Download 3.1.1.CCSSOverview

Common Core State Standards
Session 3
6-12 Mathematics
Bell Work Activity
• Handout #1
The Common Core
State Standards for
Mathematics from A to Z
• List words that begin with
each letter of the alphabet
that identify aspects of the
Common Core State
Standards for Mathematics.
2
WELCOME
Introductions
• June Campbell
• ORTTTA
• Nancy Kinard
• Palm Beach
• Michael Chase
• Volusia County
• Amy Coltharp
• BFEP
• Kim Wuellner
• St. Johns
• Martha Gioielli
• DA
Agenda
• The Common Core State
Standards for Mathematics
from A to Z
• Exploring the Standards for
Mathematical Practice
• Exploring the Common
Core State Standards for
Mathematics Critical Areas
• Exploring the Mathematics
Progressions
3
“We live in a time of vast changes that
include accelerating globalization,
mounting quantities of information,
the dominating influence of science
and technology, and the clash of
civilizations. Those changes call for
new ways of learning and thinking in
school, business, and the professions.”
-Howard Gardner
Five Minds for the Future (2007)
4
Expected Outcomes
•
Enhance knowledge base of the Common Core
Standards for Mathematics.
•
Become familiar with the structure of the
Common Core State Standards for Mathematics.
Enhance knowledge of the Common Core
Standards for Mathematical Practice.
Understand how the critical areas bring focus to
key mathematical concepts for students to learn
at each grade level.
Consider how the learning progressions can be
used to inform curriculum and guide instruction.
5
Digital Checkpoint
Session 3
6-12 Mathematics
Digital Checkpoint
• Poll Everywhere
• http://www.pollev
erywhere.com/
7
How To Vote via Texting
TIPS
1. Standard texting rates only (worst case US $0.20)
2. We have no access to your phone number
3. Capitalization doesn’t matter, but spaces and spelling do
How to Vote via Web Response
Rate your level of understanding
of the Common Core State Standards
for Mathematics?
Send to: 37607
Text Code # to respond
•
•
•
•
•
No understanding
Limited understanding
Fair understanding
Good understanding
Excellent understanding
Submit response at
http://PollEV.com
125724
125730
125803
125804
125809
10
Virtual Parking Lot
Send to: 37607
Text: 220274 plus your
message
Submit response at
http://PollEV.com
11
Digital Resources
for the Common Core
• Apple
• http://itunes.apple.com/us/app/commoncore-standards/id439424555
• Android
• https://play.google.com/store/apps/details?i
d=com.edutater.corestandards
• Common Core State Standards for
Mathematics
• http://www.corestandards.org/
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Aligned
Building
Foundation
CCSSO
Coherence
Clarity
Application Balanced
Critical Areas
Clusters
Guided
by
Principles
McCallum
Mathematical
Practice
Habits
of
Mind
International
Benchmarked
Illustrative
Mathematics
Daro
Domains
Joint
effort
Organized Progressions
National
Procedural
Focus Opportunities fluency
NGA
Proficiency
PARCC
Standards
Teachers
Timeline
Vision
Understanding
Focus
based
Fluency
Knowledge
Learnerfocused
Life-long
skills
Developmental
Levels
Evidenced-
Sensemaking
Ensuring
Education
Quality
Robust,
Relevant,
Real-world
Researchbased
Rigor
Whole
Child
Approach
X
YOU
Zimba
Domains for K-12
K
1
2
3
4
5
6
7
8
HS
Counting
and
Cardinality
(CC)
Number and Operations in Base Ten (NBT)
Number and
Operations-Fractions
(NF)
The Number System (NS)
Ratios and
Proportional
Relationships
(RP)
Number
and
Quantity
(N)
Functions (F)
Operations and Algebraic Thinking (OA)
Expressions and
Equations (EE)
Algebra
(A)
Geometry (G)
Measurement and Data (MD)
A-Z
Statistics and Probability (SP)
Grade 7 Overview
Domain
Cluster
Headings
Domain
Cluster
Headings
Domain
Cluster
Headings
Domain
Cluster
Headings
Domain
Cluster
Headings
Ratios and Proportional Relationships
•Analyze proportional relationships and use them
to solve real-world and mathematical problems.
