Mathematics K-5 FDRESA June 2013 Supporting CCGPS Leadership Academy

 How can school leader familiarity with the Standards for Mathematical Practice, Standards for Mathematical Content, content emphases, and instructional shifts impact successful implementation of CCGPS? Essential Question

“It is literally true that you can succeed best and quickest by helping others to succeed.” Napoleon Hill American author Monitoring Collaborating A Partnership

Common Core State Standards Growing Mathematically Proficient Students A Response

 Mathematics is the economy of information.  The central idea of all mathematics is to discover how knowing some things well, via reasoning, permits students to know much else…without having to commit the information to memory as a separate fact.  It is the connections… the reasoned, logical connections …that make mathematics manageable.  Common Core Georgia Performance Standards place a greater emphasis on problem solving, reasoning, representation, connections, and communication. Theory

 There is a shift toward the student applying mathematical concepts and skills in the context of authentic problems and understanding concepts rather than merely following a sequence of procedures.  In mathematics classrooms, students will learn to think critically in a mathematical way with an understanding that there are many different ways to a solution and sometimes more than one right answer in applied mathematics. Theory

 Those content standards which set an expectation of understanding are potential “points of intersection” between the Standards for Mathematical Content and the Standards for Mathematical Practice.  These points of intersection  are weighted toward central and generative concepts.  merit the most time, resources, innovative energies, and focus.  qualitatively improve the curriculum, instruction, assessment, professional development, and student achievement in mathematics. Theory

 The standards define what students should understand and be able to do in their study of mathematics.  Asking a student to understand something means asking a teacher to assess whether the student has understood it.  Mathematical understanding and procedural skill are equally important, and both are assessable using mathematical tasks of sufficient rigor. Assessment

 The Georgia Mathematics Curriculum focuses on actively engaging the students in the development of mathematical understanding by  using manipulatives and a variety of representations,  working independently and cooperatively to solve problems,  estimating and computing efficiently, and  conducting investigations and recording findings. Engagement

 Standards for Mathematical Practice  Eight standards crossing all grade levels and applied in conjunction with content standards  Standards for Mathematical Content  Multiple standards categorized in domains  Six Shifts  Teacher practices Common Core GPS

Standards for Mathematical Practice

K Modeling Geometry Measurement and Data The Number System Number and Operations in Base Ten Operations and Algebraic Thinking Geometry Number and Operations Fractions Expressions and Equations Statistics and Probability Algebra Number and Quantity Functions Statistics and Probability Ratios & Proportional Relationships Functions Counting and Cardinality © Copyright 2011 Institute for Mathematics and Education Standards for Mathematical Content

Six Shifts FOCUS: Priorities COHERENCE: Vertical Scope FLUENCY: Intensity/Frequency DEEP UNDERSTANDING: Variety/SMP APPLICATION: Relevance DUAL INTENSITY: Balance in Practice/Understanding

 MCC5.OA.2 Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them.  MCC7.EE.2 Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. For example, a+0.05a=1.05a means that “increase by 5%” is the same as “multiply by1.05.”  MCC9-12.A.SSE.1 Interpret expressions that represent a quantity in terms of its context.  MCC9-12.A.SSE.1a Interpret parts of an expression, such as terms, factors, and coefficients.  MCC9-12.A.SSE.1b Interpret complicated expressions by viewing one or more of their parts as a single entity. Coherence

Grade 3 From Grade 2  Fluent addition and subtraction to 18; foundational ideas about addition and subtraction  Foundational place value understanding  Foundational ideas about shape and position in space  Ability to compare and categorize  Understanding of quantities to 1000  Measurement as unit iteration  Foundational data ideas Later  Deep understanding of addition and subtraction, multiplication and division  Useful place value understanding  Understanding of defining attributes about shape, comparison of shape  Foundational fractional relationships  Continuation of fluency/algebraic thinking  Measurement, addition, subtraction relationships  Data analysis Coherence

Where to look…Frameworks  Concepts and Skills to Maintain  Enduring Understandings  Previous Unit  Current Unit  Evidence of Learning in Current Unit Coherence / Focus

GradePriorities in Support of Rich Instruction and Expectations of Fluency and Conceptual Understanding K-2 Addition and subtraction; measurement using whole number quantities 3-5 Multiplication and division of whole numbers and fractions 6 Ratios and proportional reasoning; early expressions and equations 7 Ratios and proportional reasoning; arithmetic of rational numbers 8 Linear algebra 9-12 Modeling Focus

GradeRequired Fluency K Add/subtract within 5 1 Add/subtract within 10 2 Add/subtract within 20; add/subtract within 100 (pencil and paper) 3 Multiply/divide within 100 ; add/subtract within Add/subtract within 1,000,000 5 Multi-digit multiplication 6 Multi-digit division ; multi-digit decimal operations 7 Solve px + q = r, p(x + q) = r 8 Solve simple 2x2 systems by inspection 9-12 Algebraic manipulation in which to understand structure. Writing a rule to represent a relationship between two quantities. Seeing mathematics as a tool to model real-world situations. Understanding quantities and their relationships. Fluency

Kindergarten 3+2=5 5-1=4 Grade 1 6+4=10 8-2=6 Grade 3 5X7=35 12÷4= = =637 Grade4 3,276+5,428=8, , ,325= 232,407 Grade 5 2,378 X 42= 99,876 Grade 2 8+7= =7 22+7= =49 Fluency

Grade 6 6(4-y)= 32 Grade 7 Solve the system of equations. 3x+2y=7 x-4y=-7 Grade 8 Fluency

Write the equation of the line 3x+2y=7 so that it can easily be graphed using the y- intercept and slope. Write the rule to express the relationship between the area of a square and its inscribed circle. Fluency High School

 FLEXIBILITY  ACCURACY  EFFICIENCY  APPROPRIATENESS Accuracy Appropriateness Flexibility Efficiency FLUENT PROBLEM SOLVER Fluency

Two Approaches  Word problems : Assigned after explanation of operations, algorithms, or rules; and students are expected to apply these procedures to the problems.  Problematic situations : Used at the beginning … for construction of understanding, for generation and exploration of mathematical ideas and strategies…offering multiple entry levels, and supportive of mathematization. (Young Mathematicians at Work, Fosnot, 2002) Application

A Delicate Balance Teachers must… … ritualize skills practice …normalize productive struggle Dual Intensity

INSTRUCTION Teacher-Focused Content Delivery Strategies HOMEWORK Distributed Practice PROCESSING Student-Focused Linked to Delivery Strategy DRILL Basic facts recall Fluency APPLICATION Making content relevant, purposeful, and meaningful REVIEW/PREVIEW Maintaining old learning Building foundations for new learning Six Elements

 How can school leader familiarity with the Standards for Mathematical Practice, Standards for Mathematical Content, content emphases, and instructional shifts impact successful implementation of CCGPS? Essential Question

Ensuring Success Leaders Supporting CCGPS A Solution Success