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

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2 Welcome…

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3 3 Let’s take our… (pages 1-2) PARCC Pre-Assessment! Activity #1 : FAQs Pre-Test

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4 HOW MANY math tests are required for HS students? Three: Algebra-I, Geometry and Algebra II (or Math-I, Math-II and Math-III) PBA Performance Based Assessment >75% of instruction EOY End of Year Assessment > 90% of instruction HOW ARE the PBAs and EOYs ALIKE? taken online divided into 2 sessions align with CCSS variety of question formats regular-ed and special-ed accommodations 4-week (20-day) window to take each test

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5 How do I know what CONTENT is included on each test? PARCC Blueprints: Algebra 1: PBA and EOY Geometry: PBA and EOY Algebra 2: PBA and EOY How many TOTAL POINTS on each test? PBA – 18-20 points EOY – 34-35 points = 52-55 What is a PROFICIENT SCORE? highly proficient score? To be determined after field tests are scored. How do I know the FORMAT of PARCC questions? Activity #2 – workbook pages 3-6 (to do soon) How many TYPES of tasks are on these tests? Activity – 3 separate packets for Type I, II and III tasks

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6 ALG.2NO Calculato r YES Calculato r Item Specific Calculato r Neutral PBA32843 EOY49199 What about calculator use? Is one session calculator active and the other not calculator active? What calculator will be available? (handout page-14A) ALG.1NO Calculato r YES Calculato r Item Specific Calculato r Neutral PBA11876 EOY391511 GEOM.NO Calculato r YES Calculato r Item Specific Calculato r Neutral PBA1617 EOY16622 Ti-84 type graphing calculator

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7SA MS/HS– PD Session 3| April 4., 2011 HOW ARE PBAs and EOYs DIFFERENT from each other? PBAEOY Hand and Machine scored Machine scored only CCSS after 75% of instruction completed CCSS after 90% of instruction completed Type I, II and III questions Type I questions only

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8 HS BLUEPRINTS for MATHEMATICS ALGEBRA-I GEOMETRY ALGEBRA-II (page 22)

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9 HS Blueprints for Mathematics MATH I MATH II MATH III (page 22)

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10 TODAY’S PLAN: Understand the overall substance, design and technical aspects of next generation PARCC assessments Experience PARCC assessment tasks and related resources Align scope-and-sequence to PARCC assessment schedule Share effective strategies to lead the transition to CCSS and PARCC assessments.

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11 “…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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12

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13 “The best time to plant a tree is twenty years ago; the second best time is today.” (Ancient Chinese Proverb)

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

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15 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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16 “Different kinds of experiences lead to different brain structures.” Dr. Bruce D. Perry, Baylor College of Medicine

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17 “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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18 21 st learning… …what should it look like?what should it look like?

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19 21 st learning… http://www.pascack.k12.nj.us/cms/lib5/NJ01000238/Centricity/Domain/87 /Writing%20Equations%202.swf

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20 Dan Meyer: Math Class Needs a Makeover

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21 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 PARCC: Partnership for Assessment of Readiness for College and Career What does it mean? “Students are on-track or ready for college and careers.”

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22 Standards of Mathematical Practices (MP) 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 WHAT’S NEW?

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23SA MS/HS– PD Session 3| April 4., 2011 MC- one right answer (traditional format) MC – more than one right answer (at least A-D) MC – yes/no true/false listed questions; multiple- standards SCR – fill-in-the blank OE – compare/contrast; explain/defend; how do you know? Activity #2 : Create different question formats Algebra, Algebra-II or Geometry (pages 3-8)

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24 A (Quick) Walk through the PARCC!

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25 PARCC Assessment Consortium PBA MATH EOY MATH

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26 Assessment Transition Timeline 26 Assessment Transition Timeline NJ ASK Spring 2012 Aligned to NJCCCS Spring 2013 Aligned to the CCSS & NJCCCS (Except Gr. 6-8 Math) Spring 2014 Aligned to the CCSS 2014-15 Full admin. of PARCC assessment “Transitional Assessments”

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27PVRSD Math TF – Work Session 1 | November 18, 2010 Understanding the Common Core State Standards …is to understand PARCC

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28 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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29 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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30 The CCSS Difference: Grade 8 Mathematics (2004) Before NJCCCS: 1. Understand and apply the Pythagorean Theorem. (2010) After CCSS 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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31 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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32 Implications of the CCSS on WHAT and HOW to teach… What are the Critical Shifts to Consider?