The Number System
•Apply and extend previous understandings of
operations with fractions to add, subtract, multiply,
and divide rational numbers.
Expressions and Equations
•Use properties of operations to generate
equivalent expressions.
Geometry
•Draw, construct and describe geometrical figures
and describe the relationships between them.
•Solve real-life and mathematical problems
involving angle measure, area, surface area, and
volume.
Statistics and Probability
•Use random sampling to draw inferences about a
population.
•Draw informal comparative inferences about two
populations.
•Investigate chance processes and develop, use,
and evaluate probability models.
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High School Conceptual Categories
• Number and Quantity (N)
• Algebra (A)
• Functions (F)
• Modeling (*)
• Geometry (G)
• Statistics and Probability (S)
http://www.corestandards.org/assets/CCSSI_Math%20Standards.pdf
A-Z
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Domain
Cluster Headings
Domain
Cluster Headings
Domain
Cluster Headings
Domain
Cluster Headings
A-Z
Domain
S
t
a
n
d
a
r
d
s
Cluster
Headings
Florida’s Numbering of
the Common Core State Standards
MACC.7.EE.1.1
Subject Grade Domain Cluster Standard
Subject
Mathematics Common Core
Grade
7
Domain
Expressions and Equations
Cluster
Use properties of operations to generate equivalent
expressions
Standard
Apply properties of operations as strategies to add, subtract,
factor, and expand linear expressions with rational coefficients.
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Florida’s Numbering of
the Common Core State Standards
MACC.912.N-RN.2.3
Subject Grade Category Domain Cluster Standard
Subject
Mathematics Common Core
Grade
9-12
Category
Number and Quantity
Domain
The Real Number System
Cluster
Use properties of rational and irrational numbers.
Standard
Explain why the sum or product of two rational numbers is
rational; that the sum of a rational number and an irrational
number is rational; and that the product of a nonzero rational
number and an irrational number is irrational.
A-Z
Standards for Mathematical Practice
“The Standards for Mathematical Practice are
unique in that they describe how teachers need to
teach to ensure their students become
mathematically proficient. We were purposeful in
calling them standards because then they won’t
be ignored.”
- Bill McCallum
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8 Standards for Mathematical Practice
Make sense of problems
and persevere in solving
them
Use appropriate tools
strategically
Reason abstractly and
quantitatively
Attend to precision
Construct viable
arguments and critique
the reasoning of others
Look for and make
sense of structure
Model with mathematics
Look for and express
regularity in repeated
reasoning
A-Z
23
Florida’s Common Core State Standards
Implementation Timeline
Year/Grade Level
K
1
2
3-8
9-12
2011-2012
FL
L
L
L
L
2012-2013
FL
FL
L
L
L
2013-2014
CCSS fully implemented
FL
FL
FL
BL
BL
2014-2015
CCSS fully implemented and
assessed
FL
FL
FL
FL
FL
F - full implementation of CCSS for all content areas
L – begin full implementation of content area literacy standards including: (1) use of
informational text, text complexity, quality and range in all grades (K-12), and (2) CCSS
Literacy Standards in History/Social Studies, Science, and Technical Subjects (6-12)
B - blended instruction of CCSS with Next Generation Sunshine State Standards (NGSSS);
last year of NGSSS assessed on FCAT 2.0
A-Z
http://www.fldoe.org/bii/pdf/CCSS-ImplementationTimeline.pdf
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Standards for Mathematical Practice
Session 3
6-12 Mathematics
Poll Question
How many Common Core Standards for
Mathematical Practice are there?
