Download CCSS Math ToT 9

Mississippi Department of Education
Common Core State Standards (CCSS)
and Assessments
Grades 9 - 12
Mathematics
Training of the Trainers
July 2012
PARCC Model Content
Frameworks for High School
Mathematics
2
PARCC Model Content Frameworks for
Mathematics
Purpose:
• To serve as a bridge between the CCSS and the
PARCC Assessments
 The PARCC Assessment will be designed to measure
conceptual understanding, procedural skill, fluency,
application and problem solving
 Questions will measure student learning across
various mathematical domains and practices
• To inform the development of item specifications
and the assessment blueprints
3
PARCC Model Content Frameworks for
Mathematics
High School Standards Analysis Structure:
(June 2012 version)
Coursespecific
Analyses
General
Analysis
Additional
Note on
Modeling
(MP.4)
Appendices
4
PARCC Model Content Frameworks for
Mathematics
Course-specific Analyses:
• Individual End-of-Course Overviews
• Examples of Key Advances from Previous Grades or
Courses
• Discussion of Mathematical Practices in Relation to Course
Content
• Fluency Recommendations
• Pathway Summary Tables (Table 1 and Table 3)
• Assessment Limit Tables (Table 2 and Table 4)
5
PARCC Model Content Frameworks for
Mathematics
General Analysis
• Examples of Opportunities for Connections
among Standards, Clusters, Domains or
Conceptual Categories
• Examples of Opportunities for Connecting
Mathematical Content and Mathematical
Practices
6
PARCC Model Content Frameworks for
Mathematics
(page 46)
Additional Note on Modeling (MP.4):
7
PARCC Model Content Frameworks for
Mathematics
(Appendices)
Appendix A: Lasting Achievements in K-8 (p. 47)
Appendix B: Starting Points for Transition to the CCSS (p. 49)
• Gives special attention to how well current materials address the
suggested starting points.
• Organizes implementation work according to progressions.
Appendix C: Rationale for the Grades 3-8 and High School Content
Emphases by Cluster (p. 51)
Appendix D: Considerations for College and Career Readiness (p. 55)
8
PARCC Model
Content
Frameworks
Common Core
State Standards
for
Mathematics
9
*All page references are from this document unless otherwise noted.
10
Design and Organization of the Common
Core State Standards (CCSS)
for Mathematics
• Introduction
• Standards for Mathematical Content
• Standards for Mathematical Practice
• Glossary
11
Introduction:
Where was American education before
CCSS?
(Refer to CCSS pp 3-4)
Too many
standards
Weak Textbooks
Poorly Aligned
Curriculum
Poor Performance
12
Standards for Mathematical
Content
Grade Level Domains
K–5
•
•
•
•
•
•
Counting and Cardinality
Operations and Algebraic Thinking
Number and Operations in Base Ten
Number and Operations – Fractions
Measurement and Data
Geometry
6–8
•
•
•
•
•
•
Ratios and Proportional Relationships
The Number System
Expressions and Equations
Functions
Geometry
Statistics and Probability
13
Standards for Mathematical
Content
High School Conceptual Categories
•
•
•
•
•
•
N = Number and Quantity
A = Algebra
F = Functions
G = Geometry
S = Statistics and Probability
Modeling
14
High School Conceptual
Categories
 Number and Quantity
• The Real Number System
• Quantities
• The Complex Number System
• Vector and Matrix Quantities
N-RN
N-Q
N-CN
N-VM
 Algebra
• Seeing Structure in Expressions
• Arithmetic with Polynomials & Rational Functions
• Creating Equations
• Reasoning with Equations and Inequalities
A-SSE
A-APR
A-CED
A-REI
15
High School Conceptual
Categories continued
 Functions
 Interpreting Functions
 Building Functions
 Linear, Quadratic, and Exponential Models
 Trigonometric Functions
F-IF
F-BF
F-LE
F-TF
 Geometry
 Congruence
 Similarity, Right Triangles, and Trigonometry
 Circles
 Expressing Geometric Properties with Equations
 Geometric Measurement and Dimension
 Modeling with Geometry
G-CO
G-SRT
G-C
G-GPE
G-GMD
G-MG
16
High School Conceptual
Categories continued
 Statistics and Probability
• Interpreting Categorical & Quantitative Data
• Making Inferences & Justifying Conclusions
• Conditional Probability & the Rules of Probability
• Using Probability to Make Decisions
S-ID
S-IC
S-CP
S-MD
17
High School Conceptual Category:
Modeling
(Refer to CCSS page 72)
18
Directions: Using the Promethean device
on your table, respond to the following
statement:
“There are a total of six domains in the
High School CCSS for Mathematics.”
