The PARCC Institute – High School Math:
Preparing for PARCC!
NJ’s Next Generation Standardized
Assessment System
FEA/NJPSA - Judith T. Brendel - Spring 2014
Welcome…
2
Let’s take our… (pages 1-2)
PARCC Pre-Assessment!
Activity #1 : FAQs Pre-Test
3
3
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?
•
•
•
•
•
•
4
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
How do I know what CONTENT is included on each test?
PARCC Blueprints: Algebra 1: PBA and EOY
Geometry: PBA and EOY
Algebra 2: PBA and EOY
How many TOTAL POINTS on each test?
PBA – 18-20 points
EOY – 34-35 points = 52-55
What is a PROFICIENT SCORE? highly proficient score?
To be determined after field tests are scored.
How do I know the FORMAT of PARCC questions?
Activity #2 – workbook pages 3-6 (to do soon)
How many TYPES of tasks are on these tests?
Activity – 3 separate packets for Type I, II and III tasks
5
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
YES
Calculato
r
Item
Specific
Calculato
r Neutral
PBA
1
18
7
6
EOY
3
9
15
11
NO
Calculato
r
YES
Calculato
r
Item
Specific
Calculato
r Neutral
PBA
16
1
7
EOY
16
6
22
NO
Calculato
r
YES
Calculato
r
Item
Specific
Calculato
r Neutral
PBA
3
28
4
3
EOY
4
9
19
9
GEOM.
ALG.2
6
Ti-84
type
graphing
calculator
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
7
SA MS/HS– PD Session 3| April 4., 2011
HS
Assessment Items Points Alg.1 Geom Alg2
BLUEPRINTS
Type
1 pt.
21
19
19
EOY
1
2 pt.
11
12
12
for
4 pt.
3
3
3
MATHEMATICS
EOY TOTAL
ALGEBRA-I
GEOMETRY
ALGEBRA-II
(page 22)
8
PBA/MYA/
MOY
Type
1
Type
2
Type
1
P/M totals Type
by course
2
Type
3
PBA/MYA TOTALS
1 pt.
2 pt.
3 pt.
4 pt.
3 pt.
6 pt.
35
10
2
2
2
2
10
34
10
2
2
2
2
10
34
10
2
2
2
3
10
4
4
5
4
4
5
18
18
20
Math Item Counts Per Form Integrated Math I, II, II
HS
Blueprints
Assessment Item
Points
Math-I
Math-II
for
Type 1
1 pt.
19
19
Mathematics EOY
MATH I
MATH II
MATH III
9
Type 1
Type 2
PBA/MYA
TOTALS
(page 22)
2 pt.
4 pt.
12
3
34
12
3
34
19
14
2
35
1 pt.
2 pt.
3 pt.
4 pt.
3 pt
6 pt.
10
2
2
2
2
10
10
2
2
2
2
10
10
2
3
2
3
10
4
4
18
4
4
18
5
5
20
EOY TOTAL
PBA/MYA
Type 1
Type 2
Type 3
PBA/MYA TOTALS
Math-III
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.
10
What should teaching and learning in
the 21st century look like?”
“…revolutionary transformation rather than
evolutionary tinkering.” US DOE, NETP 2010
11
11
12
“The best time to plant a tree is twenty
years ago; the second best time is
today.”
(Ancient Chinese Proverb)
13
13
Listen to our students!
“I am a 21st Century Learner!”
14
14
How? Fostering essential skills…
•
•
•
•
•
Communication
Collaborative
problem solving
Critical thinking
Creativity
Innovation
•
•
•
•
•
Global
competence
Content
knowledge
Entrepreneurship
Adaptability
Interpersonal
… through innovative pedagogy and
ubiquitous technology.
15
15
What conditions will
foster these skills?
“I do not teach my
students; I simply create
the conditions for their
learning.”
(Albert Einstein)
2006 Innovative Teachers Forum.
Retrieved May 10, 2010 on : http://www.edlabgroup.org/tl/resources/InnovativeTeachers2006.pdf
17
17
21st learning…
18
…what should it look like?
