Deep Dive into Math Shift 3
RIGOR
Understanding Rigor in the Common Core
State Standards for Mathematics
Using the 2013-2014 Course Descriptions
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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
We will...
1. Discuss and Find evidence of Rigor within the
Common Core Standards
2. Look specifically at fluency and the role it plays
in math instruction
3. Discuss conceptual understanding and
differentiation
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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
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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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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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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…
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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Rigor Addressed in the Standards
• Conceptual Understanding:
3.NF.1.1 Understand a fraction 1/b as the quantity
formed by 1 part when a whole is partitioned into b
equal parts; understand a fraction a/b as the
quantity formed by a parts of size 1/b.
• Procedural Skill and Fluency:
5.NBT.2.5 Fluently multiply multi-digit whole
numbers using the standard algorithm.
• Application:
4.MD.3.7 …Solve addition and subtraction
problems to find unknown angles on a diagram in
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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RIGOR is a Balancing Act
RIGOR
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Key Fluencies
Grade
Standard
Key Fluency
K
MACC.K.OA.1.5 Add/subtract within 5
1
MACC.1.OA.3.6 Add/subtract within 10
2
MACC.2.OA.2.2 Add/subtract within 20
MACC.2.NBT.2.5 Add/subtract within 100 (pencil and paper)
3
MACC.3.NBT.1.2 Add/subtract within 1,000
MACC.3.OA.3.7 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 Multi-digit multiplication
Critical Area #1 Developing fluency with addition and subtraction of
fractions
MACC.6.NS.2.2 Multi-digit division
MACC.6.NS.2.3 Multi-digit decimal operations
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MACC.7.EE.2.4a Solve px + q = r, p(x + q) = r
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MACC.8.EE.3.8b Solve simple 22 systems by inspection
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Kindergarten Fluency Progression
Represent addition and subtraction
with objects, fingers, mental images,
drawings, sounds (e.g., claps), acting
out situations, verbal explanations,
expressions, or equations (K.OA.1.1).
Solve addition and
subtraction word problems
(K.OA.1.2)
Fluently add and subtract
within 5 (K.OA.1.5)
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Grade 1 Fluency Progression
Add and subtract within 20
(1.OA.3).
Demonstrate fluency for
addition and subtraction
within 10 (1.OA.3.6).
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Grade 2 Fluency Progression
Fluently add and subtract
within 20 using mental
strategies (2.OA.2.2).
Fluently add and
subtract within 100 using
strategies based on place
value, properties of
operations, and/or the
relationship between
addition and subtraction
(2.NBT.2.5).
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Grade 3 Fluency Progression
Fluently add and subtract within 1000 using
strategies and algorithms based on place value,
properties of operations, and/or the relationship
between addition and subtraction (3.NBT.1.2).
Interpret products and quotients of
whole numbers (3.OA.1.1-3.OA.1.4)
Apply properties of operations
as strategies to multiply and
divide (3.OA.2.5)
Fluently multiply and divide within 100
using strategies such as the relationship
between multiplication and division (3.OA.3.7).
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Grade 4 Fluency Progression
Fluently add and subtract multi-digit
whole numbers using the standard
algorithm (4.NBT.2.4).
Develop fluency with efficient procedures for
multiplying whole numbers; understand and
explain why the procedures work based on
place value and properties of operations; and
use them to solve problems (Critical Area #1).
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Grade 5 Fluency Progression
Fluently multiply multi-digit whole
numbers using the standard algorithm
(5.NBT.2.5).
Develop fluency in calculating sums and
differences of fractions, and make
reasonable estimates of them (Critical Area #1)
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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?
How do you
differentiate
instruction in
your classroom?
What
instructional
shifts should
occur in our
classrooms?
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