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Parent Information Meeting ACCELERATED PATHWAYS IN MATH WALNUT CREEK SCHOOL DISTRICT MARCH 4, 2015 Information Overview of Common Core State Standards for Math (CCSSM) Course Sequences for CCSSM Course Content for CCSSM and Accelerated Pathway Criteria for Accelerated Pathway Instructional Shifts Focus: Place a strong emphasis on the grade-level and course-level standards Coherence: Think across grades and link major topics in each grade Rigor: Pursue with equal intensity Conceptual understanding Procedural skills and fluency Applications Why Students Need Common Core Math Math as a learning subject not a performance subject. Classrooms need to teach multi-dimensional mathematics. All students should be encouraged to take work to the highest level possible. Classrooms should encourage more depth, less speed. Jo Boaler – Stanford University Video: http://youcubed.stanford.edu/why-we-needcommon-core-math/ CCSS Aligned Math Courses CCSS Math 6 CCSS Math 7 CCSS Math 8 More rigorous Increased depth and complexity Increased problem solving and application of conceptual and procedural understanding True/False A number of CCSSM topics at the middle school level are repeated over various grade levels. False: The CCSSM greatly reduce the topic repetition in mathematics curriculum for grades 5-8. Each grade level has its own significant topics that are not repeated. CCSSM Math 6 Ratios and Proportional Relationships Understand ratio concepts and use ratio reasoning to solve problems. The Number System Apply and extend previous understandings of multiplication and division to divide fractions by fractions. Compute fluently with multi-digit numbers and find common factors and multiples. Apply and extend previous understandings of numbers to the system of rational numbers. Expressions and Equations Apply and extend previous understandings of arithmetic to algebraic expressions. Reason about and solve one-variable equations and inequalities. Represent and analyze quantitative relationships between dependent and independent variables. Geometry Solve real-world and mathematical problems involving area, surface area, and volume. Statistics and Probability Develop understanding of statistical variability. Summarize and describe distributions. CCSSM Math 7 Ratios and Proportional Relationships Analyze proportional relationships and use them to solve real-world and mathematical problems. The Number System Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers. Know that there are numbers that are not rational and approximate them by rational numbers. Expressions and Equations Use properties of operations to generate equivalent expressions. Solve real-life and mathematical problems using numerical and algebraic expressions and equations. Geometry Draw, construct and describe geometrical figures and describe the relationships between them. Solve real-life and mathematical problems involving angle measure, area, surface area, and volume. Solve real-life and mathematical problems involving volume of cylinders, cones, and spheres. Statistics and Probability Use random sampling to draw inferences about a population. Draw informal comparative inferences about two populations. Investigate chance processes and develop, use, and evaluate probability models. True/False The California Standards adopted in 1997 had grade- level specific standards for grade eight. False: Prior to adoption of the rigorous California CCSSM grade eight standards, there were not gradelevel specific standards for grade eight. CA Mathematics Framework 2013 True/False The 1997 California Standards Algebra I course is a less rigorous course than the CCSSM for Grade 8 course. True: Prior to the adoption of the CCSSM - Algebra I was the course name for increasing numbers of students in eighth grade. Algebra I is the course name in ninth grade for most students who moving forward will complete the CA CCSSM for grade eight – a course that is more rigorous and more demanding than earlier versions of “Algebra I.” CA Mathematics Framework 2013 CCSSM Math 8 The Number System Know that there are numbers that are not rational, and approximate them by rational numbers. Expressions and Equations Work with radicals and integer exponents. Understand the connection between proportional relationships, lines, and linear equations. Analyze and solve linear equations and pairs of simultaneous linear equations. Functions Define, evaluate, and compare functions. Use functions to model relationships between quantities. Geometry Understand congruence and similarity using physical models, transparencies, or geometry software. Understand and apply the Pythagorean Theorem. Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres. Statistics and Probability Investigate patterns of association in bivariate data. CCSSM Grade 8 – More Rigorous CCSSM Math 8 addresses the foundations of algebra: In-depth study of linear relationships and equations More formal treatment of functions Exploration of Irrational Numbers Geometry Transformations and triangle proofs Relate graphing to algebra Statistics Connect linear relationships with the representation of bivariate data Mastery of K-8 Math “Mastery of the algebra content, including attention to the Standards for Mathematical Practice, is fundamental for success in further mathematics and on college entrance examinations. Skipping over material to get students to a particular point in the curriculum will create gaps in students’ mathematical background.” CA Mathematical Framework, 2013 CCSS Accelerated Path Math 6 Pre-Algebra – Compacted CCSSM 7/8 Algebra I (Math 8) Compacted content Accelerated pace Upon successful completion students enroll in Geometry What is Compacting? To compress the content - three years of math content into two years: All content standards must be fully addressed All practice standards are fully addressed Requires a faster pace to complete the course It does not mean skipping content or opportunities for problem solving and application of conceptual and procedural understanding. Pre-Algebra /Compacted Math 7 & 8 Rational Numbers and Exponents Proportionality and Linear Relationships Introduction to Sampling Inference Creating, Comparing and Analyzing Geometric Figures Nearly all of the CCSSM for Grade 7 & 8 are included in this course with the exception of three standard sets. Algebra I Compacted CCSSM Grade 8 Algebra and Functions: Systems of equations Geometry: Congruence and similarity, triangle proofs Statistics: Statistical inferences Algebra I Number and Quantity Algebra Functions Statistics and Probability Algebra I Number and Quantity Exponents to rational exponents Properties of rational and irrational numbers. Reason quantitatively and use units to solve problems. Algebra Interpret the structure of expressions. Write expressions in equivalent forms to solve problems. Perform arithmetic operations on polynomials. Create equations that describe numbers or relationships. Understand solving equations as a process of reasoning and explain the reasoning. Solve equations and inequalities in one variable. Solve systems of equations. Represent and solve equations and inequalities graphically. Algebra I (continued) Functions Understand the concept of a function Use function notation. Interpret functions. Analyze functions using different representations. Build a function that models a relationship between two quantities. Build new functions from existing functions. Construct and compare linear, quadratic, and exponential models and solve problems. Interpret expressions for functions Statistics and Probability Summarize, represent, and interpret data on a single count or measurement variable. Summarize, represent, and interpret data on two categorical and quantitative variables. Interpret linear models. Algebra I This course whether taken in Middle School or High School builds on the CCSSM for grade 8 and is correspondingly more advanced than previous algebra courses. True/False The University of California’s A-G requirements include passing calculus in high school. False: A-G recommends a 4th year of mathematics – it is not required. Middle to High School Course Sequence CCSS Aligned Math Courses – Path 1 CCSS Aligned Math Courses – Path 2 Math 6 Math 6 Math 7 Math 7 Math 8 Math 8 Algebra I Algebra I Geometry Geometry/Honors Algebra II Algebra II/Trig Pre- Calculus Calculus AB Middle to High School Course Sequence CCSS Accelerated Path 1 CCSS Accelerated Path 2 Math 6 Math 6 Pre-Algebra Pre-Algebra Algebra I Algebra I Geometry Geometry Algebra II Pre-Calculus Calculus AB Algebra II/Trig Calculus AB Calculus BC/AP Statistics Considerations for Accelerated Placement To ensure that students are developmentally ready for accelerated content it is not recommended to compact before grade seven. Solid evidence of student’s conceptual understanding, knowledge of procedural skills, and ability to apply mathematics before moving into an accelerated pathway. CA Mathematics Framework, 2013 WCSD Criteria Grades Tests Mathematics Diagnostic Testing Project – CA State University/University of CA MARS exam Teacher Input Teacher Input Completes homework Understands complex concepts and relationships; undertakes sophisticated problem solving Is a quick learner; keenly observant, responds rapidly Perseveres in problem solving Advocates for self and asks for help Collaborates well with peers Student demonstrates motivation for learning Pre-Algebra – CCSSM 7/8 Compacted Eligible students must meet the following matrix criteria: 3 2 1 0 Grade Average Q1-Q3 95% and above 93-94.9% 92.9-90% 89.9% and below Test Average Q1-Q3 93% and above 90-92.9% 87-89.9% 86.9% and below MDTP 35-40 34 33 0-32 MARS 32-40 26-31 22-25 0-21 Algebra I Eligible students must meet the following matrix criteria: 3 2 1 0 Grade 95% and Average Q1- above Q3 93-94.9% 92.9-90% 89.9% and below Test 93% and Average Q1- above Q3 90-92.9% 87-89.9% 86.9% and below District Assessment 80% and above 75-79.9% 73-74.9% 72% and below MARS 14-16 12-13 10-11 0-9 Eligibility Criteria Case 1 Matrix Score 10-12 No zeros Case 2 Matrix Score 8-9 Teacher Input Score 28-35 No zeros Parents may appeal for students who do not meet the above criteria. Timeline 2014-2015 Sixth Grade MDTP – Week of March 9 MARS Exam – Last two weeks of April Seventh Grade Placement Exams – Week of May 4 Notification of eligibility by letter at the end of June