the parcc institute middle school and high school math preparing for parcc! nj’s next generation...
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The PARCC Institute Middle School and High School Math
Preparing for PARCC!NJ’s Next Generation Standardized
Assessment SystemJudith T. Brendel - Spring 2014
http://www.pascack.k12.nj.us[curriculum] [mathematics] [PARCC MS-HS Assessments]
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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: Grades 6, 7 8: PBA and EOY
Algebra 1: PBA and EOY Geometry: PBA and EOY Algebra 2: PBA and EOY
How many TOTAL POINTS on each test?HS: PBA – 18-20 pointsHS: EOY – 34-35 points = 52-55
What is a PROFICIENT SCORE? highly proficient score?To be determined after spring 2014 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(gr. 6-8 see
handout packet)
(HS 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
…
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
YES/NO choicesMC- 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 Middle Grades (page 8A)
24 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”
28 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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GradeFocus Areas in Support of Rich Instruction and Expectations of Fluency and Conceptual Understanding
K–2• Add/subtract within 5/ 10/ 20 (K.OA.5, 1.OA.6, 2.OA.2)• Add/subtract within 100 (2.NBT.5)• Know single-digit sums within 20 (2.OA.2)
3• Multiply/divide within 100 (know single-digit products
from memory) (3.OA.7)• Add/subtract within 1000 (3.NBT.2)
4 • Add/subtract within 1,000,000 (4.NBT.4)
5 • Multi-digit division (5.NBT.5)
6• Multi-digit division (6.NS.2)• Multi-digit decimal operations (6.NS.3)
Required Fluencies K-6 without calculators (p.13A)
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Fluencies: sample grade-3
See SAMPLE ITEM page-13B
• CONTENT STANDARD• MATH PRACTICES STANDARD
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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 …
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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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 ? (page-20A)
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Real world application – Grade 4
MORE THAN one choice
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Real world application – Grade 4
DEER in the PARK (page 20D)• What makes this problem unique?• Why might you give this problem to your upper
grade-level students?
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See what online looks like!Linking to major topics – Grade 7 (page-20B-C)
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Part B
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See what online looks like!Linking to major topics – HIGH SCHOOL (page-21)
Item 3: High School (Isabella’s Credit Card)
(Part a)
(Part b)
(Part c)
What makes this unique? Different for “your” students?
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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
Type I
(x – 2)2 + 6 = 75 solve for c: (x + c)/z = 2c(w-y)
Type II
Explain how you can use the graphs to find solutions. Estimate ….
Type III
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 (review)
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
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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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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)
Grade-6 : Slider Rule, Kelvin’s 100-Meter Dash
Grade-7: Speed, Reading Three Books
Grade-8: Length of Segment AB
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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)
84 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?
85 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?
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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?
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PICTURE FRAME http://www.parcconline.org/sites/parcc/files/HS-Alg1Math2PictureFrame.pdf
(See pages 4-6 of Type-I packet; see Details for Teacher
a Type I PARCC task
COURSE
?
DIFFICULTY?
POINTS?STANDARDS?
X + 2 in.
X in.width
length
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GREEN TEA TYPE
http://www.parcconline.org/sites/parcc/files/PARCC_SampleItems_Mathematics_HSAlgIIMathIIIGreenTeaStudy_081913_Final_0.pdf
http://www.parcconline.org/samples/mathematics/high-school-
mathematics
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:(separate packets)
PARCC TYPE-II TASKS)
Grade-6 : Proportions of Instruments (new)
Grade-7: Proportional Relationships
Grade-8: (none listed on site)
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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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Mathematics online Sample Item/Prototypes:(separate packets)
PARCC TYPE-III TASKS)
Grade-6 : Fraction Model (new)
Grade-7: (none listed on site)
Grade-8: (none listed on site)
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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.
99 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.
100 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?
105
•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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BRAINMSTORMING SESSION
WHAT are TROUBLESOME VOCABULARY for MIDDLE-SCHOOL-GRADE 9 students?
THINK: (pair-share-list)- Subject specific (quotient, ratio, proportion, rate of change)- Everyday English (adjacent)- Adult language, adult experiences (base-pay, flat-fee, commission)
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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 (p. 21A, B)
• 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
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What you SHOULD NOT see !
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ZN
x
y
>
<
Slope =
slope =
(3,6)
(3,2)
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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
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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
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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? ….)
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EXPERIENCE an ONLINE ASSESSMENT*Smarter Balanced Online Activities
• Sample online Smarter Balanced Assessments. *Select from grades 3, 4, 5, 6, 7, 8 or 11
• https://sbacpt.tds.airast.org/student/login.aspx?c=SBAC_PT
J.Brendel 11/2013
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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
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PRACTICE ONLINE w/earlier grade resources
• Order Juice (grade-4) – Dana Center (p.28-29)• Spicy Veggies (grade-7) – Dana Center (p.26-27)• Drag and Drop (Smarter-Balanced sample)• Circle; explain (Smarter-Balanced sample)• Noise Level (Smarter-Balanced sample)• Scatter Plot (Smarter-Balanced)
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SAMPLE ASSESSMENTexamples 1-12
from Smarter Balanced siteseparate hardcopy-packet
pages 15-20
and
MS and HS Reference Sheets page-12A – 13
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FINALLYPractice PARCC ONLINE tests
START NOW!http://practice.parcc.testnav.com/#
Grade-6 EOY (2 sections 34 total questions); answer keys, too.Grade-7 EOY (2 sections 32 total questions) “Grade-8 EOY (2 sections 32 total questions) “
Algebra I EOY (2 sections 35 total questions) “Geometry EOY (2 sections 32 total questions) “Algebra II EOY (2 sections 34 total questions) “
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Activity: BRAINSTORM in GROUPS
How should MS/HS math teaching change from the traditional teaching?
