The Common Core State Standards for Mathematics

Transitioning to the Common Core

K-8 Content StandardsK-8 Content StandardsGrade

Domain

Cluster

Standard

K-8 Grade Level Overview

Critical Areas Critical Areas – similar to – similar to

NCTM’s NCTM’s Curriculum Curriculum Focal PointsFocal Points

Format of K-8 Standards Grade Grade LevelLevel

DomainDomain

Format of K-8 Standards

ClusterCluster

ClusterCluster

StandardStandard

StandardStandard

Domain K 1 2 3 4 5Counting and Cardinality (CC)

Operations and Algebraic Thinking (OA)

Number and Operations in Base Ten (NBT)

Measurement and Data (MD)

Geometry (G)

Numbers and Operations- Fractions (NF)

DomainsDomains

Domain 6 7 8

Ratios and Proportional Relationships (RP)

The Number System (NS)

Expressions and Equations (EE)

Geometry (G)

Statistics and Probability (SP)

Functions (F)

DomainsDomains

High School Conceptual Categories

• The big ideas that connect mathematics across high school – such as Functions or Probability and Statistics

• A progression of increasing complexity• Description of mathematical content to be

learned elaborated through domains, clusters, and standards

• Number and Quantity • Algebra • Functions • Geometry • Statistics and Probability • Modeling

High School Conceptual Categories

Pathways

• Four model pathways:– Traditional Pathway (Algebra 1, Geometry,

Algebra 2)– Integrated Pathway– Compacted Traditional Pathway*– Compacted Integrated Pathway*

*7th, 8th, and Algebra 1 standards covered in 2 years

See CCSSM APPENDIX A for course descriptions for both pathways.

8 CCSS Mathematical Practices1. 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.

SMARTER Balanced Assessment Consortium System Highlights

Assessment Design

The Consortium will provide the following by the 2014-15 school year:

3. Formative tools and resources4. Responsible flexibility5. Distributed summative assessment

a. Content clusters throughout a courseb. Most appropriate time for each studentc. Scores rolled up

Smarter Balanced Assessment Consortium

Link to Practice StandardsFour Claims Used in Draft 2 Test Specifications

Claim 1 ≈ 40% of assessmentClaim 2 ≈ 20% of assessmentClaim 3 ≈ 20% of assessmentClaim 4 ≈ 20% of assessment

SHIFT #1: Focus

Similar to the Oregon standards in Mathematics, the intent of the CCSSM is to narrowly and deeply focus the time and energy spent in the math classroom.

The CCSSM emphasizes concepts prioritized in the

standards so that students reach strong foundational knowledge and deep conceptual understanding and are able to transfer mathematical skills and understanding across concepts and grades.

The Three-Legged Stool

In order to focus on content, you must teach to address all three legs of mathematical learning:• Conceptual

Understanding• Computational Fluency• Problem-Solving

Draft Emphases (Sample – Grade 6)Ratios and Proportional Relationships[m] Understand ratio concepts and use ratio reasoning to solve problems.

The Number System[m] Apply and extend previous understandings of multiplication and division to divide fractions by fractions.[a] Compute fluently with multi-digit numbers and find common factors and multiples.[m] Apply and extend previous understandings of numbers to the system of rational numbers.

Expressions and Equations[m] Apply and extend previous understandings of arithmetic to algebraic expressions.[m] Reason about and solve one-variable equations and inequalities.[m] Represent and analyze quantitative relationships between dependent and independent variables

Geometry[s] Solve real-world and mathematical problems involving area, surface area, and volume.

Statistics and Probability[a] Develop understanding of statistical variability.[a] Summarize and describe distributions.

Activity: Focus (find a partner or small group at your grade level)

Grades K-2• Read through the

Critical Areas page of your standards

• Discuss with a partner how you could better address all three legs of the “mathematics” stool in these areas

Grades 3-HS• Pick up the appropriate

Emphases page from the front

• Look at the “m” clusters and discuss how you could better address all three legs of the “mathematics” stool in these areas

Deep conceptual understanding of core content at each grade is critical for student success in subsequent years.

Each standard is not a new event, but an

extension of previous learning. For example, fractions and multiplication build across grade levels and students can scaffold new understanding onto foundations built in previous years.

SHIFT #2: Coherence

Activity: Coherence(with same partner or small group at your grade level)

Grades K-2• Look at the standards not

in your critical areas (may fall in the same domain but be listed at the end)

• How are these connecting to your grade level while introducing or reinforcing other grade level skills?

Grades 3-8• Look at the “s” and “a”

clusters. How are these connecting to your grade level while introducing or reinforcing other grade level skills?

Activity: Coherence (Cont)(with same partner or small group at your grade level)

High School• Only your major emphases are listed on the Emphases

handout. • Coherence may come from connecting and reinforcing

previous grade level standards. • How do the additional and supporting (non-major)

standards fit into your program(s)?

Shift #4: Modeling Modeling links classroom mathematics and statistics to

everyday life, work, and decision-making– Choose and use appropriate mathematics to analyze situations– Better understanding real-world scenarios involving math

Teachers at all grade levels should identify

opportunities for students to apply math concepts

in “real world” situations.

Activity: Modeling

1. Locate your goldenrod stations activity template.

2. Visit between 4-6 stations.Pink Cards = Elementary ContentBlue Cards = Middle/High School Content

3.While visiting stations, have others sign off on the correctness of your answer. Nobody can sign your paper

more than twice.

4. When finished, return to your seat and answer the two questions at the bottom of the page.

Performance TaskChoose a new partner or small group:

Elementary or Secondary

1. Pick up the appropriate performance task up front.

Options: Elementary (4th Grade) or High School

2. Understand purpose and placement of task in classroom instruction and assessment.

3. Read/Attempt the task.

4. Discuss implications for classroom instruction.

Contact Information

Shannon McCaw, SMc Curriculumwww.SMcCurriculum.com

mccaws@smccurriculum.com503-550-4298