21st learning…
19
http://www.pascack.k12.nj.us/cms/lib5/NJ01000238/Centricity/Domain/87
/Writing%20Equations%202.swf
19
Dan Meyer:
Math Class Needs a Makeover
20
PARCC: Partnership for
Assessment of Readiness for College and Career
What does it mean?
“Students are on-track or ready for college and careers.”
Solve problems
involving the major
content for their grade
level with connections to
practices
Solve problems
involving the additional
and supporting content
for their grade level with
connections to practices
Use the modeling
practice to solve real
world problems
21
Express mathematical
reasoning by
constructing
mathematical arguments
and critiques
Demonstrate fluency in
areas set forth in the
Standards for Content in
grades 3-6
Standards of Mathematical Practices (MP)
1.
Make sense of problems and persevere in solving them.
2.
Reason abstractly and quantitatively.
3. Construct
Constructviable
viablearguments
argumentsand
andcritique
critiquethe
thereasoning
reasoningofof
others.
others
4.
Modelwith
withmathematics.
mathematics.
Model
5.
Use appropriate tools strategically.
6.
Attend to precision.
7.
precision
Look
for and make use of structure.
8.
Look for and express regularity in repeated reasoning.
22
Activity #2 : Create different question formats
Algebra, Algebra-II or Geometry (pages 3-8)
2y = 4x - 6
MC- one right answer (traditional format)
MC – more than one right answer (at least A-D)
MC – yes/no true/false listed questions; multiplestandards
SCR – fill-in-the blank
OE – compare/contrast; explain/defend; how do you
know?
23
SA MS/HS– PD Session 3| April 4., 2011
A (Quick) Walk through the PARCC!
24
PARCC Assessment Consortium
PBA
MATH
25
EOY
MATH
Assessment Transition Timeline
NJTransition
ASK
Assessment
Timeline
“Transitional Assessments”
Spring
2012
Aligned to
NJCCCS
Aligned to the
Spring
2014
CCSS &
NJCCCS
Aligned to
the
Full
admin. of
PARCC
(Except Gr. 6-8
Math)
CCSS
assessment
Spring
2013
2014-15
26
26
Understanding the
Common Core State
Standards …is to
understand PARCC
27
PVRSD Math TF – Work Session 1 | November 18, 2010
Why Common Core State Standards?
•
Before Common Core State Standards we had
standards, but rarely did we have standards-based
instruction.
 Long
lists of broad, vague statements
 Mysterious assessments
 Coverage mentality
 Focused on teacher behaviors – “the inputs”
28
Principles of the CCSS…
•
•
•
29
FEWER - CLEARER - HIGHER
Aligned to requirements for College and
Career Readiness
Based on evidence
Honest about time
The CCSS Difference: Grade 8 Mathematics
(2004) Before NJCCCS:
1. Understand and apply the Pythagorean Theorem.
(2010) After CCSS
1. Explain a proof of the Pythagorean Theorem and its converse.
1.
Apply the Pythagorean Theorem to determine unknown side
lengths in right triangles in real-world and mathematical problems
in two and three dimensions.
1.
Apply the Pythagorean Theorem to find the distance between two
points in a coordinate system.
30
a 2 + b2
= c2
5
5
25
a=4
c=?
4
16
a
4
c
b
3
9
3
b=3
31
Implications of the CCSS on
WHAT and HOW to teach…
What are the Critical Shifts to
Consider?
32
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.
33
CC SHIFTS in ASSESSMENTS continued ….
Shift 4: Deep Understanding
Each standard will be assessed from multiple perspectives, while
not veering from the primary target of measurement for the
standard.
Shift 5: Application
Shift 6: Dual Intensity
Students will be expected to know grade-level mathematical content
with fluency and to know which mathematical concepts to employ
to solve real-world mathematics problems.
34
Three (3) Significant Shifts in Mathematics:
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
36
• application with equal intensity.
Three (3) Significant Shifts in Mathematics:
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
37
• application with equal intensity.
