In this math Common Core State Standards training, participants will learn to recognize the structure of the Common Core State Standards (CCSS) in Mathematics, identify the shifts represented in the CCSS and consider implications and implementation plans.
1. …to the CORE!
6-12 Mathematics
Teacher University
May 25, 2012
Dr. Marci Shepard Orting School District Teaching, Learning & Assessment May 2012
2. A Picture of Our Day of Learning
Dr. Marci Shepard Orting School District Teaching, Learning & Assessment May 2012
3. Learning Target
We are building awareness and gaining
familiarity with the Common Core State
Standards and assessment.
• Recognize the structure of the Common Core
State Standards (CCSS) in Mathematics
• Identify the shifts represented in the CCSS
• Consider implications and implementation plans
for OSD
Dr. Marci Shepard Orting School District Teaching, Learning & Assessment May 2012
4. Common Core State Standards - Mathematics
Dr. Marci Shepard Orting School District Teaching, Learning & Assessment May 2012
5. Placemats
Dr. Marci Shepard Orting School District Teaching, Learning & Assessment May 2012
6. Mathematics
Standards for Mathematical Practice
Carry across all grade levels
Describe habits of mind of a mathematically expert
students
Standards for Mathematical Content
K-8 standards represented by grade level, organized
into domains that progress over several grades
2-4 Focal points at each grade level
High school standards represented by conceptual
themes (Number &
Quantity, Algebra, Functions, Modeling, Geometry,
Statistics & Probability)
Dr. Marci Shepard Orting School District Teaching, Learning & Assessment May 2012
7. Mathematics
Standards for Mathematical Practice
Carry across all grade levels
Describe habits of mind of a mathematically
expert students
Page 6
Dr. Marci Shepard Orting School District Teaching, Learning & Assessment May 2012
9. Mathematics
Standards for Mathematical Practice
Carry across all grade levels
Describe habits of mind of a mathematically expert
students
Standards for Mathematical Content
K-8 standards represented by grade level, organized
into domains that progress over several grades
2-4 Focal points at each grade level
High school standards represented by conceptual
themes (Number &
Quantity, Algebra, Functions, Modeling, Geometry,
Statistics & Probability)
Dr. Marci Shepard Orting School District Teaching, Learning & Assessment May 2012
10. Content Progressions and Major Shifts
Major Shifts
Focus Coherence Application
• Fewer big ideas -- • Articulated progressions of • Being able to
- learn more topics and performances apply concepts
• Learning of that are developmental and and skills to new
concepts is connected to other situations
emphasized progressions
Dr. Marci Shepard Orting School District Teaching, Learning & Assessment May 2012
11. Critical Areas in Mathematics
PRIORITIES in Support of Rich Instruction and
Grade
Expectations of Fluency and Conceptual Understanding
Addition and subtraction, measurement using
K–2
whole number quantities
Multiplication and division of whole numbers
3–5
and fractions
Ratios and proportional reasoning; early
6
expressions and equations
Ratios and proportional reasoning; arithmetic
7
of rational numbers
8 Linear algebra
Dr. Marci Shepard Orting School District Teaching, Learning & Assessment May 2012
12. High School
Dr. Marci Shepard Orting School District Teaching, Learning & Assessment May 2012
13. Organization of the Standards
Dr. Marci Shepard Orting School District Teaching, Learning & Assessment May 2012
14. Format of K-8 Standards Grade Level
Domain
Standard
Cluster
Dr. Marci Shepard Orting School District Teaching, Learning & Assessment May 2012
15. Cross-cutting
Grade Level Introduction themes
Critical Area of
Focus
Dr. Marci Shepard Orting School District Teaching, Learning & Assessment May 2012
16. Grade Level Overview
Grade 4 Overview Mathematical Practices
Operations and Algebraic Thinking 1. Make sense of problems and
Use the four operations with whole numbers to solve problems. persevere in solving them
Gain familiarity with factors and multiples. 2. Reason abstractly and
Generate and analyze patterns. quantitatively
Number and Operations in Base Ten 3. Construct viable arguments
Generalize place value understanding for multi-digit whole and critique the reasoning of
numbers.
others
Use place value understanding and properties of operations to
perform multi-digit arithmetic. 4. Model with mathematics
Number and Operations—Fractions 5. Use appropriate tools
Extend understanding of fraction equivalence and ordering. strategically
Build fractions from unit fractions by applying and extending 6. Attend to precision
previous understandings of operations on whole numbers.
