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**FEA/NJPSA - Judith T. Brendel - Spring 2014**

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

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Welcome… WHO ARE THEY? INTRO SELF.

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**Let’s take our… (pages 1-2)**

PARCC Pre-Assessment! Activity 1 – page 2 Do alone (8 questions starting w/ What grade level … ) EXAMPLE 9 require understanding of slope from graph and table …. May skip and do easier examples in lower grades later on Activity #1 : FAQs Pre-Test 3 3

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**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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**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 – points EOY – points = 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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**What about calculator use? **

Is one session calculator active and the other not calculator active? What calculator will be available? (handout page-14A) ALG.1 NO Calculator YES Calculator Item Specific Calculator Neutral PBA 1 18 7 6 EOY 3 9 15 11 Ti-84 type graphing calculator GEOM. NO Calculator YES Calculator Item Specific Calculator Neutral PBA 16 1 7 EOY 6 22 ALG.2 NO Calculator YES Calculator Item Specific Calculator Neutral PBA 3 28 4 EOY 9 19

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**HOW ARE PBAs and EOYs DIFFERENT from each other?**

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

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**BLUEPRINTS for MATHEMATICS**

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

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**HS Blueprints for Mathematics**

MATH I MATH II MATH III (page 22)

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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. Common Core State Standards Partnership for Assessment of Readiness for College and Career

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**What should teaching and learning in the 21st century look like?”**

“…revolutionary transformation rather than evolutionary tinkering.” US DOE, NETP 2010 CONSIDER USING POLL EVERYWHERE – (1-word responses) Revolutionary transformation rather than evolutionary tinkering. 11 11

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**(Ancient Chinese Proverb)**

“The best time to plant a tree is twenty years ago; the second best time is today.” (Ancient Chinese Proverb) Both links work 11/18/13 NATION at RISK: see FINDINGS: Schools in US diff. grades, graduation requirements, college admissions, difficulty subject matter, amt. hw (2/3 say < 1hr/ nt. In HS) SCANS REPT: see What work requires of schools (p.18) … The educational side of work (p.19) US gr.11 stu. Puts in ½ of the 60 hrs a week that a Japanese peer devotes to schoolwork. …. What’s work like today (5 scenarios begin. P. 22) …. 5 competencies (p.26) … 3-part foundation (basic skills, thinking, interpersonal) … implications for learning (p.32 - ) 13 13

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

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**… through innovative pedagogy and ubiquitous technology.**

How? Fostering essential skills… Global competence Content knowledge Entrepreneurship Adaptability Interpersonal Communication Collaborative problem solving Critical thinking Creativity Innovation … through innovative pedagogy and ubiquitous technology. 15 15

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**“Different kinds of experiences lead to different brain structures.”**

Dr. Bruce D. Perry, Baylor College of Medicine LINKS NOT WORKING: Marc is a motivation education speaker … both a visionary and practical 16 16

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**What conditions will foster these skills?**

“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 : 17 17 17

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**21st learning… …what should it look like? Dr. BRIAN Chinni’s ‘ANIMOTO’**

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21st learning… The ‘link’ DOES WORK (may take awhile to upload) … you hear Erin explaining and modeling for her students … Kirkby and Erin share these resources they both create. 19 19

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**Dan Meyer: Math Class Needs a Makeover**

Dan Meyer’s is a high school math teacher. I believe this video is helpful in showing WHAT this learning looks like in the classroom. He does not address content/curriculum development specifically, …. he models high student engagement, and critical thinking in authentic learning situations. He also shares how disciplines can work collaboratively.

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**PARCC: Partnership for Assessment of Readiness for College and Career**

What does it mean? “Students are on-track or ready for college and careers.” 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

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**Standards of Mathematical Practices (MP)**

Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. Attend to precision. Look for and make use of structure. Look for and express regularity in repeated reasoning. Construct viable arguments and critique the reasoning of others Model with mathematics. WHAT’S NEW? You might think about these are you do the next activity Attend to precision 22

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**Algebra, Algebra-II or Geometry (pages 3-8)**

Activity #2 : Create different question formats Algebra, Algebra-II or Geometry (pages 3-8) 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: Pairs or small groups create differently formatted questions. Each 2-3 people create ex. to match above for Alg.I … or can change to a quadratic equation for Alg II … or use a 30/60/90 triangle for Geom. SA MS/HS– PD Session 3| April 4., 2011

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**A (Quick) Walk through the PARCC!**

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**PARCC Assessment Consortium**

PBA MATH EOY MATH Our focus today PBA and EOY MATH assessments

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**Aligned to the CCSS & NJCCCS Full admin. of PARCC assessment**

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

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**Understanding the Common Core State Standards …is to understand PARCC**

PVRSD Math TF – Work Session 1 | November 18, 2010 27

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**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” 28

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**Principles of the CCSS…**

FEWER CLEARER HIGHER Aligned to requirements for College and Career Readiness Based on evidence Honest about time 29

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**The CCSS Difference: Grade 8 Mathematics**

(2004) Before NJCCCS: Understand and apply the Pythagorean Theorem. (2010) After CCSS Explain a proof of the Pythagorean Theorem and its converse. Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions. Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. 30

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a2 + b2 = c2 a = 4 b = 3 c = ? 5 25 a b c 3 9 4 16

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**Implications of the CCSS on WHAT and HOW to teach…**

What are the Critical Shifts to Consider? 32

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**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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**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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**The Common Core Standards: Classroom Video Illustration**

High School School Click to link to online video … NYC Hillcrest HS Queens NY … see applications / hear CCSS HS concepts outlined …

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**Three (3) Significant Shifts in Mathematics:**

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. Processing the CC Math Shifts Activity Here 36

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**Three (3) Significant Shifts in Mathematics:**

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. Processing the CC Math Shifts Activity Here 37

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**Traditional U.S. Approach…**

K Number and Operations Measurement and Geometry Algebra and Functions Statistics and Probability 1 minute stretch 38 38

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**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 K 1 2 3 4 5 6 7 8 High School 1 minute stretch 39

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**Focus Areas in Mathematics (CCSS)**

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 1 minute stretch 40 40

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

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 Model Curriculum – print out from our district 41 41

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**Focus Areas in Mathematics (CCSS) - HS**

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 Model Curriculum – print out from our dist. 42 42

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**Focus Areas in Mathematics (CCSS) – HS**

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 Model Curriculum – print out from our dist. 43 43

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**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 … A.REI.10, 11 major F.IF.7/9 supporting Color codes used in Model Curriculum: Green – major Turquoise = supporting Yellow = additional A.REI.5, A.REI.6 additional Dec. 2, 2013 J.Brendel

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**Three (3) Significant Shifts in Mathematics:**

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. Processing the CC Math Shifts Activity Here 45 45

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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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**Coherence: Link to Major Topics Across Grades**

Gr.6- Apply properties One of several staircases to algebra designed in the OA domain. Gr.5-expressions Algebra begins in 6.EE.3 in its cleanest sense. Here is a beautiful illustration of the design of the standards. {read slide} Gr.3- multiply … divide Gr.1- add … subtract 47

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**Coherence: Link to Major Topics Across Grades**

One of several staircases to algebra designed in the OA domain. ALGEBRA-I ALGEBRA- II Algebra-I to II ( begins in 6.EE.3 – see progression at HS level) {read slide} 48

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**are parallelograms and rectangles have 4 acute angles **

Coherence and NEW multiple-choice questions. Activity 3: Circle all that are true. Given: All squares are parallelograms and rectangles have 4 acute angles have only 2 diagonals Area = ½ base x height Sum of consecutive angles = 180˚ Perimeter = 2 x Side length Area > area with the same perimeter. 5 3 7 25 21 SAMPLE NEW MC TYPE (multiple standards)

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**Coherence: Link to major topics within grades**

Example: HIGH SCHOOL performance task; 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. Write an equation for the total number of gallons of fuel …. How much fuel is in the tanks after the pump … 8 minutes? Graph the equation … on the coordinate plane … label …. Algebra-I Unit-1 50 50

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**Three (3) Significant Shifts in Mathematics:**

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. Processing the CC Math Shifts Activity Here 51

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**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. Processing the CC Math Shifts Activity Here Grade-2 Guess the grade level! 52

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**See the Rigor in Grade-3 Fractions on a Number Line**

* a BIG change * a move away from the circular pie to understanding fractions on a number line. A major topic focus in 3rd grade is fractions. This problem causes students to truly understand fractions and not just memorize patterns.

