Amador Public Schools Common Core Secondary Math

Common Core State StandardsThe Mathematics Standards

Our focus today is to learn about the Common Core State Standards. the CACCSS-M deals the the same standards as the CCSS-M national version, but there are some additions that make ours distinct.1States that Adopted

Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved. 2

TIME: 12 minutes (CONTINUED for Slides 4 to 8)INTENT: To provide information on the states that have adopted the CCSS___________________________________________________________________________________As of November 2011, only five states have not adopted the CCSS. This list includes the District of Columbia and the U.S. Virgin Islands.

Californias Common Core State Standards: Toolkit | Overview2WhyTo ensure that our students aremeeting 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; andprovided with rigorous content and applications of higher knowledge through higher order thinking skills.

2011 CA County Superintendents Educational Services Association3

TIME: 12 minutes (CONTINUED for Slides 4 to 8)INTENT: To provide a background on why the new standards were written___________________________________________________________________________________The standards were written to ensure that our students are:[click] meeting college and career expectations; While reading demands in college, workforce training programs, and life in general have held steady or increased over the last half century, K12 texts have actually declined in sophistication, and relatively little attention has been paid to students ability to read complex texts independently. Furthermore, students in college are expected to read complex texts with substantially greater independence (i.e., much less scaffolding) than students in typical K12 programs.[click] provided a vision of what it means to be an academically literate person in the twenty-first century;[click] prepared to succeed in our global economy and society; andStudents must be prepared for both our domestic economy and, more so than ever before, for our global economy.[click] provided with rigorous content and applications of higher knowledge through higher order thinking skills.This means our students must master ever more rigorous content and be prepared to apply that content to succeed.Californias Common Core State Standards: Toolkit | Overview3The CCSS for Mathematicsare 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

4Whats 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)

5So What is Different?Focus on College & Career PathwaysEmphasis on Mathematical ModelingStandards of Mathematical PracticeMultiple Formats for Testing

Take a minute and think aboutWhat does it mean to be college ready?

What does it mean to be career ready?7

Spend some time allowing for participants to talk. Then (if time allows) share out some ideas.7College & Career ReadinessACT 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. ACTs 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.www.act.org/commoncore/pdf/FirstLook.pdf

American College Testing Program Common Core State StandardsTwo types of mathematics standards

Standards for ContentStandards for Practice9

Share both sets of Standards with Participants.

CCSS have two sets of Standards for Mathematics. Both types of standards will be assessed and both need to be a part of regular instruction and teachers need to understand and be familiar with both types of standards. This session is designed to introduce participants to the mathematical practiceswhat they are and what they might mean for their instruction and assessment.

10Standards of Mathematical PracticeGrades K-5Grades 6-8High School MathGrade 8 CCSSGrade Level Standards

As of January 2012, Instructional Quality Commission has removed almost all of the 15% additions because the additions were either too specific or it was repetitive. This includes the removal of Algebra 1 at the 8th Grade. The recommendation is to provide a K-8th grade curriculum. Acceleration is still possible, but not to offer an Algebra 1 or beyond course at the middle school level.10California Grade 8 Algebra 1

Standards for 8th grade2011 CA County Superintendents Educational Services Association11

TIME: 5 minutes (for Slide 50)INTENT: To understand the CCSS grade 8 options___________________________________________________________________________________In California, the goal for 8th grade students is Algebra 1. The CCSS has standards for grades K-8 organized by domain, and the courses/clusters begin in grade 9. Each state was able to add an additional 15% to the original CCSS. California added a grade 8 Algebra 1 Course. As a result, there are 2 options for grade 8 students in California. While it is the goal for California 8th graders to take Algebra, students can take the grade 8 course as outlined by the national document or they can take the Algebra 1 course that California designed for 8th grade students. Each option will prepare students for college and career. INSTRUCTOR NOTE:The grade 8 CCSS course is not a remedial course. It is a course that contains rich mathematics and is not aligned to the California Algebra Readiness Program currently designed for grades 8 and above.The SMARTER Balanced Consortium is creating assessments for the 8th grade CCSS Course and not the 8th grade Algebra 1 Course that was designed by California. K-7 standards as augmented prepare students for either set of standards. Californias Common Core State Standards: Toolkit | Overview11Standards for Mathematical PracticeThe 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 Standards12

TIME: 2 minutes (for Slide 47)INTENT: To understand that the Standards for Mathematical Practice describe two types of student learning: 1) thinking process and habits of mind; and 2) mathematical content___________________________________________________________________________________The Standards for Mathematical Practice describe the thinking processes, habits of mind, and dispositions that students need to develop a deep, flexible, and enduring understanding of mathematics.For example, in Standards for Mathematical Practice 1, students will need to engage in tasks that have them analyze givens, constraints, relationships, and goals. They need to monitor and evaluate their progress and be able to change course if necessary. Californias Common Core State Standards: Toolkit | Overview12Part 1: Standards for Mathematical PracticeMake sense of problems and persevere in solving themstart by explaining the meaning of a problem and looking for entry points to its solutionReason abstractly and quantitativelymake sense of quantities and their relationships to problem situationsConstruct viable arguments and critique the reasoning of othersunderstand and use stated assumptions, definitions, and previously established results in constructing argumentsModel with mathematicscan apply the mathematics they know to solve problems arising in everyday life, society, and the workplace2011 CA County Superintendents Educational Services Association13