Understand decimal notation for fractions, and compare decimal
7. Look for and make use of
fractions. structure
Measurement and Data 8. Look for and express
Solve problems involving measurement and conversion of regularity in repeated
measurements from a larger unit to a smaller unit. reasoning
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.
Dr. Marci Shepard Orting School District Teaching, Learning & Assessment May 2012
17. CCSS for High School Mathematics
• Organized in “Conceptual Categories”
▫ Number and Quantity
▫ Algebra
▫ Functions
▫ Modeling
▫ Geometry
▫ Statistics and Probability
• Conceptual categories are not courses
• Additional mathematics for advanced
courses indicated by (+)
• Standards with connections to
modeling indicated by (★)
Dr. Marci Shepard Orting School District Teaching, Learning & Assessment May 2012
18. Format of High School Standards
Domain
Cluster
Standard
Advanced
Dr. Marci Shepard Orting School District Teaching, Learning & Assessment May 2012
19. Format of Standards
Dr. Marci Shepard Orting School District Teaching, Learning & Assessment May 2012
22. High School Conceptual Categories
• Numbers and quantities
• Algebra
• Functions
• Geometry
• Statistics and probability
Dr. Marci Shepard Orting School District Teaching, Learning & Assessment May 2012
23. High School Mathematical Pathways
Typical
in U.S.
• Two main pathways:
▫ Traditional: Two algebra courses and a geometry
course, with statistics and probability in each
▫ Integrated: Three courses, each of which includes
algebra, geometry, statistics, and probability
Typical
• Both pathways: outside U.S.
▫ Complete the Common Core in the third year
▫ Include the same “critical areas”
▫ Require rethinking high school mathematics
▫ Prepare students for a menu of fourth-year courses
Dr. Marci Shepard Orting School District Teaching, Learning & Assessment May 2012
24. Two Main Pathways
Dr. Marci Shepard Orting School District Teaching, Learning & Assessment May 2012
25. Pathway Overview
Dr. Marci Shepard Orting School District Teaching, Learning & Assessment May 2012
26. Course Overview: Critical Areas (units)
Dr. Marci Shepard Orting School District Teaching, Learning & Assessment May 2012
27. Course Detail by Unit (critical area)
Dr. Marci Shepard Orting School District Teaching, Learning & Assessment May 2012
28. Dr. Marci Shepard Orting School District Teaching, Learning & Assessment May 2012
29. May 2012
Dr. Marci Shepard Orting School District Teaching, Learning & Assessment May 2012
30. Before…
Dr. Marci Shepard Orting School District Teaching, Learning & Assessment May 2012
31. After…
Dr. Marci Shepard Orting School District Teaching, Learning & Assessment May 2012
32. 2010-2011
Training for
PowerStandards
• K-5 math
• 6-8 Math
• Algebra &
Geometry
• 9-12 ELA
Communication
• Instructional
Council
• Key
Communicator
• PD/Meetings
Dr. Marci Shepard Orting School District Teaching, Learning & Assessment May 2012
33. 2011-2012
CCSS Workgroup
• Overview for all
• Math
• ELA
• Implementation planning
OSPI/ESD Trainings
• Marci and teachers attend 2-day math
training
• Marci and teachers attend 2-day ELA
training
Teacher University
• Provided printed standards
• Overview of standards and
assessment
Communication
• Teacher University
• OSD Website
• Key Communicator
• Twitter
• Presentation to the school board
• Teacher meeting with Superintendent
• Instructional Council
• PD/Meetings
Dr. Marci Shepard Orting School District Teaching, Learning & Assessment May 2012
34. 2012-2013
Math Transition OPS
• K-Counting and Cardinality (CC);
Operations and Algebraic
Thinking (OA)
• 1&2-Operations and Algebraic
Thinking (OA); Number and
Operations in Base Ten (NBT)
PtR
• Number and Operations-
Fractions (NF); Operations and
Algebraic Thinking (OA)
OMS
• 6&7-Ratio and Proportion
Relationship (RP); Number
System (NS); Expressions and
Equations (EE)
• 8-Number System (NS);
Expressions and Equations (EE);
Functions (F)
OHS
• Algebra 1&Geometry-Unit 1;
Unit 2; Unit 4
Dr. Marci Shepard Orting School District Teaching, Learning & Assessment May 2012
35. Math Transition
2013-2014
OPS
• Measurement and Data (MD);
Geometry (G)
PtR
• Number and Operations in
Base Ten (NBT);
Measurement and Data (MD)
OMS
• Geometry (G); Statistics and
Probability (SP)
OHS
• Algebra 1-Unit 3; Unit 5
• Geometry – Unit 3, Unit 5;
Unit 6
Dr. Marci Shepard Orting School District Teaching, Learning & Assessment May 2012
36. Full Implementation 2014-2015
Math Transition
• All domains