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33 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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34 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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35 The Common Core Standards: Classroom Video Illustration High School School

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36 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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37 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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38 K 12 Number and Operations Measurement and Geometry Algebra and Functions Statistics and Probability Traditional U.S. Approach…

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39 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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40 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 Focus Areas in Mathematics (CCSS)

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41 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 Focus Areas in Mathematics (CCSS)- MS/HS

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42 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 Focus Areas in Mathematics (CCSS) - HS

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43 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 Focus Areas in Mathematics (CCSS) – HS

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44 FOCUS AREAS: High School 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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45 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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46 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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47 One of several staircases to algebra designed in the OA domain. Coherence: Link to Major Topics Across Grades 47 Gr.3- multiply … divide Gr.5-expressions Gr.6- Apply properties Gr.1- add … subtract

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48 One of several staircases to algebra designed in the OA domain. Coherence: Link to Major Topics Across Grades 48 ALGEBRA-I ALGEBRA- II

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49 Coherence and NEW multiple-choice questions. Activity 3: 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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50 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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51 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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52 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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53 See the Rigor in Grade-3 Fractions on a Number Line http://www.illustrativemathematics.org/standards/hs * a BIG change * a move away from the circular pie to understanding fractions on a number line.

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54 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 * a BIG change * Students will have online tools to use that simulate hands-on tools

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55 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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56 See the Rigor – High School Part A

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57 Part B Describ e Compare Write

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58 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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59 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. 59

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60 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. 60

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61 See what online looks like! Real world application – Grade ?

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62 Real world application – Grade 4 MORE THAN one choice

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63 See what online looks like! Linking to major topics – Grade 7 (page-26-27)

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64 Part B

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65 See what online looks like! HS Teachers outside of math use grade-level-appropriate math

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66 Part B

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67 Part C

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68 Part D

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69 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. Handout page-25

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70 What do you mean 3 TYPES of TASKS? No, not differently formatted No, not different levels-of-difficulty

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71 TASK TYPES – PARCC (x – 2) 2 + 6 = 75 solve for c: (x + c)/z = 2c(w-y) Explain how you can use the graphs to find solutions. Estimate …. Compare the 3 sets of data (graph, chart, and equation) and defend the argument that ….

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72 Let’s take a quick break!

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73 TASK TYPES – PARCC I – Computation, Skills, Process (x – 2) 2 + 6 = 75 solve for c: (x + c)/z = 2c(w-y) II – Mathematical Reasoning Explain how you can use the graphs to find solutions. Estimate …. III – Modeling, Combined Standards, Applications Compare the 3 sets of data (graph, chart, and equation) and defend the argument that ….

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74 TASK TYPE-I Tasks assess 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 Performance Based and End-of-Year Assessments

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75December 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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76December 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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77 TYPE-I PARCC TASKS Tasks assess concepts, skills and procedures. All are machine score-able.

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78 Mathematics online Sample Item/Prototypes: (separate packets) 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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79J. Brendel 12.3.2013 Functions http://www.parcconline.org/samples/mathematics/high-school- functions http://www.parcconline.org/samples/mathematics/high-school- functions (first page of Type-I Task package; see graph and table) Given f(x) as a graphed parabola and g(x) as table of values 1.Compare y-intercepts 1.Compare f(3) and g(3) 1.Compare maximum values of each w/in range -5 ≤ x ≤ 5 1.Compare A Type-I PARCC task COURSE ? DIFFICULTY? POINTS? STANDARDS?

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80J. Brendel 12.3.2013 Seeing Structure in a Quadratic Equations http://www.parcconline.org/samples/mathematics/high-school-seeing- structure-quadratic-equation (second page in Type-I packet) (3x - 2) 2 = 6x – 4 a Type-I PARCC task COURSE ? DIFFICULTY? POINTS? STANDARDS?