Traditional U.S. Approach…
K
12
Number and
Operations
Measurement
and Geometry
Algebra and
Functions
Statistics and
38
Probability
38
Focusing attention within Number and Operations
Operations and Algebraic Thinking 
Number and Operations—Base
Ten

K
1
2
3
4
Algebra

The Number
System
Number and
Operations—
Fractions
39
Expressions and

Equations

5
6
7
8
High School
Focus Areas in Mathematics (CCSS)
Grade
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
7
40
Focus Areas in Support of Rich Instruction and
Expectations of Fluency and Conceptual Understanding
8
Ratios and proportional reasoning; early expressions and
equations
Ratios and proportional reasoning; arithmetic of rational
numbers
Linear algebra, linear functions
40
Focus Areas in Mathematics (CCSS)- MS/HS
ALG. - 1
41
Focus Areas in Support of Rich Instruction and
Expectations of Fluency and Conceptual Understanding
UNIT-1
Relationships Between Quantities and Reasoning with Equations
UNIT-2
Linear Relationships
UNIT-3
Expressions and Equations
UNIT-4
Quadratic Functions and Modeling
UNIT-5
Functions and Descriptive Statistics
41
Focus Areas in Mathematics (CCSS) - HS
GEOMETRY
42
Focus Areas in Support of Rich Instruction and
Expectations of Fluency and Conceptual Understanding
UNIT-1
Congruence, Proof, and Constructions
UNIT-2
Similarity, Proof, and Trigonometry
UNIT-3
Extending to Three Dimensions
UNIT-4
Connecting Algebra and Geometry Through Coordinates
UNIT-5
Circles With and Without Coordinates
UNIT-6
Applications of Probability
42
Focus Areas in Mathematics (CCSS) – HS
ALG. - 2
Focus Areas in Support of Rich Instruction and
Expectations of Fluency and Conceptual Understanding
UNIT-1
Polynomial, Rational, and Radical Relationships
UNIT-2
Trigonometric Functions
UNIT-3
Modeling with Functions
Inferences and Conclusions from Data
UNIT-4
43
43
FOCUS AREAS: High School
ALGEBRA-I: Unit 2 – LINEAR RELATIONSHIPS
Find approximate solutions to linear
equations by making a table of values, using
technology to graph and successive approximations.
•F.IF.7/9 supporting Graph functions by hand (in simple
cases) and with technology ….
•A.REI.5, A.REI.6 additional Solve systems of linear
equations in two variables …
•A.REI.10, 11 major
44
Dec. 2, 2013 J.Brendel
Three (3) Significant Shifts in Mathematics:
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
45
• application with equal intensity.
45
COHERENCE
Integrative tasks draw on multiple standards to ensure
students are making important connections.
The Standards are not treated as a checklist.
46
Coherence: Link to Major Topics Across Grades
Gr.6- Apply properties
One of several staircases to
algebra designed in the
OA domain.
•
Gr.5-expressions
Gr.3- multiply … divide
Gr.1- add … subtract
47
47
Coherence: Link to Major Topics Across Grades
One of several staircases to algebra designed in the OA domain.
ALGEBRA-I
ALGEBRA- II
48
48
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
25 5
C. have only 2 diagonals
3
5
D. Area
= ½ base x height
21 7
E. Sum of consecutive angles = 180˚
F. Perimeter
= 2 x Side length
G. Area
> area
with the same perimeter.
49
Coherence: Link to major topics within grades
Example: HIGH SCHOOL performance task; Algebra-I unit 1
A large truck has two fuel tanks, each with a capacity of 150
gallons. One of the tanks is half full, and the other is empty. Fuel is
pumped into the tanks until both tanks are full. The pump delivers
fuel at a constant rate of 5¾ gallons per minute.
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 ….
50
Algebra-I Unit-1
50
Three (3) Significant Shifts in Mathematics:
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
51
• application with equal intensity.
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.
52
Guess the grade level!
See the Rigor in Grade-3
Fractions on a Number Line
* a BIG change *
a move away from
the circular pie to
understanding
fractions on a
number line.
http://www.illustrativemathematics.org/standards/hs
53
See Rigor in Grade 6: Ratios
* a BIG change *
Students will
have online tools
to use that
simulate hands-on
tools
PARCC - Grade-6 Slider
Ruler: type-I
http://www.parcconline.org/
samples/mathematics/grade6-slider-ruler
54
See the Rigor in Middle Grades
Understanding of Fractions
Write a number that is greater than
1
5
and less than
Hint: Find equivalent fractions for
denominators of 40 or 100.