19
Mississippi Mathematics Framework (MMF)
Content Strands vs. CCSS High School
Conceptual Categories
Numbers
Algebra
Measurement
Geometry
Functions
Modeling
Statistics
and Data
MMF Content Strands
CCSS High School
Conceptual Categories
20
Structure Sample from Grade 3
(Refer to CCSS page 5)
Cluster
Heading
(According to PARCC)
21
Structure Sample from High School
(Refer to CCSS page 71)
Conceptual Category
Trigonometric Functions
Domain
F - TF
Extend the domain of trigonometric functions using the unit circle.
1. Understand radian measure of an angle as the length of
the arc on the unit circle subtended by the angle.
Standard
Plus
Standard
2.
Cluster
Heading
Explain how the unit circle in the coordinate plane enables
the extension of trigonometric functions to all real
numbers, interpreted as radian measures of angles
traversed counterclockwise around the unit
Circle.
3. (+) Use special triangles to determine geometrically the
values of sine, cosine, tangent for π/3, π/4 and π/6, and
use the unit circle to express the values of sine, cosines,
and tangent for x, π+x, and 2π–x in terms of their values
for x, where x is any real number.
4. (+) Use the unit circle to explain symmetry (odd and even)
and periodicity of trigonometric functions.
Cluster
22
Reading the Grade Level
Standards
• Conceptual Categories are larger groups of related domains
that portray a coherent view of high school mathematics.
* Note: Standards from different conceptual categories may sometimes be closely
related.
• Domains are larger groups of related standards.
*Note: Standards from different domains may sometimes be closely related.
• Cluster Heading is indicated in bold and summarizes the
major skills and concepts taught in a group of standards.
• Clusters are groups of related standards.
*Note: Standards from different clusters may sometimes be closely related.
23
Reading the High School
Standards
• Standards define what students should understand and be
able to do.
• Plus Standards represent additional standards that
students should learn in order to take advanced courses.
*Note: These standards will not be tested in Grades 9-11. They will, however, appear in
the 4th year course: Common Core Plus. Courses without a (+) symbol should appear in
the common math curriculum for all students (Algebra I, Algebra II, and Geometry).
24
Referencing the CCSS for
Mathematics
F-BF.2
F-BF.2 - Functions Conceptual Category
F-BF.2 - Building Functions Domain
F-BF.2 - Standard Number
N-CN.5
N-CN.5 - Numbers and Quantity Conceptual Category
N-CN.5 - The Complex Number System Domain
N-CN.5 - Standard Number
25
Referencing the CCSS for
Mathematics
(Refer to CCSS page 71)
What is the reference for the following
standard?
“Interpret the parameters in a linear or
exponential function in terms of a context.”
Answer: ____________
26
Referencing the CCSS for
Mathematics
(Refer to CCSS page 71)
F-LE.5
•
What is the conceptual category?
•
What is the domain?
•
What is the standard number?
•
What is the cluster heading?
Functions
Linear, Quadratic, and Exponential Models (*)
5
Interpret expressions for functions in
terms of the situation they model
27
Referencing the CCSS for
Mathematics
Using F-LE.5,the facilitator will model how to
use the PARCC Model Content Frameworks
for High School Mathematics to inform
implications for instruction.
