift 4: Deep Understanding Each standard will be assessed from multiple perspectives, while not veering from the primary target of measurement for the standard. Shift 5: Application Shift 6: Dual Intensity Students will be expected to know grade-level mathematical content with fluency and to know which mathematical concepts to employ to solve real-world mathematics problems.

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41PVRSD Math TF – Work Session 1 | November 18, 2010 PARCC sample prototypes with Task Type

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42 TASK TYPES – PARCC I – Computation, Skills, Process (x – 2) 2 + 6 = 75 2x 2 - 5x – 6 = 0 II – Mathematical Reasoning xxx xxxx III – Modeling, Combined Standards, Applications Compare the 3 sets of data (graph, chart, and equation) and defend the argument that ….

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43December 2, 2013 TASK TYPE-I Tasks assessing concepts, skills and procedures. - include a balance of conceptual understanding, fluency, and application. These tasks can involve any or all mathematical practice standards. - will be machine scorable and will include innovative, computer- based formats. -will appear on the End-of-Year and Performance Based Assessment components and generate evidence for measuring major, additional, and supporting content with connections to the mathematical practices as indicated in the PARCC Model Content Frameworks for Mathematics.*

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44December 2, 2013 Mathematics online Sample Item/Prototypes: PARCC TYPE-I TASKS (1, 2, or 4 point questions) HS – FunctionsSFunctionsS HS – Seeing Structure in Quadratic EquationSeeing Structure in Quadratic Equation HS – Picture Frame (Algebra-I/Math 2)Picture Frame http://www.parcconline.org/sites/parcc/files/HS-Alg1Math2PictureFrame.pdf HS – Myla’s Swimming Poole (Algebra-I)Myla’s Swimming Poole HS – Green Tea Observation Study (Algebra-2/Math 3)Green Tea Observation Study

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45December 2, 2013 TYPE II: Tasks assessing expressing mathematical reasoning. - tasks call for written arguments/justifications, critique of reasoning, or precision in mathematical statements (MP. 3, 6). These tasks can also involve other mathematical practice standards. - tasks may include a mix of innovative, machine scored and hand scored responses. - tasks will be included on the Performance Based Assessment component and generate evidence for measuring mathematical reasoning with connections to content.

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46 Dec. 2, 2013 Mathematics online Sample Item/Prototypes: PARCC TYPE-II TASKS (4 point questions) HS – Graphs of Functions (Algebra-II/Math III) Nov. 2013Graphs of Functions HS.C.6.2, A.REI.D, MP.3, 7 with 4-point scoring rubric http://www.parcconline.org/sites/parcc/files/HighSchoolAlg2Math3-GraphsofFunctions.pdf HS – Michelle’s Conjectures (Algebra-II/Math III)Michelle’s Conjectures http://www.parcconline.org/sites/parcc/files/PARCC_SampleItems_Mathematics_HSAlgIMathIIMi chelleConjecture_081913_Final_0.pdf HS – Geometric Construction Connection (Geometry/Math III)Geometric Construction PARCC_SampleItems_Mathematics_HSGeoMathIIIGeometricConnection_081913_Final_0.pdf http://www.parcconline.org/sites/parcc/files

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47December 2, 2013 TYPE III: Tasks assessing modeling/applications. (3 or 6 point questions) - tasks call for modeling/application in a real-world context or scenario (MP.4) and can also involve other mathematical practice standards. - tasks may include a mix of innovative, machine scored and hand scored responses. -tasks will be included on the Performance Based Assessment component and generate evidence for measuring mathematical modeling/application with connections to content.

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48SA MS/HS– PD Session 3| April 4., 2011 TYPE-I PARCC TASKS include a balance of conceptual understanding, fluency, and application, and can involve any or all Math Practice Standards. will be machine scorable and will include innovative, computer- based formats. will appear on the End of Year and Performance Based Assessment components and generate evidence for measuring major, additional, and supporting content with connections to the mathematical practices as indicated in the PARCC Model Content Frameworks for MathematicsPARCC Model Content Frameworks for Mathematics.*

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49J. Brendel 12.3.2013 Functions http://www.parcconline.org/samples/mathematics/high-school- functions http://www.parcconline.org/samples/mathematics/high-school- functions Given f(x) as a graphed parabola and g(x) as table of values 1.Compare y-intercepts 2.Compare f(3) and g(3) 3.Compare maximum values of each w/in range -5 ≤ x ≤ 5 4.Compare A type I PARCC task COURSE ? DIFFICULTY? POINTS? STANDARDS?

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50J. Brendel 12.3.2013 Seeing Structure in a Quadratic Equations http://www.parcconline.org/samples/mathematics/high-school-seeing- structure-quadratic-equation (3x - 2) 2 = 6x – 4 a Type-I PARCC task COURSE ? DIFFICULTY? POINTS? STANDARDS?