1
5
and
1
4
1
4
with
Why wasn’t it helpful to use 20 as a denominator? (JB)
55
See the Rigor – High School
Part A
56
Part B
Describe
Write
Compare
57
Required Fluencies in K-6
Grade
Standard
K
K.OA.5
Add/subtract within 5
1
1.OA.6
Add/subtract within 10
2.OA.2
Add/subtract within 20 (know single-digit sums from memory)
2.NBT.5
Add/subtract within 100
Multiply/divide within 100 (know single-digit products from
memory)
2
3
58
3.OA.7
3.NBT.2
Required Fluency
Add/subtract within 1000
4
4.NBT.4
Add/subtract within 1,000,000
5
5.NBT.5
Multi-digit multiplication
6
6.NS.2,3
Multi-digit division
Multi-digit decimal operations
58
Application
• Students can use appropriate concepts and procedures for
application even when not prompted to do so..
•
Teachers provide opportunities at all grade levels for students
to apply math concepts in “real world” situations, recognizing
this means different things in K-5, 6-8, and HS.
•
Teachers in content areas outside of math, particularly science,
ensure that students are using grade-level-appropriate math to
make meaning of and access science content.
59
59
Application
• Students can use appropriate concepts and procedures for
application even when not prompted to do so..
•
Teachers provide opportunities at all grade levels for students
to apply math concepts in “real world” situations, recognizing
this means different things in K-5, 6-8, and HS.
•
Teachers in content areas outside of math, particularly science,
ensure that students are using grade-level-appropriate math to
make meaning of and access science content.
60
60
See what online looks like!
Real world application – Grade ?
61
Real world application – Grade 4
62
MORE THAN one choice
See what online looks like!
Linking to major topics – Grade 7 (page-26-27)
63
Part
B
64
See what online looks like!
HS Teachers outside of math
use grade-level-appropriate math
65
Part B
66
Part C
67
Part D
68
Activity No. 3: Shifts Happen - Mathematics
What is this
shift?
Why this shift?
Opportunities
Focus: Focus strongly
where the Standards focus.
Coherence: Think across
grades, and link to major
topics within grades.
69
Rigor: In major topics,
pursue conceptual
understanding, procedural
skill and fluency, and
application with equal
intensity.
Handout page-25
Challenges
What do you mean 3 TYPES of
TASKS?
No, not differently formatted
No, not different levels-of-difficulty
70
TASK TYPES – PARCC
(x – 2)2 + 6 = 75 solve for c: (x + c)/z = 2c(w-y)
Explain how you can use the graphs to find
solutions. Estimate ….
Compare the 3 sets of data (graph, chart, and
equation) and defend the argument that ….
71
Let’s take a quick break!
72
TASK TYPES – PARCC
I – Computation, Skills, Process
(x – 2)2 + 6 = 75 solve for c: (x + c)/z = 2c(w-y)
II – Mathematical Reasoning
Explain how you can use the graphs to find
solutions. Estimate ….
III – Modeling, Combined Standards, Applications
Compare the 3 sets of data (graph, chart, and
equation) and defend the argument that ….
73
TASK TYPE-I
Tasks assess concepts, skills and procedures.
-include a balance of conceptual understanding, fluency, and
application. These tasks can involve any or all mathematical practice
standards.
-will be machine scorable and will include innovative, computerbased formats.
-will appear on the Performance Based and End-of-Year
Assessments
74
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.
75
December 2, 2013
TYPE III:
Tasks assessing modeling/applications.
(3 or 6 point questions)
- tasks call for modeling/application in a real-world context or
scenario (MP.4) and can also involve other mathematical practice
standards.
- tasks may include a mix of innovative, machine scored and hand
scored responses.
- tasks will be included on the Performance Based Assessment
component and generate evidence for measuring mathematical
modeling/application with connections to content.
76
December 2, 2013
TYPE-I PARCC TASKS
Tasks assess concepts, skills and procedures.
All are machine score-able.