28
Referencing the CCSS for
Mathematics
Directions:
• Locate F-IF.4 and N-VM.5 in the CCSS and the
PARCC Model Content Frameworks for
Mathematics.
• As a group, briefly discuss the implications for
instruction for both of these standards.
29
Referencing the CCSS for
Mathematics
Facilitator will discuss implications for
instruction for F-IF.4 and N-VM.5
30
Work Session 1
CCSS K-12 Mathematics Progression of
Domains
Directions:
• Locate Work Session 1 Activity Sheet.
• Complete Work Session 1 Activity Sheet
as a group.
31
Work Session 1
continued
The facilitator will select several groups to
report out.
32
Work Session 1
continued
33
Reviewing the CCSS for
Mathematics Glossary
Directions:
• Locate pages 85-90 of the CCSS for
Mathematics.
• Note the following:
List of Terms: (pp 85 – 87)
Table 1: (p. 88)
Table 2: (p. 89)
Tables 3, 4, and 5: (p. 90)
34
A Snapshot of the Glossary
(Refer to List of Terms CCSS page 85)
Glossary
Additive inverses. Two numbers whose sum is 0 are additive inverses of one
another. Example: 3/4 and – 3/4 are additive inverses of one another because
3/4 + (– 3/4) = (– 3/4) + 3/4 = 0.
Associative property of addition. See Table 3 in this Glossary.
Associative property of multiplication. See Table 3 in this Glossary.
Bivariate data. Pairs of linked numerical observations. Example: a list of heights
and weights for each player on a football team.
Box plot. A method of visually displaying a distribution of data values by using
the median, quartiles, and extremes of the data set. A box shows the middle
50% of the data.1
35
A Snapshot of the Glossary
(Refer to Table 1 CCSS page 88)
36
A Snapshot of the Glossary
(Refer to Table 2 CCSS page 89)
37
A Snapshot of the Glossary
(Refer to Table 3 CCSS page 90)
Table 3. The properties of operations. Here a, b and c stand for arbitrary numbers in a given number system. The
properties of operations apply to the rational number system, the real number system, and the complex number system.
Associative property of addition
(a + b) + c = a + (b + c)
Commutative property of addition
a+b=b+a
Additive identity property of 0
a+0=0+a=a
Existence of additive inverses
For every a there exists –a so that a + (–a) = (–a) + a = 0.
Associative property of multiplication
(a × b) × c = a × (b × c)
Commutative property of multiplication
Multiplicative identity property of 1
a×b=b×a
a×1=1×a=a
Existence of multiplicative inverses
For every a ≠ 0 there exists 1/a so that a × 1/a = 1/a × a = 1.
Distributive property of multiplication over addition
a × (b + c) = a × b + a × c
38
Work Session 2: CCSS for
Mathematics “Scavenger Hunt”
Directions:
• Locate Work Session 2 Activity Sheet.
• Knowing where to find information in the
Standards is just as important as knowing
the information itself. Using the CCSS for
Mathematics, work in pairs to find the
answers to the questions.
39
Work Session 2
continued
Facilitator will discuss answers for Work
Session 2.
40
PARCC Model Content Frameworks
for Mathematics
(page 43)
(Work Session 2, item #14)
Examples of Opportunities for
Connections among Standards, Clusters,
Domains or Conceptual Categories:
Connections among Statistics, Functions and
Modeling. Functions may be used to describe
data; if the data suggest a linear relationship, the
relationship can be modeled with a regression line,
and its strength and direction can be expressed
through a correlation coefficient.
41
The Heart of the CCSS for
Mathematics:
Standards for
Mathematical Practice
42
Standards for Mathematical
Practice
(Refer to CCSS pp 6 - 8)
The Standards for Mathematical Practice describe
ways in which developing student practitioners of
the discipline of mathematics increasingly ought to
engage with the subject matter as they grow in
mathematical maturity and expertise throughout
the elementary, middle and high school years.
Designers of curricula, assessments, and
professional development should all attend to the
need to connect the mathematical practices to
mathematical content in mathematics
instruction.
