Deep Dive into Math Shift 3

RIGOR

Understanding Rigor in the Common Core State Standards for Mathematics Using the 2013-2014 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

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 PARCC fluency recommendations for High School 3. Determine what instructional shifts must occur as we increase the rigor 3

Building Fluency

What is meant by fluency?

Mathematics Fluency: A Balanced Approach (1:56)

http://www.youtube.com/watch?v=ZFUAV00bTwA&list=PLD7F4C7DE7 CB3D2E6&index=13&feature=plpp_video http://youtu.be/ZFUAV00bTwA 4

Fluency

What is it?

Skill in carrying out procedures flexibly, accurately, efficiently and appropriately

What the Student Does…

• Spends time practicing, with intensity, skills (in high volume)

What the Teacher Does…

• 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 5

Deep Understanding

What is it?

Comprehension of Mathematical Concepts

What the Student Does…

• Show mastery of material at a deep level

What the Teacher Does…

• Respond to student answers by eliciting student explanations and reasoning • Articulate mathematical

reasoning

• Ensure that all students reach understanding • Demonstrate deep conceptual understanding of priority

concepts

• View concepts being taught as a coherent continuum instead of as isolated topics 6

Application

What is it?

Bringing mathematical skill and understanding together and applying it to real-world situations and in new contexts

What the Student Does…

•

Apply math in other

content areas and situations, as relevant

What the Teacher Does…

• Apply math content to other content areas(i.e. science) • Choose the right math concept to solve a problem when not necessarily prompted to do so • Provide students with

real world experiences

and opportunities to apply what they have learned 7

Rigor ous 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?

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Florida 2013-2014 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

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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

…

Rigor Requires Balance

Conceptual Understanding + Procedural Skill and Fluency + Application = RIGOR

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Grade

K 1 2

Key Fluencies

Key Fluency Standard

MACC.K.OA.1.5 Add/subtract within 5 MACC.1.OA.3.6 Add/subtract within 10 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 5 6 MACC.4.2.4

Critical Area #1 Add/subtract within 1,000,000 Develop fluency with efficient procedures for multiplying whole numbers MACC.5.NBT.2.5

Critical Area #1 MACC.6.NS.2.2

MACC.6.NS.2.3

Multi-digit multiplication Developing fluency with addition and subtraction of fractions Multi-digit division Multi-digit decimal operations MACC.7.EE.2.4a Solve px + q = r, p(x + q) = r 7 MACC.8.EE.3.8b Solve simple 2  2 systems by inspection 8 12

HS Fluency

• The words

fluently and fluency

in the HS Standards are not found • 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

Understand Describe Relate Justify Recognize Explain Represent Solve Interpret Use Identify

Application

Solve Real World Problem Mathematical Problem Word Problem Apply Model(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

Course

HS Fluency Recommendations

Algebra 1 Geometry Algebra 2

Standard

A/G A-APR.1.1 A-SSE.1.1b G-SRT.2.5 G-GPE.2.4, 5, 7 G-CO.4.12 A-APR.4.6 A-SSE.1.2 F-IF.1.3

Key Fluency

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 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 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 http://www.parcconline.org/sites/parcc/files/PARCCMCFMathematicsNovember201 2V3_FINAL.pdf

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RIGOR is a Balancing Act

RIGOR

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Rigor in the Standards for

Mathematical Practice

http://www.insidemathematics.org/index.php/classroom-video-visits/public-lessons properties-of-quadrilaterals/300-properties-of-quadrilaterals-tuesday-group-work part-a ? 19

Group Discussion

Which of the 8 Standards for Mathematical Practice are evidenced?

Where was the rigor?

What shifts need to occur in your classroom?

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