Download Begin with the End in Mind: Common Core State Standards

Begin with the End in Mind:
Common Core State Standards
and Next Generation Assessments
Susan A Gendron
Senior Fellow
International Center for Leadership in Education
July 2011
What will our Students need to:
Know
 Do

EXTERNAL DRIVERS
• Education Trends
• Changing
Society/Workplace
• Technology
• Global Competition
Of Walmart’s 6,000
suppliers, 5,000 are in China
Source: National Academy of Science
Global Economics
• Software written in India . . .
• MRI’s read moments later by
radiologist in Australia
• Pilots in U.S. guide unmanned
aircraft in Afghanistan
Source: National Academy of Science
U.S. now ranks 22nd worldwide
in the density of broadband
Internet penetration
and
72nd . . . density of mobile
telephone subscriptions
Source: National Academy of Science
GE has now located the
majority of its R & D
personnel outside the U.S.
Source: National Academy of Science
In a survey of global firms
planning to build new R & D
facilities, 77% say they will
build in China or India
Source: National Academy of Science
EXTERNAL DRIVERS
• Education Trends
• Changing
Society/Workplace
• Technology
• Global Competition
Economic Growth
• Innovation
• Entrepreneurship
Source: National Academy of Science
EXTERNAL DRIVERS
• Education Trends
• Changing
Society/Workplace
• Technology
• Global Competition
• Economic Trends
• Focus on Math and Science
The great majority of newly
created jobs are the indirect
or direct result of
advancements in science
and technology
Source: National Academy of Science
The World Economic Forum
ranks the U.S. 48th in quality
of mathematics and science
education
Source: National Academy of Science
The U.S. ranks 27th among
developed nations in the
proportion of college students
receiving undergraduate
degrees in science or
engineering
Source: National Academy of Science
Arkansas Workforce
Between 2008 and 2018, new jobs in
Arkansas requiring postsecondary
education and training will grow by 86,000
while jobs for high school graduates and
dropouts will grow by 63,000.
Arkansas Workforce
• Between 2008 and 2018;
419,000 job vacancies
217,000 - postsecondary
credentials
150,000 for high school
graduates
52,000 for high school dropouts.
Arkansas Workforce
Arkansas Workforce 2018
By 2018, 52% (750,000 jobs) of jobs in
Arkansas will require postsecondary
education. This is 11 percentage points
below the national average of 63%.
Arkansas ranks 49th in postsecondary
education intensity for 2018.
Arkansas Workforce 2018
•
•
•
•
•
•
•
•
Management and Professional Office (126,000
STEM (52,000)
Community Service (35,000)
Healthcare (126,000)
Education (90,000)
Food and Personal Services (116,000)
Sales (151,000)
Office administration (206,000)
Arkansas Workforce 2018
• Blue collar jobs
– Farming (16,000)
– Construction (70,000)
– Installation (62,000)
– Production (146,000)
– Transportation (120,000)
1
Shanghai-China
556
2
Korea
539
3
Finland
536
4
Hong Kong-China
533
5
Singapore
526
6
Canada
524
7
New Zealand
521
8
Japan
520
9
Australia
515
10
Netherlands
508
17
United States
500
20
Germany
497
21
Ireland
496
22
France
496
25
United Kingdom
494
33
Spain
481
43
Russian Federation
459
48
Mexico
425
53
Brazil
412
57
Indonesia
402
PISA
2009
Overall
Reading
Scale
Significantly
Above OECD
Average
Not
Significantly
Different
(OECD
Average 493)
Significantly
below OECD
Average
1
Shanghai-China
600
2
Singapore
562
3
Hong Kong-China
555
4
Korea
546
6
Finland
541
9
Japan
529
10
Canada
527
11
Netherlands
526
13
New Zealand
519
15
Australia
514
16
Germany
513
22
France
497
28
United Kingdom
492
31
United States
487
32
Ireland
487
34
Spain
483
38
Russian Federation
468
51
Mexico
419
57
Brazil
386
61
Indonesia
371
PISA
2009
Overall
Math
Scale
Significantly
Above OECD
Average
Not
Significantly
Different
(OECD
Average 496)
Significantly
below OECD
Average
1
Shanghai-China
575
2
Finland
554
3
Hong Kong-China
549
4
Singapore
542
5
Japan
539
6
Korea
538
7
New Zealand
532
8
Canada
529
10
Australia
527
11
Netherlands
522
13
Germany
520
16
United Kingdom
514
20
Ireland
508
23
United States
502
27
France
498
36
Spain
488
39
Russian Federation
478
50
Mexico
416
53
Brazil
405
60
Indonesia
383
PISA
2009
Overall
Science
Scale
Significantly
Above OECD
Average
Not
Significantly
Different
(OECD
Average 501)
Significantly
below OECD
Average
Skills Gap
Why – What - How
Rigor/Relevance
For
All Students
Knowledge Taxonomy
1.
2.
3.
4.
5.
6.
Awareness
Comprehension
Application
Analysis
Synthesis
Evaluation
Application Model
1.
2.
3.
4.
Knowledge in one discipline
Application within discipline
Application across disciplines
Application to real-world
predictable situations
5. Application to real-world
unpredictable situations
Levels
Bloom’s
6
5
4
3
2
1
C
D
A
B
1
2 3 4 5
Application
Students gather and store bits of knowledge/information and are
expected to remember or understand this acquired knowledge.
Application
3
A
Comprehension
Awareness
2
Acquisition
1
Low-level Knowledge
1
2
Knowledge
in one
discipline
Apply
knowledge
in one
discipline
A Quadrant
Verbs
•
•
•
•
•
•
•
•
•
•
name
label
define
select
identify
list
memorize
recite
locate
record
•
•
•
•
•
•
•
•
•
Products
definition
worksheet
list
quiz
test
workbook
true-false
reproduction
recitation
Students use acquired knowledge to solve problems,
design solutions, and complete work.
Application
3
B
Comprehension
Awareness
2
Application
1
Low-level Application
3
4
5
Apply
knowledge
across
disciplines
Apply to
real-world
predictable
situation
Apply to
real-world
unpredictable
situation
B Quadrant
Verbs
•
•
•
•
•
•
•
•
•
•
apply
sequence
demonstrate
interview
construct
solve
calculate
dramatize
interpret
illustrate
Products
•
•
•
•
•
•
•
•
•
scrapbook
summary
interpretation
collection
annotation
explanation
solution
demonstration
outline
Students extend and refine their knowledge so that they can use it
automatically and routinely to analyze and solve problems and create
solutions.