Send to: 37607
Text: 129153 plus your
message
Submit response at
http://PollEV.com/
26
Standards for Mathematical Practice
Overarching Habits of Mind of a
Productive Mathematical Thinker
1. Make sense of problems and persevere in solving them
6. Attend to precision
Reasoning
and
Explaining
Modeling
and
Using Tools
2. Reason abstractly
and quantitatively
3. Construct viable
arguments and
critique the reasoning
of others
4. Model with
mathematics
5. Use appropriate
tools strategically
Seeing
Structure and
Generalizing
7. Look for and make
use of structure
8. Look for and
express regularity in
repeated reasoning
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Standards for Mathematical Practice
• Develops dispositions and habits of mind
“Characteristic of an educated person”
•
•
•
•
Precision in thought
Precision in the use of language and terms
Precision of argument
Sense making happens through conversations
http://www.youtube.com/watch?v=9pKcO9E4Flw&feature=relmfu
http://youtu.be/9pKcO9E4Flw
A-Z
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The Standards for
Mathematical Practice
• Please locate the Common Core State
Standards for Mathematics.
Page 6
• Take a moment to examine the first three
words of the narrative description for each of
the 8 mathematical practices.
• What do you notice?
Mathematically Proficient Students…
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Digital Task
Your Digital Task is to:
• Read your assigned Mathematical Practice.
• Identify the words (verbs) that illustrate the
student actions for this practice.
• Text the words on one continuous line with
spaces between each word.
Example: #..... create
analysis model describe
demonstrate….
30
Digital Task Text Numbers
Send to: 37607
Text a CODE # to respond
Submit responses at
http://PollEV.com
Practice #1 – code 130116
Practice #2 – code 50983
Practice #3 – code 71040
Practice #4 – code 71234
Practice #5 – code 71681
Practice #6 – code 71867
Practice #7 – code 72038
Practice #8 – code 6381
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Mathematical Practice 1 - Make sense of
problems and persevere in solving them.
Text 130116 to 37607
Submit responses at
http://PollEV.com
Mathematical Practice 2 - Reason
Abstractly and Quantitatively
Text 50983 to 37607
Submit responses at
http://PollEV.com
Mathematical Practice 3 - Construct
viable arguments and critique the
reasoning of others.
Text 71040 to 37607
Submit responses at
http://PollEV.com
Mathematical Practice 4 - Model with
mathematics.
Text 71234 to 37607
Submit responses at
http://PollEV.com
Mathematical Practice 5 - Use
appropriate tools strategically.
Text 71681 to 37607
Submit responses at
http://PollEV.com
Mathematical Practice 6 - Attend to
precision.
Text 71867 to 37607
Submit responses at
http://PollEV.com
Mathematical Practice 7 - Look for and
make sense of structure.
Text 72038 to 37607
Submit responses at
http://PollEV.com
Mathematical Practice 8 - Look for and
express regularity in repeated reasoning.
Text 6381 to 37607
Submit responses at
http://PollEV.com
http://www.wordle.net/show/wrdl/5360414/Mathematical_Practice_Actions
40
Consider the Learners
• Over 240,000 ELLs in Florida
• Almost every district has ELLs
• 300 languages are spoken among ELLs
• 79% of ELLs are in Mainstream/Inclusion
model classrooms
• ELLs are learning in the same classrooms
as non-ELLs
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Making the Content Comprehensible
• Use the standards vocabulary as a teaching tool.
“Generalize, develop, describe, analyze, apply,
measure,” etc. are all words ELLs will hear in the
classroom and need to understand.
• ELLs may know how to perform the skill using
their language, they just may not yet have the
English vocabulary.
• Use pictures, graphs, and charts whenever
possible.
• Make use of root words and cognates.
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Classroom Strategies
• Group ELLs with non-ELLs to work together.
• Allow more wait time for ELLs to respond.
– Silence does not necessarily mean the
student does not know the answer, the ELL
may be translating the answer and needs
more time.
• Remember that ELLs from different countries
may display mathematical functions in different
ways.