43
Standards for Mathematical
Practice
Provide
connected,
engaging
instruction
Practice with
the content
and mature
mathematically
The Role of
the Teacher
The Role of
the Student
Mathematical
Practices
The Learning
Environment
44
Standards for Mathematical
Practice
Directions:
• Locate CCSS pages 6 – 8.
• Review the eight Standards for Mathematical
Practice.
• As a group, create a list of three words that
capture the essence of each Standard for
Mathematical Practice.
45
Standards for Mathematical
Practice
The facilitator will select several groups to
report out.
46
Standards for Mathematical
Practice
(Refer to CCSS pp. 6 - 8)
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.
47
Standards for Mathematical
Practice
The Standards for Mathematical Practice
should not be used as a checklist nor
should they be used in isolation. Rather,
the Mathematical Practices should be
interwoven into every lesson where they
overlap and interact with each other
constantly.
48
Work Session 3:
Connecting Mathematical Practices to
Instruction
Directions:
• Locate Work Session 3.
• Locate the large “card” on your table.
The number on the front indicates the
Mathematical Practice your group will
discuss.
• Complete Work Session 3 as a group.
49
Work Session 3
continued
The facilitator will select several groups to
report out on their responses to item #3 of
the Work Session Activity.
50
Work Session 3
continued
Directions: Using the Promethean device
on your table, respond to the following
statement:
“When teaching a particular CCSS, one
of the Mathematical Practices may be
more dominant than the others.”
Standard for Mathematical Practices in the classroom:
https://sites.google.com/a/dpi.wi.gov/disciplinary-literacy-in-mathematics/
51
CCSS
Student
Learning
PARCC Model
Content
Frameworks
Mathematical
Practices
52
Unpacking the CCSS for
Mathematics
and Creating
Essential Questions
53
Steps for Unpacking CCSS for
Mathematics
1.
“Study” the standard as a Professional Learning Community (PLC).
2.
Identify prerequisite skills.
3.
Identify the key terms and verbs directly (or indirectly) stated within
the standard.
4.
Give a definition for each term and verb.
5.
Provide “student-friendly language” for each term and verb.
6.
Create a series of “I can” statements in “student friendly language”.
7.
Create a series of Essential Questions.
54
What is an
Essential Question?
•
An Essential Question is a Question that:
Causes genuine and relevant inquiry into the big ideas and core
content.
•
Provokes deep thought, lively discussion, sustained inquiry, and new
understanding.
•
Requires students to consider alternatives, weigh evidence, support
their ideas, and justify their answers.
•
Sparks meaningful connections with prior learning and personal
experiences.
•
Creates opportunities for transfer to other situations and disciplines.
55
Why Do We Need Essential
Questions?
• Guides instruction for the teacher and the students.
• Assists students in seeing the relevancy of a topic of study.
• Serves as a framework to provide and sustain student
interest.
• Fosters a literacy and vocabulary-rich environment.
• Links to other essential questions and topics.
• Ensures utility of the Standards for Mathematical Practice.
56
Constructing Essential
Questions
1.
“Study” the standard in your PLC.
--Examine your teaching objectives and goals within the
standard.
--Identify the key words.
--Tie to prerequisite skills.
--Ask yourself “why” is this question important?
2.
Possibly write the standard as a question or a series of smaller
questions.
3.
Think:
concept → skill → application → understanding
57
Work Session 4:
Unpacking Sample for CCSS G-SRT.2
Directions:
• Locate Work Session 4 “Unpacking Sample
for G-SRT.2.”
• Facilitator will discuss the Unpacking Sample.
58
Work Session 4 Activity 4a:
Unpacking CCSS for High School and
Creating Essential Questions
Directions:
• Locate Work Session Activity Sheet 4a.
• As a group, complete Activity Sheet 4a for
one of the standards listed below.
A-SSE.2
F-TF.3
F-TF.5
G-GPE.1
59
Work Session 4 Activity 4a
continued
Directions:
• Locate the large “card” on your table. The back
of the card indicates which section from Activity
Sheet 4a your group will record on chart paper.
