The PARCC Institute – High School Math:

Preparing for PARCC!NJ’s Next Generation Standardized

Assessment SystemFEA/NJPSA - Judith T. Brendel - Spring 2014

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Welcome…

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Let’s take our… (pages 1-2)

PARCC Pre-Assessment!

Activity #1 : FAQs Pre-Test

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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 – 18-20 pointsEOY – 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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ALG.2 NO Calculato

r

YESCalculato

r

Item Specific

Calculator Neutral

PBA 3 28 4 3

EOY 4 9 19 9

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 Calculato

r

YESCalculato

r

Item Specific

Calculator Neutral

PBA 1 18 7 6

EOY 3 9 15 11

GEOM. NO Calculato

r

YESCalculato

r

Item Specific

Calculator Neutral

PBA 16 1 7

EOY 16 6 22

Ti-84 type graphing calculator

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

HOW ARE PBAs and EOYs DIFFERENT from each other?

PBA EOY

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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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.

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“…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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“The best time to plant a tree is twenty years ago; the second best time is today.”

(Ancient Chinese Proverb)

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Listen to our students!

“I am a 21st Century Learner!”

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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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“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

What conditions will foster these skills?

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21st learn

ing

…

…what should it look like?

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21st learn

ing

…

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

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Dan Meyer:Math Class Needs a Makeover

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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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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 othersModel with mathematics.

Attend to precision

WHAT’S NEW?

23 SA 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-standardsSCR – fill-in-the blankOE – 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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A (Quick) Walk through the PARCC!

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PARCC Assessment Consortium

PBA MATH

EOY MATH

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Assessment Transition Timeline

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Assessment Transition TimelineNJ ASK

Spring 2012

Aligned to

NJCCCS

Spring 2013Aligned to the

CCSS & NJCCCS(Except Gr. 6-8

Math)

Spring 2014

Aligned to the

CCSS

2014-15

Full admin. of

PARCC assessment

“Transitional Assessments”

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

Understanding the Common Core State Standards …is to understand PARCC

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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”

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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

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The CCSS Difference: Grade 8 Mathematics

(2004) Before NJCCCS:

1. Understand and apply the Pythagorean Theorem.

(2010) After CCSS

2. Explain a proof of the Pythagorean Theorem and its converse.

3. Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.

4. Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.

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a2 + b2 = c2

a

b

c

3

3

9

4 16

4

5 5

25

a = 4

b = 3

c = ?

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Implications of the CCSS on WHAT and HOW to teach…

What are the Critical Shifts to Consider?

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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 UnderstandingEach 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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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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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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K 12Number and Operations

Measurement and Geometry

Algebra and Functions

Statistics and Probability

Traditional U.S. Approach…

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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

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GradeFocus 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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ALG. - 1Focus 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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GEOMETRYFocus 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-6Applications of Probability

Focus Areas in Mathematics (CCSS) - HS

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ALG. - 2Focus 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-4Inferences and Conclusions from Data

Focus Areas in Mathematics (CCSS) – HS

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FOCUS AREAS: High SchoolALGEBRA-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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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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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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•

One of several staircases to algebra designed in the OA domain.

Coherence: Link to Major Topics Across Grades

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Gr.3- multiply … divide

Gr.5-expressions

Gr.6- Apply properties

Gr.1- add … subtract

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One of several staircases to algebra designed in the OA domain.

Coherence: Link to Major Topics Across Grades

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ALGEBRA-I

ALGEBRA- II

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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

525

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Coherence: Link to major topics within gradesExample: 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 ….

b. How much fuel is in the tanks after the pump … 8 minutes?

c. Graph the equation … on the coordinate plane … label ….

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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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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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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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See Rigor in Grade 6: Ratios

PARCC - Grade-6 Slider Ruler: type-I 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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See the Rigor in Middle GradesUnderstanding 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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See the Rigor – High School Part A

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Part B

Describe

Compare

Write

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Required Fluencies in K-6Grade Standard Required Fluency

K K.OA.5 Add/subtract within 5

1 1.OA.6 Add/subtract within 10

22.OA.2

2.NBT.5

Add/subtract within 20 (know single-digit sums from memory)

Add/subtract within 100

33.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.2,3Multi-digit division

Multi-digit decimal operations

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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.

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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.

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

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Real world application – Grade 4

MORE THAN one choice

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

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Part B

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See what online looks like! HS Teachers outside of math

use grade-level-appropriate math

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Part B

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Part C

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Part D

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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

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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 ….