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51J. Brendel 12.3.2013 Seeing Structure in Equations http://www.parcconline.org/samples/mathematics/high-school-seeing-structure-equation http://www.parcconline.org/samples/mathematics/high-school-seeing-structure-equation 24 + 10x – x 2 = p – (x – 5) 2 Solve for p a Type I PARCC task COURSE ? DIFFICULTY? POINTS? STANDARDS?

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52J. Brendel 12.3.2013 PICTURE FRAME http://www.parcconline.org/sites/parcc/files/HS-Alg1Math2PictureFrame.pdf a Type I PARCC task COURSE ? DIFFICULTY? POINTS? STANDARDS?

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53J. Brendel 12.3.2013 GREEN TEA TYPE http://www.parcconline.org/sites/parcc/files/PARCC_SampleItems_Mathematics_HS AlgIIMathIIIGreenTeaStudy_081913_Final_0.pdf a Type I PARCC task COURSE ? DIFFICULTY? POINTS? STANDARDS?

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54 TYPE-II PARCC TASKS call for written arguments/justifications, critique of reasoning, or precision in mathematical statements (MP. 3, 6). These tasks can also involve other mathematical practice standards. may include a mix of innovative, machine scored and hand scored responses. will be included on the Performance Based Assessment component and generate evidence for measuring mathematical reasoning with connections to content.

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55 GRAPH of FUNCTIONS (posted November 2013) http://www.parcconline.org/sites/parcc/files/HighSchoolAlg2Math3- GraphsofFunctions.pdf http://www.parcconline.org/sites/parcc/files/HighSchoolAlg2Math3- GraphsofFunctions.pdf a Type-II PARCC Task COURSE ? POINTS ? DIFFICULTY? STANDARDS?

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56 GEOMETRY CONSTRUCTION CONNECTION http://www.parcconline.org/sites/parcc/files/PARCC_SampleItems_Mathematics_HS GeoMathIIIGeometricConnection_081913_Final_0.pdf a Type-II PARCC Task POINTS ? DIFFICULTY? STANDARDS?

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57 MICHELLE’S CONJECTURES (Aug.19, 2013) http://www.parcconline.org/sites/parcc/files/PARCC_SampleItems_Mathematics_HSAlgIMat hIIMichelleConjecture_081913_Final_0.pdf a Type-II PARCC Task COURSE ? POINTS ? DIFFICULTY? STANDARDS?

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58 TYPE-III PARCC TASKS call for modeling/application in a real-world context or scenario (MP.4) and can also involve other mathematical practice standards. may include a mix of innovative, machine scored and hand scored responses. will be included on the Performance Based Assessment component and generate evidence for measuring mathematical modeling/application with connections to content.

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59 MINI GOLF PRICES (November, 2013) http://www.parcconline.org/sites/parcc/files/HSAlg1Math2MiniGolfPrices.pdf a Type-III PARCC Task COURSE ? POINTS ? DIFFICULTY? STANDARDS?

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60 BRETT’S RACE (November, 2013) http://www.parcconline.org/sites/parcc/files/HSMathematicsSampleItemBR.pdf a Type-III PARCC Task COURSE ? POINTS ? DIFFICULTY? STANDARDS?

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61 a Type-III PARCC Task POPCORN INVENTORY (NOVEMBER 2013) http://www.parcconline.org/sites/parcc/files/HSAlg1Math1PopcornInventory.pdf COURSE ? POINTS ? DIFFICULTY?

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62 a Type-III PARCC Task TEMPERATURE CHANGES http://www.parcconline.org/sites/parcc/files/PARCC_SampleItems_Mathematics_HS AlgIIMathIIITemperatureChange_081913_Final_0.pdf COURSE ? POINTS ? DIFFICULTY?

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64 PARCC RELEASED TASKS include elsewhere? Use this slide to ‘hold’ sites file://localhost/Users/jbrendel/Desktop/PARCC%20HS%20Functions.h tmlfile://localhost/Users/jbrendel/Desktop/PARCC%20HS%20Functions.h tml (November/December 2013)

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65SA MS/HS– PD Session 3| April 4., 2011 https://www.teachingchannel.org/videos/laws-of-sines-cosines- lesson#https://www.teachingchannel.org/videos/laws-of-sines-cosines- lesson# 14-min lesson “fly quadcopters” math/science/engineering … a 4-month project … Ms. Brookins and Mr. James GRADE-11 How/if...include here? https://www.teachingchannel.org/videos/statistical-analysis-lesson Statistical analysis to rank baseball players GRADES 11-12 CCSS Standards: Math SID. 1, 2 and 3

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66 What you SHOULD NOT see !