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**See Rigor in Grade 6: Ratios**

* a BIG change * Students will have online tools to use that simulate hands-on tools Ratios is one of the major topics of focus for 6th grade. This is not your typical ratio problem. Students must build upon their solid knowledge of fractions, established primarily in 3rd grade, and apply it to what they have learned about ratios. This problem not only demonstrates Shift 1, focus where the standards focus, but also Shift 2 – Coherence within and across grade levels. PARCC - Grade-6 Slider Ruler: type-I

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**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) Processing the CC Math Shifts Activity Here 55

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**See the Rigor – High School Part A**

A high school example, again demonstrating coherence within and across grade bands.

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**Part B Describe Write Compare**

Students must be able to apply the skills used to solve Part A to create a new example and must be able to explain. General note: Students are expected to recognize and compare functions seen within a scenario, as an algebraic equation, a table, or graph. (Relate to how do you compare fractions with different denominators … or numbers seen as decimals, percents, and fractions.)

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**Required Fluencies in K-6**

Grade Standard Required Fluency K K.OA.5 Add/subtract within 5 1 1.OA.6 Add/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 4 4.NBT.4 Add/subtract within 1,000,000 5 5.NBT.5 Multi-digit multiplication 6 6.NS.2,3 Multi-digit division Multi-digit decimal operations Processing the CC Math Shifts Activity Here 58 58

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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. Using mathematics in problem solving contexts is the third leg of the stool supporting the learning that is going on in the math classroom. This is the “why we learn math” piece, right? We learn it so we can apply it in situations that require mathematical knowledge. There are requirements for application all the way throughout the grades in the CCSS. {read slide} But again, we can’t just focus solely on application—we need also to give students opportunities to gain deep insight into the mathematical concepts they are using and also develop fluency with the procedures that will be applied in these situations. The problem-solving aspect of application is what’s at stake here—if we attempt this with a lack of conceptual knowledge and procedural fluency, the problem just becomes three times harder. At the same time, we don’t want to save all the application for the end of the learning progression. Application can be motivational and interesting, and there is a need for students at all levels to connect the mathematics they are learning to the world around them.

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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. Using mathematics in problem solving contexts is the third leg of the stool supporting the learning that is going on in the math classroom. This is the “why we learn math” piece, right? We learn it so we can apply it in situations that require mathematical knowledge. There are requirements for application all the way throughout the grades in the CCSS. {read slide} But again, we can’t just focus solely on application—we need also to give students opportunities to gain deep insight into the mathematical concepts they are using and also develop fluency with the procedures that will be applied in these situations. The problem-solving aspect of application is what’s at stake here—if we attempt this with a lack of conceptual knowledge and procedural fluency, the problem just becomes three times harder. At the same time, we don’t want to save all the application for the end of the learning progression. Application can be motivational and interesting, and there is a need for students at all levels to connect the mathematics they are learning to the world around them.

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

Relatable, real-world problems will engage students and demand they apply their conceptual understandings in new and rigorous ways.

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**Real world application – Grade 4**

Relatable, real-world problems will engage students and demand they apply their conceptual understandings in new and rigorous ways. MORE THAN ONE right answer: people = bus+ 4 vans = = vans + 11 cars = = bus.+3 vans + 4cars = = 108 MORE THAN one choice

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**See what online looks like**

See what online looks like! Linking to major topics – Grade 7 (page-26-27) This two-part problem illustrates coherence within and across grade levels. You see major topics covered previously as well as multiple grade level concepts being connected to each other..

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Part B Are these the types of questions we are asking in our classrooms or are we just leading our children through rote practice applying memorized algorithms with little or no conceptual understanding?

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**See what online looks like**

See what online looks like! HS Teachers outside of math use grade-level-appropriate math This is a high school prototype, which asks students to connect math and science, demonstrates beautifully the application component of Shift 3. This problem has 4 parts, the last of which asks students to explain their thinking in detail and connect it to prior learning.

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Part B In Part B of the same problem, students must move the tiles to write a recursive definition using the chart at the top.

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Part C In Part C, students must recognize statements that are true after applying the formula.