TIME: 7 minutes (for Slides 44 to 46)INTENT: To understand the Standards for Mathematical Practice as outlined in the CCSS___________________________________________________________________________________Have participants locate the CCSS for Mathematics handout and turn to the Standards for Mathematical Practice found on pp.1-2. Briefly discuss each of the Standards for Mathematical Practice. HANDOUTS:CCSS for Mathematics

Explain Mathematical modeling as applications.Californias Common Core State Standards: Toolkit | Overview13Part 2: Standards for Mathematical PracticeUse appropriate tools strategicallyconsider the available tools when solving a mathematical problemAttend to precisioncommunicate precisely using clear definitions and calculate accurately and efficientlyLook for and make use of structurelook closely to discern a pattern or structureLook for and express regularity in repeated reasoningnotice if calculations are repeated, and look for both general methods and for shortcuts2011 CA County Superintendents Educational Services Association14

TIME: 7 minutes (CONTINUED for Slides 44 to 46)INTENT: To understand the Standards for Mathematical Practice as outlined in the CCSS___________________________________________________________________________________Continued from previous slide. Briefly discuss Standards 5-8.HANDOUTS:CCSS for MathematicsCalifornias Common Core State Standards: Toolkit | Overview14CCSS Domains K-5DomainK12345Counting 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)

Point out that there15CCSS Domains 6-8Domain678Ratio and Proportional Relationships (RP)The Number System (NS)Expressions and Equations (EE)Geometry (G)Statistics and Probability (SP)Functions (F)

Point out that there is a focus on fractions. One entire domain is dedicated to it.16Domains and Conceptual CategoriesDistribution

Findell & Foughty (2011)College and Career-Readiness through the Common Core State Standards for Mathematics17

TIME: 10 minutes (CONTINUED for Slides 51 to 54)INTENT: To understand how domains and conceptual categories are distributed across the grade levels ___________________________________________________________________________________This diagram illustrates how the domains are distributed across the CCSS. This diagram does not show how a domain may impact multiple domains in future grades. An example is K-5 Measurement and Data, which splits into Statistics and Probability and Geometry in grade 6. Likewise, Operations and Algebraic Thinking in K-5 provides a foundation for Ratios and Proportional Relationships, The Number System, Expressions and Equations, and Functions in grades 6-8.Californias Common Core State Standards: Toolkit | Overview17Focusing Attention Within Number and OperationsBriars & Mitchell (2010)Getting Started with the Common Core State StandardsOperations and Algebraic ThinkingNumber and Operations - Base TenNumber and Operations - FractionsExpressions and EquationsThe NumberSystem

Algebra

K-56-8High School18

TIME: 5 minutes (CONTINUED for Slides 48 to 49)INTENT: To understand that the Standards for Mathematical Practice use mathematical progression to help ensure success as students progress through grade levels, practices, and content___________________________________________________________________________________The content of the K-5 domains and the 6-8 domains lead students to be ready for algebra. The big ideas have been backward mapped and build upon each other as students move up the grades. This is the critical nature of mathematical progressions. Californias Common Core State Standards: Toolkit | Overview1819

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202013-2014Amador Public SchoolsCommon Core Secondary Math

Six Conceptual CategoriesNumber and quantityAlgebraFunctionsModelingGeometryStatistics and probability

The six conceptual categories are number and quantity, algebra, functions, modeling, geometry, and statistics and probability. Conceptual categories portray a coherent view of higher mathematics and cross traditional course boundaries. There are no standards listed in the conceptual category of modeling. Instead, specific modeling standards appear throughout the other conceptual categories and are indicated by a star symbol ().

22To be college and career readyAlgebra 1GeometryAlgebra 2

Algebra II is the new standard. As of now, the Smarter Balanced Assessment tests once in high school for math. That is eleventh grade and that test will be based on Algebra II standards.23Preparation for advanced mathCalculusAdvanced statisticsDiscrete Statistics

When reading the standards ALL standards without a (+) are for all students to be college and career ready.

Local districts determine which course offerings and sequences best meet the needs of their students. The table provides guidance on possible course-taking sequences in higher mathematics. It is not intended to be an exhaustive list of courses or sequences of courses that students could take.25The Standards are differentEither Pathway

High School Model Algebra 1Deepen and extend understanding of linear and exponential relationshipsContrast linear and exponential relationships with each other and engage in methods for analyzing solving and using quadratic functionsExtend the laws of exponents to square and cube rootsApply linear models to data that exhibits a linear trend.

Instructional time should focus on four critical areas.27

By the end of eighth grade, students have learned to solve linear equations in one variable and have applied graphical and algebraic methods to analyze and solve systems of linear equations in two variables. In Algebra I, students analyze and explain the process of solving an equation and justify the process used in solving a system of equations. Students develop fluency writing, interpreting, and translating among various forms of linear equations and inequalities, and use them to solve problems. They master the solution of linear equations and apply related solution techniques and the laws of exponents to the creation and solution of simple exponential equations.

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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 IIrelate arithmetic of rational expressions to arithmetic of rational numbers expand understandings of functions and graphing to include trigonometric functionssynthesize and generalize functions and extend understanding of exponential functions to logarithmic functionsrelate data display and summary statistics to probability and explore a variety of data collection methods

Instructional time should focus on four critical areas.371. Relate arithmetic of rational expressions to arithmetic of rational numbers.

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

Building on their previous work with functions and on their work with trigonometric ratios and circles in the Model Geometry course, students now use the coordinate plane to extend trigonometry to model periodic phenomena. 393. Synthesize and generalize functions and extend understanding of exponential functions to logarithmic functions

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

41Please take some time nowTo review theCDE Draft math Framework

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