Evaluation
6
Synthesis
5
Analysis
4
Application
3
C
Assimilation
High-level Knowledge
1
2
Knowledge
in one
discipline
Apply
knowledge
in one
discipline
C Quadrant
Verbs
•
•
•
•
•
•
•
•
•
•
•
sequence
annotate
examine
report
criticize
paraphrase
calculate
expand
summarize
classify
diagram
Products
essay
abstract
blueprint
inventory
report
plan
chart
questionnaire
classification
diagram
discussion
collection
annotation
Students think in complex ways and apply acquired knowledge and
skills, even when confronted with perplexing unknowns, to find
creative solutions and take action that further develops their skills and
knowledge.
Evaluation
6
D
Synthesis
5
Adaptation
Analysis
Application
4
High-level Application
3
3
4
5
Apply
Apply to
Apply to
knowledge real-world
real-world
across predictable unpredictable
disciplines situation
situation
D Quadrant
Verbs
•
•
•
•
•
•
•
•
•
•
evaluate
validate
justify
rate
referee
infer
rank
dramatize
argue
conclude
Products
•
•
•
•
•
•
•
•
•
•
•
•
•
•
evaluation
newspaper
estimation
trial
editorial
radio program
play
collage
machine
adaptation
poem
debate
new game
invention
Current
Assessments
Next Generation
Assessments
Bloom’s
6
5
4
3
2
1
C
D
A
B
1 2 3 4 5
Application
Now
State
Standards
State
Tests
A
State
Standards
State
Tests
A
Standards Charge
Common Core Standards Criteria
•
•
•
•
•
•
•
Rigorous
Clear and specific
Teachable and learnable
Measurable
Coherent
Grade by grade standards
Internationally benchmarked
• Individually complete the Characteristics
of Standards and Alignment Checklists
• Compare your choices with team
• Underline items rated Pervasive or
Considerable
• Circle items rated Initiated or Absent
• Come to consensus on item (s) of
concern
Common Core State Standards
Fewer, Clearer, Higher
Lexile Framework® for Reading Study
Summary of Text Lexile Measures
Interquartile Ranges Shown (25% - 75%)
Text Lexile Measure (L)
1600
1400
1200
1000
800
600
High
School
Literature
College
Literature
* Source of National Test Data: MetaMetrics
College
High
School Textbooks
Textbooks
Military
Personal Entry-Level
Use
Occupations
SAT 1,
ACT,
AP*
MetaMetrics Survey 2000
Arkansas Democrat Gazette
1230 L
Associated Press
1310 L
LA Times
1330 L
Miami Herald
New York Post
Oakland Tribune
Raleigh News & Observer
Wall Street Journal
USA Today
1200 L
1280 L
1210 L
1220 L
1320 L
1200 L
What is Proficiency?
Proficiency
Grade 4 Reading
NAEP
Proficient
New York
Florida
Arkansas
Louisiana
Tennessee
Massachusetts
Mississippi
NAEP Average
State Score
36 %
36 %
29%
18 %
28 %
47 %
224
226
216
207
217
234
22 %
211
Proficiency
Grade 8 Reading
NAEP
Proficient
New York
Florida
Arkansas
Louisiana
Tennessee
Massachusetts
Mississippi
NAEP Average
State Score
33 %
32 %
27 %
20 %
28 %
43 %
264
264
258
253
261
274
19 %
251
Proficiency
Grade 4 Mathematics
NAEP
Proficient
New York
Florida
Arkansas
Louisiana
Tennessee
Massachusetts
Mississippi
NAEP Average
State Score
40 %
40 %
36 %
23 %
28 %
57 %
241
242
238
229
232
252
22 %
227
Proficiency
Grade 8 Mathematics
NAEP
Proficient
New York
Florida
Arkansas
Louisiana
Tennessee
Massachusetts
Mississippi
NAEP Average
State Score
34 %
29 %
27 %
20 %
25 %
52 %
283
279
276
272
275
299
15 %
265
16 Career Clusters
Department of Education
Agriculture and Natural Resources
Arts, Audiovisual Technology, and
Communications
Business and Administration
Architecture and Construction
Education and Training
Finance
Health Science
Hospitality and Tourism
Human Services
Information Technology
Law and Public Safety
Manufacturing
Government and Public Administration
Retail, Wholesale, and Service
Scientific Research and Engineering
Transportation, Distribution, and Logistics
Reading Requirements
Findings

Entry-level



Highest in 6/16
Second Highest in 7/16
Consistent Across
Country
Advanced
Lexile Reading Level Range: 850-930
Intermediate
Lexile Reading Level Range: 940-1090
Entry Level
Human Services
Lexile Reading Level Range: 1000-1140
Advanced
Lexile Reading Level Range: 1310-1390
Intermediate
Lexile Reading Level Range: 1250-1340
Entry Level
Construction
Lexile Reading Level Range: 1310-1350
Advanced
Lexile Reading Level Range: 1310-1440
Intermediate
Lexile Reading Level Range: 1280-1310
Entry Level
Manufacturing
Lexile Reading Level Range: 1280-1330
Lexile
1,500
1,400
1,300
1,200
1,100
1,000
900
800
On-the Job
Lexile Requirements
National Adult Literacy Study 1992
International Center for Leadership in Education 2009
College and Career Readiness Defined
• Cognitive strategies: Intellectual openness; inquisitiveness;
analysis; interpretation; precision and accuracy; problem solving;
and reasoning, argumentation, and proof.
• Content knowledge: Understanding the structures and large
organizing concepts of the academic disciplines, resting upon
strong research and writing abilities.
• Academic behaviors: Self-management, time management,
strategic study skills, accurate perceptions of one’s true
performance, persistence, ability to utilize study groups, selfawareness, self-control, and intentionality.
• Contextual skills and knowledge: Facility with application and
financial-aid processes and the ability to acculturate to college.
