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Deep Dive into Math Shift 3RIGOR

Understanding Rigor in the Common Core State Standards for Mathematics

Using the 2013-2014 Course Descriptions

Shift #3: RigorWhat 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.

RIGORConceptual U

nderstanding

Fluency

Application

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Today’s AgendaRigor 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

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Building Fluency

What is meant by fluency?

http://www.youtube.com/watch?v=ZFUAV00bTwA&list=PLD7F4C7DE7CB3D2E6&index=13&feature=plpp_video

http://youtu.be/ZFUAV00bTwA

Mathematics Fluency: A Balanced Approach (1:56)

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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

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Deep UnderstandingWhat is it? Comprehension of Mathematical

ConceptsWhat 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

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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

ApplicationWhat is it? Bringing mathematical skill and

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

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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?

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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

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…

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Rigor Requires Balance

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Conceptual Understanding +

Procedural Skill and Fluency +

Application

=RIGOR

Grade Standard Key FluencyK MACC.K.OA.1.5 Add/subtract within 51 MACC.1.OA.3.6 Add/subtract within 10

2 MACC.2.OA.2.2MACC.2.NBT.2.5

Add/subtract within 20Add/subtract within 100 (pencil and paper)

3 MACC.3.NBT.1.2MACC.3.OA.3.7

Add/subtract within 1,000Multiply/divide within 100

4MACC.4.2.4

Critical Area #1Add/subtract within 1,000,000 Develop fluency with efficient procedures for multiplying whole numbers

5MACC.5.NBT.2.5Critical Area #1

Multi-digit multiplicationDeveloping fluency with addition and subtraction of fractions

6 MACC.6.NS.2.2MACC.6.NS.2.3

Multi-digit divisionMulti-digit decimal operations

7 MACC.7.EE.2.4a Solve px + q = r, p(x + q) = r

8 MACC.8.EE.3.8b Solve simple 22 systems by inspection

Key Fluencies

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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

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Evidence of Rigor in the Standards

key words within the standardsConceptual Understanding

Understand Recognize InterpretDescribe Explain UseRelateRepresent IdentifyJustifySolve

ApplicationSolve Word Problem Real World Problem ApplyMathematical Problem Model(ing)

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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.”

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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

Activity

Course Standard 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 casesSee structure in expressions and use this structure to rewrite expressions Translate sequences and series between recursive definitions and closed forms

HS Fluency Recommendations

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http://www.parcconline.org/sites/parcc/files/PARCCMCFMathematicsNovember2012V3_FINAL.pdf

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RIGOR is a Balancing Act

RIGOR

Fluency

Application

ConceptualUnderstanding

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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?

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Group Discussion

Where was the rigor?

Which of the 8 Standards for Mathematical Practice are evidenced?

What shifts need to occur

in your classroom?