Dr. Marci Shepard Orting School District Teaching, Learning & Assessment May 2012
37. ELA Transition
2012-2013
ELA teachers (K-5 & 6-12)
• Foundational Skills (K-5)
• Reading Standards – Literary
and Informational
• Language Standards #4-6 –
Vocabulary Acquisition and Use
• And…
Other content area teachers (6-12)
• College and Career Readiness
(CCR) Anchor Standards for
Reading & Reading Standards
for Literacy in the content areas
• Emphasis on #10 – Text
Complexity
• Emphasis on #4 –
Academic Vocabulary
Dr. Marci Shepard Orting School District Teaching, Learning & Assessment May 2012
38. 2013-2014
ELA Transition ELA teachers (K-5 & 6-12)
• Writing Standards
• Language Standards #1-3 –
Conventions of Standard
English
• Speaking and Listening
Standards
• And…
Other content area teachers (6-12)
• College and Career Readiness
(CCR) Anchor Standards for
Writing & Writing Standards for
Literacy in the content areas
• Emphasis on #1 –
Arguments focused on
discipline-specific content
• Reading #10 – Balance of
informational and literary texts
Dr. Marci Shepard Orting School District Teaching, Learning & Assessment May 2012
39. Full Implementation 2014-2015
Math Transition
• All domains
ELA Transition
ELA teachers
• All reading, writing, language
and speaking & listening
standards
6-12 Other content area teachers
• All CCR Reading standards
• All CCR Writing standards
Dr. Marci Shepard Orting School District Teaching, Learning & Assessment May 2012
40. Technology and Multi-Media Skills
2012-2013
Develop a K-12 skills
continuum
Dr. Marci Shepard Orting School District Teaching, Learning & Assessment May 2012
41. Full Implementation 2014-2015
Math Transition
• All domains
ELA Transition
ELA teachers
• All reading, writing, language
and speaking & listening
standards
6-12 Other content area teachers
• All CCR Reading standards
• All CCR Writing standards
Technology/Multi-media
Skills
All teachers
• Incorporate technology and
multi-media to
gather, research, develop and
publish information
Dr. Marci Shepard Orting School District Teaching, Learning & Assessment May 2012
42. Recommended PD
2012-2013
K-5
• 1-2 days release time for CCSS
mathematics shift
• PLC Facilitators meet 5 times
(4 reading topics and 1
language) then lead learning in
PLCs
• IA’s join PLCs when it’s a
literacy focus
6-12
• 1-2 days release time for ELA
and Math teachers
All teachers (TU):
• CCR Reading – focus on text
complexity and academic
vocabulary
Dr. Marci Shepard Orting School District Teaching, Learning & Assessment May 2012
43. Recommended PD 2013-2014
K-5
• 1-2 days release time for CCSS
mathematics shift
• PLC Facilitators meet times (4
writing topics, 1 language and 1
speaking & listening) then lead
learning in PLCs
• IA’s join PLCs when it’s a
literacy focus
6-12
• 1-2 days release time for ELA
and Math teachers
All teachers:
• CCR writing – focus on
arguments and balance of
literary & information texts
Dr. Marci Shepard Orting School District Teaching, Learning & Assessment May 2012
44. 2012-2013 2013-2014 2014-2015
ELA Teachers Foundational Skills (K-5) Writing Standards • All reading,
K-5 & Reading Standards – Literary and Informational Language Standards #1-3 – Conventions of Standard writing, language
6-12 Language Standards #4-6 – Vocabulary Acquisition and English and speaking &
Use Speaking and Listening Standards listening
And “other content area teachers” And “other content area teachers” standards
Other Content • College and Career Readiness (CCR) Anchor • College and Career Readiness (CCR) Anchor • All CCR Reading
Teachers Standards for Reading & Reading Standards for Standards for Writing & Writing Standards for standards
Literacy in the content areas Literacy in the content areas • All CCR Writing
• Emphasis on #10 – Text Complexity • Emphasis on #1 – Arguments focused on standards
• Emphasis on #4 – Academic Vocabulary discipline-specific content
• Emphasis on Reading #10 – Balance of
informational and literary texts
Math OPS OPS • All domains
• K-Counting and Cardinality (CC); Operations and • Measurement and Data (MD); Geometry (G)
Algebraic Thinking (OA) PtR
• 1&2-Operations and Algebraic Thinking (OA); • Number and Operations in Base Ten (NBT);
Number and Operations in Base Ten (NBT) Measurement and Data (MD)
PtR OMS
Number and Operations-Fractions (NF); Operations and • Geometry (G); Statistics and Probability (SP)
Algebraic Thinking (OA) OHS
OMS • Algebra 1-Unit 3; Unit 5
6&7-Ratio and Proportion Relationship (RP); Number • Geometry – Unit 3, Unit 5; Unit 6
System (NS); Expressions and Equations (EE)