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67 Z N x y > < Slope =slope = (3,6) (3,2)

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68SA MS/HS– PD Session 3| April 4., 2011 BRAINSTORM in GROUPS What should teachers NOT be doing?

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69 READING CCSS and Mathematics

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70 In “Casey at the Bat,” Casey strikes out. Describe a time when you failed at something. In “Letter from a Birmingham Jail,” Dr. King discusses nonviolent protest. Discuss, in writing, a time when you wanted to fight against something that you felt was unfair. In “The Gettysburg Address” Lincoln says the nation is dedicated to the proposition that all men are created equal. Why is equality an important value to promote? What makes Casey’s experiences at bat humorous? What can you infer from King’s letter about the letter that he received? “The Gettysburg Address” mentions the year 1776. According to Lincoln’s speech, why is this year significant to the events described in the speech? Not Text-Dependent in ELAText-Dependent in ELA

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71 Text-Dependent in mathematics December 2, 2013 author: J. Brendel Material not to be duplicated.

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72 Regular Practice with Complex Text and its Academic Language

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73 Regular Practice with Complex Text and its Academic Language Cramer’s Rule for solving systems of equations uses determinants to solve for each variable. D is the determinant of the coefficient matrix. Dy is the determinant formed by replacing the coefficients of y in D with the constant terms. Algebra-II Sample academic language in a basic statistics task: measure of central tendency, skewed, mean, median, mode, outlier, bimodal, quartiles, box-and-whisker plot, percentile, random sample, … New to Pre-Algebra, Algebra I or II

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74 Regular Practice with Complex Text and its Academic Language (“Adult Language”) Example: Phone company ‘A’ charges an initiation fee plus a charge per minute. The cost of using 300 minutes (plus initiation fee) is $25 and the cost of 700 minutes (plus initiation fee) is $33. Write an equation to represent the cost. What is the initiation fee? What is the cost per minute? Is this company’s offer better than the new phone company ‘B’s? Explain or compare with charts and graphs. Pre-Algebra, Algebra

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75 Regular Practice with Complex Text and its Academic Language Basic constructions w/triangles using protractors, compasses or online with simulation tools: Students construct, do proofs and solve problems involving: Medians, vertex angle, balancing point, centroid Altitudes, acute triangles, obtuse triangles, right triangles, orthocenter, interior, exterior or …. Perpendicular Bisectors, concurrent lines, point of concurrency, circumcenter of a triangle Angle Bisectors, incenter, equidistant, …. Geometry

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76 Adjusting Math Language to the CCSS Old habit to eliminate: Defining equality as “same as.” The problem: This is mathematically incorrect and leads to misconceptions. New habit to adopt: Defining equality as “same value as.” Old habit to eliminate: “Addition makes things get bigger.” The problem: When negative numbers are introduced, the old habit has to be debugged. New habit to adopt: Addition is about combining. Old habit to eliminate: “Subtraction makes things get smaller.” The problem: As with addition, negative numbers make this wrong. New habit to adopt: Subtraction is about difference.

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77 Regular Practice With Complex Text and its Academic Language: Why? Gap between complexity of college and high school texts is huge. What students can read, in terms of complexity is greatest predictor of success in college (ACT study). Too many students are reading at too low a level.

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78 What are the Features of Complex Text? Subtle and/or frequent transitions Multiple and/or subtle themes and purposes Density of information Unfamiliar settings, topics or events Lack of repetition, overlap or similarity in words and sentences Complex sentences

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79 What are the Features of Complex Text? (cont.) Uncommon vocabulary Lack of words, sentences or paragraphs that review or pull things together for the student Longer paragraphs Any text structure which is less narrative and/or mixes structures

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80 It all boils down to… Texts Worth Reading…and Questions Worth Answering!

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81 Let’s take a quick break!

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82PVRSD Math TF – Work Session 1 | November 18, 2010 Understanding the Common Core Math Standards …is to understand PARCC Math!

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83 The Common Core Standards: Classroom Video Illustration High School School

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84 The Standards are NOT new names for old ways of doing things…

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85 A different topic every day Every topic/concept treated as equally important Elementary students dipping into advanced topics at the expense of mastering fundamentals Infinitesimal advance in each grade; endless review Incoherence and illogic – bizarre associations, or lacking a thread NOT …

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86 Dan Meyer: Math Class Needs a Makeover

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87 NOT Lack of rigor Reliance on rote learning at expense of concepts Aversion to repetitious practice Severe restriction to stereotyped problems lending themselves to mnemonics or tricks Lack of quality applied problems and real-world contexts Lack of variety in what students produce E.g., overwhelmingly only answers are produced, not arguments, diagrams, models, etc. From....To…. 856 = ___ hundreds, ___ tens, ___ ones1 hundredth = ___ tenths x 2 + 10x + 21 = 0¾ c(c –1) = c