David Conley
STANDARDS FOR
ENGLISH LANGUAGE ARTS
&
LITERACY IN HISTORY/SOCIAL STUDIES,
SCIENCE, AND TECHNICAL SUBJECTS
JUNE 2010
http://www.corestandards.org
Design and Organization
Three main sections
K-5 (cross-disciplinary)
6-12 English Language Arts
6-12 Literacy in History/Social Studies,
Science, and Technical Subjects
Design and Organization
Three appendices
A: Research and evidence; glossary of key
terms
B: Reading text exemplars; sample
performance tasks
C: Annotated student writing samples
Design and Organization
Shared responsibilities for
students’ literacy development
Design and Organization
Focus on results rather than
means
Design and Organization
Media skills blended
throughout
Design and Organization
Four strands:
– Reading (including Reading
Foundational Skills)
– Writing
– Speaking and Listening
– Language
Reading Design and
Organization
Three sections:
1. Literature
2. Informational Text
3. Foundational Skills (K-5)
Literary/Informational Text
Literature
Literature
Literature
Informational
Text
Stories
Drama
Poetry
Literary
Nonfiction and
Historical,
Scientific, and
Technical Texts
Includes children’s
adventure stories,
folktales, legends,
fables, fantasy, realistic
fiction, and myth
Includes staged
dialogue and brief
familiar scenes
Includes nursery
rhymes and the
subgenres of the
narrative poem,
limerick, and free verse
poem
Includes biographies
and autobiographies;
books about history,
social studies, science,
and the arts; technical
texts, including
directions, forms, and
information displayed in
graphs, charts, or
maps; and digital
sources on a range of
topics
Design and Organization
K−12 standards
• Grade-specific end-of-year
expectations
• Developmentally appropriate,
cumulative progression of skills
and understandings
• One-to-one correspondence with
CCR standards
College and Career Readiness
Standards for Reading
Correspond to the College and Career
Readiness anchor stand organized in
four key areas:
1. Key Ideas and Details
2. Craft and Structure
3. Integration of Knowledge and
Ideas
4. Range of reading and Level of
Text Complexity
College and Career Readiness
Standards for Reading
Key Ideas and Details
1. Read closely to determine what the text says explicitly
and to make logical inferences from it; cite specific
textual evidence when writing or speaking to support
conclusions drawn from the text.
2. Determine central ideas or themes of a text and
analyze their development; summarize the key
supporting details and ideas.
3. Analyze how and why individuals, events, and ideas
develop and interact over the course of a text.
College and Career Readiness
Standards for Reading
Craft and Structure
4. Interpret words and phrases as they are used in a text,
including determining technical, connotative, and figurative
meanings, and analyze how specific word choices shape
meaning or tone.
5. Analyze the structure of texts, including how specific
sentences, paragraphs, and larger portions of the text (e.g.,
a section, chapter, scene, or stanza) relate to each other and
the whole.
6. Assess how point of view or purpose shapes the content
and style of a text.
College and Career Readiness
Standards for Reading
Integration of Knowledge and Ideas
7. Integrate and evaluate content presented in diverse media and
formats, including visually and quantitatively, as well as in
words.
*8. Delineate and evaluate the argument and specific claims in a
text, including the validity of the reasoning as well as the
relevance and sufficiency of the evidence.
9. Analyze how two or more texts address similar themes or
topics in order to build knowledge or to compare the
approaches the authors take.
College and Career Readiness
Standards for Reading
Range of Reading and Level of Text
Complexity
10 .Read and comprehend complex literary and
informational texts independently and proficiently.
Table Discussion:
How does your current
curriculum align to the
CCR Anchor standards
in Reading?
Which of the concepts and skills
required in the Common Core
State Standards are included in
your state’s standards?
Reading Framework for NAEP
2009
Grade
Literary
Informational
4
50%
50%
8
45%
55%
12
30%
70%
How will you engage all
content teachers in
understanding and
implementing reading
expectations?
Text Complexity Matters
• ACT 2006 Reading Between the Lines:
• Students who reached benchmark score
and did well in college:
– Ability to make inferences while reading or
answering questions
– Ability to answer questions associated with
complex text
Text Complexity Grade Bands and
Associated Lexile Ranges
Text Complexity Grade
Band in the Standards
Old Lexile Ranges
Lexile Ranges Aligned to
CCR expectations
K-1
N/A
N/A
2-3
450-725
450-790
4-5
645-845
770-980
6-8
860-1010
955-1155
9-10
960-1115
1080-1305
11-CCR
1070-1220
1215-1355
Lexile Literature
1500 - On Ancient Medicine
1400 - The Scarlet Letter
1300 - Brown vs. Board of Ed.
1200 - War and Peace
1100 - Pride and Prejudice
1000 - Black Beauty
900 - Tom Swift in the Land of Wonders
800 - The Adventures of Pinocchio
700 - Bunnicula: A Rabbit Tale of Mystery
600 - A Baby Sister for Frances
500 - The Magic School Bus Inside the Earth
400 - Frog and Toad are Friends
300 - Clifford’s Manners
Lexile Analyzer
http://www.lexile.com/analyz
er/
Overview of Text Complexity
Reading Standards include over exemplar texts (stories and literature, poetry,
and informational texts) that illustrate appropriate level of complexity by grade
Text complexity is defined by:
1. Qualitative measures – levels of meaning,
structure, language conventionality and
clarity, and knowledge demands
2. Quantitative measures – readability and
other scores of text complexity
3. Reader and Task – background knowledge
of reader, motivation, interests, and
complexity generated by tasks assigned
Reader and Task
84
Levels of Meaning
Single

Multiple levels of meaning
Explicitly stated purpose  Implicit
purpose, may be hidden or obscure
Structure
•
•
•
•
•
•
•
Simple  Complex
Explicit  Implicit
Conventional  Unconventional (Literary)
Chronological order  Unconventional order
Common genre  Specific to a discipline (I)
Simple graphics  Sophisticated graphics
Graphics unnecessary  Graphics essential to
text
Language Conventionality and Clarity
•
•
•
•
Literal  Figurative or ironic
Clear  Ambiguous
Contemporary  Archaic or unfamiliar
Conversational  General academic and
domain specific
Knowledge Demands: Life Experiences
(literary text)
• Simple theme  Complex or sophisticated
themes
• Single themes  Multiple
• Common everyday experiences
Experiences distinctly different from one’s
own
• Single perspective  Multiple
• Perspective like one’s own  Perspective
unlike or in opposition to one’s own
Knowledge Demands:
Content/Discipline
(Informational)
• Everyday knowledge/genre conventions
required  Extensive specific content
knowledge required
• Fe citations of other texts  Many
references to citations of other text
Performance Task
Students explain how Melvin Berger uses
reasons and evidence in his book
Discovering Mars: The Amazing Story of
the Red Planet to support particular points
regarding the topology of the planet.
[RI.4.8]
Performance Task
• Students determine the figurative and
connotative meanings of words such as
wayfaring, laconic, and taciturnity as well as of
phrases such as hold his peace in John
Steinbeck’s Travels with Charley: In Search of
America. They analyze how Steinbeck’s specific
word choices and diction impact the meaning
and tone of his writing and the characterization
of the individuals and places he describes.
[RI.7.4]
Reading Standards: Foundational
Skills
Four categories (standards 1-4)
•
•
•
•
Print concepts ( K-1)
Phonological awareness (K-1)
Phonics and word recognition (K-5)
Fluency (K-5)
Not an end in and of themselves
Differentiated instruction
Teach what they need, not what they know
Reading Standards:
Foundational Skills (K–2)
Kindergarten
Grade One
Print Concepts
1.Demonstrate understanding of the
organization and basic features of
print.
a. Follow words from left to right, top
to bottom, and page by page.
b. Recognize that spoken words are
represented in written language by
specific sequences of letters.
c. Understand that words are
separated by spaces in print.
d. Recognize and name all upper- and
lowercase letters of the alphabet.