43
Critical Areas and Mathematics Progressions
Session 3
6-12 Mathematics
K-12 Domains and Critical Areas
6th Grade Domains






Ratios and Proportional Relationships
The Number System
Expressions and Equations
Geometry
Statistics and Probability





7th Grade Domains
Ratios and Proportional Relationships
The Number System
Expressions and Equations
Geometry
Statistics and Probability







8th





Grade Domains
The Number System
Expressions and Equations
Functions
Geometry
Statistics and Probability










Algebra 1 Domains
The Real Number System
Quantities
Seeing Structure in Expressions
Arithmetic with Polynomials and Rational Expressions
Creating Equations
Reasoning with Equations and Inequalities
Interpreting Functions
Building Functions
Linear, Quadratic, and Exponential Models
Interpreting Categorical and Quantitative Data








6th Grade Critical Areas
Connecting ratio and rate to whole number multiplication and division
using concepts of ratio and rate to solve problems.
Completing understanding of division of fractions and extending the
notation of numbers to the system of rational numbers which includes
negative numbers.
Writing, interpreting, and using expressions and equations.
Developing understanding of statistical thinking.
7th Grade Critical Areas
Developing understanding of and applying proportional relationships.
Developing understanding of operations with rational numbers and
working with expressions and linear equations.
Solving problems involving scale drawings and informal geometric
constructions, and working with two-and three-dimensional shapes to
solve problems involving area, surface area, and volume.
Drawing inferences about populations based on samples.
8th Grade Critical Areas
Formulating and reasoning about expressions and equations, including
modeling an association in bivariate data with a linear equation, and
solving linear equations and systems of linear equations.
Grasping the concept of a function and using functions to describe
quantitative relationships.
Analyzing two-and-three dimensional space and figures using distance,
angle, similarity, and congruence, and understanding and applying
Pythagorean Theorem.
Algebra 1 Critical Areas
Relationships between Quantities and Reasoning with Equations; Analyze
and explain the process of solving an equation.
Linear and Exponential Relationships; Learn function notation and develop
the concept of domain and range.
Descriptive Statistics; Learn formal means of assessing how a model fits
(data regression techniques, graphical representations and goodness of
fit.)
Expressions and Equations; Create and solve equations, inequalities, and
45
systems of equations involving quadratic expressions.
Quadratic Functions and Modeling; Comparing key characteristics.
Four critical areas in 6th Grade
1.
Connecting ratio and rate to whole number
multiplication and division and using concepts of
ratio and rate to solve problems
2.
Completing understanding of division of fractions and
extending the notion of number to the system of
rational numbers, which includes negative numbers
3.
Writing, interpreting, and using expressions and
equations
4.
Developing understanding of statistical thinking
http://www.corestandards.org/thestandards/mathematics/grade-6/introduction/
Page 39
46
Identify the
th
6
Grade Critical Area
Cluster Heading
Understand ratio concepts and use ratio reasoning to
solve problems.
Summarize and describe distributions.
Compute fluently with multi-digit numbers and find
common factors and multiples.
Reason about and solve one-variable equations and
inequalities.
Apply and extend previous understandings of arithmetic
to algebraic expressions.
Apply and extend previous understandings of numbers to
the system of rational numbers.
Represent and analyze quantitative relationships between
dependent and independent variables.
Develop understanding of statistical variability.
Critical Area
1-Ratio
4-Statistics
3-Equations
2-Rational #
3-Equations
2-Rational #
3-Equations
4-Statistics
Apply and extend previous understandings of
multiplication and division to divide fractions by fractions. 2-Rational47#
Four critical areas in 7th Grade
1.
Developing understanding of and applying
proportional relationships
2.
Developing understanding of operations with
rational numbers and working with expressions and
linear equations
3.
Solving problems involving scale drawings and
informal geometric constructions, and working with
two- and three-dimensional shapes to solve
problems involving area, surface area, and volume
4.
Drawing inferences about populations based on
samples
Page 46
http://www.corestandards.org/thestandards/mathematics/grade7/introduction/
48
Identify the 7th Grade Critical Areas
Cluster Heading
Analyze proportional relationships and use them to
solve real-world and mathematical problems.
Critical Area
1-Proportions,
2-Rational
Draw, construct and describe geometrical figures and
describe the relationships between them.
3-Geometry
Apply and extend previous understandings of
operations with fractions to add, subtract, multiply, and
divide rational numbers.
2-Rational
Use random sampling to draw inferences about a
population.