What non-math type skills are essential?
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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
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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
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The Specs, Accountability, and Resources:
What We Know Now!
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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 [email protected]
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Performance Based Assessment
ELA/Literacy Math TOTAL
Grade Literacy Analysis
Research Narrative Session 1
Session 2
6-8Estimated
Time on Task(minutes)
80 85 50 50 50 315
Estimated Time on Task: Grade 6-8
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End-of-Year (EOY) Assessment
ELA/Literacy Math TOTAL
Grade Session 1
Session 2
Session 1
Session 2
6-8Estimated
Time on Task(minutes)
70 70 55 55 250
Estimated Time on Task: Grade 6-8
Grade 6-8 Summative Total: 9 Hours, 25 minutes
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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
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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
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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
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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
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GRADES 6-8 (2 packets each grade)
ALGEBRA-I PBA and EOY (2 packets)
GEOMETRY PBA and EOY (2 packets) ALGEBRA-2 PBA and EOY (2 packets)
ALGEBRA-I PBA vs EOY (packet)
HOW will I know what should be ‘learned’ before the PBA? before the EOY? (Activity)
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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…
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What Else…
Accessibility Features for ALL students• Audio Amplification• Blank Paper (provided by test administrator)
• Eliminate Answer Choices• Flag Items to Review• General Administration Directions (provided by test administrator)
• General Administration Directions Read Aloud and Repeated (provided by test administrator)
Accommodations / Modifications for Special Education students (55 page manual)
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What Else…
Accessibility Features for ALL students continued• Highlight tool• Headphones• Magnification/Enlargement Device• Notepad• Pop-Up Glossary• Redirect Student to Test (provided by test administrator)
• Spell Checker• Writing Tool
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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
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Modifications Accommodations NOT permitted
Modifications involve changes in the conditions under which a student takes an assessment that result in unacceptable changes to the test itself, or what the test measures (e.g., reducing or changing expectations for students) and are therefore not permitted on PARCC assessments.
Examples of modifications that will result in invalidated results on PARCC include:• Requiring a student to be assessed on less content matter than
other students because he has been taught less material;• Reducing the scope of assessments so a student needs to complete
only a limited number of problems or items;
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• Modifying the complexity of assessments to make them easier (e.g., deleting half of the response choices on a multiple-choice test so that a student selects from two options instead of four);
• Giving hints, clues, or other coaching that directs the student to
correct responses on assignments and tests;
• Adults defining vocabulary on the test or explaining test items;
• Allowing the student to complete an assessment of English
language arts in a language other than English; and
• Using dictionaries that provide definitions (rather than an
acceptable word-to-word dual-language dictionary).
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Accountability:What We Know Now!
146
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
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What does “distinguished” (Level 5) mean?“Students performing at this level demonstrate a distinguished command of the knowledge, skills, and practices embodied by the Common Core State Standards for English language arts/literacy assessed at grade 11.
They are academically well prepared to engage successfully in entry-level, credit-bearing courses in College English Composition, Literature, and technical courses requiring college-level reading and writing.
Students performing at this level are exempt from having to take and pass placement tests in two- and four-year public institutions of higher education designed to determine whether they are academically prepared for such courses without need for remediation.”
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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.”
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What does it mean to be CCR? (cont.)Will be used as a benchmark against which the CCR cut score on the PARCC assessments will be validated through empirical research.
• WHY - a “C” is the minimum grade needed to earn credit for a course
• WHY - a reasonably high standard but not unattainable.
• WHY - similar to the criteria used by ACT,
• WHY - other important CCR skills will not be measured by PARCC assessments.
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What are the cut scores for each level?
As/PARCC, “the vendor selected through the RFP will
also work with state leaders, educators and eternal
experts to determine the cut scores to establish the five
PARCC Performance levels for each grade-level
assessment.
RFP for “Operational Assessment”
Vendor proposals were due by Dec. 11, 2013.
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Timelines and Resources:What We Know Now!
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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)
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PARCC Timeline…
*Over the next year, PARCC will develop five online training modules for teachers, school leaders, and school site testing coordinators – each with a unique purpose.
PARCC will produce modules with the following foci:
1. PARCC Common Assessments Overview
2. Introduction to the PARCC Mid-Year Assessment
3. Introduction to the PARCC Diagnostic Assessment
4. Introduction to the PARCC Speaking/Listening Assessment
5. PARCC Accessibility System
*It is anticipated that modules will be available in June 2014.
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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)
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HIGHER ED FOCUS
June 16-17, 2014 convening
The focus will be on policy associated with student scores that signal on track; that signal a student is ready for entry level, college-bearing credit classes.
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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
158December 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)
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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
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TEXTBOOK PUBLISHERS are beginning to develop new programs to assist districts as they transition to technology-based assessments:
Many now have all resources online including assessment options.
Sample: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]
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Self-Evaluation, Action Planning and Next Steps
Roadblocks Action Planning
Next Steps
162
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Let’s take our… (last page in packet)
PARCC POST-Assessment!
Activity : FAQs POST-Test
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Questions?Concerns (silly question)?
Discussion/Debrief
164
SINCERE THANKS…For your participation, collaboration and dedicated efforts!!!
Judy [email protected] or contact NJPSA/FEA