Post on 30-Dec-2015
description
Session 36-12 Mathematics
Common Core State Standards
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.
Handout #1
Common Core From A to Z
Handout #1
Common Core From A to Z
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
• Become familiar with the structure of the Common Core State Standards for Mathematics.2
Enhance knowledge of the Common Core Standards for Mathematical Practice. 3
4Understand how the critical areas bring focus to key mathematical concepts for students to learn at each grade level.
5 Consider how the learning progressions can be used to inform curriculum and guide instruction.
• Enhance knowledge base of the Common Core Standards for Mathematics.1
5
Session 36-12 Mathematics
Digital Checkpoint
Digital Checkpoint
• Poll Everywhere• http://www.pollev
erywhere.com/
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How To Vote via Texting
1. Standard texting rates only (worst case US $0.20)2. We have no access to your phone number3. Capitalization doesn’t matter, but spaces and spelling do
TIPS
EXAMPLE
How to Vote via Web Response
Rate your level of understanding of the Common Core State Standards
for Mathematics?
• No understanding 125724• Limited understanding 125730• Fair understanding 125803• Good understanding 125804• Excellent understanding 125809
Submit response at http://PollEV.com
Send to: 37607Text Code # to respond
10
Virtual Parking Lot
Submit response at http://PollEV.com
Send to: 37607Text: 220274 plus your message
11
Digital Resources for the Common Core
• Apple
• http://itunes.apple.com/us/app/com
mon-core-standards/id439424555
• Android
• https://play.google.com/store/apps/
details?id=com.edutater.corestand
ards
• Common Core State Standards for
Mathematics
• http://www.corestandards.org/
12
Understanding Teachers
Aligned
McCallum
Guided by Principles
Standards
National Focus NGA
Habits of
Mind
Organized
International Benchmarked
Building Foundation
CCSSO Daro
Progressions
Joint effort
Vision
Quality
Knowledge
Zimba
Robust, Relevant,
Real-world
Whole Child
Approach
Learner-focused Life-long
skills
Ensuring Education Focus
BalancedClarity
Critical Areas
ClustersDomains
Evidenced-based
Illustrative Mathematics
Sense-making
Rigor
Research-based
Procedural fluency
ProficiencyPARCC
OpportunitiesMathematical Practice
XYOU
FluencyApplication
Coherence
Timeline
DevelopmentalLevels
Domains for K-12K 1 2 3 4 5 6 7 8 HS
Counting
and Cardinality
(CC)
Number and
Quantity(N)
Number and Operations in Base Ten (NBT) The Number System (NS)
Number and Operations-Fractions
(NF)
Ratios and Proportional Relationships
(RP)
Operations and Algebraic Thinking (OA)Functions (F)
Expressions and Equations (EE)
Algebra(A)
Geometry (G)
Measurement and Data (MD)
Statistics and Probability (SP)A-Z
Domain
Domain
Domain
Domain
Cluster Headings
Cluster Headings
Cluster Headings
Cluster Headings
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Grade 7 Overview
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.
Domain
Cluster Headings
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High School Conceptual Categories
http://www.corestandards.org/assets/CCSSI_Math%20Standards.pdf
• Number and Quantity (N)
• Algebra (A)
• Functions (F)
• Modeling (*)
• Geometry (G)
• Statistics and Probability (S)A-Z
Cluster Headings
Cluster Headings
Cluster Headings
Cluster Headings
Domain
Domain
Domain
Domain
A-Z
Cluster Headings
Standards
Domain
Florida’s Numbering ofthe 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 ofthe Common Core State Standards
MACC.912.N-RN.2.3
Subject Grade Category Domain Cluster StandardSubject 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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Use appropriate tools strategically5
Attend to precision6
Look for and make sense of structure
7
Look for and express regularity in repeated reasoning
8
8 Standards for Mathematical Practice
Make sense of problems and persevere in solving them
1
Reason abstractly and quantitatively2
Construct viable arguments and critique the reasoning of others
3
Model with mathematics4
23A-Z
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 F L F L L L L
2013-2014CCSS fully implemented
F L F L F L B L B L
2014-2015CCSS fully implemented and
assessed
F L F L F L F L F L
F - full implementation of CCSS for all content areasL – 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
http://www.fldoe.org/bii/pdf/CCSS-ImplementationTimeline.pdf 24A-Z
Session 36-12 Mathematics
Standards for Mathematical Practice
Poll Question
How many Common Core Standards for Mathematical Practice are there?
