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Math at La Cañada H.S. LCHS AND THE NEW COMMON CORE STANDARDS— PARADIGM SHIFT

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21 st century workforce skills, the Common Core State Standards and the changing assessments

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Fortune 500 Survey On Needed Workforce Skills Critical Thinking/Problem Solving Oral and written communication Teamwork/Collaboration Diversity Information Technology Application Leadership Creativity/Innovation Lifelong Learning/Self-direction Professionalism/Work ethic Ethics/Social Responsibility

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10 th grade CST Geometry Standard: 10.0 Students compute areas of polygons, including rectangles, scalene triangles, equilateral triangles, rhombi, parallelograms, and trapezoids. 9.0 Students compute the volumes and surface areas of prisms, pyramids, cylinders, cones, and spheres; and students commit to memory the formulas for prisms, pyramids, and cylinders Common Core State Standards for Mathematics: 6.G.1 Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems. 7.G.6 Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. G-GMD.1 Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone. Use dissection arguments, Cavalieri’s principle, and informal limit arguments. G-GMD. 4 Identify the shapes of two-dimensional cross-sections of three-dimensional objects, and identify three- dimensional objects generated by rotations of two-dimensional objects.

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Grade 11 Common Core Performance Task – Math Speeding Tickets New York state wants to change its system for assigning speeding fines to drivers. The current system allows a judge to assign a fine that is within the ranges shown in Table 1. Table 1. New York Speeding FinesTable 2. Massachusetts Speeding Fines Miles per Hour over Speed Limit Minimum Fine 1-10$45 11-30$90 31 or more$180 Miles per Hour over Speed Limit Fines 1-10$100 flat charge 11 or more$100 flat charge plus $10 for each additional mph above the first 10 mph

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Performance Task Continued Some people have complained that the New York speeding fine system is not fair. The New Drivers Association (NDA) is recommending a new speeding fine system. The NDA is studying the Massachusetts system because of the claims that it is fairer than the New York system. In this task, you will: Analyze the speeding fine systems for both New York and Massachusetts. Use data to propose fairer speeding fine system for New York.

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Sample Problem with Performance Task

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Sample Problem – Algebra

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Sample Problem - Geometry

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Implementatio n of the CCSS Requires Time Resources Patience Perseverance

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The Common Core State Standards We have a script for a different play…

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The Common Core State Standards Actors and Directors need training like…

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The Key to Drive Successful Implementation Teacher Professional Development and On-Going Support Teachers Development Group (TDG)

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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

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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

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MATHEMATICAL HABITS OF MIND MAKE SENSE JUSTIFY GENERALIZE Regularity Patterns Structure Mathematical Representation Connections Mistakes and Stuck Points Metacognit ion and Reflection Persevere and Seek More

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MATHEMATI CAL HABITS OF INTERACTIO N Private Reasoning Time Explain Listen to Understand Genuine Questions

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Fixed Mindset vs. Growth Mindset Carol Dweck Fixed MindsetGrowth Mindset Believe that ability is fixed and being good at math is a “gift” Believe that math “smartness” grows with hard work 18

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How to help your child at home Your job is to help your child move towards an answer, not solve the problem for him or her. Have your child explain to you how he or she is thinking and reasoning about the problem. Let them grapple. Resist the temptation to rescue your child. Praise your child for qualities they can control like effort and perseverance.

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How to help your child at home Ask open-ended questions: “Explain your thinking.” “How do you know?” “What confuses you?” “What do you understand?” “What do you know about the problem?” “What are you being asked to do?” “If your math teacher were here, what would he or she say?” “What ideas do you have for solving the problem (i.e. drawing, using manipulatives, role playing, etc.) Source: Some of the slides have been taken from Torrey Pines Elementary School’s Math Night Presentation.

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Implementatio n of the CCSS Requires Community, Students, Teachers, Staff coming together

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Common Core Mathematical Practices. People who are good in math… Make sense of problems.

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