77
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)
78
Functions http://www.parcconline.org/samples/mathematics/high-schoolfunctions
(first page of Type-I Task package; see graph and table)
Given f(x) as a graphed parabola and g(x) as table of values
1. Compare y-intercepts
1. Compare f(3) and g(3)
DIFFICULTY?
1. Compare maximum values of each w/in range -5 ≤ x ≤ 5
1. Compare
f (5)- f (2)
g(5)- g(2)
and
5- 2
5- 2
STANDARDS?
A Type-I PARCC task
79
J. Brendel 12.3.2013
Seeing Structure in a Quadratic Equations
http://www.parcconline.org/samples/mathematics/high-school-seeingstructure-quadratic-equation
(second page in Type-I packet)
(3x - 2)2 = 6x – 4
STANDARDS?
80
J. Brendel 12.3.2013
a Type-I PARCC task
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
STANDARDS?
81
J. Brendel 12.3.2013
a Type I PARCC task
PICTURE FRAME
http://www.parcconline.org/sites/parcc/files/HS-Alg1Math2PictureFrame.pdf
(See pages 4-6 of Type-I packet; see Details for Teacher
width
X in.
X + 2 in.
length
STANDARDS?
82
J. Brendel 12.3.2013
a Type I PARCC task
GREEN TEA TYPE
http://www.parcconline.org/sites/parcc/files/PARCC_SampleItems_Mathematics_HS
AlgIIMathIIIGreenTeaStudy_081913_Final_0.pdf
STANDARDS?
a Type I PARCC task
83
J. Brendel 12.3.2013
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.
84
Mathematics online Sample Item/Prototypes:
PARCC TYPE-II TASKS (4 point questions)
• HS – Graphs of Functions (Algebra-II/Math III) Nov. 2013
HS.C.6.2, A.REI.D, MP.3, 7 with 4-point scoring rubric
http://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_HSAlgIMathIIMichelle
Conjecture_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
85
Dec. 2, 2013
GRAPH of FUNCTIONS
(posted November 2013)
(See first 3 pages of Type-II packet
See two-page details for teacher)
http://www.parcconline.org/sites/parcc/files/HighSchoolAlg2Math3GraphsofFunctions.pdf
STANDARDS?
86
a Type-II PARCC Task
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_HS
GeoMathIIIGeometricConnection_081913_Final_0.pdf
STANDARDS?
87
a Type-II PARCC Task
MICHELLE’S CONJECTURES
(Aug.19, 2013)
(See last 3-pages in Type-II packet; see details for teacher)
http://www.parcconline.org/sites/parcc/files/PARCC_SampleItems_Mathematics_HSAlgIMat
hIIMichelleConjecture_081913_Final_0.pdf
Investigate the effect on the vertex of the graph
f(x) = x2 + 6 when f(x) is replaced by f(x + k)
POINTS ?
88
a Type-II PARCC Task
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.
89
MINI GOLF PRICES
(November, 2013)
(See first four pages in Type-III packet)
http://www.parcconline.org/sites/parcc/files/HSAlg1Math2MiniGolfPrices.pdf
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 …
STANDARDS?
90
a Type-III PARCC Task
BRETT’S RACE
(November, 2013)
(See pages 5-8 in Type-III packet)
http://www.parcconline.org/sites/parcc/files/BRHSSampleItem.pdf
Part A: … write an equation for each person that ….
Part B: Based on your equation … who will win ... ?
Justify your answer.
STANDARDS?
91
a Type-III PARCC Task
POPCORN INVENTORY
(NOVEMBER 2013)
http://www.parcconline.org/sites/parcc/files/HSAlg1Math1
PopcornInventory.pdf
Read scenario, understand table, read additional facts
…
Estimate the amount of popcorn …
Show or explain the reasoning you used to determine
your estimate.
POINTS ?
92
a Type-III PARCC Task
TEMPERATURE CHANGES
(See last 4 pages in Type-II packet)
http://www.parcconline.org/sites/parcc/files/PARCC_SampleItems_M
athematics_HSAlgIIMathIIITemperatureChange_081913_Final_0.pdf
Part A: Which model is linear?
Which model is best for the range … ?
Explain why the other model …
Part B: Construct a function ….
POINTS ?