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Let’s take a quick break!

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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 ….

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TASK TYPE-ITasks 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

75 December 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.

76 December 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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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) http://www.parcconline.org/sites/parcc/files/HS-Alg1Math2PictureFrame.pdf

HS – Myla’s Swimming Poole (Algebra-I)

HS – Green Tea Observation Study (Algebra-2/Math 3)

79 J. Brendel 12.3.2013

 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

2. Compare f(3) and g(3)

3. Compare maximum values of each w/in range -5 ≤ x ≤ 5

4. Compare

A Type-I PARCC task

COURSE ?

DIFFICULTY?

POINTS?

STANDARDS?

80 J. 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?

81 J. Brendel 12.3.2013

Seeing Structure in Equations http://www.parcconline.org/samples/mathematics/high-school-seeing-structure-equation

(see third page in Type-I packet)

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

a Type I PARCC task

COURSE

?DIFFICULTY?

POINTS?STANDARDS?

82 J. 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

83 J. Brendel 12.3.2013

GREEN TEA TYPE

http://www.parcconline.org/sites/parcc/files/PARCC_SampleItems_Mathematics_HSAlgIIMathIIIGreenTeaStudy_081913_Final_0.pdf

a Type I PARCC task

COURSE

? DIFFICULTY?POINTS?

STANDARDS?

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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 rubrichttp://www.parcconline.org/sites/parcc/files/HighSchoolAlg2Math3-GraphsofFunctions.pdf

• HS – Michelle’s Conjectures (Algebra-II/Math III)http://www.parcconline.org/sites/parcc/files/PARCC_SampleItems_Mathematics_HSAlgIMathIIMichelleConjecture_081913_Final_0.pdf

• HS – Geometric Construction Connection (Geometry/Math III)PARCC_SampleItems_Mathematics_HSGeoMathIIIGeometricConnection_081913_Final_0.pdf

http://www.parcconline.org/sites/parcc/files

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GRAPH of FUNCTIONS (posted November 2013)

(See first 3 pages of Type-II packetSee 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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  GEOMETRY CONSTRUCTION CONNECTION

(See 4th-6th page in Type-II packet; see details for teacher.)

http://www.parcconline.org/sites/parcc/files/PARCC_SampleItems_Mathematics_HSGeoMathIIIGeometricConnection_081913_

Final_0.pdf

a Type-II PARCC Task

POINTS ?

DIFFICULTY?STANDARDS?

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  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_HSAlgIMathIIMichelleConjecture_081913_Final_0.pdf

 

a Type-II PARCC Task

COURSE

?POINTS ?

DIFFICULTY?

STANDARDS?

Investigate the effect on the vertex of the graphf(x) = x2 + 6 when f(x) is replaced by f(x + k)

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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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 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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  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.

92 a Type-III PARCC Task

POPCORN INVENTORY (NOVEMBER 2013)

COURSE

? POINTS ?

DIFFICULTY?

http://www.parcconline.org/sites/parcc/files/HSAlg1Math1PopcornInventory.pdf

Read scenario, understand table, read additional facts …Estimate the amount of popcorn … Show or explain the reasoning you used to determine your estimate.

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_Mathematics_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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Help Students and Teachers

Prepare for the Change

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READING CCSS and Mathematics

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Regular Practice with Complex Text and its Academic Language

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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?

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•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 ELA Text-Dependent in ELA

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Text-Dependent in mathematics

December 2, 2013 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

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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

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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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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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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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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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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

109

What you SHOULD NOT see !

110

ZN

x

y

>

<

Slope =

slope =

(3,6)

(3,2)

111

The Mathematics Common Core ToolboxMathematics 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. 24-25)

• 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

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 http://www.parcconline.org/sites/parcc/files HSAlg1Math1PopcornInventory.pdf

113

Sample Online Performance TasksMathematics 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? ….)

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

• https://sbacpt.tds.airast.org/student/login.aspx?c=SBAC_PT

J.Brendel 11/2013

115

EXPERIENCE ONLINE TASKSjust released; similar to testing environment

*PARCC Online Activities

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

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)

117 December 2, 2013

SAMPLE ASSESSMENTexamples 1-12

from Smarter Balanced siteseparate hardcopy-packet

pages 15-20

and

High School Reference Sheet page-13

118

Activity: BRAINSTORM in GROUPS

How should high school math teaching change from the traditional teaching?