1.Demonstrate understanding of the
organization and basic features of
print.
a. Recognize the distinguishing
features of a sentence (e.g., first word,
capitalization, ending punctuation).
Reading Standards: Foundational Skills (K–2)
Kindergarten
Grade One
Phonological awareness
2.Demonstrate understanding of spoken
words, syllables, and sounds (phonemes).
a. Recognize and produce rhyming words.
b. Count, pronounce, blend, and segment
syllables in spoken words.
c. Blend and segment onsets and rimes of
single-syllable spoken words.
d. Isolate and pronounce the initial, medial
vowel, and final sounds (phonemes) in
three-phoneme (consonent-vowelconsonent, or CVC) words.* (This does not
include CVCs ending with /l/, /r/, or /x/.)
e.Add or substitute individual sounds
(phonemes) in simple, one-syllable words
to make new words.
2.Demonstrate understanding of spoken
words, syllables, and sounds
(phonemes).
a. Distinguish long from short vowel
sounds in spoken single-syllable
words.
b. Orally produce single-syllable words
by blending sounds (phonemes),
including consonant blends.
c. Isolate and pronounce initial, medial
vowel, and final sounds (phonemes) in
spoken single-syllable words.
d. Segment spoken single-syllable
words into their complete sequence of
individual sounds (phonemes).
Reading Foundational Skills K-2
Kindergarten
Grade One
Grade Two
3.Know and apply grade-level
phonics and word analysis skills
in decoding words
a. spelling-sound
correspondences for
common consonant
digraphs.
b. Decode regularly spelled onesyllable words
c.Know final -e and common
vowel team conventions for
representing long vowel
sounds
D .Use knowledge that every
syllable must have a vowel
sound to determine the
number of syllables in a
printed word.
e.Decode two-syllable words
following basic patterns by
breaking the words into
syllables
.f.Read words with inflectional
endings.
g.Recognize and read grade-
3. Know and apply grade-level
phonics and word analysis skills
in decoding
.a.Distinguish long and short
vowels when reading regularly
spelled one-syllable words.
b.Know spelling-sound
correspondences for additional
common vowel teams.
c.Decode regularly spelled twosyllable words with long vowels.
d.Decode words with common
prefixes and suffixes.
e.Identify words with
inconsistent but common
spelling-sound
correspondences.
f.Recognize and read gradeappropriate irregularly spelled
words.
Phonics and Word
Recognition
3.Know and apply grade-level
phonics and word analysis skills
in decoding words.
a. One-to-one letter-sound
correspondences by producing
the primary or many of the most
frequent sound for each
consonant.
b.Associate the long and short
sounds with common spellings
(graphemes) for the five major
vowels.
c.Read common high-frequency
words by sight (e.g., the, of, to,
you, she, my, is, are, do, does).
d.Distinguish between similarly
spelled words by identifying the
sounds of the letters that differ.
Reading Foundational Skills K-2
Kindergarten
Grade One
Grade Two
4. Read with sufficient
accuracy and fluency to
support comprehension.
a.Read on-level text with
purpose and
understanding
.b.Read on-level text
orally with accuracy,
appropriate rate, and
expression on
successive readings.
c.Use context to confirm
or self-correct word
recognition and
understanding, rereading
as necessary.
4. Read with sufficient
accuracy and fluency to
support comprehension.
a.Read on-level text with
purpose and
understanding.
b.Read on-level text
orally with accuracy,
appropriate rate, and
expression on
successive readings.
c.Use context to confirm
or self-correct word
recognition and
understanding, rereading
as necessary.
Fluency
4. Read emergentreader texts with
purpose and
understanding.
Writing Standards
College and Career Readiness
Writing Standards
Text Types and Purposes
1.Write arguments to support claims in an analysis of
substantive topics or texts, using valid reasoning and
relevant and sufficient evidence.
2.Write informative/explanatory texts to examine and
convey complex ideas and information clearly and
accurately through the effective selection, organization,
and analysis of content.
3.Write narratives to develop real or imagined
experiences or events using effective techniques, wellchosen details, and well-structured event sequences.
Table Discussion
Why is the student’s ability to
write sound arguments on
substantive topics and issues
important?
NAEP 2011 Writing Framework
Grade
To Persuade
To Explain
To Convey
Experience
4
30%
35%
35%
8
35%
35%
30%
12
40%
40%
20%
College and Career Readiness
Writing Standards
Production and Distribution of Writing
4. Produce clear and coherent writing in which the
development, organization, and style are appropriate
to task, purpose, and audience.
5. Develop and strengthen writing as needed by
planning, revising, editing, rewriting, or trying a new
approach.
6. Use technology, including the Internet, to produce and
publish writing and to interact and collaborate with
others.
College and Career Readiness
Writing Standards
Research to Build and Present Knowledge
7. Conduct short, as well as more sustained research
projects based on questions, demonstrating
understanding of the subject under investigation.
8. Gather relevant information from multiple print and
digital sources, assess the credibility and accuracy of
each source, and integrate the information while
avoiding plagiarism.
9. Draw evidence from literary or informational texts to
support analysis, reflection, and research.
College and Career Readiness
Writing Standards
Range of Writing
10. Write routinely over extended time frames (time for
research, reflection, and revision) and shorter time
frames (a single sitting or a day or two) for a range of
tasks, purposes, and audiences.
Writing Standards/Research
First Grade
• 7. Participate in shared research and
writing projects (e.g., explore a number
of “how-to” books on a given topic and
use them to write a sequence of
instructions).
• 8. With guidance and support from
adults, recall information from
experiences or gather information from
provided sources to answer a question.
• 9. (Begins in grade 4)
Writing Standards/Research
Third Grade
7. Conduct short research projects that build
knowledge about a topic.
8. Recall information from experiences or
gather information from print and digital
sources; take brief notes on sources and
sort evidence into provided categories.
9. (Begins in grade 4)
Writing Standards/Research
Grade 5
7. Conduct short research projects that use several sources to
build knowledge through investigation of different aspects of a
topic.
8. Recall relevant information from experiences or gather relevant
information from print and digital sources; summarize or
paraphrase information in notes and finished work, and provide
a list of sources.
9. Draw evidence from literary or informational texts to support
analysis, reflection, and research. Apply grade 5 Reading
standards to literature (e.g., “Compare and contrast two or
more characters, settings, or events in a story or a drama,
drawing on specific details in the text [e.g., how characters
interact]”). Apply grade 5 Reading standards to informational
texts (e.g., “Explain how an author uses reasons and evidence
to support particular points in a text, identifying which reasons
and evidence support which point[s]”).