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81J. 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 (see third page in Type-I packet) 24 + 10x – x 2 = p – (x – 5) 2 Solve for p a Type I PARCC task COURSE ? DIFFICULTY? POINTS? STANDARDS?

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82J. Brendel 12.3.2013 PICTURE FRAME http://www.parcconline.org/sites/parcc/files/HS-Alg1Math2PictureFrame.pdf (See pages 4-6 of Type-I packet; see Details for Teacher a Type I PARCC task COURSE ? DIFFICULTY? POINTS? STANDARDS? X + 2 in. X in.width length

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83J. 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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84 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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85 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_HSAlgIMathIIMichelle Conjecture_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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86 GRAPH of FUNCTIONS (posted November 2013) (See first 3 pages of Type-II packet See two-page details for teacher) http://www.parcconline.org/sites/parcc/files/HighSchoolAlg2Math3- GraphsofFunctions.pdf a Type-II PARCC Task COURSE ? POINTS ? DIFFICULTY? STANDARDS?

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87 GEOMETRY CONSTRUCTION CONNECTION (See 4 th -6 th page in Type-II packet; see details for teacher.) 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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88 MICHELLE’S CONJECTURES (Aug.19, 2013) (See last 3-pages in Type-II packet; see details for teacher) 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? Investigate the effect on the vertex of the graph f(x) = x 2 + 6 when f(x) is replaced by f(x + k)

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89 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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90 MINI GOLF PRICES (November, 2013) (See first four pages in Type-III packet) http://www.parcconline.org/sites/parcc/files/HSAlg1Math2MiniGolfPrices.pdf a Type-III PARCC Task COURSE ? POINTS ? DIFFICULTY? STANDARDS? Part A: … write a liner function to model … Part B: … write a quadratic function for … Part C: … maximum possible weekly revenue is what percent greater than the weekly revenue …

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91 BRETT’S RACE (November, 2013) (See pages 5-8 in Type-III packet) http://www.parcconline.org/sites/parcc/files/BRHSSampleItem.pdf a Type-III PARCC Task COURSE ? POINTS ? DIFFICULTY? STANDARDS? Part A: … write an equation for each person that …. Part B: Based on your equation … who will win... ? Justify your answer.

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92 a Type-III PARCC Task POPCORN INVENTORY (NOVEMBER 2013) COURSE ? POINTS ? DIFFICULTY? http://www.parcconline.org/sites/parcc/files/HSAlg1Math1 PopcornInventory.pdf Read scenario, understand table, read additional facts … Estimate the amount of popcorn … Show or explain the reasoning you used to determine your estimate.

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93 a Type-III PARCC Task TEMPERATURE CHANGES (See last 4 pages in Type-II packet) http://www.parcconline.org/sites/parcc/files/PARCC_SampleItems_M athematics_HSAlgIIMathIIITemperatureChange_081913_Final_0.pdf COURSE ? POINTS ? DIFFICULTY? Part A: Which model is linear? Which model is best for the range … ? Explain why the other model … Part B: Construct a function ….

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95 Help Students and Teachers Prepare for the Change

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96 READING CCSS and Mathematics

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97 Regular Practice with Complex Text and its Academic Language

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98 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? 98 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? Not Text-Dependent in ELAText-Dependent in ELA

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

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100 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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101 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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102 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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103 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. (2)(2) is equivalent to √16 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. (-4) + (-5) 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. (-4) - (-8)

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104 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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105 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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106 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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107 The Standards are NOT new names for old ways of doing things…

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108 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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109 What you SHOULD NOT see !

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

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111 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 K. I. S. S. CHANGE PROCESS Keep content SIMPLE

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112 The Mathematics Common Core Toolbox Mathematics Sample Item/Prototypes: PARCC online at the Dana Center Grade 4 (Deer in the Park) Grade 6 (Gasoline Consumption) High School (Isabella’s Credit Card) ( page-21) High School (Isabella’s Credit Card) High School (Popcorn Inventory) new Nov. 2013 http://www.parcconline.org/sites/parcc/files HSAlg1Math1PopcornInventory.pdf

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113 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., surface area, minimum surface area) Grade 7 - Food Basket (calories, grams, protein) Grade 8 - Heartbeats (scatter plot ….) Grade 11- Speeding Ticket (graph, what is fair? ….)