Solve real-life and mathematical problems involving
angle measure, area, surface area, and volume.
Draw informal comparative inferences about two
populations.
Use properties of operations to generate equivalent
expressions.
Solve real-life and mathematical problems using
numerical and algebraic expressions and equations.
4-Statistics
3-Geometry
4-Statistics
2-Rational
2-Rational,
3-Geometry
49
Three critical areas in 8th Grade
1.
Formulating and reasoning about expressions
and equations, including modeling an
association in bivariate data with a linear
equation, and solving linear equations and
systems of linear equations
2.
Grasping the concept of a function and using
functions to describe quantitative relationships
3.
Analyzing two- and three-dimensional space
and figures using distance, angle, similarity,
and congruence, and understanding and
applying the Pythagorean Theorem
Page 52
http://www.corestandards.org/thestandards/mathematics/grade8/introduction/
50
Mathematics Progressions
Ratio and Proportion in Grades 6-8:
Connections to College and Career Skills
<iframe width="560"
height="315"
src="http://www.youtube.
com/embed/5pBOnvzC_Y
w" frameborder="0"
allowfullscreen></iframe>
http://youtu.be/5pBOnvzC_Yw
http://www.youtube.com/watch?v=5pBOnvzC_Y
w&feature=BFa&list=UUF0pa3nE3aZAfBMT8pq
M5PA
http://commoncoretools.files.
wordpress.com/2011/12/ccss
_progression_sp_68_2011_12
_26_bis.pdf
51
Five critical areas in Algebra 1
1.
Relationships Between Quantities and Reasoning
with Equations
2.
Linear and Exponential Relationships
3.
Descriptive Statistics
4.
Expressions and Equations
5.
Quadratic Functions and Modeling
Page 15
http://www.corestandards.org/thestandards/mathematics/high-school52
algebra/introduction/
Six critical areas in Geometry
1.
Congruence, Proof, and Constructions
2.
Similarity, Proof, and Trigonometry
3.
Extending to Three Dimensions
4.
Connecting Algebra and Geometry Through
Coordinates
5.
Circles With and Without Coordinates
6.
Applications of Probability
Page 27
http://www.corestandards.org/thestandards/mathematics/high-schoolgeometry/introduction/
53
Four critical areas in Algebra 2
1.
Polynomial, Rational, and Radical
Relationships
2.
Trigonometric Functions
3.
Modeling with Functions
4.
Inferences and Conclusions from Data
Page 36
http://www.corestandards.org/thestandards/mathematics/highschool-algebra/introduction/ 54
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
55
Key Fluencies
Grade
Standard
K
MACC.K.OA.1.5
1
MACC.1.OA.3.6
Key Fluency
Add/subtract within 5
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
7
8
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
MACC.7.EE.2.4a Solve px + q = r, p(x + q) = r
MACC.8.EE.3.8b Solve simple 22 systems by inspection
A-Z
56
Mathematics Progressions
The Importance of
Mathematics Progressions
Gathering Momentum for Algebra
http://www.youtube.com/watch?v=ONPADo_Nt14&list=UUF0pa3nE3a
ZAfBMT8pqM5PA&index=6&feature=plcp
57
Mathematics Progressions Project
• Kindergarten Counting and Cardinality
• K-5 Number and Operations in Base Ten
• 3-5 Number and Operations—Fractions
• K–5 Operations and Algebraic Thinking
• K-5 Measurement and Data (Data part)
• Geometry Progression (coming soon!)
• 6-8 Expressions and Equations
• 6-7 Ratios and Proportional Relationships
• 6-8 Statistics and Probability
• High school Statistics and Probability
http://commoncoretools.me/category/progressions/
58
Give me a lever long enough
and a fulcrum to place it on,
and I can move the world.
‐‐Archimedes
59
Reflective Thoughts
How will you use the Common Core Standards for
Mathematical Practices to inform your curriculum
and guide your instruction?
How will the Critical Areas and the Cluster headings
help to inform your curriculum and guide your
instruction?
How will you use the Learning Progressions to
inform your curriculum and guide your instruction?
60