Writing Standards/Research
Grade 7
7. Conduct short research projects to answer a question,
drawing on several sources and generating additional
related, focused questions for further research and
investigation.
8. Gather relevant information from multiple print and digital
sources, using search terms effectively; assess the
credibility and accuracy of each source; and quote or
paraphrase the data and conclusions of others while
avoiding plagiarism and following a standard format for
citation.
9. Draw evidence from literary or informational texts to support
analysis, reflection, and research. Apply grade 7 Reading
standards to literature (e.g., “Compare and contrast a
fictional portrayal of a time, place, or character and a
historical account of the same period as a means of
understanding how authors of fiction use or alter history”).
Apply grade 7 Reading standards to literary nonfiction (e.g.
“Trace and evaluate the argument and specific claims in a
Writing Standards/Research
Grade 9-10
7. Conduct short as well as more sustained research projects to
answer a question (including a self-generated question) or solve a
problem; narrow or broaden the inquiry when appropriate;
synthesize multiple sources on the subject, demonstrating
understanding of the subject under investigation.
8. Gather relevant information from multiple authoritative print and
digital sources, using advanced searches effectively; assess the
usefulness of each source in answering the research question;
integrate information into the text selectively to maintain the flow
of ideas, avoiding plagiarism and following a standard format for
citation.
9. Draw evidence from literary or informational texts to support
analysis, reflection, and research. Apply grades 9–10 Reading
standards to literature (e.g., “Analyze how an author draws on
and transforms source material in a specific work [e.g., how
Shakespeare treats a theme or topic from Ovid or the Bible or
how a later author draws on a play by Shakespeare]”). Apply
grades 9–10 Reading standards to literary nonfiction (e.g.,
“Delineate and evaluate the argument and specific claims in a
text, assessing whether the reasoning is valid and the evidence is
What types of writing are your students
engaged in? Is it sufficient? What
might you need to consider?
College and Career Readiness Anchor
Standards for Speaking and Listening
Comprehension and Collaboration
1. Range of conversations and collaborations, diverse
partners, building on others’ ideas and expressing their
own clearly and persuasively.
2. Integrate and evaluate information presented in diverse
media and formats, including visually, quantitatively, and
orally.
3. Evaluate a speaker’s point of view, reasoning, and use
of evidence and rhetoric.
College and Career Readiness Anchor
Standards for Speaking and Listening
Presentation of Knowledge and Ideas
4. Present information, findings, and supporting evidence such
that listeners can follow the line of reasoning and the
organization, development, and style are appropriate to task,
purpose, and audience.
5. Make strategic use of digital media and visual displays of data
to express information and enhance understanding of
presentations.
6. Adapt speech to a variety of contexts and communicative
tasks, demonstrating command of formal English when indicated
or appropriate.
College and Career Readiness
Anchor Standards for Language
Conventions of Standard English
1. When writing or speaking.
2. Use capitalization, punctuation, and spelling when writing.
Knowledge of Language
3. To comprehend more fully when reading or listening.
Vocabulary Acquisition and Use
4. Determine or clarify the meaning of unknown and multiple-meaning words
and phrases by using context clues, analyzing meaningful word parts,
5. Demonstrate understanding of figurative language, word relationships, and
nuances in word meanings
6. Acquire and use accurately a range of general academic and domainspecific words
911
Reading Standards for Literacy in
History/Social Studies, Science and
Technical Subjects 6-12
 Reading critical to building knowledge
 Appreciation for the norms and conventions
 Evidence
 Understanding of domain specific words
 Analyze, evaluate intricate argument,
synthesize
 Complement the disciplines
Reading Standards for Literacy in
History/Social Studies 6–12
Common Core Reading
Standard for
Grades 9-10
Informational Text
Anchor Standard
Grades 11-12
Key Ideas & Details
Key Ideas & Details
Key Ideas & Details
1. Read closely to
determine what the text
says explicitly and to
make logical inferences
from it; cite specific
textual evidence when
writing or speaking to
support conclusions
drawn from the text.
1. Cite specific textual
evidence to support
analysis of primary and
secondary sources,
attending to such
features as the date and
origin of the information
1. Cite specific textual
evidence to support
analysis of primary and
secondary sources,
connecting insights
gained from specific
details to an
understanding of the text
as a whole.
Literacy in Science and Technical
Subjects
Common Core Reading
Standard for
Informational Text
Anchor Standard
Reading Standards for
Literacy in Science and
Technical Subjects
Grades 9-10
Reading Standards for
Literacy in Science and
Technical Subjects
Grades 11-12
Key Ideas & Details
Key Ideas & Details
Key Ideas & Details
1. Read closely to
determine what the text
says explicitly and to
make logical inferences
from it; cite specific
textual evidence when
writing or speaking to
support conclusions
drawn from the text.
1 .Cite specific textual
evidence to support
analysis of science and
technical texts, attending
to the precise details of
explanations or
descriptions
1. Cite specific textual
evidence to support
analysis of science and
technical texts, attending
to important distinctions
the author makes and to
any gaps or
inconsistencies in the
account.
CCR Students in Reading, Writing,
Speaking, Listening, and Language
 They demonstrate independence
 They build strong content knowledge
 They respond to varying demands of audience,
task, purpose, and discipline
 They comprehend as well as critique
 They value evidence
 They use technology and digital media
 They understand other perspectives and cultures
What is not included:
•
•
•
•
How teachers should teach
All that can or should be taught
The nature of advanced work beyond the core
The interventions needed for students well below
grade level
• The full range of support for English language learners
and students with special needs
• Everything needed to be college and career ready
• Complete the Rigor and Relevance, and
Literacy Checklist independently
• Discuss with team
• Identify 2-3 key focus areas
• Develop action steps
• Who will be responsible
• Timeline
• How will it be measured?
Quantile Framework


Numbers and Operations
Algebra / Patterns &
Functions

Data Analysis & Probability

Measurement

Geometry
2005-06 Quantile Framework® for Math
Interquartile Ranges Shown (25% - 75%)
1500
1400
Quantile Measure (Q)
1300
1200
11th
10th
1100
1000
8th
900
800
700
600
500
Personal Use
Employment
High School
First-Year College
STANDARDS FOR
MATHEMATICS
JUNE 2010
Characteristics
•
•
•
•
•
•
Fewer and more rigorous.
Aligned with college and career expectations – prepare
all students for success upon graduating from high
school.
Internationally benchmarked, so that all students are
prepared for succeeding in our global economy and
society.