What non-math type skills are essential?

119

J. Brendel 11/2013

Other Resources

CIRCLEShttp://sampleitems.smarterbalanced.org/itempreview/ModernShell.aspx?config=SBAC%5CContent%5CCircle1.json

MATH II - WALLShttp://sampleitems.smarterbalanced.org/itempreview/ModernShell.aspx?config=SBAC%5CContent%5CRoomWall.json

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# 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-lessonStatistical analysis to rank baseball players GRADES 11-12CCSS Standards: Math SID. 1, 2 and 3

121

The Specs, Accountability, and Resources:

What We Know Now!

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 11EOY – 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

123

Performance Based Assessment

ELA/Literacy Math TOTAL

Grade Literacy Analysis

Research Narrative Session 1

Session 2

9-10

Alg I/ Math IGeo/

Math II

Estimated Time on

Task(minutes)

80 85 5050 50

315

Estimated Time on Task: Grade 9-10

124

End-of-Year (EOY) Assessment

ELA/Literacy Math TOTAL

Grade Session 1

Session 2

Session 1

Session 2

9-10

Alg I/ Math IGeo/ Math II

Estimated Time on

Task(minutes)

70 7065 65

270

Estimated Time on Task: Grade 9-10

Grade 9-10 Summative Total: 9 Hours, 45 minutes

125

Performance Based Assessment

ELA/Literacy Math TOTAL

Grade Literacy Analysis

Research Narrative

Session 1

Session 2

11

Alg II/Math III

Estimated Time on

Task(minutes)

80 85 5065 65

345

Estimated Time on Task: Grade 11

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 7055 55

250

Estimated Time on Task: Grade 11

Grade 11 Summative Total: 9 Hours, 55 minutes

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)

128

What Else…

• 20 Day Window…for both the PBA and EOY summative assessments (performance based and end-of-year)

• Summative Assessments Retest OpportunitiesGrades 3-8 - 1 retest opportunity/yearHS - up to 3 retest opps/year for each assessment

• Computer-based (w/paper version available in rare circumstances), contingency back-up

• PBA delay? No…

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)

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

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 Assessmentshttp://parcconline.org/parcc-accessibility-accommodations-and-fairness

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; 

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). 

134

Accountability:What We Know Now!

135

Results Types…

Performance Level Description

Level 5* Distinguished Command

Level 4* Strong Command

Level 3 Moderate Command

Level 2 Partial Command

Level 1 Minimal Command

Proficiency (PLDs) On-Track-to-College and

Career Readiness (CCRDs) Growth Data

Performance Level Descriptors (PLDs)

*Achieved CCR Performance Threshold

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.”

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.”

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.

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.

140

140

Timelines and Resources:What We Know Now!

141

PARCC Timeline…

 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

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)

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.

143

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. (2014-15 school year)

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.

145

www.achievethecore.org

146

Links to Model Math Curriculum Sites

Sample Assessments by grade:http://www.achievethecore.corg/

Common Core and Special Education Studentshttp://www.ode.state.or.us/search/page/?id=3741

Common Core Practice Testhttps://sbacot.tds.airast.org/student/login.aspz?c=SBAC.PThttp://sbac.portal.airast.org/practice-test/

Common Core Resources to use with studentshttp://www.illustrativemathematics.org

Dana Center Resources http://www.ccsstoolbox.org/http://ccsstoolbox.agilemind.com/pdf/DanaCenter_YAG_HS.pdf

147December 2013 J.Brendel

COMPANIES are developing new programs to assist districts:

ACUITY: a comprehensive K-12 assessment programTom 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)

148

COMPANIES are developing new programs to assist districts as they transition to technology-based assessments:

Pearson’s online Assessment Roadmap 2014www.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/NextGenRoadmapBryan Bleil (VP, online & tech), Ellen Stain Seymore

J. Brendel 11/2013

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

150

Self-Evaluation, Action Planning and Next Steps

Roadblocks Action Planning

Next Steps

151

151

Let’s take our… (last page in packet)

PARCC POST-Assessment!

Activity : FAQs POST-Test

152

Questions?Concerns (silly question)?

Discussion/Debrief

153

SINCERE THANKS…For your participation, collaboration and dedicated efforts!!!

Judy jbrendel@pascack.k12.nj.us or contact NJPSA/FEA