93
a Type-III PARCC Task
Task
Type
1
1
1
PARCC PROTOTYPE SAMPLE TASKS
As of 12/5/2013
Algebra-I/Math I
Geometry/Math II
Algebra-II / Math III
Seeing Structure in
Equations
(1 point)
Picture Frame
(2 points)
Myla’s Swimming Pool
(2 points)
2
Michele’s Conjectures
3
Popcorn Inventory
(6 points)
3
Brett’s Race
(3 points)
Golf Prices
(6 points)
3
94
Seeing Structure in
Functions
Quadratic Equation
(1 point)
Green Tea
(2 points)
Geometry
Construction
(3 points)
Graph function
(4 points)
Temperature
Changes
(3 points)
Help Students
and Teachers
Prepare for the Change
95
READING CCSS and Mathematics
96
Regular Practice with Complex Text and
its Academic Language
97
Not Text-Dependent in ELA
•In “Casey at the Bat,” Casey strikes out.
Describe a time when you failed at
something.
•In “Letter from a Birmingham Jail,” Dr.
King discusses nonviolent protest.
Discuss, in writing, a time when you
wanted to fight against something that
you felt was unfair.
•In “The Gettysburg Address” Lincoln
says the nation is dedicated to the
proposition that all men are created
equal. Why is equality an important
98value to promote?
98
Text-Dependent in ELA
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?
Text-Dependent in mathematics
TOSHIE’S SISTER CHIE
6)
· Circle the floors in the building
Chie is learning about odd and
that have laundry rooms.
even numbers in school. Help
her do the two problems in
1 2 3 4 5 6 7 8 9
example 6).
Remember, the laundry rooms
are on floors with even
numbers.
The parking garages are on
floors with odd numbers.
99
December 2, 2013 author: J. Brendel Material not to be duplicated.
10
·
11
12
13
14
15
16
Circle the floors in the building
that have parking garages.
1
10
2
11
3
4
5
6
12
13
14
7
8
15
9
16
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, ….
100
Geometry
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, …
101
New to Pre-Algebra, Algebra I or II
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.
•
•
•
•
•
102
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
Adjusting Math Language to the CCSS
• Old habit to eliminate: Defining equality as “same as.” The
problem: This is mathematically incorrect and leads to
misconceptions. (2)(2) is equivalent to √16
New habit to adopt: Defining equality as “same value as.”
• Old habit to eliminate: “Addition makes things get bigger.”
The problem: When negative numbers are introduced, the old habit
has to be debugged. (-4) + (-5)
New habit to adopt: Addition is about combining.
• Old habit to eliminate: “Subtraction makes things get smaller.”
The problem: As with addition, negative numbers make this wrong.
New habit to adopt: Subtraction is about difference. (-4) - (-8)
103
Regular Practice With Complex Text and its
Academic Language: Why?
104
•
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.
What are the Features of Complex Text?
105
•
•
•
•
•
Subtle and/or frequent transitions
•
Complex sentences
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
What are the Features of Complex Text? (cont.)
106
•
•
Uncommon vocabulary
•
•
Longer paragraphs
Lack of words, sentences or paragraphs that review
or pull things together for the student
Any text structure which is less narrative and/or
mixes structures
What you SHOULD NOT see !
109
y
m = y1 - y
6-2 4
= =
x1 - x2 3- 3 0
(3,6)
N
Z
0
slope =
4
110
Slope =
(3,2)
>
4
0
x
<
The Mathematics Common Core Toolbox
K. I. S. S.
Mathematics Sample Item/Prototypes:
PARCC online at the Dana Center
•Grade 4 (Deer in the Park) p. 23
CHANGE PROCESS
•Grade 6 (Gasoline Consumption)
•High School (Isabella’s Credit Card) *p. 24-25)
Keep content SIMPLE
•High School (Popcorn Inventory) new Nov. 2013
http://www.parcconline.org/sites/parcc/files HSAlg1Math1PopcornInventory.pdf
111
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
112
Sample Online Performance Tasks
Mathematics Sample online Item/Prototypes:
Smarter Balanced: link on next slide
•Grade 3 - Lemonade Sale
•Grade 4 - Family Trip to the Zoo
•Grade 6 - Cereal Box (vol., surface area, minimum surface area)
•Grade 7 - Food Basket (calories, grams, protein)
•Grade 8 - Heartbeats (scatter plot ….)
•Grade 11- Speeding Ticket (graph, what is fair? ….)
113
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=S
BAC_PT
J.Brendel 11/2013
114
EXPERIENCE ONLINE TASKS
just 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
115
PRACTICE ONLINE w/earlier grade resources
•
•
•
•
•
•
116
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)
SAMPLE ASSESSMENT
examples 1-12
from Smarter Balanced site
separate hardcopy-packet
pages 15-20
and
High School Reference Sheet
page-13
117
December 2, 2013
Activity: BRAINSTORM in GROUPS
How should high school math teaching change
from the traditional teaching?
What non-math type skills are essential?
118
Other Resources
CIRCLES
http://sampleitems.smarterbalanced.org/itempreview/ModernShell.asp
x?config=SBAC%5CContent%5CCircle1.json
MATH II - WALLS
http://sampleitems.smarterbalanced.org/itempreview/ModernShell.asp
x?config=SBAC%5CContent%5CRoomWall.json
J. Brendel 11/2013
119
PARCC RELEASED TASKS include elsewhere?
file://localhost/Users/jbrendel/Desktop/PARCC%20HS%20Functi
ons.html (November/December 2013)
https://www.teachingchannel.org/videos/laws-of-sines-cosineslesson#
14-min lesson “fly quadcopters”
math/science/engineering … a 4-month project … Ms. Brookins
and Mr. James GRADE-11
https://www.teachingchannel.org/videos/statistical-analysis-lesson
Statistical analysis to rank baseball players GRADES 11-12
CCSS Standards: Math SID. 1, 2 and 3
120
The Specs, Accountability,
and Resources:
What We Know Now!
121
FIELD TESTING this SPRING (2014)
>1 million students across PARCC states and Washington DC
>10,000 students / 1,276 schools / 445 districts in NJ
PBA – anytime between March 24 – April 11
EOY – anytime between May 5 – June 6
Results: not individual student or school results
Sample online test available “spring” 2014
Field Test questions: Dr. Jeffrey B. Hauger assessment@doe.state.nj.us
122
Estimated Time on Task: Grade 9-10
Performance Based Assessment
ELA/Literacy
Grade
9-10
Alg I/
Math I
Geo/
Math II
123
Estimated
Time on
Task
(minutes)
Math
Literacy
Analysis
Research
Narrative
80
85
50
Session
1
50
TOTAL
Session
2
50
315
Estimated Time on Task: Grade 9-10
End-of-Year (EOY) Assessment
ELA/Literacy
Grade
9-10
Alg I/ Math I
Geo/ Math II
Estimated
Time on
Task
(minutes)
Session
1
Session
2
70
70
Math
Session
1
65
Grade 9-10 Summative Total:
124
TOTAL
Session
2
65
270
9 Hours, 45 minutes
Estimated Time on Task: Grade 11
Performance Based Assessment
ELA/Literacy
Grade
11
Alg II/
Math III
125
Estimated
Time on
Task
(minutes)
Math
Literacy
Analysis
Research
Narrativ
e
80
85
50
Session
1
65
TOTAL
Session
2
65
345
Estimated Time on Task: Grade 11
End-of-Year (EOY) Assessment
ELA/Literacy
Grade
11
Alg II/
Math III
Estimated
Time on
Task
(minutes)
Session
1
Session
2
70
70
Math
Session
1
55
TOTAL
Session
2
55
250
Grade 11 Summative Total:
126
9 Hours, 55 minutes
HOW will I know what should be ‘learned’
before the PBA? before the EOY? (Activity)
ALGEBRA-I PBA and EOY (2 packets)
GEOMETRY PBA and EOY (2 packets)
ALGEBRA-2 PBA and EOY (2 packets)
ALGEBRA-I PBA vs EOY (packet)
127
What Else…
128
• 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…
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)
129
What Else…
Accessibility Features for ALL students continued
•
•
•
•
•
•
•
•
130
Highlight tool
Headphones
Magnification/Enlargement Device
Notepad
Pop-Up Glossary
Redirect Student to Test (provided by test administrator)
Spell Checker
Writing Tool
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
131
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;
132
•
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).