• Upon completion, designate one person to post
your work in the designated area.
• The facilitator will select several groups to report
out.
60
PARCC Model Content Frameworks
for Mathematics
(page 17)
(Work Session 4a, CCSS G-GPE-1)
Examples of Key Advances from Previous
Grades or Courses:
In grade 8, students learned the Pythagorean theorem
and used it to determine distances in a coordinate
system (8.G.6–8). In Geometry, students proved
theorems using coordinates(G-GPE.4–7). In Algebra II,
students will build on their understanding of distance in
coordinate systems and draw on their growing
command of algebra to connect equations and graphs
of conic sections (e.g., G-GPE.1).
61
PARCC Model Content Frameworks
for Mathematics
(page 18)
(Work Session 4a, CCSS A-SSE.2)
Discussion of Mathematical Practices in
Relation to Course Content:
Look for and make use of structure (MP.7). The structure theme
in Algebra I centered on seeing and using the structure of
algebraic expressions. This continues in Algebra II, where
students delve deeper into transforming expressions in ways
that reveal meaning. The example given in the standards — that
x4 – y4 can be seen as the difference of squares — is typical of
this practice. This habit of seeing subexpressions as single
entities will serve students well in areas such as trigonometry,
where, for example, the factorization of x4 – y4 described above
can be used to show that the functions cos4x – sin4x and
cos2x – sin2x are, in fact, equal (A-SSE.2).
62
PARCC Model Content Frameworks
for Mathematics
(page 19)
(Work Session 4a, CCSS A-SSE.2)
Fluency Recommendations:
A-SSE.2
The ability to see structure in expressions
and to use this structure to rewrite
expressions is a key skill in everything
from advanced factoring (e.g., grouping)
to summing series to the rewriting of
rational expressions to examine the end
behavior of the corresponding rational
function.
63
Work Session 4 Activity 4a
continued
Directions: Using the Promethean
device on your table, respond to the
following statement:
“The Unpacking Activity could be used
by students, as well as teachers, prior
to teaching a lesson.”
64
Focusing on a High School
CCSS:
A-REI.11
65
A-REI.11
Explain why the x-coordinates of the points
where the graphs of the equations y = f(x)
and y = g(x) intersect are the solutions of the
equation f(x) = g(x); find the solutions
approximately, e.g., using technology to
graph the functions, make tables of values, or
find successive approximations. Include
cases where f(x) and/or g(x) are linear,
polynomial, rational, absolute value,
exponential, and logarithmic functions. ★
66
Instructional Notes for CCSS
A-REI.11
• This is a “cross-cutting” standard.
• Limits and clarifications:
– Algebra I assessment will not include exponential or logarithmic
functions.
– In Algebra I “finding the solutions approximately” is limited to
cases where f(x) and g(x) are polynomial functions.
• In Algebra I and Algebra II: (
______________________ ).
• Common misconception: When a pair of equations intersect at
more than one point, some students mistakenly use the y-coordinate
of the first point as the other possible solution to their system.
67
Work Session 5 Activity 5a:
Focusing on a High School CCSS
(A-REI.11)
Directions:
• Locate Work Session 5a Activity Sheet.
• As a group, complete Work Session 5a
Activity Sheet.
• View the video.
68
Work Session 5 Activity 5a
continued
(A-REI.11)
Facilitator will discuss answers for Work
Session 5a.
69
Work Session 5 Activity 5b: Instructional
Strategy for CCSS A-REI.11
Directions:
• Locate Work Session 5b Activity Sheet.
• Complete Work Session 5b as a group.
70
Work Session Activity 5b
continued
Directions:
• Each group will post their work from the
bottom of the A-REI.II Template.
• Facilitator will select several groups to
report out on the Activity.
71
Example of Progression in the CCSS
Grade K – High School using A-REI.11
A-REI.11:
Explain why the x-coordinates of the points where the graphs of the equations y = f(x)
and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g.,
using technology to graph the functions, make tables of values, or find successive approximations.
Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and
logarithmic functions.★
8.EE.8a:
Understand that solutions to a system of two linear equations in two variables correspond
to points of intersection of their graphs, because points of intersection satisfy both equations
simultaneously.
5.G.1:
Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the
intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in
the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first
number indicates how far to travel from the origin in the direction of one axis, and the second number
indicates how far to travel in the direction of the second axis, with the convention that the names of the
two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate).
72
Focusing on a High School
CCSS:
G-SRT.2
73
G-SRT.2
Given two figures, use the definition of
similarity in terms of similarity
transformations to decide if they are similar;
explain using similarity transformations the
meaning of similarity for triangles as the
equality of all corresponding pairs of angles
and the proportionality of all corresponding
pairs of sides.
74
Instructional Notes for CCSS
G-SRT.2
• This standard will only be assessed at the end of the Geometry
course.
• In Geometry: (
________________________________ ).
• Allow adequate time for hands-on activities to explore dilations
visually and physically.
• Common misconceptions: 1) some students do not recognize that
congruence is a special case of similarity; and, 2) some students do
not list the vertices of similar triangles in order.
75
PARCC Model Content Frameworks
for Mathematics
(page 13)
Examples of Key Advances from
Previous Grades or Courses:
Because concepts such as rotation, reflection and
translation were treated in the Grade 8 standards
mostly in the context of hands-on activities, and
with an emphasis on geometric intuition, high
school Geometry will put equal weight on precise
definitions.
76
Work Session 6 Activity 6a:
Focusing on a High School CCSS
(G-SRT. 2)
Directions:
• Locate Work Session 6a Activity Sheet.
• As a group, complete Work Session 6a
Activity Sheet.
• View the video.
77
Work Session 6 Activity 6a
continued
(G-SRT.2)
Facilitator will discuss answers for Work
Session 6a.
78
Work Session 6 Activity 6b:
Instructional Strategy for CCSS G-SRT.2
Directions:
• Locate Work Session 6b Activity Sheet.
• Complete Work Session 6b as a group.
• Upon completion, the facilitator will select
several groups to report out on the
Activity.
79
Work Session 6b
continued
Directions: Using the Promethean device
on your table, respond to the following
statement:
“This standard (G-SRT.2) is eligible for
assessment on two or more end-ofcourse assessments.”
80
Focusing on a High School
CCSS:
F-BF.1a
81
F-BF.1a
1. Write a function that describes a
relationship between two quantities.
a. Determine an explicit
expression, a recursive
process, or steps for
calculation from a context.
82
Instructional Notes for CCSS
F-BF.1a
• This is a “cross-cutting” standard.
• In Algebra I: (
__________________________________ ).
• In Algebra II: (
_________________________________ ).
• Focus on one representation and its related language—recursive or
explicit—at a time so that students do not confuse the formats.
• Common misconceptions: 1) Students may believe that the best (or only)
way to generalize a table of data is by using a recursive formula; and,
2) students may only “look down” a table to determine the pattern.
83
Work Session 7 Activity 7a:
Focusing on a High School CCSS
(F-BF.1a)
Directions:
• Locate Work Session 7a Activity Sheet.
• As a group, complete Work Session 7a
Activity Sheet.
• View the video.
84
Work Session 7 Activity 7a
continued
(F-BF.1a)
Facilitator will discuss answers for Work
Session 7a.
85
Work Session 7 Activity 7b:
Instructional Strategy for CCSS F-BF.1a
Directions:
• Locate Work Session 7b Activity Sheet.
• Complete Work Session 7b as a group.
86
Work Session 7 Activity 7b
continued
Directions:
• Designate one person to show your work
for items # 8 and #9 on chart paper and
post it.
• The facilitator will select several groups to
report out.
87
Work Session 7 Activity 7b
continued
Facilitator will discuss answers for Work
Session 7b.
