Common Core State Standards THE MATHEMATICS STANDARDS

States that Adopted © Copyright National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved. 2

Why To ensure that our students are… meeting college and career expectations (Text Complexity needs to be increased K-12); provided a vision of what it means to be an academically literate person in the twenty-first century; prepared to succeed in our global economy and society; and provided with rigorous content and applications of higher knowledge through higher order thinking skills © CA County Superintendents Educational Services Association 3

The CCSS for Mathematics ……are not a mile wide & an inch deep…… are focused, coherent, and rigorous aim for clarity and specificity balance mathematical understanding & procedural skills stress conceptual understanding of key ideas are internationally benchmarked are research based

What’s different about CCSS? These Standards are not intended to be new names for old ways of doing business. They are a call to take the next step. It is time for states to work together to build on lessons learned from two decades of standards based reforms. It is time to recognize that standards are not just promises to our children, but promises we intend to keep. — CCSS (2010, p.5)

So What is Different? o Focus on College & Career Pathways o Emphasis on Mathematical Modeling o Standards of Mathematical Practice o Multiple Formats for Testing

Take a minute and think about… What does it mean to be college ready? What does it mean to be career ready? 7

College & Career Readiness ACT defines college & career readiness as the acquisition of the knowledge & skills a student needs to enroll & succeed in credit-bearing, first year courses at a postsecondary institution without the need for remediation. ACT’s definition of college & career readiness was adopted by the Common Core State Standards Initiative & provides a unifying goal upon which educators & policymakers now must act. ook.pdf

Common Core State Standards Two types of mathematics standards Standards for Content Standards for Practice 9

10 Standards of Mathematical Practice Grades K-5Grades 6-8 High School Math Grade 8 CCSS Grade Level Standards

California Grade 8 Algebra 1 Standards for 8th grade 2011 © CA County Superintendents Educational Services Association 11

Standards for Mathematical Practice The Eight Standards for Mathematical Practice place an emphasis on student demonstrations of learning that describe the thinking processes, habits of mind, and dispositions that students need to develop. adapted from Briars & Mitchell (2010) Getting Started with the Common Core State Standards 12

Part 1: Standards for Mathematical Practice 1. Make sense of problems and persevere in solving them …start by explaining the meaning of a problem and looking for entry points to its solution 2. Reason abstractly and quantitatively …make sense of quantities and their relationships to problem situations 3. Construct viable arguments and critique the reasoning of others …understand and use stated assumptions, definitions, and previously established results in constructing arguments 4. Model with mathematics …can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace 2011 © CA County Superintendents Educational Services Association 13

Part 2: Standards for Mathematical Practice 5. Use appropriate tools strategically …consider the available tools when solving a mathematical problem 6. Attend to precision …communicate precisely using clear definitions and calculate accurately and efficiently 7. Look for and make use of structure …look closely to discern a pattern or structure 8. Look for and express regularity in repeated reasoning …notice if calculations are repeated, and look for both general methods and for shortcuts 2011 © CA County Superintendents Educational Services Association 14

CCSS Domains K-5 Domain K12345 Counting and Cardinality (CC) ✓ Operations and Algebraic Thinking (OA) ✓✓✓✓✓✓ Number and Operations in Base 10 (NBT) ✓✓✓✓✓✓ Measurement and Data (MD) ✓✓✓✓✓✓ Geometry (G) ✓✓✓✓✓✓ Number and Operation – Fractions (NF) ✓✓✓

CCSS Domains 6-8 Domain 678 Ratio and Proportional Relationships (RP) ✓✓ The Number System (NS) ✓✓✓ Expressions and Equations (EE) ✓✓✓ Geometry (G) ✓✓✓ Statistics and Probability (SP) ✓✓✓ Functions (F) ✓

Domains and Conceptual Categories Distribution Findell & Foughty (2011) College and Career-Readiness through the Common Core State Standards for Mathematics 17

Focusing Attention Within Number and Operations Briars & Mitchell (2010) Getting Started with the Common Core State Standards Operations and Algebraic Thinking Number and Operations - Base Ten Number and Operations - Fractions Expressions and Equations The Number System Algebra K-56-8High School 18

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Amador Public Schools Common Core Secondary Math

Six Conceptual Categories Number and quantity Algebra Functions Modeling Geometry Statistics and probability

To be college and career ready Algebra 1 Geometry Algebra 2

Preparation for advanced math Calculus Advanced statistics Discrete Statistics When reading the standards ALL standards without a (+) are for all students to be college and career ready.

THE STANDARDS ARE DIFFERENT Either Pathway

High School Model Algebra 1 1. Deepen and extend understanding of linear and exponential relationships 2. Contrast linear and exponential relationships with each other and engage in methods for analyzing solving and using quadratic functions 3. Extend the laws of exponents to square and cube roots 4. Apply linear models to data that exhibits a linear trend.

Establish a criteria for congruence of triangles based on rigid motions

Establish criteria for similarity of triangles based on dilations and proportional reasoning.

Informally develop explanations of circumference, area and volume formulas.

Pythagorean Theorem

Prove basic geometric theorems

Extend work with probability

High School Model Algebra II 1. relate arithmetic of rational expressions to arithmetic of rational numbers 2. expand understandings of functions and graphing to include trigonometric functions 3. synthesize and generalize functions and extend understanding of exponential functions to logarithmic functions 4. relate data display and summary statistics to probability and explore a variety of data collection methods

1. Relate arithmetic of rational expressions to arithmetic of rational numbers.

2. Expand understandings of functions and graphing to include trigonometric functions

3. Synthesize and generalize functions and extend understanding of exponential functions to logarithmic functions

4. Relate data display and summary statistics to probability and explore a variety of data collection methods

PLEASE TAKE SOME TIME NOW TO REVIEW THE CDE “DRAFT MATH FRAMEWORK” A LINK HAS BEEN PROVIDED