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 fluency recommendations
for Middle 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…
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
5
Deep Understanding
What is it? Comprehension of Mathematical
Concepts
What the Student Does…
What the Teacher Does…
•Shows mastery of material at
a deep level
•Responds to student answers
by eliciting student
explanations and reasoning
•Articulates mathematical
reasoning
•Demonstrates deep
conceptual understanding of
priority concepts
•Ensures that all students reach
understanding
•Views concepts being taught
as a coherent continuum
instead of as isolated topics
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What the Student Does…
What the Teacher Does…
•Applies math in other
content areas and situations,
as relevant
•Applies math content to
other content areas (i.e.
science)
•Chooses the right math
concept to solve a problem
when not necessarily
prompted to do so
•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/Practice
20 minutes: Application
10 minutes: Review
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EXAMPLE:
NY Common Core Mathematics Curriculum
Model
Lesson Structure
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How do we address rigor while
building fluency?
Rigor Breakdown - Sprints - Fluency in Action(6:07)
http://www.engageny.org/resource/nti-november-2012-rigorbreakdown-sprints-fluency-in-action
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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
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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.
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Rigor Requires Balance
Conceptual Understanding
+
Procedural Skill and Fluency
+
Application
=
RIGOR
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Evidence of Rigor in the Standards
key words within the standards
Conceptual Understanding
Understand
Describe
Relate
Justify
Recognize
Explain
Represent
Solve
Interpret
Use
Identify
Procedural Skill and Fluency
Fluently
Fluency
Application
Solve
Real World Problem
Mathematical Problem
Word Problem
Apply
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
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RIGOR is a Balancing Act
RIGOR
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Grade
Standard
Key Fluency
K
MACC.K.OA.1.5 Add/subtract within 5
1
MACC.1.OA.3.6 Add/subtract within 10
MACC.2.OA.2.2
Add/subtract within 20
2
MACC.2.NBT.2.
Add/subtract within 100 (pencil and paper)
5
MACC.3.NBT.1.
Add/subtract within 1,000
3
2
Multiply/divide within 100
MACC.3.OA.3.7
MACC.4.2.4
Add/subtract within 1,000,000
4
Critical Area #1 Develop fluency with efficient procedures for multiplying
whole numbers
MACC.5.NBT.2.
Multi-digit multiplication
5
5
Developing fluency with addition and subtraction of
Critical Area #1
fractions
6
7
8
MACC.6.NS.2.2
MACC.6.NS.2.3
MACC.7.EE.2.4
a
MACC.8.EE.3.8
b
Multi-digit division
Multi-digit decimal operations
Solve px + q = r, p(x + q) = r
Solve simple 22 systems by inspection
Advance
to next
slide
Grade 6 Fluency Progression
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
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Grade 7 Fluency Progression
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 onevariable equations of the form px + q =
r and p(x + q) = r, fluently. 7.EE.2.4a
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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/buildingmath-confidence
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Group Discussion
Where was the
rigor?
What strategies
and structures
are applicable
to MS?
What shifts
need to happen
in our
classrooms?
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