88
PARCC Model Content Frameworks
for Mathematics
(page 45)
(Work Session 7b, item #2)
Examples of Opportunities for
Connecting Mathematical Content and
Mathematical Practices:
Students might use spreadsheets or similar
technology in modeling situations to compute and
display recursively defined functions (e.g., a
function that gives the balance Bn on a credit card
after n months given the interest rate, starting
balance and regular monthly payment) (F-BF.1a; F-LE).
.
89
Work Session 7 Activity 7b
continued
Directions: Using the Promethean device
on your table, respond to the following
statement:
“For this standard (F-BF.1a), assessment
tasks on the Algebra I end-of-course
assessment will be limited to domains
in the set of integers.”
90
Conclusion:
Impact of CCSS for
Mathematics on Instruction
at the Local Level
91
Guidance Regarding the Use of
Resources in Mathematics
School districts should consider the following when reviewing existing
resources or developing materials:
Materials should:
•
•
•
•
•
•
Align to the CCSS
Foster the Standards for Mathematical Practice
Connect the CCSS and Mathematical Practices
Be mathematically correct
Motivate students
Demand conceptual understanding, procedural skill and fluency, and
application
• Provide strategies for helping students who have special needs
(students with disabilities, English language learners, and gifted
students)
• Provide strategies for integrating literacy
Note: Refer to PARCC Model Content Framework Grades K – 8 (pp 8 – 10) October 2011
92
Note: Notice that coverage is not in the
aforementioned list. Materials that are
excellent but narrow in scope still have
value; they can be combined with other like
resources and supplemented as needed.
Don’t settle for a single mediocre resource
that claims to cover all content.
93
Considerations and Decisions
Think-Pair-Share
Directions:
• Locate one person from a different
district/school and respond to each of the five
questions on the next slide.
• The facilitator will select several participants to
report out.
94
Considerations and Decisions
• What strategies must be introduced into classroom
instruction?
• What must happen to encourage conceptual understanding
with skills and fluency?
• How will you (administrator or teacher) have to change?
• How will you support instruction that must change to meet
what is required of students by Common Core assessments?
• How will your everyday decisions be affected by adjustments
that will be considered for the positive effects they will have
on student learning?
95
• Intentional
Planning
• Scope and Sequence/Pace
• Collaborative
• Student Centered
Instruction
• Literacy and Vocabulary Rich
• Engaging
96
Reflections
97
Reflections
Directions:
• Locate the Graphic Organizer Puzzle
Shapes document.
• Using the “KEY” on the next slide, select
three shapes that indicate your comfort
level with the High School Common Core
State Standards for Mathematics.
98
Reflections
continued
“Graphic Organizer Puzzle Shapes Key”
Related to CCSS
•
•
•
•
•
•
•
•
•
•
•
•
Lightening Bolt:
Light Bulb:
Quotation Mark:
Heart:
Question Mark:
Diamond:
Double arrow:
Rectangle:
Square:
Circle:
Arrow
Oval
“Something that struck you or something that you are charged –up about”
“Something that enlightened you or an “aha” moment”
“A quote or statement that you remember someone saying”
“Something you fell in love with”
“A question that you still have”
“Identify something that you learned that is very valuable to you”
“Something that you are still going back and forth about”
“Draw the ideal classroom set-up for implementing the CCSS”
“Identify four things that are ‘square’ with you.”
“List 2 things that are still ‘circling around ‘in your head”
“Identify one area that you are ready to ‘go forward’ with”
“Oh my!”
99
Reflections
continued
The facilitator will select several participants
to report out.
100
Directions: Using the Promethean device
on your table, respond to the following
statement:
“The Graphic Organizer Puzzle Shapes
can be used by students as a formal or
informal assessment.”
101
“Planning is bringing the future
into the present so that you can
do something about it now.”
Alan Lakein
102
Websites and Contact
Information
Common Core Website
www.corestandards.org
MDE website
PARCC Website
www.mde.k12.ms.us
www.PARCConline.org
Office of Curriculum and Instruction
[email protected]
(dedicated email address)
Marla D. Davis
Office Director II, Mathematics
[email protected]
(601) 359-2586
103