8-Number System (NS); Expressions and Equations (EE);
Functions (F)
OHS
Algebra 1&Geometry-Unit 1; Unit 2; Unit 4
Technology and Develop a K-12 skills continuum • Incorporate
Multi-Media technology and
Skills multi-media to
gather, research,
develop and
Dr. Marci Shepard Orting School District Teaching, Learning & Assessment May 2012 publish
information
45. OSD Website
Dr. Marci Shepard Orting School District Teaching, Learning & Assessment May 2012
46. Dr. Marci Shepard Orting School District Teaching, Learning & Assessment May 2012
47. Wrap up:
Go-around and share one word…
I’m feeling _________________ to the CORE!
Dr. Marci Shepard Orting School District Teaching, Learning & Assessment May 2012
Notes de l'éditeur
Handouts: Content Progressions & Shifts slideMathematical Practices slideMath Practices descriptionsThis slide up as groups report.
Handouts: Content Progressions & Shifts slideMathematical Practices slideMath Practices descriptionsThis slide up as groups report.
Handouts: Content Progressions & Shifts slideMathematical Practices slideMath Practices descriptionsThis slide up as groups report.
These critical areas in K-8 mathematics are intended to establish a firm foundation for high school algebraGreat implications on instructional practice – many instructional materials are surface and don’t provide the depth of practiceApproach mathematics in a different way – dive deep into a core area to develop habits of mind in those areas versus rushing through materialsWhat does critical area mean? Focus DAILY on the 2-4 focal point areas.
HS
Each K-8 grade is made up of domains, clusters and standards.Domain names are in the shaded band; overarching ideas that continue across multiple grades; illustrates a progression of increasing complexity Clusters are underneath in bold with the standards numbered under each of the clusters; describes the big idea of a group of related standardsStandards are numbered and describe what students should know and be able to do at each grade level
(Each grade in K-8 begins with an Introduction.These introductions identify the critical areas, which cut across topics, in the gradeThe numbered description of each critical area illustrates the focus for the learning.
The second page of each grade is an Overview. It identifies the domains and clusters in that grade also reminding readers of the mathematical practices.
High school has an added level in the hierarchy – the Conceptual Category. These Conceptual Categories are: Number and Quantity, Algebra, Functions, Geometry, Statistics and Probability and Modeling. Modeling actually does not have Standards; it is embedded within the other Conceptual Categories. Standards connected to Modeling are indicated by asterisks. Conceptual Categories are not courses. Standards marked with a plus sign are standards that are necessary for advanced mathematics. This means that any student who intends to pursue advanced mathematics needs these experiences.
Within each Conceptual Category the structure parallels K-8. There are Domains or big ideas. The bolded statements are the Clusters. The Standards are numbered and further describe the Cluster. An added element is the (+) standards which identify standards that are needed for advanced study. They are not intended to be required for all students.
Like the K-8 grade level introduction, the Conceptual Category Introduction describes the mathematics within the Conceptual Category and places that mathematics within the K-16 perspective.
The Conceptual Category Overview serves as an outline of the conceptual category, listing the domains with their clusters, and reminding readers of the mathematical practices.
An Achieve committee organized the high school standards into course sequences.
Each Pathway prepares students for a menu of fourth-year courses such as:Pre-calculus (or AP Calculus)AP StatisticsDiscrete MathematicsAdvanced Quantitative ReasoningAnd courses designed for particular career technical pathways
Each of the Pathways has an overview that details the content addressed in each course. The columns represent each course with the related domains, clusters and standards.
The critical areas are fleshed out as the units within each course. The overview By the end of the third course in each pathway, all of the critical areas have been addressed.
Unit details are elaborated with the addition of unit overviews containing instructional notes. These notes are seen in italics and further clarify the related clusters and standards.