26
Submit response at http://PollEV.com/
Send to: 37607Text: 129153 plus your message
27
Standards for Mathematical Practice
Reasoning and
Explaining
Seeing Structure and Generalizing
Overarching Habits of Mind of a Productive Mathematical Thinker
2. Reason abstractly and quantitatively
3. Construct viable arguments and
critique the reasoning of others
Modeling and
Using Tools
4. Model with mathematics
5. Use appropriate tools strategically
7. Look for and make use of structure
8. Look for and express regularity in repeated reasoning
1. Make sense of problems and persevere in solving them6. Attend to precision
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Standards for Mathematical Practice
http://www.youtube.com/watch?v=9pKcO9E4Flw&feature=relmfu http://youtu.be/9pKcO9E4Flw
• 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
28A-Z
The Standards for Mathematical Practice
• Please locate the Common Core State Standards for Mathematics.
• 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…
Page 6
29
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Digital TaskYour 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….
Digital Task Text Numbers
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
Submit responses at http://PollEV.com
Send to: 37607Text a CODE # to respond
31
Mathematical Practice 1 - Make sense of problems and persevere in solving them.
Submit responses at http://PollEV.com
Text 130116 to 37607
Mathematical Practice 2 - Reason Abstractly and Quantitatively
Submit responses at http://PollEV.com
Text 50983 to 37607
Mathematical Practice 3 - Construct viable arguments and critique the
reasoning of others.
Submit responses at http://PollEV.com
Text 71040 to 37607
Mathematical Practice 4 - Model with mathematics.
Submit responses at http://PollEV.com
Text 71234 to 37607
Mathematical Practice 5 - Use appropriate tools strategically.
Submit responses at http://PollEV.com
Text 71681 to 37607
Mathematical Practice 6 - Attend to precision.
Submit responses at http://PollEV.com
Text 71867 to 37607
Mathematical Practice 7 - Look for and make sense of structure.
Submit responses at http://PollEV.com
Text 72038 to 37607
Mathematical Practice 8 - Look for and express regularity in repeated reasoning.
Submit responses at http://PollEV.com
Text 6381 to 37607
http://www.wordle.net/show/wrdl/5360414/Mathematical_Practice_Actions40
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. 42
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.
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Session 36-12 Mathematics
Critical Areas and Mathematics Progressions
K-12 Domains and Critical Areas
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6th Grade Domains 6th Grade Critical Areas
Ratios and Proportional Relationships The Number System Expressions and Equations Geometry Statistics and Probability
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 Domains 7th Grade Critical Areas Ratios and Proportional Relationships The Number System Expressions and Equations Geometry Statistics and Probability
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 Domains 8th Grade Critical Areas The Number System Expressions and Equations Functions Geometry Statistics and Probability
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 Domains Algebra 1 Critical Areas 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
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 systems of equations involving quadratic expressions.
Quadratic Functions and Modeling; Comparing key characteristics.
Geometry Domains Geometry Critical Areas
Handout #2
Handout #2
Four critical areas in 6th GradeConnecting ratio and rate to whole number multiplication and division and using concepts of ratio and rate to solve problems
1.
Completing understanding of division of fractions and extending the notion of number to the system of rational numbers, which includes negative numbers
2.
Writing, interpreting, and using expressions and equations3.
Developing understanding of statistical thinking4.
46
http://www.corestandards.org/the-standards/mathematics/grade-6/introduction/
Page 39
Identify the 6th Grade Critical AreaCluster Heading Critical Area
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.
Apply and extend previous understandings of multiplication and division to divide fractions by fractions.
3-Equations
3-Equations
2-Rational #
1-Ratio
4-Statistics
3-Equations
2-Rational #
47
4-Statistics
2-Rational #
48
Four critical areas in 7th Grade
Page 46
http://www.corestandards.org/the-standards/mathematics/grade-7/introduction/
Developing understanding of and applying proportional relationships1.