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88 1. Focus: Focus strongly where the Standards focus. 2. Coherence: Think across grades, and link to major topics within grades. 3. Rigor: In major topics, pursue: conceptual understanding; procedural skill and fluency; and application with equal intensity. Three (3) Significant Shifts in Mathematics:

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89 Activity No. 3: Shifts Happen - Mathematics What is this shift? Why this shift? OpportunitiesChallenges Focus: Focus strongly where the Standards focus. Coherence: Think across grades, and link to major topics within grades. Rigor: In major topics, pursue conceptual understanding, procedural skill and fluency, and application with equal intensity.

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90 1. Focus: Focus strongly where the Standards focus. 2. Coherence: Think across grades, and link to major topics within grades. 3. Rigor: In major topics, pursue: conceptual understanding; procedural skill and fluency; and application with equal intensity. Three (3) Significant Shifts in Mathematics:

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91 FOCUS continued 70% or more of the assessment will measure the major work in grades 3-8 Focus allows for a variety of problem types (task types) to get at a concept in multiple ways. Students will have more time to master concepts at a deeper level.

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92 Mathematics topics intended at each grade by at least two-thirds of A+ countries Mathematics topics intended at each grade by at least two-thirds of 21 U.S. states The shape of math in A+ countries… 1 Schmidt, Houang, & Cogan, “A Coherent Curriculum: The Case of Mathematics.” (2002).

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93 K 12 Number and Operations Measurement and Geometry Algebra and Functions Statistics and Probability Traditional U.S. Approach…

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94 Focusing attention within Number and Operations Operations and Algebraic Thinking Expressions and Equations Algebra Number and Operations—Base Ten The Number System Number and Operations— Fractions K12345678High School

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95 Grade Focus Areas in Support of Rich Instruction and Expectations of Fluency and Conceptual Understanding K–2 Addition and subtraction - concepts, skills, and problem solving and place value 3–5 Multiplication and division of whole numbers and fractions – concepts, skills, and problem solving 6 Ratios and proportional reasoning; early expressions and equations 7 Ratios and proportional reasoning; arithmetic of rational numbers 8 Linear algebra, linear functions Priorities in Mathematics (CCSS)

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96 ALG. - 1 Focus Areas in Support of Rich Instruction and Expectations of Fluency and Conceptual Understanding UNIT-1 Relationships Between Quantities and Reasoning with Equations UNIT-2 Linear Relationships UNIT-3 Expressions and Equations UNIT-4 Quadratic Functions and Modeling UNIT-5 Functions and Descriptive Statistics Priorities in Mathematics (CCSS)- MS/HS

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97 GEOMETRY Focus Areas in Support of Rich Instruction and Expectations of Fluency and Conceptual Understanding UNIT-1 Congruence, Proof, and Constructions UNIT-2 Similarity, Proof, and Trigonometry UNIT-3 Extending to Three Dimensions UNIT-4 Connecting Algebra and Geometry Through Coordinates UNIT-5 Circles With and Without Coordinates UNIT-6 Applications of Probability Priorities in Mathematics (CCSS) - HS

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98 ALG. - 2 Focus Areas in Support of Rich Instruction and Expectations of Fluency and Conceptual Understanding UNIT-1 Polynomial, Rational, and Radical Relationships UNIT-2 Trigonometric Functions UNIT-3 Modeling with Functions UNIT-4 Inferences and Conclusions from Data Priorities in Mathematics (CCSS) – HS

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99 1. Focus: Focus strongly where the Standards focus. 2. Coherence: Think across grades, and link to major topics within grades. 3. Rigor: In major topics, pursue: conceptual understanding; procedural skill and fluency; and application with equal intensity. Three (3) Significant Shifts in Mathematics:

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100 COHERENCE Integrative tasks draw on multiple standards to ensure students are making important connections. The Standards are not treated as a checklist.

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101 COHERENCE Need to include h.s. task(s) that incorporate multiple standards to show connections.