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Part D We must not teach students to take tests but rather prepare them to solve problems creating and explaining their own solutions. FROM Kimberley Harrington, Director of Standards, NJ Department of Education

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**Activity No. 3: Shifts Happen - Mathematics**

What is this shift? Why this shift? Opportunities Challenges 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 Handout page-25 Processing the CC Math Shifts Activity Here 69

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**What do you mean 3 TYPES of TASKS?**

No, not differently formatted No, not different levels-of-difficulty

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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 …. Whole group discuss … Ask what is being assessed I, how is II different from I? …

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**Let’s take a quick break!**

1 minute stretch 72

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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 …. Whole group discuss … Ask what is being assessed I, how is II different from I? …

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**Tasks assess concepts, skills and procedures.**

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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**Tasks assessing expressing mathematical reasoning.**

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. December 2, 2013

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**Tasks assessing modeling/applications.**

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. December 2, 2013

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**TYPE-I PARCC TASKS Tasks assess concepts, skills and procedures.**

All are machine score-able.

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**Mathematics online Sample Item/Prototypes: (separate packets) **

PARCC TYPE-I TASKS (1, 2, or 4 point questions) HS – FunctionsS HS – Seeing Structure in Quadratic Equation HS – Picture Frame (Algebra-I/Math 2) HS – Myla’s Swimming Poole (Algebra-I) HS – Green Tea Observation Study (Algebra-2/Math 3) As of Nov. 14, 2013

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** (first page of Type-I Task package; see graph and table)**

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 Compare y-intercepts Compare f(3) and g(3) Compare maximum values of each w/in range -5 ≤ x ≤ 5 Compare DIFFICULTY? POINTS? GO TO LINK – SEE PARABOLA – DO IN PAIRS – THEN DISCUSS Solutions: What course? Alg.II Level of difficulty? Low … medium … high (1, 2, 3, 4) No Points: 4? What standards: A.REI.D What is different? COURSE ? STANDARDS? A Type-I PARCC task J. Brendel

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** Seeing Structure in a Quadratic Equations**

(second page in Type-I packet) (3x - 2)2 = 6x – 4 DIFFICULTY? COURSE ? Solutions: What course? Alg.II Level of difficulty? Low … medium … high (1, 2, 3, 4) No Points: 1 What standards: What is different? POINTS? STANDARDS? a Type-I PARCC task J. Brendel

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**24 + 10x – x2 = p – (x – 5)2 Solve for p**

Seeing Structure in Equations (see third page in Type-I packet) x – x2 = p – (x – 5)2 Solve for p COURSE ? DIFFICULTY? Course: Algebra-I/Math I Points: 1 Standards: POINTS? STANDARDS? a Type I PARCC task J. Brendel

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**(See pages 4-6 of Type-I packet; see Details for Teacher**

PICTURE FRAME (See pages 4-6 of Type-I packet; see Details for Teacher X + 2 in. X in. width length DIFFICULTY? COURSE ? Algebra-I/Math-II Standard: ASSE 1-2 Points: 2 Length of picture alone in inches = X + 2 Length of frame in inches = X + 4 Area of picture alone = x (x+2) … they don’t ask student to solve ... could be x2 + 2x Area of picture and frame together = (x+4) ( x+2) … “ ‘ …. Could be x2 + 12x + 8 Scoring: all 4 parts correct = 2 points, 3 parts correct = 1 point POINTS? STANDARDS? a Type I PARCC task J. Brendel

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**GREEN TEA TYPE COURSE ? DIFFICULTY? POINTS? STANDARDS?**

COURSE ? DIFFICULTY? POINTS? Algebra II/Math II Standard: S.IC.3-1,3 MP.4 (S.IC.3) Scoring: 2 points 1-point: Part A – “is associated with,” and “the women in the study only.” 1-point: Part B = “be asked to drink green tee;” “be asked not to drink green tea,” and “at random.” STANDARDS? a Type I PARCC task J. Brendel

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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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**Mathematics online Sample Item/Prototypes:**

PARCC TYPE-II TASKS (4 point questions) HS – Graphs of Functions (Algebra-II/Math III) Nov. 2013 HS.C.6.2, A.REI.D, MP.3, 7 with 4-point scoring rubric HS – Michelle’s Conjectures (Algebra-II/Math III) HS – Geometric Construction Connection (Geometry/Math III) PARCC_SampleItems_Mathematics_HSGeoMathIIIGeometricConnection_081913_Final_0.pdf As of Nov. 14, 2013 Dec. 2, 2013