Developing understanding of operations with rational numbers and working with expressions and linear equations
2.
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
3.
Drawing inferences about populations based on samples
4.
Identify the 7th Grade Critical AreasCluster Heading Critical Area
Analyze proportional relationships and use them to solve real-world and mathematical problems.
Draw, construct and describe geometrical figures and describe the relationships between them.
Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.
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.
1-Proportions, 2-Rational
2-Rational
4-Statistics
3-Geometry
2-Rational, 3-Geometry
3-Geometry
4-Statistics
2-Rational
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Three critical areas in 8th GradeFormulating 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
1.
Grasping the concept of a function and using functions to describe quantitative relationships2.
Analyzing two- and three-dimensional space and figures using distance, angle, similarity, and congruence, and understanding and applying the Pythagorean Theorem
3.
50
http://www.corestandards.org/the-standards/mathematics/grade-8/introduction/Page 52
Mathematics ProgressionsRatio and Proportion in Grades 6-8:
Connections to College and Career Skills
Ratio and Proportion in Grades 6-8
Common Core Progressions Project
http://www.youtube.com/watch?v=5pBOnvzC_Yw&feature=BFa&list=UUF0pa3nE3aZAfBMT8pqM5PA
51
<iframe width="560" height="315" src="http://www.youtube.com/embed/5pBOnvzC_Yw" frameborder="0" allowfullscreen></iframe>
http://youtu.be/5pBOnvzC_Yw
http://commoncoretools.files.wordpress.com/2011/12/ccss_progression_sp_68_2011_12_26_bis.pdf
Five critical areas in Algebra 1Relationships Between Quantities and Reasoning
with Equations 1.
Linear and Exponential Relationships2.
Descriptive Statistics 3.
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http://www.corestandards.org/the-standards/mathematics/high-school-algebra/introduction/Page 15
Expressions and Equations 4.
Quadratic Functions and Modeling 5.
Six critical areas in GeometryCongruence, Proof, and Constructions1.
Similarity, Proof, and Trigonometry2.
Extending to Three Dimensions3.
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http://www.corestandards.org/the-standards/mathematics/high-school-geometry/introduction/Page 27
Connecting Algebra and Geometry Through Coordinates4.
Circles With and Without Coordinates5.
Applications of Probability 6.
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Four critical areas in Algebra 2
Page 36
http://www.corestandards.org/the-standards/mathematics/high-school-algebra/introduction/
Polynomial, Rational, and Radical Relationships
1.
Trigonometric Functions2.
Modeling with Functions3.
Inferences and Conclusions from Data4.
55
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)
Grade Standard Key FluencyK MACC.K.OA.1.5 Add/subtract within 5
1 MACC.1.OA.3.6 Add/subtract within 10
2MACC.2.OA.2.2MACC.2.NBT.2.5
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.4.2.4Critical Area #1
Add/subtract within 1,000,000 Develop fluency with efficient procedures for multiplying whole numbers
5MACC.5.NBT.2.5Critical 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
7 MACC.7.EE.2.4a Solve px + q = r, p(x + q) = r8 MACC.8.EE.3.8b Solve simple 22 systems by inspection
Key Fluencies Handout #3
Handout #3
56A-Z
Mathematics Progressions
The Importance of Mathematics Progressions
http://www.youtube.com/watch?v=ONPADo_Nt14&list=UUF0pa3nE3aZAfBMT8pqM5PA&index=6&feature=plcp
Handout #4
Handout #4
57
Gathering Momentum for Algebra
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
http://commoncoretools.me/category/progressions/ 58
• High school Statistics and Probability
Give me a lever long enoughand a fulcrum to place it on,and I can move the world. ‐‐Archimedes
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Reflective Thoughts
How will the Critical Areas and the Cluster headings help to inform your curriculum and guide your instruction?
2
3 How will you use the Learning Progressions to inform your curriculum and guide your instruction?
How will you use the Common Core Standards for Mathematical Practices to inform your curriculum and guide your instruction?
1
Handout #5
Handout #5
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