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102 Coherence and NEW multiple-choice questions. Circle all that are true. Given: All squares A. are parallelograms and rectangles B. have 4 acute angles C. have only 2 diagonals D. Area = ½ base x height E. Sum of consecutive angles = 180˚ F. Perimeter = 2 x Side length G. Area > area with the same perimeter. 5 3 7 5 25 21

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103 *Activity 4: Work with your group (p. 15. Ex. 8) What skills and understandings are assessed here? Do they come from only one standard? One domain? A.subtraction w/decimals B. addition then subtraction C.write % as a decimal; multiply D.read carefully, add and subtract money E.know how to find an average F.know to ÷ or x; compute accurately G.know to add lowest, then highest; understand concept, recognize > and < symbols

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104 Coherence: Link to major topics within grades Example: HIGH SCHOOL performance task; Algebra-I unit 1 Algebra-I Unit-1 A large truck has two fuel tanks, each with a capacity of 150 gallons. One of the tanks is half full, and the other is empty. Fuel is pumped into the tanks until both tanks are full. The pump delivers fuel at a constant rate of 5¾ gallons per minute. a.Write an equation for the total number of gallons of fuel …. a.How much fuel is in the tanks after the pump … 8 minutes? b.Graph the equation … on the coordinate plane … label ….

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105 1. Focus: Focus strongly where the Standards focus. 2. Coherence: Think across grades, and link to major topics within grades. 3. Rigor: In major topics, pursue: conceptual understanding; procedural skill and fluency; and application with equal intensity. Three (3) Significant Shifts in Mathematics:

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106 RIGOR Need to include h.s. task(s) that incorporate multiple standards to show connections.

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107 See the Rigor – Early Elementary Grades Ray’s father has 129 plants in his garden. Billy’s father has 230 plants in his garden. Ray says his father has more plants because 9 is bigger than 2. Is Ray correct? Yes ___ No ___ Explain how you know. Guess the grade level!

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108 See the Rigor in Grade-3 Fractions on a Number Line http://www.illustrativemathematics.org/standards/hs

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109 See the Rigor in Middle Grades Understanding of Fractions Write a number that is greater than and less than Hint: Find equivalent fractions for and with denominators of 40 or 100. Why wasn’t it helpful to use 20 as a denominator? (JB)

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110 See Rigor in Grade 6: Ratios PARCC - Grade-6 Slider Ruler: type-I http://www.parcconline.org/ samples/mathematics/grade- 6-slider-ruler http://www.parcconline.org/ samples/mathematics/grade- 6-slider-ruler

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111 ONLINE http://www.parcconline.org/samples/item-task- prototypes Grade-3 Fractions on a Number Line: type- I http://www.parcconline.org/samples/mathematics/grade-3- mathematics-number-line http://www.parcconline.org/samples/mathematics/grade-3- mathematics-number-line Grade-4 Fraction model: type-II http://www.parcconline.org/sites/parcc/files/PARCC_SampleItems_ Mathematics_G4FractionModel_081913_Final.pdf http://www.parcconline.org/sites/parcc/files/PARCC_SampleItems_ Mathematics_G4FractionModel_081913_Final.pdf Grade-6 Slider Ruler: type-I http://www.parcconline.org/samples/mathematics/grade-6-slider- ruler http://www.parcconline.org/samples/mathematics/grade-6-slider- ruler

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112 See the Rigor in High School Math

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113 Linking to major topics – Grade 7

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114 Part B

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115 Linking to major topics – High School Part A

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116 Part B Describ e Compare Write

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117 REQUIRED FLUENCIES SA MS/HS– PD Session 3| April 4., 2011

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118 Required Fluencies in K-6 GradeStandardRequired Fluency KK.OA.5Add/subtract within 5 11.OA.6Add/subtract within 10 2 2.OA.2 2.NBT.5 Add/subtract within 20 (know single-digit sums from memory) Add/subtract within 100 3 3.OA.7 3.NBT.2 Multiply/divide within 100 (know single-digit products from memory) Add/subtract within 1000 44.NBT.4Add/subtract within 1,000,000 55.NBT.5Multi-digit multiplication 66.NS.2,3 Multi-digit division Multi-digit decimal operations

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119 HS EXPECTATIONS ALGEBRA-I: Unit 2 – LINEAR RELATIONSHIPS Find approximate solutions to linear equations by making a table of values, using technology to graph and successive approximations. Graph functions by hand (in simple cases) and with technology …. Solve systems of linear equations in two variables … Dec. 2, 2013 J.Brendel A.REI.5, A.REI.6 additional A.REI.10, 11 major F.IF.7/9 supporting

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120 One of several staircases to algebra designed in the OA domain. Coherence: Link to Major Topics Across Grades 120 1. add … subtract 3. multiply … divide 5. expressions 6. Apply properties

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121 One of several staircases to algebra designed in the OA domain. Coherence: Link to Major Topics Across Grades 121 ALGEBRA-I ALGEBRA- II

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122 Application Students can use appropriate concepts and procedures for application even when not prompted to do so. Teachers provide opportunities at all grade levels for students to apply math concepts in “real world” situations, recognizing this means different things in K-5, 6-8, and HS. Teachers in content areas outside of math, particularly science, ensure that students are using grade-level-appropriate math to make meaning of and access science content. 122

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123 Fluency FLUENCY and new type of MC question

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124 Real world application – Grade 4

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125 HS Teachers outside of math use grade-level-appropriate math

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126 Part B

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127 Part C

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128 Part D

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129 Standards of Mathematical Practices 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. Construct viable arguments and critique the reasoning of others Model with mathematics. Attend to precision

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130 Analysis of the PARCC Mathematics Assessment: Design Shifts (Activity No. 4)

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131 Shift No. 1…Focus where Standards Focus Advance: PARCC assessments will focus strongly where the Standards focus (70% or more on the major work in grades 3-8). Focus allows for a variety of problem types to get at concept in multiple ways. Students will have more time to master concepts at a deeper level.