Includes rigorous content and application of higherorder skills.
Builds upon strengths and lessons of current state
standards.
Research based
Coherence
• Articulated progressions of topics and
performances that are developmental and
connected to other progressions
• Conceptual understanding and procedural skills
emphasized equally
• NCTM states coherence also means that
instruction, assessment, and curriculum are
aligned
Focus
• Key ideas, understandings, and skills are identified
• Deep learning of concepts is stressed
– That is, time is spent on a topic and on learning it
well. This counters the “mile wide, inch deep”
criticism leveled at most current U.S. standards.
Clarity and Specificity
• Skills and concepts are clearly defined
• Being able to apply concepts and skills to
new situations is expected
Intent of Common Core
• The same goals for all students
• Coherence
• Focus
• Clarity and Specificity
Grade-Level Standards
 K-8 grade-by-grade standards
organized by domain
 9-12 high school standards
organized by conceptual
categories
Grade-Level Standards
 K-8 grade-by-grade standards
organized by domain
 9-12 high school standards
organized by conceptual
categories
The K-5 standards:
whole numbers
addition
subtraction
multiplication
division
fractions and decimals
6-8 standards:
geometry
algebra
probability and statistics
High school standards:
Number & Quantity
Algebra
Functions
Modeling
Geometry
Statistics & Probability
Standards for Mathematical
Practice
 Describe mathematical “habits
of mind”
 Standards for mathematical
proficiency: reasoning, problem
solving, modeling, decision
making, and engagement
 Connect with content standards
in each grade
Mathematics/Standards for
Mathematical Practice
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
Mathematical Practices
1. Make sense of problems and persevere in
solving them:
– Use concrete objects or pictures to help solve
problems
– Proficient students can explain the meaning of
the problem
– Identify how to enter the problem
– Make a plan on how to solve the problem
– Monitor progress
Mathematical Practices
2. Reason abstractly and quantitatively:
– Make sense of quantities and their
relationship in problems
– Use concrete manipulatives to demonstrate
an understanding of the problem
• Units involved
• Understanding the meaning of quantities
• Knowing and using different properties of
operations
Mathematical Practices
3. Construct viable arguments and critique
the reasoning of others:
– Can construct solutions using concrete
objects such as drawings, diagrams and
actions
– Students develop strategies to solve
problems, question them to understand their
thinking and understanding
Mathematical Practices
4. Model with mathematics:
– Apply the math they know to solving problems
– Being able to write equations to describe a
situation
Mathematical Practices
5. Use appropriate tools strategically
– Students use a variety of methods and tools
to compute, including objects, mental
computation, estimation, paper and pencil,
and calculators.
Mathematical Practices
6. Attend to Precision
– Communicate clearly how they solved the
problem
– Know the symbol
– Check answers
– Ask lots of question to understand how
students are tackling the problem
Mathematical Practices
7. Look for and make use of structure
– Recognize patterns or structure (3+7 is the
same as 7+3)
Mathematical Practices
8. Look for and express regularity in
repeated reasoning:
– Watch for repeated patterns, numbers
– Able to identify shortcuts
Common Core Format
Domains are larger groups of related standards.
Standards from different domains may
sometimes be closely related.
Clusters are groups of related standards.
Standards from different clusters may
sometimes be closely related, because
mathematics is a connected subject.
Standards define what students should be able to
understand and be able to do.
Common Core Format
K-8
High School
Grade
Conceptual Category
Domain
Cluster
Standards
Domain
Cluster
Standards
Grade Level Overview
Grade Level Overview
Critical Areas –
similar to
NCTM’s
Curriculum
Focal Points
Format of K-8 Standards
Grade Level
Domain
Format of K-8 Standards
Domain
Statement
Standard
Cluster
Domain
Statement
Cluster
Standard
Kindergarten
• Understanding base ten system – drawing
special attention to 10
• Children learn to view 11-19 as ten ones
and some more
• Decompose 10 into pairs such as 1 + 9,
2 + 8, 3 + 7 and find the umber that makes
10 when added to a given number
Kindergarten
Grade 1 Focus Areas
1. Developing understanding of addition,
subtraction, and strategies for addition and
subtraction within 20;
2. Developing understanding of whole number
relationships and place value, including
grouping in tens and ones;
3. Developing understanding of linear
measurement and measuring lengths as
iterating length units; and
4. Reasoning about attributes of, and composing
and decomposing geometric shapes.
Grade 2 Focus
1. Extending understanding of base-ten notation
Counting by 5s, 10s, and multiples of 100s, 10s, and
ones
Multiple digits up to 1000
2. Building fluency with + and – (within 1000)
3. Using standard units of measure (centimeter
and inch)
4. Describing and analyzing shapes
Foundation for understanding area, volume,
congruence, similarity, and symmetry in later grades.
Grade 2 Overview
• Operations and Algebraic Thinking
– Represent and solve problems involving
addition and subtraction
– Add and Subtract within 20
– Work with equal groups of objects to gain
foundations for multiplication
Grade 2 Overview
• Number and Operations in Base Ten
– Understand place value
– Use place value understanding and properties
of operations to add and subtract
Grade 2 Overview
• Measurement and Data
– Measure and estimate lengths in standard
units
– Relate addition and subtraction to length
– Work with time and money
– Represent and interpret data
• Geometry
– Reason with shapes and their attributes
Common Addition and
Subtraction Situations
Results
Unknown
Change
Unknown
Start Unknown
Add to
Sally has 4 rocks.
John gave her 6
more rocks. How
many rocks does
S
Sally had 4 rocks.
How many rocks
does she need to
have 10 rocks
altogether?
Sally had some
rocks. John gave
her 6 more rocks.
Now she has 10
rocks. How many
rocks did Sally
have to start with?
Take from
Sally had 10
rocks. She gave 4
to John. How
many rocks does
Sally have left?
Sally had 10
rocks. She gave
some to John.
Now she has 6
rocks left. How
many rocks did
Sally give to
John?
Sally had some
rocks. She gave 4
to John. Now she
has 6 rocks left.
How many rocks
did Sally have to
start with?
Common addition and
subtraction situations
Total Unknown
Put Together/Take Sally has 4 red
apart
rocks and 6 blue
rocks. How many
rocks does she
have?
4+6=?
Added Unknown
Both Addends
Unknown
Sally has 10
rocks. 4 are red
and the rest are
blue. How many
blue rocks does
Sally have?
4 + ? = 10
Sally has 10
rocks. How many
can she put in the
blue box and how
many in her red
box?
10 = 0 +10, 10=10
+0
10 = 5 + 5
10 = 6 + 4
Compare Addition and
Subtraction situations
Compare
Differences
Unknown
Bigger Unknown
Smaller
Unknown
Sally has 10
rocks. John has 6
rocks. How many
more rocks does
Sally have than
John?