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114 EXPERIENCE an ONLINE ASSESSMENT *Smarter Balanced Online Activities Sample online Smarter Balanced Assessments. *Select from grades 3, 4, 5, 6, 7, 8 or 11 Sample online Smarter Balanced Assessments. https://sbacpt.tds.airast.org/student/login.aspx?c=S BAC_PT https://sbacpt.tds.airast.org/student/login.aspx?c=S BAC_PT J.Brendel 11/2013

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115 EXPERIENCE ONLINE TASKS just released; similar to testing environment *PARCC Online Activities http://practice.parcc.testnav.com/#http://practice.parcc.testnav.com/# * difficulty levels vary item types vary users are encouraged to work w/items across grades additional online functionality … in coming weeks. J.Brendel 3/8/14

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116 PRACTICE ONLINE w/earlier grade resources Order Juice (grade-4) – Dana Center (p.28-29) Spicy Veggies (grade-7) – Dana Center (p.26-27) Drag and Drop (Smarter-Balanced sample) Circle; explain (Smarter-Balanced sample) Noise Level (Smarter-Balanced sample) Scatter Plot (Smarter-Balanced)

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117December 2, 2013 SAMPLE ASSESSMENT examples 1-12 from Smarter Balanced site separate hardcopy-packet pages 15-20 and High School Reference Sheet page-13

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118 Activity: BRAINSTORM in GROUPS How should high school math teaching change from the traditional teaching? What non-math type skills are essential?

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119 J. Brendel 11/2013 Other Resources 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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120 PARCC RELEASED TASKS include elsewhere? file://localhost/Users/jbrendel/Desktop/PARCC%20HS%20Functi ons.htmlfile://localhost/Users/jbrendel/Desktop/PARCC%20HS%20Functi ons.html (November/December 2013) 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 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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121 The Specs, Accountability, and Resources: What We Know Now!

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122 FIELD TESTING this SPRING (2014) >1 million students across PARCC states and Washington DC >10,000 students / 1,276 schools / 445 districts in NJ PBA – anytime between March 24 – April 11 EOY – anytime between May 5 – June 6 Results: not individual student or school results Sample online test available “spring” 2014 Field Test questions: Dr. Jeffrey B. Hauger assessment@doe.state.nj.us assessment@doe.state.nj.us

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123 Performance Based Assessment ELA/Literacy Math TOTAL Grade Literacy Analysis ResearchNarrative Session 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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124 End-of-Year (EOY) Assessment ELA/Literacy Math 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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125 Performance Based Assessment ELA/Literacy Math TOTAL Grade Literacy Analysis ResearchNarrativ e Session 1 Session 2 11 Alg II/ Math III Estimated Time on Task (minutes) 808550 65 345 Estimated Time on Task: Grade 11

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126 End-of-Year (EOY) Assessment ELA/Literacy Math 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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127 ALGEBRA-I PBA and EOY (2 packets) GEOMETRY PBA and EOY (2 packets) ALGEBRA-2 PBA and EOY (2 packets) ALGEBRA-I PBA vs EOY (packet) HOW will I know what should be ‘learned’ before the PBA? before the EOY? (Activity)

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128 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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129 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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130 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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131 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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132 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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133 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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134 Accountability: What We Know Now!

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135 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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136 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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137 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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138 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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139 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 were due by Dec. 11, 2013.

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140 Timelines and Resources: What We Know Now!

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141 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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142 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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143 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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144 HIGHER ED FOCUS June 16-17, 2014 convening The focus will be on policy associated with student scores that signal on track; that signal a student is ready for entry level, college-bearing credit classes.

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145 www.achievethecore.org

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146 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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147 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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148 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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149 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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150 Self-Evaluation, Action Planning and Next Steps Roadblocks Action Planning Next Steps

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151 Let’s take our… (last page in packet) PARCC POST-Assessment! Activity : FAQs POST-Test

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

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153 SINCERE THANKS… For your participation, collaboration and dedicated efforts!!! Judy jbrendel@pascack.k12.nj.us or contact NJPSA/FEA

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