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**GRAPH of FUNCTIONS COURSE ? DIFFICULTY? POINTS ? STANDARDS? **

GRAPH of FUNCTIONS (posted November 2013) (See first 3 pages of Type-II packet See two-page details for teacher) COURSE ? DIFFICULTY? POINTS ? POINTS: 2- 4? Algebra-II/Math 3? Standards: A.REI.D STANDARDS? a Type-II PARCC Task

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**GEOMETRY CONSTRUCTION CONNECTION**

GEOMETRY CONSTRUCTION CONNECTION (See 4th-6th page in Type-II packet; see details for teacher.) POINTS ? STANDARDS? DIFFICULTY? Points 3 Geometry//Math 3 Task type 2 Standards G-CO.D a Type-II PARCC Task

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**Investigate the effect on the vertex of the graph **

MICHELLE’S CONJECTURES (Aug.19, 2013) (See last 3-pages in Type-II packet; see details for teacher) Investigate the effect on the vertex of the graph f(x) = x when f(x) is replaced by f(x + k) DIFFICULTY? COURSE ? Points 3 Algebra-II//Math 3 Points POINTS ? STANDARDS? a Type-II PARCC Task

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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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**(See first four pages in Type-III packet)**

MINI GOLF PRICES (November, 2013) (See first four pages in Type-III packet) 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 … DIFFICULTY? ALGEBRA-I/Math-II Points: 6 Standards: FBF-I COURSE ? POINTS ? STANDARDS? a Type-III PARCC Task

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**(See pages 5-8 in Type-III packet)**

BRETT’S RACE (November, 2013) (See pages 5-8 in Type-III packet) Part A: … write an equation for each person that …. Part B: Based on your equation … who will win ... ? Justify your answer. ALGEBRA-I Level-3 Standards D.205, A.CED, A.CED.A Problem-Based Task assessment only Points: 3 Part A . 1 pt. – formulate mode y = 81/3x + 20 … or y = 100/12 = 20 x= 9.6; Olympian y = 100, 100 = 10x, 10 = xOlympian’s distance is related to time y = 10x Points: Part B. 1 pt – correct winner …and … correct margin of victory … Brett = 0.4 seconds DIFFICULTY? COURSE ? POINTS ? STANDARDS? a Type-III PARCC Task

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**POPCORN INVENTORY DIFFICULTY? COURSE ? POINTS ?**

(NOVEMBER 2013) Read scenario, understand table, read additional facts … Estimate the amount of popcorn … Show or explain the reasoning you used to determine your estimate. COURSE: ALGEBRA-I LEVEL III Points: 6 Standards HS Di-I 7.RP.2,3 DIFFICULTY? COURSE ? POINTS ? a Type-III PARCC Task

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**(See last 4 pages in Type-II packet)**

TEMPERATURE CHANGES (See last 4 pages in Type-II packet) Part A: Which model is linear? Which model is best for the range … ? Explain why the other model … Part B: Construct a function …. COURSE: Algebra-II/Math III Level III Points 3 (can be scored 0, 1, 2, or 3) Standards: F.BF.A, F.IF.4 DIFFICULTY? COURSE ? POINTS ? a Type-III PARCC Task

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**As of 12/4/2013 IN HANDOUT PACKET**

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**Help Students and Teachers Prepare for the Change**

95

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**READING CCSS and Mathematics**

97
**Regular Practice with Complex Text and**

its Academic Language Attendees make a list of 10 Vocab words specific to hs math 97

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**Not Text-Dependent in ELA Text-Dependent in ELA**

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 According to Lincoln’s speech, why is this year significant to the events described in the speech? Examples of questions that take students outside and inside the text. Text-dependent questions require students to pay attention to the text at hand and to draw evidence from that text. What does this look like in the classroom? Teachers insist that classroom experiences stay deeply connected to the text on the page and that students develop habits for making evidentiary argument both in conversation, as well as in writing to assess comprehension of a text. Students have rich and rigorous conversations and develop writing that are dependent on a common text.

