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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?
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