133
Accountability:
What We Know Now!
134
Results Types…
 Proficiency (PLDs)
 On-Track-to-College and
Career Readiness (CCRDs)
 Growth Data
Performance
Level
Descriptors
Performance Level
(PLDs)
135
Description
Level 5*
Distinguished Command
Level 4*
Strong Command
Level 3
Moderate Command
Level 2
Partial Command
Level 1
Minimal Command
*Achieved CCR Performance Threshold
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.”
136
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.”
137
What does it mean to be CCR? (cont.)
Will be used as a benchmark against which the CCR cut score on
the PARCC assessments will be validated through empirical
research.
• WHY - a “C” is the minimum grade needed to earn credit for a
course
•
WHY - a reasonably high standard but not unattainable.
•
WHY - similar to the criteria used by ACT,
•
WHY - other important CCR skills will not be measured by
PARCC assessments.
138
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.
139
RFP for “Operational Assessment”
Vendor proposals were due by Dec. 11, 2013.
Timelines and Resources:
What We Know Now!
140
140
PARCC Timeline…
•
Jan – Aug 2013
2013-2014
2014-2015
141
•
Release of 2nd set of prototype assessment and instructional tasks
(spring 2013)
Release of online professional learning modules (spring 2013) (update:
expected June 2014)
Item tryouts (spring 2013) – see next slide
•
•
•
•
Full-scale pilot/field testing (spring 2014)
Partnership Resource Center launches (spring 2013)
Optional performance tasks for K-2 available (February 2014)
College readiness tools available (spring 2014)
•
•
•
Diagnostic assessments release (September 2014)
Full operational administration of PARCC assessments (spring 2015)
Setting of achievement levels, including college-ready performance
levels (late spring 2015 (post-administration)
•
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.
142
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)
143
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.
144
www.achievethecore.org
145
Links to Model Math Curriculum Sites
Sample Assessments by grade:
http://www.achievethecore.corg/
Common Core and Special Education Students
http://www.ode.state.or.us/search/page/?id=3741
Common Core Practice Test
https://sbacot.tds.airast.org/student/login.aspz?c=SBAC.PT
http://sbac.portal.airast.org/practice-test/
Common Core Resources to use with students
http://www.illustrativemathematics.org
Dana Center Resources http://www.ccsstoolbox.org/
http://ccsstoolbox.agilemind.com/pdf/DanaCenter_YAG_HS.pdf
146
COMPANIES are developing new programs to assist districts:
ACUITY: a comprehensive K-12 assessment program
Tom Moellering from McGraw Hills as/DA/District Administration
(30 minute video/conversation)
• pre-built assessments (diagnostic) – or item banks to create your
own;
• can be delivered online or in print; scan in software …
• automatically scores and results to teacher quickly
• teacher can see individual/class(es)/school/district results
• teacher can assign specific tasks
• instruction resources in general (including Performance Tasks)
December 2013 J.Brendel
147
COMPANIES are developing new programs to assist districts
as they transition to technology-based assessments:
Pearson’s online Assessment Roadmap 2014
www.Commoncore.pearsoned.com/index.cfm?locator=PS11Uz
Step-1: Conducting a Needs Analysis
Step-2: Developing a Transition Strategy
Step-3: Ensuring Interoperability
Step-4: Communicating Proactively
Step-5: Anticipating Ongoing Change
www.PearsonAssessments.com/NextGenRoadmap
Bryan Bleil (VP, online & tech), Ellen Stain Seymore
148
J. Brendel 11/2013
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]
149
J. Brendel 11/2013
Self-Evaluation, Action Planning
and Next Steps
Roadblocks
Action Planning
Next Steps
150
Let’s take our…
(last page in packet)
PARCC POST-Assessment!
Activity : FAQs POST-Test
151
151
Questions?
Concerns (silly question)?
Discussion/Debrief
152
SINCERE THANKS…
For your participation,
collaboration and dedicated
efforts!!!
Judy
jbrendel@pascack.k12.nj.us
or contact
NJPSA/FEA
153