Deep Dive into Math Shift 3 RIGOR Understanding Rigor in the Common Core State Standards for Mathematics Using the Course Descriptions 1

Shift #3: Rigor What is meant by rigor? The CCSSM require a balance of:  Solid conceptual understanding  Procedural skill and fluency  Application of skills in problem solving situations Pursuit of all three requires equal intensity in time, activities, and resources. RIGOR Conceptual Understanding Fluency Application

Today’s Agenda Rigor in the CCSSM 1.Discuss Rigor and Find evidence of it within the Florida Math Course Descriptions 2.Look specifically at PARCC fluency recommendations for High School 3.Determine what instructional shifts must occur as we increase the rigor 3

4 Building Fluency What is meant by fluency? CB3D2E6&index=13&feature=plpp_video Mathematics Fluency: A Balanced Approach (1:56)

What the Student Does…What the Teacher Does… Spends time practicing, with intensity, skills (in high volume) Pushes students to know basic skills at a greater level of fluency Focuses on the listed fluencies by grade level Uses high quality problem sets, in high volume Fluency What is it? Skill in carrying out procedures flexibly, accurately, efficiently and appropriately 5

Deep Understanding What is it? Comprehension of Mathematical Concepts 6 What the Student Does…What the Teacher Does… Show mastery of material at a deep level Articulate mathematical reasoning Demonstrate deep conceptual understanding of priority concepts Respond to student answers by eliciting student explanations and reasoning Ensure that all students reach understanding View concepts being taught as a coherent continuum instead of as isolated topics

What the Student Does…What the Teacher Does… Apply math in other content areas and situations, as relevant Choose the right math concept to solve a problem when not necessarily prompted to do so Apply math content to other content areas(i.e. science) Provide students with real world experiences and opportunities to apply what they have learned Application What is it? Bringing mathematical skill and understanding together and applying it to real-world situations and in new contexts 7

Rigorous Group Discussion 1.Share examples of relevant real-world experiences you use to make important connections to the concepts you teach. 2.How do these applications relate back to both fluency and conceptual understanding? 8

Florida Math Instruction Blended Instruction between the CCSS and a subset of NGSSS (assessed by State EOC). Algebra I and Geometry assessed by the Florida EOC Exams. Transitional Shifts Increased rigor Classroom assessment to include PARCC-like tasks 9

Rigor Addressed in the Standards Conceptual Understanding: 912.N-VM.3.9 Understand that, unlike multiplication of numbers, matrix multiplication for square matrices is not a commutative operation, but still satisfies the associative and distributive properties. Application: 912.G-MG.1.2 Apply concepts of density based on area and volume in modeling Procedural Skill and Fluency: 7.EE.2.4a …..Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently… 10

Rigor Requires Balance 11 Conceptual Understanding + Procedural Skill and Fluency + Application = RIGOR

GradeStandard Key Fluency KMACC.K.OA.1.5Add/subtract within 5 1MACC.1.OA.3.6Add/subtract within 10 2 MACC.2.OA.2.2 MACC.2.NBT.2.5 Add/subtract within 20 Add/subtract within 100 (pencil and paper) 3 MACC.3.NBT.1.2 MACC.3.OA.3.7 Add/subtract within 1,000 Multiply/divide within MACC Critical Area #1 Add/subtract within 1,000,000 Develop fluency with efficient procedures for multiplying whole numbers 5 MACC.5.NBT.2.5 Critical Area #1 Multi-digit multiplication Developing fluency with addition and subtraction of fractions 6 MACC.6.NS.2.2 MACC.6.NS.2.3 Multi-digit division Multi-digit decimal operations 7MACC.7.EE.2.4aSolve px + q = r, p(x + q) = r 8MACC.8.EE.3.8b Solve simple 2  2 systems by inspection Key Fluencies 12

HS Fluency The words fluently and fluency are not found in the HS Standards Fluencies are indicated by culminating standards which mark the end of learning progressions Recommended fluencies are identified in the PARCC Model Content Frameworks 13

Evidence of Rigor in the Standards key words within the standards Conceptual Understanding UnderstandRecognizeInterpret DescribeExplainUse RelateRepresentIdentify JustifySolve Application SolveWord Problem Real World ProblemApply Mathematical ProblemModel(ing) 14

Fluency Progression Culminating in Algebra 1 As early as grades 6 and 7, students begin to use the properties of operations to generate equivalent expressions (6.EE.3, 7.EE.1). By grade 7, they begin to recognize that rewriting expressions in different forms could be useful in problem solving (7.EE.2). In Algebra I, these aspects of algebra carry forward as students continue to use properties of operations to rewrite expressions, gaining fluency and engaging in what has been called “mindful manipulation.” 15

Locating Evidence of Rigor in the Standards Read each standard in your course description Look for and underline or highlight key words or phrases indicating RIGOR – Understand – Solve Real World problems or word problems Locate an indicated fluency by finding at least one progression and culminating standard Post your questions and comments to the Parking Lot 16 Activity

CourseStandard Key Fluency Algebra 1 A/G A-APR.1.1 A-SSE.1.1b Solve characteristic problems involving the analytic geometry of lines Add. subtract, and multiply polynomials Transform expressions and see parts of an expression as a single object Geometry G-SRT.2.5 G-GPE.2.4, 5, 7 G-CO.4.12 Triangle congruence and similarity Use coordinates to establish geometric results, calculate length and angle, and use geometric representations as a modeling tool Use construction tools, physical and computational Algebra 2 A-APR.4.6 A-SSE.1.2 F-IF.1.3 Divide polynomials with remainder by inspection in simple cases See structure in expressions and use this structure to rewrite expressions Translate sequences and series between recursive definitions and closed forms HS Fluency Recommendations V3_FINAL.pdf

RIGOR is a Balancing Act RIGOR Fluency Application Conceptual Understanding 18

Rigor in the Standards for Mathematical Practice 19 properties-of-quadrilaterals/300-properties-of-quadrilaterals-tuesday-group-work- part-ahttp:// properties-of-quadrilaterals/300-properties-of-quadrilaterals-tuesday-group-work- part-a?

Group Discussion Where was the rigor? 20 Which of the 8 Standards for Mathematical Practice are evidenced? What shifts need to occur in your classroom?