John has 6 rocks.
Sally has 4 more
than John. How
many rocks does
Sally have?
Sally has 10
rocks. She has 6
more rocks than
John. How many
rocks does John
have?
10 – 6 = ?
6+4=?
? + 6 = 10
6 + ? = 10
4+6=?
10 – 6 = ?
Grade 3 Focus
(1) developing understanding of multiplication and
division and strategies for multiplication and
division within 100;
(2) developing understanding of fractions,
especially unit fractions (fractions with
numerator 1);
(3) developing understanding of the structure of
rectangular arrays and of area; and
(4) describing and analyzing two-dimensional
shapes
Grade Three Overview
• Operations and Algebraic Thinking
– Represent and solve problems involving
multiplication and division.
– Understand properties of multiplication and
the relationship between multiplication and
division.
– Multiply and divide within 100
– Solve problems involving the four operations,
and identify and explain patterns in arithmetic.
Grade Three Overview
• Number and Operation in Base Ten
– Use place value understanding and properties
of operations to perform multi-digit arithmetic.
• Number and Operation – Fractions
– Develop understanding of fractions as
numbers.
Grade Three Overview
• Measurement and Data
– Solve problems: estimation of intervals of
time, liquid volumes, and masses of objects.
– represent and interpret data.
– Geometric measurement: concepts of area
and relate area to multiplication and to
addition.
– Geometric measurement: recognize perimeter
as an attribute of plane figures and distinguish
between linear and area measures.
Grade Three Overview
• Geometry
– Reason with shapes and their attributes.
Grade Four Focus Areas
(1) Develop understanding and fluency with multi-digit
multiplication, and developing understanding of dividing
to find quotients involving multi-digit dividends;
(2) Develop understanding of fraction equivalence, addition
and subtraction of fractions with like denominators, and
multiplication of fractions by whole numbers;
(3) Understanding that geometric figures can be analyzed
and classified based on their properties, such as having
parallel sides, perpendicular sides, particular angle
measures, and symmetry.
Grade Four Overview
• Operations and Algebraic thinking
– Use the four operations with whole numbers
to solve problems.
– Gain familiarity with factors and multiples.
– Generate and analyze patterns.
Grade Four Overview
• Number and operations in Base ten
– Generalize place value understanding for multi- digit
whole numbers.
– Use place value understanding and properties of
operations to perform multi-digit arithmetic.
• Number and operations—fractions
– extend understanding of fraction equivalence and
ordering.
– Build fractions from unit fractions by applying and
extending previous understandings of operations on
whole numbers.
– Understand decimal notation for fractions, and
compare decimal fractions.
Grade Four Overview
• Measurement and data
– Solve problems involving measurement and
conversion of measurements from a larger unit to a
smaller unit.
– Represent and interpret data.
– Geometric measurement: understand concepts of
angle and measure angles.
• Geometry
– Draw and identify lines and angles, and classify
shapes by properties of their lines and angles.
Grade Five Focus
(1) developing fluency with addition and subtraction of
fractions, and developing understanding of the
multiplication of fractions and of division of fractions in
limited cases (unit fractions divided by whole numbers
and whole numbers divided by unit fractions);
(2) extending division to 2-digit divisors, integrating
decimal fractions into the place value system and
developing understanding of operations with decimals
to hundredths, and developing fluency with whole
number and decimal operations; and
(3) developing understanding of volume.
Grade Five Overview
• Operations and Algebraic Thinking:
Write and interpret numerical expressions
Analyze patterns and relationships.
• Number and Operations in Base ten
Understand the place value system.
Perform operations with multi-digit whole
numbers and with decimals to hundredths.
Common multiplication and
division situations
Problem Types
Multiplication
Partition
Division
Measurement
Division
Equal Group
(Whole unknown)
Mark has 4 bags of
apples. There are 5
apples in each
bag. How many
apples does Mark
have altogether
(Size of groups
unknown) Mark
has 20 apples. He
wants to share
them equally
among his 4
friends. How many
apples will each
friend receive?
(Number of groups
unknown) Mark
has 20 apples. He
puts them in bags
with 5 apples in
each. How many
bags did he use?
Equal Group
Problems (rate
(Whole unknown)
If apples cost 4
cents each, how
much would 5
apples cost?
(Size of groups
unknown) Jill paid
20 cents for 5
apples. What is the
cost of 1 apple?
(Number of groups
unknown) Jill
bought apples for
4 cents each. She
spent 20 cents.
How many apples
did she buy?
Common multiplication and
division situations
Equal Group
Problems (rate)
(Whole
unknown) Peter
walked for 5
hours at 4 miles
per hour. How
far did he walk?
(Size of groups
unknown) Peter
walked 20 miles
in 5 hours. How
fast was he
walking (in miles
per hour)?
(Number of
groups
unknown) Peter
walked 20 miles
at a rate of 4
miles per hour.
How long did he
walk for?
Compare
Problems
(Product
unknown) Jill
picked 4 apples.
Bill picked 5
times as many.
How many
apples did Bill
pick?
(Set size
unknown) Mark
picked 20
apples. He
picked 4 times
as many as Jill.
How many
apples did Jill
pick?
(Multiplier
Unknown) Mark
Picked 20 apples
and Jill picked
only 4. How
many times as
many apples did
Mark pick as Jill
did?
Grade Five Overview
• Number and Operations—Fractions
• Use equivalent fractions as a strategy
to add and subtract fractions.
• Apply and extend previous
understandings of multiplication and
division to multiply and divide
fractions.
Grade Five Overview
• Measurement and Data:
Convert like measurement units within a
given measurement system.
Represent and interpret data.
Geometric measurement: understand
concepts of volume and relate volume to
multiplication and to addition.
Grade Five Overview
Geometry:
• Graph points on the coordinate plane to solve
real-world and mathematical problems.
• Classify two-dimensional figures into
categories based on their properties.
K-5 Learning Progressions
http://commoncoretools.wordpress
.com/
http://www.esd112.org/smerc/
mpat_detail.cfm
Sample math performance tasks
Grade 6 Focus
• (1) connecting ratio and rate to whole number
multiplication and division and using concepts of
ratio and rate to solve problems;
• (2) completing understanding of division of
fractions and extending the notion of number to
the system of rational numbers, which includes
negative numbers;
• (3) writing, interpreting, and using expressions
and equations; and
• (4) developing understanding of statistical
thinking.
Grade Six Overview
• Ratios and Proportional relationship
• Understand ratio concepts and use ratio reasoning
to solve problems.
