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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 fluency recommendations for Middle 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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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 UnderstandingWhat is it? Comprehension of Mathematical

Concepts

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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

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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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One Instructional Model

Assuming a 60 minute math class:

10 minutes: Fluency Activities, formative assessment

20 minutes: Conceptual Development/Practice20 minutes: Application10 minutes: Review

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EXAMPLE:NY Common Core Mathematics Curriculum

ModelLesson Structure

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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)

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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

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

Rigor Requires Balance

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Conceptual Understanding +

Procedural Skill and Fluency +

Application

=RIGOR

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Evidence of Rigor in the Standards

key words within the standardsConceptual Understanding

Understand Recognize InterpretDescribe Explain UseRelate Represent IdentifyJustify Solve

Procedural Skill and FluencyFluently Fluency

ApplicationSolve Word Problem Real

World Problem ApplyMathematical Problem Model(ing)

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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

Activity

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RIGOR is a Balancing Act

RIGOR

Fluency

Application

ConceptualUnderstanding

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

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

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

3MACC.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

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MACC.5.NBT.2.5

Critical Area #1

Multi-digit multiplicationDeveloping fluency with addition and subtraction of fractions

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

Multi-digit divisionMulti-digit decimal operations

7MACC.7.EE.2.4a

Solve px + q = r, p(x + q) = r

8MACC.8.EE.3.8b

Solve simple 22 systems by inspection

Advance to next

slide

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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

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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

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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

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Rethinking Rigor

• Building Confidence through Problem Solving• Grades 3-5, Math, Number Fluency

https://www.teachingchannel.org/videos/building-math-confidence

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Group DiscussionWhere was the rigor?

What strategies

and structures are applicable to

MS?

What shifts need to

happen in our classrooms?