FEA/PSA - Judith T. Brendel - Spring 2014

The PARCC Institute – High School Math:

Preparing for PARCC!NJ’s Next Generation Standardized

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

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Welcome…

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Desired outcomes…

•understand the overall substance, design and technical aspects of next generation PARCC assessments

•gain access and practice with PARCC tasks and related resources

•better enable educators to effectively lead the transition to CCSS and PARCC assessments.

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“…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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Education for a Contemporary Age

Preparing a Globally Competent and Innovative Workforce

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A Changing World…

A growing need for a paradigm shift in the way we teach and learn…

• A Nation at Risk (1983) http://www2.ed.gov/pubs/NatAtRisk/findings.html

http://www.ed.gov/pubs/NatAtRisk/index.html

• SCANS Report and America 2000 http://wdr.doleta.gov/SCANS/whatwork/whatwork.pdf

(What Work Requires of Schools)

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

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A Changing Student… (recommended resources)

• Digital Natives, Digital Immigrants – Parts I and II – Do They Really Think Differently? (Prensky, 2001) http://www.marcprensky.com/writing/default.asp

• Marc Prensky’s Essential 21st Century Skills http://www.marcprensky.com/writing/Prensky-Essential_21stCenturySkills.pdf

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

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A Changing Student… (recommended resources)

•Authentic Intellectual Work and Standardized Tests: Conflict or Coexistence (2001) http://ccsr.uchicago.edu/content/publications.php?pub_id=38#

•How People Learn: Brain, Mind, Experience and School (1999, 2003) http://www.nap.edu/openbook.php?record_id=6160

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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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Common standards,…

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

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Reflection…•What trends will continue to shape the world in which our students will live and work?

•What skills will our students need to succeed in their future?

•What type of learning environments would best support to development of these skills?

…what are your thoughts?

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Let’s take a (quick) break!

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Let’s get to work…

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Let’s take our… (page-3)

PARCC Pre-Assessment!

Item 9: grade-7 level math w/new CCSS (What’s different?)ADD H.S. EXAMPLE

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A (Quick) Walk through the PARCC!

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Race to the Top Assessment Grants:• $350 million of Race-to-the-Top Fund to consortia of states to design and

develop common K-12 assessment systems aligned to CCSS

• In September 2010, the U.S. Department of Education awarded grants to:

• Partnership for Assessment of Readiness for College and Careers (PARCC) – 18 States, & DC

• Smarter Balanced Assessment Consortium (SBAC)

• Winning consortia - four years - to develop assessments systems,

• States participating will administer new assessments statewide by 2014-2015

• ACHIEVE was selected through a competitive bid process, by PARCC to be the Project Manager.

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Race to the Top Assessment Grants:

• New Jersey is PARCC Governing Board State:

• Will administer the assessment system statewide 2014-15 school year.

• Will field test assessment items spring 2014.

• Governing Board meets quarterly. The chief state school officer for each of the governing states sits on the PARCC Governing Board. This to make major policy, operational, design and financial decisions regarding PARCC.

• Executive Committee meets weekly. (Governing Board Members from 6 states)

• ACHIEVE won competitive bid, selected by PARCC to be the Project Manager.

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Why New Common Assessments?

Current Assessment Systems…

• Too many tests, often with disconnected purposes (e.g., instructional improvement vs. accountability vs. college admissions)

• Not challenging enough to measure CCR

• Do not measure the full range of college- and career-ready knowledge and skills (such as research, analysis, critical thinking, and collaboration)

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Current Assessment Systems…

• Fail to generate information for educators and students quickly enough or at all

• Are widely inconsistent across states making results impossible to compare

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Next-Generation Common Assessment Systems will…

• Measure students’ mastery of Common Core State Standards

• Provide a common measure of college and career readiness

• Include a range of item types that allow for the assessment of higher-order skills

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Next-Generation Common Assessment Systems will…

• Leverage new technologies in assessment and reporting to get actionable student data to educators and parents in real time

• Mitigate challenges associated with student mobility by ensuring students will have the same expectations wherever they live

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PARCC Assessment Consortium

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K-2 formative assessment

being developed,

aligned to the PARCC system

Timely student achievement data showing students, parents and educators

whether ALL students are on-track to college and

career readiness

ONGOING STUDENT SUPPORTS/INTERVENTIONS

College readiness score to identify who

is ready for college-level coursework

SUCCESS IN FIRST-YEAR,

CREDIT-BEARING,

POSTSECONDARY COURSEWORK

Targeted interventions &

supports:•12th-grade bridge courses• PD for educators

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

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Assessment Transition Timeline

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Assessment Transition Timeline

Spring 2012

NJ ASK Aligned to NJCCCS

Spring 2013

NJ ASK

Aligned to the CCSS and NJCCCS

(Except Gr. 6-8 Math)

Spring 2014

NJ ASK

Aligned to the CCSS

SY 2014-15

Full administration

of PARCC assessments

“Transitional Assessments”

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The PARCC Commitment…

PARCC is designed to promote quality instruction aligned to the CC Standards, so the assessment is worthy of preparation rather than a distraction from good work.

TEACHING to the TEST may be a GOOD THING!

32 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?

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"The standards are designed to be robust and relevant to the real world, reflecting the knowledge and skills that our young people need for success in college and careers," which will place American students in a position in which they can compete in a global economy.

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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

Before: NJCCCS (2004)

1. Understand and apply the Pythagorean Theorem.

After: CCSS (2010)

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

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

• 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

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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.


PARCC sample prototypes with Task Type

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TASK TYPES – PARCC

I – Computation, Skills, Process

(x – 2)2 + 6 = 75 2x2 - 5x – 6 = 0

II – Mathematical Reasoning

xxx

xxxx

III – Modeling, Combined Standards, Applications

Compare the 3 sets of data (graph, chart, and equation) and defend the argument that ….

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TASK TYPE-ITasks assessing concepts, skills and procedures.

- include a balance of conceptual understanding, fluency, and application. These tasks can involve any or all mathematical practice standards.

- will be machine scorable and will include innovative, computer-based formats.

-will appear on the End-of-Year and Performance Based Assessment components and generate evidence for measuring major, additional, and supporting content with connections to the mathematical practices as indicated in the PARCC Model Content Frameworks for Mathematics.*

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Mathematics online Sample Item/Prototypes:

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)

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TYPE II: Tasks assessing expressing mathematical reasoning.

- tasks call for written arguments/justifications, critique of reasoning, or precision in mathematical statements (MP. 3, 6). These tasks can also involve other mathematical practice standards.

- tasks may include a mix of innovative, machine scored and hand scored responses.

- tasks will be included on the Performance Based Assessment component and generate evidence for measuring mathematical reasoning with connections to content.

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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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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.

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

TYPE-I PARCC TASKSinclude a balance of conceptual understanding, fluency, and application, and can involve any or all Math Practice Standards. will be machine scorable and will include innovative, computer-based formats. will appear on the End of Year and Performance Based Assessment components and generate evidence for measuring major, additional, and supporting content with connections to the mathematical practices as indicated in the

PARCC Model Content Frameworks for Mathematics.*

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Functions http://www.parcconline.org/samples/mathematics/high-school-functions

Given f(x) as a graphed parabola and g(x) as table of values

1.Compare y-intercepts 2.Compare f(3) and g(3)3.Compare maximum values of each w/in range -5 ≤ x ≤ 54.Compare

A type I PARCC task

COURSE

?

DIFFICULTY?

POINTS?

STANDARDS?

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

(3x - 2)2 = 6x – 4

a Type-I PARCC task

COURSE

?DIFFICULTY

?POINTS?

STANDARDS?

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

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

a Type I PARCC task

COURSE

?DIFFICULTY

?

POINTS?STANDARDS?

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PICTURE FRAME http://www.parcconline.org/sites/parcc/files/HS-Alg1Math2PictureFrame.pdf

a Type I PARCC task

COURSE

?DIFFICULTY

?POINTS?

STANDARDS?

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GREEN TEA TYPEhttp://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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GRAPH of FUNCTIONS (posted November 2013)

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

http://www.parcconline.org/sites/parcc/files/PARCC_SampleItems_Mathematics_HSGeoMathIIIGeometricConnection_081913

_Final_0.pdf


POINTS ?

DIFFICULTY

?STANDARDS?

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MICHELLE’S CONJECTURES (Aug.19, 2013)

http://www.parcconline.org/sites/parcc/files/PARCC_SampleItems_Mathematics_HSAlgIMathIIMichelleConjecture_081913_Final_0.pdf


COURSE

? POINTS ?

DIFFICULTY?

STANDARDS?

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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)

http://www.parcconline.org/sites/parcc/files/HSAlg1Math2MiniGolfPrices.pdf

a Type-III PARCC Task

COURSE

? POINTS ?

DIFFICULTY?

STANDARDS?

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BRETT’S RACE

(November, 2013)

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

a Type-III PARCC Task

COURSE

? POINTS ?DIFFICULTY

?

STANDARDS?

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POPCORN INVENTORY (NOVEMBER 2013)

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

COURSE

? POINTS ?

DIFFICULTY?

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TEMPERATURE CHANGES

http://www.parcconline.org/sites/parcc/files/PARCC_SampleItems_Mathematics_HSAlgIIMathIIITemperatureChange_081913_

Final_0.pdf

COURSE

? POINTS ?

DIFFICULTY?

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PARCC RELEASED TASKS include elsewhere? Use this slide to ‘hold’ sites

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

How/if .. .include here?

https://www.teachingchannel.org/videos/statistical-analysis-lessonStatistical analysis to rank baseball players GRADES 11-12CCSS Standards: Math SID. 1, 2 and 3

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What you SHOULD NOT see !

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ZN

x

y

>

<

Slope =

slope =

(3,6)

(3,2)


BRAINSTORM in GROUPS

What should teachers NOT be doing?

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READING CCSS and Mathematics

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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?

What makes Casey’s experiences at bat humorous?

What can you infer from King’s letter about the letter that he received?

“The Gettysburg Address” mentions the year 1776. According to Lincoln’s speech, why is this year significant to the events described in the speech?

Not Text-Dependent in 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

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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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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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Adjusting Math Language to the CCSS• Old habit to eliminate: Defining equality as “same as.” The problem: This is mathematically incorrect and leads to

misconceptions. New habit to adopt: Defining equality as “same value as.”

• Old habit to eliminate: “Addition makes things get bigger.” The problem: When negative numbers are introduced, the old habit

has to be debugged. New habit to adopt: Addition is about combining.

• Old habit to eliminate: “Subtraction makes things get smaller.” The problem: As with addition, negative numbers make this wrong. New habit to adopt: Subtraction is about difference.

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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

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It all boils down to…

Texts Worth Reading…and

Questions Worth Answering!

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Let’s take a quick break!


Understanding the Common Core Math Standards …is to understand PARCC Math!

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The Common Core Standards: Classroom Video Illustration

High School School

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

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• A different topic every day

• Every topic/concept treated as equally important

• Elementary students dipping into advanced topics at the expense of mastering fundamentals

• Infinitesimal advance in each grade; endless review

• Incoherence and illogic – bizarre associations, or lacking a thread

NOT …

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Dan Meyer:Math Class Needs a Makeover

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NOT

Lack of rigor

• Reliance on rote learning at expense of concepts

• Aversion to repetitious practice

• Severe restriction to stereotyped problems lending themselves to mnemonics or tricks

• Lack of quality applied problems and real-world contexts

• Lack of variety in what students produce

• E.g., overwhelmingly only answers are produced, not arguments, diagrams, models, etc.

From.... To….856 = ___ hundreds, ___ tens, ___ ones 1 hundredth = ___ tenths

x2 + 10x + 21 = 0 ¾ c(c –1) = c

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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:

1.conceptual understanding;

2.procedural skill and fluency; and

3.application with equal intensity.

