Introduction to the Math Common Core Presented by Dr. Nicki Newton
Introduction • Welcome • Introductions • Overview • Logistics – blog, pearltree, twitter • Conference Handbook
Goals of the Workshop • Learn Practical Strategies to Implement CCSS Standards A. Mathematical Practices B. Domains 2. Scaffold Instruction • Meaningfully Integrate Technology • Meaningfully Integrate Literature
Essential Questions • How does the New Math CCSS change the way we think about teaching and learning math? • How do I teach the mathematical practices? • What’s different about the content in the Domains?
History of the Common Core • A Nation at Risk, 1983 • NCTM, 1989 • Goals 2000 • Achieve, Inc. • No Child Left Behind • The NGA/CCSSO Standards Initiative
Why the CCSS? • Preparation: The standards are college- and career-ready. They will help prepare students with the knowledge and skills they need to succeed in education and training after high school.
Why the CCSS? • Competition: The standards are internationally benchmarked. Common standards will help ensure our students are globally competitive.
Why the CCSS? • Equity: Expectations are consistent for all – and not dependent on a student’s zip code.
Why the CCSS? • Clarity: The standards are focused, coherent, and clear. Clearer standards help students (and parents and teachers) understand what is expected of them.
Why the CCSS? • Collaboration: The standards create a foundation to work collaboratively across states and districts, pooling resources and expertise, to create curricular tools, professional development, common assessments and other materials
Who is involved? As of October, 2011
Key Points in Math • The K-5 standards provide students with a solid foundation in whole numbers, addition, subtraction, multiplication, division, fractions and decimals—which help young students build the foundation to successfully apply more demanding math concepts and procedures, and move into applications. Source: http://www.corestandards.org/about-the-standards/key-points-in-mathematics
Key Points in Math • The K-5 standards build on the best state standards to provide detailed guidance to teachers on how to navigate their way through knotty topics such as fractions, negative numbers, and geometry, and do so by maintaining a continuous progression from grade to grade. Source: http://www.corestandards.org/about-the-standards/key-points-in-mathematics
Key Points in Math • The standards stress not only procedural skill but also conceptual understanding, to make sure students are learning and absorbing the critical information they need to succeed at higher levels Source: http://www.corestandards.org/about-the-standards/key-points-in-mathematics
Key Points in Math • - rather than the current practices by which many students learn enough to get by on the next test, but forget it shortly thereafter, only to review again the following year. Source: http://www.corestandards.org/about-the-standards/key-points-in-mathematics
Math Components • Mathematical Practices • Critical Areas • Domains
Big Ideas for Grades 3 - 5 Measurement and Data Number and Operations in Base Ten Operations in Algebraic Thinking
Must Look at CCSS Progressions • Content Progressions • *Good resource is NC • ckingeducation.com
Critical Areas – Grade 3 Instructional time should focus on four critical areas: • developing understanding of multiplication and division and strategies for multiplication and division within 100 (i.e. sticks, circles and squares; divide and ride) • developing understanding of fractions, especially unit fractions (fractions with numerator 1) (math stories –numerator/denominator dogs)(find your match)
Critical Areas – Grade 3 Instructional time should focus on four critical areas: (3) developing understanding of the structure of rectangular arrays and of area (4) describing and analyzing two-dimensional shapes (Tell me all you can).
Critical Areas – Grade 4 Instructionaltime should focus on three critical areas: • developing understanding and fluency with multi-digit multiplication, and developing understanding of dividing to find quotients involving multi-digit dividends (base ten block division; equal groups; dots and dashes) • developing an understanding of fraction equivalence, addition and subtraction of fractions with like denominators, and multiplication of fractions by whole numbers (Show video of models)(show fraction man)(fraction bingo) • Understanding that geometric figures can be analyzed and classified based on their properties, such as having parallel sides, perpendicular sides, particular angle measures, and symmetry. (show matrices)
Critical Areas – Grade 5 Instructional time should focus on three critical areas: • developing fluency with addition and subtraction of fractions, and developing understanding of the multiplication of fractions and of division of fractions in limited cases (unit fractions divided by whole numbers and whole numbers divided by unit fractions) (show video) • extending division to 2-digit divisors, integrating decimal fractions into the place value system and developing understanding of operations with decimals to hundredths, and developing fluency with whole number and decimal operations (show videos) • developing understanding of volume
Processes & Proficiencies NCTM: • Problem Solving • Reasoning and Proof • Communication • Connections • Representation Adding it Up: • Conceptual Understanding • Procedural Fluency • Strategic Competence • Adaptive Reasoning • Mathematical Reasoning
Make sense of problems and persevere in solving them. • Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals.
Make sense of problems and persevere in solving them. • They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt.
Make sense of problems and persevere in solving them. • They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution.
Make sense of problems and persevere in solving them. • They monitor and evaluate their progress and change course if necessary.
Make sense of problems and persevere in solving them. • Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, “Does this make sense?”
Make sense of problems and persevere in solving them. • They can understand the approaches of others to solving complex problems and identify correspondences between different approaches.
Let’s Make Sense of a Problem and Persevere in Solving it! • Timothy’s Dice Problem
Level 1 of Problem Solving(O& Ap.25) • Level 1 is making and counting all of the quantities involved in a multiplication or division. As before, the quantities can be represented by objects or with a diagram, but a diagram affords reflection and sharing when it is drawn on the board and explained by a student.
Level 2 of Problem Solving(O& Ap.25) • Level 2 is repeated counting on by a given number, such as for 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30. The count-bys give the running total. The number of 3s said is tracked with fingers or a visual or physical (e.g., head bobs) pattern. For 8x 3, you know the number of 3s and count by 3 until you reach 8 of them. For 24/3, you count by 3 until you hear 24, then look at your tracking method to see how many 3s you have. Because listening for 24 is easier than monitoring the tracking method for 8 3s to stop at 8, dividing can be easier than multiplying.
Level 3 of Problem Solving(O& Ap.25) • Level 3 methods use the associative property or the distributive property to compose and decompose. These compositions and de- compositions may be additive (as for addition and subtraction) or multiplicative. For example, students multiplicatively compose or decompose:
Reason abstractly and quantitatively. • Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships:
Reason abstractly and quantitatively. • the ability to decontextualize—to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents—
Reason abstractly and quantitatively. • —and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved.
Reason abstractly and quantitatively. • Quantitative reasoning entails habits of creating a coherent representation of the problem at hand;
Reason abstractly and quantitatively. • considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects.