1. Deep Dive into Math Shift 3 RIGOR Understanding Rigor in the Common Core State Standards for Mathematics Using the 2013-2014 Course Descriptions 1

2. 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

3. Today’s Agenda Rigor in the CCSSM 1.Discuss Rigor and Find evidence of it within the 2013-2014 Florida Math Course Descriptions 2.Look specifically at fluency recommendations for Middle School 3.Determine what instructional shifts must occur as we increase the rigor 3

4. 4 Building Fluency What is meant by fluency? http://www.youtube.com/watch?v=ZFUAV00bTwA&list=PLD7F4C7DE7 CB3D2E6&index=13&feature=plpp_video http://youtu.be/ZFUAV00bTwA Mathematics Fluency: A Balanced Approach (1:56)

5. 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

6. What the Student Does…What the Teacher Does… Shows mastery of material at a deep level Articulates mathematical reasoning Demonstrates deep conceptual understanding of priority concepts Responds to student answers by eliciting student explanations and reasoning Ensures that all students reach understanding Views concepts being taught as a coherent continuum instead of as isolated topics Deep Understanding What is it? Comprehension of Mathematical Concepts 6

7. What the Student Does…What the Teacher Does… Applies math in other content areas and situations, as relevant Chooses the right math concept to solve a problem when not necessarily prompted to do so Applies math content to other content areas (i.e. science) Provides students with real world experiences and opportunities to apply what they have learned 7

8. 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

9. One Instructional Model Assuming a 60 minute math class: 10 minutes: Fluency Activities, formative assessment 20 minutes: Conceptual Development/Practice 20 minutes: Application 10 minutes: Review 9

10. EXAMPLE: NY Common Core Mathematics Curriculum Model Lesson Structure 10

11. 11 How do we address rigor while building fluency? http://www.engageny.org/resource/nti-november-2012-rigor- breakdown-sprints-fluency-in-action Rigor Breakdown - Sprints - Fluency in Action (6:07)

12. Florida 2013-2014 Math Instruction Blended Instruction between the CCSS and a subset of NGSS (assessed by FCAT 2.0). Grades 3-8 will be assessed by FCAT 2.0 Algebra I and Geometry will be assessed by the Florida EOC Exams. Transitional Shifts Increased rigor Classroom assessment to include PARCC-like tasks 12

13. Rigor Addressed in the Standards Conceptual Understanding: 6.NS.3.7 Understand ordering and absolute value of rational numbers. 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… Application: 8.G.3.9 Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real world and mathematical problems. 13

14. Rigor Requires Balance 14 Conceptual Understanding + Procedural Skill and Fluency + Application = RIGOR

15. Evidence of Rigor in the Standards key words within the standards Conceptual Understanding UnderstandRecognizeInterpret DescribeExplainUse RelateRepresentIdentify JustifySolve Procedural Skill and Fluency Fluently Fluency Application SolveWord Problem Real World ProblemApply Mathematical ProblemModel(ing) 15

16. Locating Evidence of Rigor in the Standards In grade-level teams: Read each standard in your course description Look for and underline or highlight key words or phrases indicating RIGOR – Understand – Fluently – Solve Real World problems or word problems Post your questions and comments to the Parking Lot 16 Activity

17. RIGOR is a Balancing Act RIGOR Fluency Application Conceptual Understanding 17

18. 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 100 4 MACC.4.2.4 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 7 MACC.7.EE.2.4 a Solve px + q = r, p(x + q) = r 8 MACC.8.EE.3.8 b Solve simple 2  2 systems by inspection Advance to next slide

19. Interpret and compute quotients of fractions and solve word problems involving division of fractions by fractions. 6.NS.1.1 Fluently divide multi-digit numbers using the standard algorithm. 6.NS.2.2 Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation. 6.NS.3 Grade 6 Fluency Progression 19

20. Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers. 7.NS.1.1–2 Students solve multistep problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. 7.EE.2.3 Solve word problems leading to one- variable equations of the form px + q = r and p(x + q) = r, fluently. 7.EE.2.4a Grade 7 Fluency Progression 20

21. Grade 8 Fluency Progression Solve linear equations in one variable. 8.EE.3.7 Analyze and solve pairs of simultaneous linear equations....Solve simple cases by inspection. 8.EE.3.8b 21

22. Rethinking Rigor Building Confidence through Problem Solving Grades 3-5, Math, Number Fluency https://www.teachingchannel.org/videos/building- math-confidence 22

23. Group Discussion Where was the rigor? 23 What strategies and structures are applicable to MS? What shifts need to happen in our classrooms?