Three (3) Significant Shifts in Mathematics:

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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.

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• conceptual understanding;

• procedural skill and fluency; and

• application with equal intensity.


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FOCUS continued

70% or more of the assessment will measure the major work in grades 3-8

Focus allows for a variety of problem types (task types) to get at a concept

in multiple ways.

Students will have more time to master concepts at a deeper level.

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Mathematics topics intended at each grade by at least two-thirds of A+ countries

Mathematics topics intended at each grade by at least two-thirds of 21 U.S. states

The shape of math in A+ countries…

1 Schmidt, Houang, & Cogan, “A Coherent Curriculum: The Case of Mathematics.” (2002).

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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–2Addition and subtraction - concepts, skills, and problem solving and place value

3–5Multiplication and division of whole numbers and fractions – concepts, skills, and problem solving

6Ratios and proportional reasoning; early expressions and equations

7Ratios and proportional reasoning; arithmetic of rational numbers

8Linear algebra, linear functions

Priorities 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

Priorities 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

Priorities 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-4 Inferences and Conclusions from Data

Priorities in Mathematics (CCSS) – HS

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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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COHERENCENeed to include h.s. task(s) that incorporate multiple standards to show connections.

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Coherence and NEW multiple-choice questions.Circle all that are true.

Given: All squaresA.are parallelograms and rectanglesB.have 4 acute anglesC.have only 2 diagonals D.Area = ½ base x height E.Sum of consecutive angles = 180˚F.Perimeter = 2 x Side lengthG.Area > area with the same perimeter.

5 3

7

525

21

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*Activity 4: Work with your group (p. 15. Ex. 8)

What skills and understandings are assessed here?

Do they come from only one standard? One domain?

A. subtraction w/decimals

B. addition then subtraction

C. write % as a decimal; multiply

D. read carefully, add and subtract money

E. know how to find an average

F. know to ÷ or x; compute accurately

G. know to add lowest, then highest; understand concept, recognize > and < symbols

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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 ….

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

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

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RIGOR

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

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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

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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 Rigor in Grade 6: Ratios

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

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ONLINE http://www.parcconline.org/samples/item-task-prototypesGrade-3 Fractions on a Number Line: type- I http://www.parcconline.org/samples/mathematics/grade-3-mathematics-number-line

Grade-4 Fraction model: type-II http://www.parcconline.org/sites/parcc/files/PARCC_SampleItems_Mathematics_G4FractionModel_081913_Final.pdf

Grade-6 Slider Ruler: type-I http://www.parcconline.org/samples/mathematics/grade-6-slider-ruler

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See the Rigor in High School Math

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Linking to major topics – High School Part A

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Part B

Describe

Compare

Write

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REQUIRED FLUENCIES

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

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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

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

119

HS EXPECTATIONSALGEBRA-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

120

•

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

Coherence: Link to Major Topics Across Grades

120

1. add … subtract

3. multiply … divide

5. expressions

6. Apply properties

121

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

Coherence: Link to Major Topics Across Grades

121

ALGEBRA-I

ALGEBRA- II

122

Application

• Students can use appropriate concepts and procedures for application even when not prompted to do so.

• Teachers provide opportunities at all grade levels for students to apply math concepts in “real world” situations, recognizing this means different things in K-5, 6-8, and HS.

• Teachers in content areas outside of math, particularly science, ensure that students are using grade-level-appropriate math to make meaning of and access science content.

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123

Fluency

FLUENCY and new type of MC question

125

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

126

Part B

127

Part C

128

Part D

129

Standards of Mathematical Practices1. 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

130

Analysis of the PARCC Mathematics Assessment:

Design Shifts(Activity No. 4)

131

Shift No. 1…Focus where Standards Focus

Advance: PARCC assessments will focus strongly where the Standards focus (70% or more on the major work in grades 3-8).