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**Text-Dependent in mathematics**

Use a high school EXAMPLE not grade-2 December 2, author: J. Brendel Material not to be duplicated.

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**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 Teacher (mid Nov in cp Geometry) … students had hands-on construction practice w/compass & protractor … for 3 different special line segments … and they never used the terminology. Not discovery-based … followed teacher step-by-step … (The could have done wax-paper folding as informal discovery … and will do Geometer’s Sketchpad constructions following week). May have been more effective to do more w/’medians’ first and include applications and real-life problem scenarios. 100

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**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 101

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 Or “base salary” plus “commission” – similar vocab. students rarely know 102

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) Kappan article re elementary mathematics and ‘habits to change.’ OTHER PROBLEMS: focus on interesting students/getting them moving/ motivated … but … improper math habits and language! Relate TV video Excellent Teaching (saw Nov. 28, 2013) … model classroom experiences … mid school … students survey time classmates spent each day (1-week) using diff. forms of technology, reading, etc. … Teacher ‘told them’ just put minutes over 60 and get decimal number … then she read decimal number as “point 45” … no discussion of estimated and comparing to ‘half,’ … no discussion of what “point 45” really meant … Students mimicked the teacher’s terminology. 103

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**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. 104

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**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 105

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**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 106

107
**The Standards are NOT new names for old ways of doing things…**

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**NOT … 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 108 108

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What you SHOULD NOT see !

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

111
**The Mathematics Common Core Toolbox**

K. I. S. S. CHANGE PROCESS Keep content SIMPLE The Mathematics Common Core Toolbox Mathematics Sample Item/Prototypes: PARCC online at the Dana Center Grade 4 (Deer in the Park) p. 23 Grade 6 (Gasoline Consumption) High School (Isabella’s Credit Card) *p ) High School (Popcorn Inventory) new Nov. 2013 HSAlg1Math1PopcornInventory.pdf Online to see all … hardcopy of Grade-4 and HS in packet Look at Popcorn Inventory … discuss …. What skills students’ need … how to transition to these types of problems? 111

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 (Popcorn Inventory) new Nov. 2013 HSAlg1Math1PopcornInventory.pdf Online to see all … hardcopy of Grade-4 and HS in packet Look at Popcorn Inventory … discuss …. What skills students’ need … how to transition to these types of problems? 112

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? ….) Do one … then see grade-2 hardcopy …. Students CAN PRACTICE off-line, too. Have HS students begin w/MS resources (KISS) new process/easy content. 113

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**EXPERIENCE an ONLINE ASSESSMENT *Smarter Balanced Online Activities**

Sample online Smarter Balanced Assessments *Select from grades 3, 4, 5, 6, 7, 8 or 11 https://sbacpt.tds.airast.org/student/login.aspx?c=SBAC_PT Link to Smarter Balanced site to experience Performance Task … Discuss skills and experiences students need to develop … PARCC expected to make sample assessments available late spring 2014. J.Brendel 11/2013

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**http://practice.parcc.testnav.com/# ***

EXPERIENCE ONLINE TASKS just released; similar to testing environment *PARCC Online Activities * difficulty levels vary item types vary users are encouraged to work w/items across grades additional online functionality … in coming weeks. Link to PARCC site to experience tasks that were available before, but now they ‘simulate’ what it will be like taking these online … with drag-and-drop, etc. New February 2014. J.Brendel 3/8/14

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**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)

117
**from Smarter Balanced site**

SAMPLE ASSESSMENT examples 1-12 from Smarter Balanced site separate hardcopy-packet pages 15-20 and High School Reference Sheet page-13 Distribute sample Algebra-I Unit-I test w/rubric … and HS Reference sheet December 2, 2013

118
**Activity: BRAINSTORM in GROUPS**

How should high school math teaching change from the traditional teaching? What non-math type skills are essential?

119
**Other Resources CIRCLES MATH II - WALLS**

MATH II - WALLS J. Brendel 11/2013

120
**PARCC RELEASED TASKS include elsewhere?**

file://localhost/Users/jbrendel/Desktop/PARCC%20HS%20Functions.html (November/December 2013) https://www.teachingchannel.org/videos/laws-of-sines-cosines-lesson# 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

121
**The Specs, Accountability,**

and Resources: What We Know Now! 121

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 Dec. 17, 2013 letter from NJDOE ; Bari Anhalt Erlichson, Asst. Commissioner/Chief Performance Officer Field Test questions: Dr. Jeffrey B. Hauger

123
**Estimated Time on Task: Grade 9-10 Performance Based Assessment**

ELA/Literacy Math TOTAL Grade Literacy Analysis Research Narrative Session 1 2 9-10 Alg I/ Math I Geo/ Math II Estimated Time on Task (minutes) 80 85 50 315

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**Estimated Time on Task: Grade 9-10 End-of-Year (EOY) Assessment**

ELA/Literacy Math TOTAL Grade Session 1 2 9-10 Alg I/ Math I Geo/ Math II Estimated Time on Task (minutes) 70 65 270 Grade 9-10 Summative Total: 9 Hours, 45 minutes

125
**Estimated Time on Task: Grade 11 Performance Based Assessment**

ELA/Literacy Math TOTAL Grade Literacy Analysis Research Narrative Session 1 2 11 Alg II/ Math III Estimated Time on Task (minutes) 80 85 50 65 345

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**Estimated Time on Task: Grade 11 End-of-Year (EOY) Assessment**

ELA/Literacy Math TOTAL Grade Session 1 2 11 Alg II/ Math III Estimated Time on Task (minutes) 70 55 250 Grade 11 Summative Total: 9 Hours, 55 minutes

127
**HOW will I know what should be ‘learned’ before the PBA? before the EOY? (Activity)**

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)

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 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… 128

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**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) 129

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 130

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 131

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**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;

133
**Modifying the complexity of assessments to make them easier (e. g**

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).

134
Accountability: What We Know Now! 134

135
**Distinguished Command**

Results Types… Proficiency (PLDs) On-Track-to-College and Career Readiness (CCRDs) Growth Data Performance Level Descriptors (PLDs) Performance Level Description Level 5* Distinguished Command Level 4* Strong Command Level 3 Moderate Command Level 2 Partial Command Level 1 Minimal Command *Achieved CCR Performance Threshold 135

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**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.” Acuplacer test (Typical Community College placement test) no need to be taken if student “passes” the PARCC test in h.s. 136

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 probability of earning college credit by attaining at least a grade of C or its equivalent in those courses.” 137

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**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. 138

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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**Timelines and Resources:**

What We Know Now! 140 140

141
**PARCC Timeline… Jan – Aug 2013**

Jan – Aug 2013 Release of 2nd 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 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) 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) “It is anticipated … that the PARCC ONLINE PD modules will be available in June as/site below 11/29/13. 141

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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: PARCC Common Assessments Overview Introduction to the PARCC Mid-Year Assessment Introduction to the PARCC Diagnostic Assessment Introduction to the PARCC Speaking/Listening Assessment PARCC Accessibility System *It is anticipated that modules will be available in June 2014. (above on site as of 11/29/13)

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**PARCC Timeline… NJ 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. ( school year) 143

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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.

146
**Links to Model Math Curriculum Sites**

Sample Assessments by grade: Common Core and Special Education Students Common Core Practice Test https://sbacot.tds.airast.org/student/login.aspz?c=SBAC.PT Common Core Resources to use with students Dana Center Resources

147
**ACUITY: a comprehensive K-12 assessment program**

COMPANIES are developing new programs to assist districts: ACUITY: 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) NOT recommending any … just be aware of what will eventually be available …consider when creating budgets December J.Brendel

148
**Pearson’s online Assessment Roadmap 2014**

COMPANIES are developing new programs to assist districts as they transition to technology-based assessments: Pearson’s online Assessment Roadmap 2014 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 Bryan Bleil (VP, online & tech), Ellen Stain Seymore J. Brendel 11/2013

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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: Teacher username and password Select Subject: [Algebra-I CC Standards National] Select Standards: [National] [Assess] [Algebra-I] [Create a New Test] User name: JUDITHB39 J. Brendel 11/2013

150
**Self-Evaluation, Action Planning and Next Steps**

Roadblocks Action Planning Next Steps

151
**PARCC POST-Assessment!**

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

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

153
**For your participation, collaboration and dedicated efforts!!!**

SINCERE THANKS… For your participation, collaboration and dedicated efforts!!! Judy or contact NJPSA/FEA

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