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132 Shift No. 2…Coherence across/within grades Advance: The assessment design is informed by multi-grade progressions in the Standards and the Model Content Frameworks. Key beginnings are stressed: e.g., ratio concepts in grade 6, e.g., fluency with the multiplication table in grade 3 Become key endpoints and takeaway skills

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133 Shift No. 2…Coherence across/within grades Advance: Integrative tasks draw on multiple standards to ensure students are making important connections. The Standards are not treated as a checklist.

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134 Shift No. 3…Rigor Advance: PARCC assessments will reach the rigor in the Standards through innovations in technology and item design.

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135December 2, 2013 SAMPLE ALGEBRA-1 UNIT-I ASSESSMENT and High School Reference Sheet (separate packet) Solution Guide With notes to teachers Sample responses and scoring

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136 The Mathematics Common Core Toolbox Mathematics Sample Item/Prototypes: PARCC online at the Dana Center Grade 4 (Deer in the Park) p. 23 Grade 4 (Deer in the Park) Grade 6 (Gasoline Consumption) High School (Isabella’s Credit Card) *p. 24-25) High School (Isabella’s Credit Card) High School (Popcorn Inventory) new Nov. 2013 http://www.parcconline.org/sites/parcc/files HSAlg1Math1PopcornInventory.pdf Activity: grade-2 (p. 26-27) *What makes it unique? ….

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137 Performance Based Assessment (PBA) Type I items (machine-scorable) Type II items (Mathematical Reasoning/hand-scored) Type III items (Mathematical Modeling/hand scored and/or machine-scored End-of-Year Assessment (EOA) Type I items only (All machine-scorable)

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138 Sample Online Performance Tasks Mathematics Sample online Item/Prototypes: Smarter Balanced: link on next slide Grade 3 - Lemonade Sale Grade 4 - Family Trip to the Zoo Grade 6 - Cereal Box (vol., surf.area, min s.a.) Grade 7 - Food Basket (calories, grams, protein) Grade 8 - Heartbeats (scatter plot ….) Grade 11- Speeding Ticket (graph, what is fair? ….) Grade 2 hardcopy-Trip to Zoo (gr. 4 modified; J. Brendel Barron’s) (page 27-28)

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139 EXPERIENCE an ASSESSMENT Activity 6 https://sbacpt.tds.airast.org/student/login.aspx?c=SB AC_PT https://sbacpt.tds.airast.org/student/login.aspx?c=SB AC_PT Sample online Smarter Balanced Assessments. Select from grades 3, 4, 5, 6, 7, 8 or 11 Sample online Smarter Balanced Assessments. Select Examples or Performance Tasks J.Brendel 11/2013

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140 J. Brendel 11/2013 CIRCLES http://sampleitems.smarterbalanced.org/itempreview/ModernShell.asp x?config=SBAC%5CContent%5CCircle1.json MATH II - WALLS http://sampleitems.smarterbalanced.org/itempreview/ModernShell.asp x?config=SBAC%5CContent%5CRoomWall.json

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141 The Specs, Accountability, and Resources: What We Know Now!

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142 PARCC Assessment Consortium

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143 Dynamic Learning Maps (DLM) Alternate Assessment Consortium

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144 Performance Based Assessment ELA/LiteracyMath TOTAL Grade Literacy Analysis ResearchNarrativeSession 1 Session 2 9-10 Alg I/ Math I Geo/ Math II Estimated Time on Task (minutes) 808550 315 Estimated Time on Task: Grade 9-10

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145 End-of-Year (EOY) Assessment ELA/LiteracyMath TOTAL Grade Session 1 Session 2 Session 1 Session 2 9-10 Alg I/ Math I Geo/ Math II Estimated Time on Task (minutes) 70 65 270 Estimated Time on Task: Grade 9-10 Grade 9-10 Summative Total: 9 Hours, 45 minutes

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146 Performance Based Assessment ELA/LiteracyMath TOTAL Grade Literacy Analysis ResearchNarrativ e Session 1 Session 2 11 Alg II/ Math III Estimated Time on Task (minutes) 80855065 345 Estimated Time on Task: Grade 11