Focus allows for a variety of problem types to get at concept in multiple ways.Students will have more time to master concepts at a deeper level.

132

Shift No. 2…Coherence across/within grades

Advance: The assessment design is informed by multi-grade progressions in the Standards and the Model Content Frameworks.Key beginnings are stressed:

e.g., ratio concepts in grade 6, e.g., fluency with the multiplication table in

grade 3Become key endpoints and takeaway skills

133

Shift No. 2…Coherence across/within grades

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

134

Shift No. 3…Rigor

Advance: PARCC assessments will reach the rigor in the Standards through innovations in technology and item design.

135 December 2, 2013

SAMPLE ALGEBRA-1 UNIT-I ASSESSMENT

and High School Reference Sheet(separate packet)

• Solution Guide

• With notes to teachers

• Sample responses and scoring

136

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

Activity: grade-2 (p. 26-27) *What makes it unique? ….

137

Performance Based Assessment (PBA)

•Type I items (machine-scorable)

•Type II items (Mathematical Reasoning/hand-scored)

•Type III items (Mathematical Modeling/hand scored and/or machine-scored

End-of-Year Assessment (EOA)•Type I items only (All machine-scorable)

138

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., surf.area, min s.a.)•Grade 7 - Food Basket (calories, grams, protein)•Grade 8 - Heartbeats (scatter plot ….)•Grade 11- Speeding Ticket (graph, what is fair? ….)

•Grade 2 hardcopy-Trip to Zoo (gr. 4 modified; J. Brendel Barron’s)(page 27-28)

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EXPERIENCE an ASSESSMENTActivity 6

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

• Sample online Smarter Balanced Assessments. Select from grades 3, 4, 5, 6, 7, 8 or 11

• Select Examples or Performance Tasks J.Brendel 11/2013

140

J. Brendel 11/2013

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

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The Specs, Accountability, and Resources:

What We Know Now!

142

PARCC Assessment Consortium

143

Dynamic Learning Maps (DLM) Alternate Assessment Consortium

144

Performance Based Assessment

ELA/Literacy Math TOTAL

Grade Literacy Analysis

Research Narrative Session 1

Session 2

9-10Alg I/

Math IGeo/

Math II

Estimated Time on

Task(minutes)

80 85 50 50 50 315

Estimated Time on Task: Grade 9-10

145

End-of-Year (EOY) Assessment


Grade Session 1

Session 2

Session 1

Session 2

9-10Alg I/ Math IGeo/ Math II

Estimated Time on

Task(minutes)

70 70 65 65 270

Estimated Time on Task: Grade 9-10

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

146

Performance Based Assessment


Grade Literacy Analysis

Research Narrative

Session 1

Session 2

11Alg II/

Math III

Estimated Time on

Task(minutes)

80 85 50 65 65 345

Estimated Time on Task: Grade 11

147

End-of-Year (EOY) Assessment


Grade Session 1

Session 2

Session 1

Session 2

11Alg II/

Math III

Estimated Time on

Task(minutes)

70 70 55 55 250

Estimated Time on Task: Grade 11

Grade 11 Summative Total: 9 Hours, 55 minutes

148

~ 1/3 total points = PBA

End-of-Year machine scored

149

~ 1/3 total points =

PBA

End-of-Year machine scored

150

What Else… 20 Day Window…for both the PBA and EOY

summative assessments (performance based and end-of-year) Summative Assessments Retest Opportunities

Grades 3-8 - 1 retest opportunity/year HS - up to 3 retest opps/year for each assessment

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

PBA delay? No…

151

What Else…Accessibility Features for ALL students•Audio Amplification•Blank Paper (provided by test administrator)

•Eliminate Answer Choices•Flag Items to Review•General Administration Directions (provided by test administrator)

•General Administration Directions Read Aloud and Repeated (provided by test administrator)

Accommodations / Modifications for Special Education students (55 page manual)

152

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

•Spell Checker•Writing Tool

153

What Else…Accommodations / Modifications for Special Education Students (from the 55-page PARCC Accessibility manual)

Accessibility Features Identified in Advance• Answer Masking• Background/Font Color (Color Contrast)• General Masking• Line Reader Tool• Text-to-Speech for the Mathematics Assessments

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

154

Modifications Accommodations NOT permittedModifications 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;

155

• Modifying the complexity of assessments to make them easier (e.g., deleting half of the response choices on a multiple-choice test so that a student selects from two options instead of four);

• Giving hints, clues, or other coaching that directs the student to correct

responses on assignments and tests; • Adults defining vocabulary on the test or explaining test items; • Allowing the student to complete an assessment of English language arts

in a language other than English; and • Using dictionaries that provide definitions (rather than an acceptable

word-to-word dual-language dictionary).

156

156

Accountability:What We Know Now!

157

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

158

What does “distinguished” (Level 5) mean?“Students performing at this level demonstrate a distinguished command of the knowledge, skills, and practices embodied by the Common Core State Standards for English language arts/literacy assessed at grade 11.

They are academically well prepared to engage successfully in entry-level, credit-bearing courses in College English Composition, Literature, and technical courses requiring college-level reading and writing.

Students performing at this level are exempt from having to take and pass placement tests in two- and four-year public institutions of higher education designed to determine whether they are academically prepared for such courses without need for remediation.”

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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.”

160

What does it mean to be CCR? (cont.)Will be used as a benchmark against which the CCR cut score on the PARCC assessments will be validated through empirical research.

•WHY - a “C” is the minimum grade needed to earn credit for a course

•WHY - a reasonably high standard but not unattainable.

•WHY - similar to the criteria used by ACT,

•WHY - other important CCR skills will not be measured by PARCC assessments.

161

What are the cut scores for each level?

As/PARCC, “the vendor selected through the RFP will

also work with state leaders, educators and eternal

experts to determine the cut scores to establish the five

PARCC Performance levels for each grade-level

assessment.

RFP for “Operational Assessment”

Vendor proposals are due by Dec. 11, 2013.

162

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Timelines and Resources:What We Know Now!

163

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)

164

PARCC Timeline…

*Over the next year, PARCC will develop five online training modules for teachers, school leaders, and school site testing coordinators – each with a unique purpose.

PARCC will produce modules with the following foci:

1. PARCC Common Assessments Overview

2. Introduction to the PARCC Mid-Year Assessment

3. Introduction to the PARCC Diagnostic Assessment

4. Introduction to the PARCC Speaking/Listening Assessment

5. PARCC Accessibility System

*It is anticipated that modules will be available in June 2014.

165

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)

166

NJDOE Model Curricula(handouts Algebra-I, Geometry, Algebra-II)

PARCC Model Content Frameworks

167

INITIAL QUESTIONS to CONSIDER

when choosing or developing a

Quality Math Assessment.

See handout page-31

JB modified from: http://www.state.nj.us/education/AchieveNJ/teacher/SGOGuidebook.pdf

168

GENERAL TEST PREP:

What does this look like?

See handout pages 32-33

•Know the test in terms of the following:•10 Considerations for Success

169

www.achievethecore.org

170

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

171December 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)

172

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

173

TEXTBOOK PUBLISHERS are beginning to develop new programs to assist districts as they transition to technology-based assessments:

Many now have all resources online including assessment options.

Sample:http://www.connected.mcgraw-hill.com

•Teacher username and password

•Select Subject: [Algebra-I CC Standards National]

•Select Standards: [National] [Assess] [Algebra-I]

[Create a New Test]

J. Brendel 11/2013

174

Two Activities

Self-Evaluation, Action Planning and Next Steps

Response Priority Comments Roadblocks (pages 28-29)

Action Planning/Next Steps (page 30)

175

Questions?Concerns (silly question)?

Discussion/Debrief

176

SINCERE THANKS…

For your participation, collaboration and dedicated efforts!!!

Judy [email protected]

[email protected]

Documents

FEA/PSA - Judith T. Brendel - Spring 2014