COMMON CORE STATE

STANDARDS9-12Overview

Dr Kwaku Adu-Gyamfi

Stefanie Smith

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INTRODUCTORY ACTIVITY

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INTRODUCTORY ACTIVITY Work with your group

Who did you work with?What did you learn about them?Their knowledge of mathematicsTheir problem solving techniquesTheir mathematical preferences?

Present your Solutions

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POSSIBLE SOLUTION

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EXTENSION PROBLEM

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EXTENSION PROBLEM

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DISCUSSION Mathematics involved in the task Pedagogy experienced Connecting task to CCSSM and the

mathematical Practices Adjusting the task for your class needs

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FOUNDATIONAL OVERVIEW OF THE CCSSM Goal

Identify the domains, clusters and concept categories included in the standards

Identify and connect the standards for mathematical practice to the National Council of Teachers of Mathematics process standards

COMMON CORE STATE STANDARDS?

Aligned with college and work expectations

Maintains focus on what matters most for readiness

Include rigorous content and application of knowledge through high-order skills

Build upon strengths and lessons of current state standards

Internationally benchmarked so that all students are prepared to succeed in our global economy and society

State led

GENERAL OVERVIEW OF WHAT THE STANDARDS DEFINE Focus and coherence• Focus on key topics at each grade level.• Coherent progressions across grade levels. Balance of concepts and skills• Content standards require both conceptual

understanding and procedural fluency. Mathematical practices• Foster reasoning and sense-making in mathematics. College and career readiness• Level is ambitious but achievable.

What the Standards do NOT define 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 learners and

students with special needs Everything needed to be college and

career ready

STANDARDS: IMPORTANT BUT INSUFFICIENT

To be effective in improving education and getting all students ready for college, workforce training, and life, the Standards must be partnered with a content-rich curriculum and robust assessments, both aligned to the Standards.

NC Curriculum MATH1 /MATH2

Algebra1/Algebra2 Integrated

NC Themes Algebra Theme

Geometry Theme Functions Theme Statistics Theme

STANDARDS FOR HIGH SCHOOL

MATHEMATICS9-12

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STANDARDS FOR MATHEMATICAL CONTENT

Part 1

DESIGN AND ORGANIZATION

Standards for Mathematical Content Defines what students should understand and be

able to do (conceptual categories)

Standards for Mathematical Practice Describes habits of mind of a mathematically

proficient student

CCSS= Math content + Math practices

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HIGH SCHOOL: STANDARDS FOR MATHEMATICAL CONTENT Organized by conceptual categories

The big ideas that connect mathematics across high school Number and Quantity Algebra Functions Modeling Geometry Statistics and Probability

Elaborated through domains, clusters and standards

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COLLEGE READINESS CONNECTION

College High School

Linear Algebra Calculus Abstract Algebra Introduction to

proof Geometry Statistics and

Probability

Number and Quantity

Algebra Functions Modeling Geometry Statistics and

Probability

COMMON CORE LANGUAGE

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Content standard

Domain

Cluster

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COMMON CORE LANGUAGE

Domains: are larger groups that progress across grades (Big Idea)

Content standards: defines what students should understand and be able to do with the big idea (Objectives)

Clusters are groups of related standards (content needed to be covered for the said objective)

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DOMAIN CONTENT CLUSTERS CYCLE

Domain

Content

Clusters

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DOMAIN CONTENT CLUSTERS CLASS ACTIVITY

Work with your partner (from the race track activity)

Go to the function section of the common core (CCSSM) document

Pick out a domain, identify the standards and clusters associated with the domain

Create a chart/visual or concept map that helps address the connection between Domain Content Clusters

Color code your chart… Post your Chart Paper Gallery Walk…

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STANDARDS FOR MATHEMATICAL PRACTICES

Part 2

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STANDARDS FOR MATHEMATICAL PRACTICE Make sense of problems and persevere

in solving them Reason abstractly and quantitatively Construct viable arguments and critique

the reasoning of others Model with mathematics Use appropriate tools strategically Attend to precision Look for and make use of structure Look for an express regularity in

repeated reasoning

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STANDARDS FOR MATHEMATICS PRACTICES Describes varieties of expertise that

proficient mathematics students naturally have

Practices that all teachers should develop in their students

Practices rests on important processes and proficiencies of importance in mathematics educationProcess standardsMathematical proficiency strands

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NATIONAL COUNCIL OF TEACHERS OF MATHEMATICS (NCCTM)

Process StandardsProblem SolvingReasoning and Proof

CommunicationConnectionsRepresentations

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CONNECTION WITH THE STANDARDS

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STRANDS OF MATHEMATICAL PROFICIENCY

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STRANDS OF MATHEMATICAL PROFICIENCY Conceptual Understanding-

comprehension of mathematical concepts, operations and relations

Procedural Fluency- skill in carrying out procedures flexibly, accurately,

efficiently and appropriately Strategic Competence-

ability to formulate, represent and solve mathematical problems

Adaptive Reasoning- capacity for logical thought, reflection, explanation and

justification Productive disposition-

inclination to see mathematics as sensible useful and worthwhile, coupled with a belief in diligence and one’s own efficacy

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GROUP Take a moment to examine the first

three words of each of the 8 mathematical practices..what do you notice?

What are the verbs that illustrate the student actions for an identified mathematical practice?Circle, highlight or underline them for your

assigned practiceDiscuss with a partner, what jumps out at

you?

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STANDARDS FOR MATHEMATICAL PRACTICE ACTIVITY Stay in the same groups as for the

previous activity Each group is assigned 1-3

mathematical practices to review Each group construct tasks that reflect

their assigned practices Write tasks on chart paper Discuss challenges with regard to

developing tasks

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What I Know about the CCSSM

What I want to Know about the CCSSM

What I learned about the CCSM

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THINK PAIR SHARE

A function or not a function activity

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CARD SORT TASK

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REAL LIFE FUNCTION TASK

Overview of Mathematics Task Types

PARCC mathematics assessments will include three types of tasks.

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Task Type Description of Task TypeI. Tasks assessing concepts, skills and procedures

• Balance of conceptual understanding, fluency, and application• Can involve any or all mathematical practice standards• Machine scorable including innovative, computer-based formats• Will appear on the End of Year and Performance Based Assessment

componentsII. Tasks assessing expressing mathematical reasoning

• Each task calls for written arguments / justifications, critique of reasoning, or precision in mathematical statements (MP.3, 6).

• Can involve other mathematical practice standards• May include a mix of machine scored and hand scored responses• Included on the Performance Based Assessment component

III. Tasks assessing modeling / applications

• Each task calls for modeling/application in a real-world context or scenario (MP.4)

• Can involve other mathematical practice standards.• May include a mix of machine scored and hand scored responses• Included on the Performance Based Assessment component

For more information see PARCC Item Development ITN Appendix D.