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147 End-of-Year (EOY) Assessment ELA/LiteracyMath TOTAL Grade Session 1 Session 2 Session 1 Session 2 11 Alg II/ Math III Estimated Time on Task (minutes) 70 55 250 Estimated Time on Task: Grade 11 Grade 11 Summative Total: 9 Hours, 55 minutes

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148 ~ 1/3 total points = PBA End-of-Year machine scored

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149 ~ 1/3 total points = PBA End-of-Year machine scored

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150 What Else… 20 Day Window…for both the PBA and EOY summative assessments (performance based and end-of-year) Summative Assessments Retest Opportunities Grades 3-8 - 1 retest opportunity/year HS - up to 3 retest opps/year for each assessment Computer-based (w/paper version available in rare circumstances), contingency back-up PBA delay? No…

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151 What Else… Accessibility Features for ALL students Audio Amplification Blank Paper (provided by test administrator) Eliminate Answer Choices Flag Items to Review General Administration Directions (provided by test administrator) General Administration Directions Read Aloud and Repeated (provided by test administrator) Accommodations / Modifications for Special Education students (55 page manual)

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152 What Else… Accessibility Features for ALL students continued Highlight tool Headphones Magnification/Enlargement Device Notepad Pop-Up Glossary Redirect Student to Test (provided by test administrator) Spell Checker Writing Tool

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153 What Else… Accommodations / Modifications for Special Education Students (from the 55-page PARCC Accessibility manual) Accessibility Features Identified in Advance Answer Masking Background/Font Color (Color Contrast) General Masking Line Reader Tool Text-to-Speech for the Mathematics Assessments http://parcconline.org/parcc-accessibility-accommodations-and-fairness

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154 Modifications Accommodations NOT permitted Modifications involve changes in the conditions under which a student takes an assessment that result in unacceptable changes to the test itself, or what the test measures (e.g., reducing or changing expectations for students) and are therefore not permitted on PARCC assessments. Examples of modifications that will result in invalidated results on PARCC include: Requiring a student to be assessed on less content matter than other students because he has been taught less material; Reducing the scope of assessments so a student needs to complete only a limited number of problems or items;

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155 Modifying the complexity of assessments to make them easier (e.g., deleting half of the response choices on a multiple-choice test so that a student selects from two options instead of four); Giving hints, clues, or other coaching that directs the student to correct responses on assignments and tests; Adults defining vocabulary on the test or explaining test items; Allowing the student to complete an assessment of English language arts in a language other than English; and Using dictionaries that provide definitions (rather than an acceptable word-to-word dual-language dictionary).

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156 Accountability: What We Know Now!

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157 Results Types… Performance LevelDescription Level 5*Distinguished Command Level 4*Strong Command Level 3Moderate Command Level 2Partial Command Level 1Minimal Command Proficiency ( PLDs ) On-Track-to-College and Career Readiness (CCRDs) Growth Data Performance Level Descriptors (PLDs) *Achieved CCR Performance Threshold

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158 What does “distinguished” (Level 5) mean? “Students performing at this level demonstrate a distinguished command of the knowledge, skills, and practices embodied by the Common Core State Standards for English language arts/literacy assessed at grade 11. They are academically well prepared to engage successfully in entry-level, credit-bearing courses in College English Composition, Literature, and technical courses requiring college-level reading and writing. Students performing at this level are exempt from having to take and pass placement tests in two- and four-year public institutions of higher education designed to determine whether they are academically prepared for such courses without need for remediation.”

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159 What does it mean to be CCR? (Level-4) “Students who earn a PARCC College- and Career-Ready Determination by performing at Level 4 in mathematics and enroll in College Algebra, Introductory College Statistics, and technical courses requiring an equivalent level of mathematics have approximately a 0.75 probability of earning college credit by attaining at least a grade of C or its equivalent in those courses.”

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160 What does it mean to be CCR? (cont.) Will be used as a benchmark against which the CCR cut score on the PARCC assessments will be validated through empirical research. WHY - a “C” is the minimum grade needed to earn credit for a course WHY - a reasonably high standard but not unattainable. WHY - similar to the criteria used by ACT, WHY - other important CCR skills will not be measured by PARCC assessments.

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161 What are the cut scores for each level? As/PARCC, “the vendor selected through the RFP will also work with state leaders, educators and eternal experts to determine the cut scores to establish the five PARCC Performance levels for each grade-level assessment. RFP for “Operational Assessment” Vendor proposals are due by Dec. 11, 2013.

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162 Timelines and Resources: What We Know Now!