• The Number System
• apply and extend previous understandings of
multiplication and division to divide fractions by fractions.
• Compute fluently with multi-digit numbers and find
common factors and multiples
.• apply and extend previous understandings of numbers
to the system of rational numbers.
Grade Six Overview
• Expressions and Equations
• apply and extend previous understandings of
arithmetic to algebraic expressions.
• reason about and solve one-variable equations
and inequalities.
• represent and analyze quantitative
relationships between dependent and
independent variables.
Grade Six Overview
• Geometry
• Solve real-world and mathematical
problems involving area, surface area, and
volume.
Statistics and Probability
• develop understanding of statistical
variability.
• Summarize and describe distributions.
Fractions, Grades 3–6
 3. Develop an understanding of fractions as numbers.






4. Extend understanding of fraction equivalence and ordering.
4. Build fractions from unit fractions by applying and extending
previous understandings of operations on whole numbers.
4. Understand decimal notation for fractions, and compare decimal
fractions.
5. Use equivalent fractions as a strategy to add and subtract
fractions.
5. Apply and extend previous understandings of multiplication and
division to multiply and divide fractions.
6. Apply and extend previous understandings of multiplication and
division to divide fractions by fractions.
Grade 7 Focus
(1) Develop understanding of and applying
proportional relationships;
(2) Develop understanding of operations with rational
numbers and working with expressions and linear
equations;
(3) Solve problems involving scale drawings and
informal geometric constructions, and working with
two- and three-dimensional shapes to solve
problems involving area, surface area, and volume;
and
(4) Draw inferences about populations based on
samples.
Grade 7 Overview
Ratios and Proportional relationships
• Analyze proportional relationships and use
them to solve real-world and mathematical
problems.
The Number System
• Apply and extend previous understandings of
operations with fractions to add, subtract,
multiply, and divide rational numbers.
Grade 7 Overview
Expressions and Equations
• Use properties of operations to generate equivalent
expressions.
• Solve real-life and mathematical problems using
numerical and algebraic expressions and equations.
Geometry
• Draw, construct and describe geometrical figures and
describe the relationships between them.
• Solve real-life and mathematical problems involving
angle measure, area, surface area, and volume.
Grade 7 Overview
Statistics and Probability
• Use random sampling to draw inferences
about a population.
• Draw informal comparative inferences
about two populations.
• Investigate chance processes and
develop, use, and evaluate probability
models.
Grade 8 Focus
(1) formulating and reasoning about expressions and
equations, including modeling an association in
bivariate data with a linear equation, and solving
linear equations and systems of linear equations;
(2) grasping the concept of a function and using
functions to describe quantitative relationships;
(3) analyzing two- and three-dimensional space and
figures using distance, angle, similarity, and
congruence, and understanding and applying the
Pythagorean Theorem.
Grade 8 Overview
The Number System
• Know that there are numbers that are not rational,
and approximate them by rational numbers.
Expressions and Equations
• Work with radicals and integer exponents.
• Understand the connections between proportional
relationships, lines, and linear equations
.• Analyze and solve linear equations and pairs of
simultaneous linear equations.
Grade 8 Overview
Functions
• Define, evaluate, and compare functions.
• Use functions to model relationships
between quantities.
Grade 8 Overview
Geometry
• Understand congruence and similarity using
physical models, transparencies, or geometry
software.
• Understand and apply the Pythagorean
theorem.
• Solve real-world and mathematical problems
involving volume of cylinders, cones and
spheres.
Grade 8 Overview
Statistics and Probability
• Investigate patterns of association in
bivariate data.
HS Pathways
1.) Traditional (US) – 2 Algebra, Geometry
and Data, probability and statistics included
in each course
2.) International (integrated) three courses
including number , algebra, geometry,
probability and statistics each year
3.) Compacted version of traditional –
grade 7/8 and algebra completed by end of
8th grade
4.) Compacted integrated model, allowing
students to reach Calculus or other college
level courses
Number and Quantity Overview
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•
•
•
Real Number System
Quantities
Complex Number System
Vector and Matrix Quantities
Algebra Overview
• Seeing Structure in Expressions
• Arithmetic with Polynomials and Rational
Expressions
• Creating Equations
• Reasoning with Equations and Inequalities
Functions
•
•
•
•
Interpreting Functions
Building Functions
Linear, Quadratic and Exponential Models
Trigonometric Functions
Modeling
•
•
•
•
•
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Identify the problem
Formulate a model
Analyze and perform operations
Interpret results
Validate the conclusion
Report on the conclusion
Geometry
• Congruence
• Similarity, Right Triangles, and
Trigonometry
• Circles
• Expressing Geometric Properties with
Equations
• Geometric Measurement and Dimension
• Modeling and Geometry
Statistics and Probability
• Interpreting Categorical and Quantitative
Data
• Making Inferences and Justifying
Conclusions
• Conditional Probability and the Rules of
Probability
• Using Probability to Make Decisions
Resources
• Progressions Project,
ime.math.arizona.edu/progressions/
• Mathematics Project website,
http://illustrativemathematics.org.
• NCTM, NCSM, AMTE, and ASSM will be
developing additional resources watch http://commoncoretools.wordpress.com
Recommended Professional
Development
• Grades K–2, Counting and Cardinality and Number and
Operations in Base
• Grades K–5 Operations and Algebraic Thinking
• Grades 3–5 Number and Operations—Fractions
• Grades 6–7 Ratios and Proportional Reasoning
• Grade 8 Geometry
Key Advances
Focus and coherence
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•
Focus on key topics at each grade level.
Coherent progressions across grade levels.
Balance of concepts and skills
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Content standards require both conceptual
understanding and procedural fluency.
Mathematical practices
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Foster reasoning and sense-making in
mathematics.
College and career readiness
•
Level is ambitious but achievable.
• Individually complete the Mathematics
Characteristics Checklist
• Compare your choices with team
• Underline items rated Pervasive or
Considerable
• Circle items rated Initiated or Absent
• Come to consensus on item (s) of
concern
State
Standards
State
Tests
NESS
Common
Core
Standards
C
A
State
Standards
C
State
Tests
NESS
Common
Core
Standards
State
Standards
State
Tests
NESS
Common
Core
Standards
Consortium
Assessment
3 Years
State
Standards
State
Tests
NESS
Common
Consortium
Core
Assessment
Standards
D
State
Standards
State
Tests
NESS
Common
Core
Standards
Consortium
Assessment
A
State
Standards
State
Tests
D
NESS
Common
Core
Standards
Consortium
Assessment
Now
State
Standards
State
Tests
NESS
C
A
3 Years
State
Standards
State
Tests
NESS
Common
Consortium
Core
Assessment
Standards
C
D
C
D
A
B