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163 PARCC Timeline… Jan – Aug 2013 Release of 2 nd set of prototype assessment and instructional tasks (spring 2013) Release of online professional learning modules (spring 2013) (update: expected June 2014) Item tryouts (spring 2013) – see next slide 2013-2014 Full-scale pilot/field testing (spring 2014) Partnership Resource Center launches (spring 2013) Optional performance tasks for K-2 available (February 2014) College readiness tools available (spring 2014) 2014-2015 Diagnostic assessments release (September 2014) Full operational administration of PARCC assessments (spring 2015) Setting of achievement levels, including college-ready performance levels (late spring 2015 (post-administration)

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164 PARCC Timeline… *Over the next year, PARCC will develop five online training modules for teachers, school leaders, and school site testing coordinators – each with a unique purpose. PARCC will produce modules with the following foci: 1.PARCC Common Assessments Overview 2.Introduction to the PARCC Mid-Year Assessment 3.Introduction to the PARCC Diagnostic Assessment 4.Introduction to the PARCC Speaking/Listening Assessment 5.PARCC Accessibility System *It is anticipated that modules will be available in June 2014.

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165 PARCC Timeline… NJ SpotlightNJ Spotlight (Nov. 20, 2013) For the first time since 1989, New Jersey will next year suspend its requirement that high school graduates pass a state test in language arts and math to receive their diplomas. (No HSPA) But that doesn't mean there will be fewer tests, just that they'll be used for different purposes. For instance, current eighth, ninth, and 10th graders will be tested in language arts and math now in three separate tests, and while passing the exams will not be required for graduation, the scores will be included in a student’s permanent transcript. (2014-15 school year)

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166 NJDOE Model Curricula (handouts Algebra-I, Geometry, Algebra-II) PARCC Model Content Frameworks PARCC Model Content Frameworks

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167 INITIAL QUESTIONS to CONSIDER when choosing or developing a Quality Math Assessment. See handout page-31 JB modified from: http://www.state.nj.us/education/AchieveNJ/teacher/ SGOGuidebook.pdf http://www.state.nj.us/education/AchieveNJ/teacher/ SGOGuidebook.pdf

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168 GENERAL TEST PREP: What does this look like? See handout pages 32-33 Know the test in terms of the following: 10 Considerations for Success

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169 www.achievethecore.org

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170 Links to Model Math Curriculum Sites Sample Assessments by grade: http://www.achievethecore.corg/ Common Core and Special Education Students http://www.ode.state.or.us/search/page/?id=3741 Common Core Practice Test https://sbacot.tds.airast.org/student/login.aspz?c=SBAC.PT http://sbac.portal.airast.org/practice-test/ Common Core Resources to use with students http://www.illustrativemathematics.org Dana Center Resources http://www.ccsstoolbox.org/http://www.ccsstoolbox.org/ http://ccsstoolbox.agilemind.com/pdf/DanaCenter_YAG_HS.pdf

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171 December 2013 J.Brendel COMPANIES are developing new programs to assist districts: ACUITY: a comprehensive K-12 assessmentACUITY: a comprehensive K-12 assessment program Tom Moellering from McGraw Hills as/DA/District Administration (30 minute video/conversation) pre-built assessments (diagnostic) – or item banks to create your own; can be delivered online or in print; scan in software … automatically scores and results to teacher quickly teacher can see individual/class(es)/school/district results teacher can assign specific tasks instruction resources in general (including Performance Tasks)

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172 COMPANIES are developing new programs to assist districts as they transition to technology-based assessments: Pearson’s online Assessment Roadmap 2014 www.Commoncore.pearsoned.com/index.cfm?locator=PS11Uz Step-1: Conducting a Needs Analysis Step-2: Developing a Transition Strategy Step-3: Ensuring Interoperability Step-4: Communicating Proactively Step-5: Anticipating Ongoing Change www.PearsonAssessments.com/NextGenRoadmap Bryan Bleil (VP, online & tech), Ellen Stain Seymore J. Brendel 11/2013

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173 TEXTBOOK PUBLISHERS are beginning to develop new programs to assist districts as they transition to technology-based assessments: Many now have all resources online including assessment options. Sample: http://www.connected.mcgraw-hill.com Teacher username and password Select Subject: [Algebra-I CC Standards National] Select Standards: [National] [Assess] [Algebra-I] [Create a New Test] J. Brendel 11/2013

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174 Two Activities Self-Evaluation, Action Planning and Next Steps Response Priority Comments Roadblocks (pages 28-29) Action Planning/Next Steps (page 30)

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175 Questions? Concerns (silly question)? Discussion/Debrief

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176 SINCERE THANKS… For your participation, collaboration and dedicated efforts!!! Judy jbrendel@pascack.k12.nj.us Brian bchinni@tmieducation.com

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