Session 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. 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. Enhance knowledge base of the Common Core Standards for Mathematics. 5

Session Mathematics Digital Checkpoint

Poll Everywhere erywhere.com/ erywhere.com/ 7

How To Vote via Texting 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 TIPS EXAMPLE

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Rate your level of understanding of the Common Core State Standards for Mathematics? No understanding Limited understanding Fair understanding Good understanding Excellent understanding Submit response at Send to: Text Code # to respond 10

Virtual Parking Lot Submit response at Send to: Text: plus your message 11

Digital Resources for the Common Core Apple core-standards/id http://itunes.apple.com/us/app/common- core-standards/id Android d=com.edutater.corestandardshttps://play.google.com/store/apps/details?i d=com.edutater.corestandards Common Core State Standards for Mathematics 12

Understanding Teachers Aligned McCallum Guided byPrinciples Standards National Focus NGA Habits of Mind Organized International Benchmarked Building Foundation CCSSO Daro Progressions Joint effort Vision Quali ty Knowledge Zimb a Robust, Relevant, Real-world Whole Child Approach Learner- focused Life-long skills Ensuring Education Focus Balanced Clarity Critical Areas Clusters Domains Evidenced- based Illustrative Mathematics S ense- making Rigor Research- based Procedural fluency Proficiency PARCC Opportunities Mathematical Practice X YOU Fluency Application Coherence Timeline Developmental Levels

Domains for K-12 K 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 Cluster Headings 16 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

High School Conceptual Categories 17 Number and Quantity (N) Algebra (A) Functions (F) Modeling (*) Geometry (G) Statistics and Probability (S) A-Z

Cluster Headings Domain A-Z

Cluster Headings StandardsStandards Domain

Florida’s Numbering of the Common Core State Standards MACC.7.EE.1.1 Subject Grade Domain Cluster Standard SubjectMathematics Common Core Grade7 DomainExpressions and Equations Cluster Use properties of operations to generate equivalent expressions StandardApply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. 20

Florida’s Numbering of the Common Core State Standards MACC.912.N-RN.2.3 Subject Grade Category Domain Cluster Standard SubjectMathematics Common Core Grade9-12 CategoryNumber and Quantity DomainThe Real Number System ClusterUse properties of rational and irrational numbers. StandardExplain 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. 21 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 22

Use appropriate tools strategically Attend to precision Look for and make sense of structure Look for and express regularity in repeated reasoning 8 Standards for Mathematical Practice Make sense of problems and persevere in solving them Reason abstractly and quantitatively Construct viable arguments and critique the reasoning of others Model with mathematics 23 A-Z

Florida’s Common Core State Standards Implementation Timeline Year/Grade LevelK FLLLLL F L LLL CCSS fully implemented F L B L CCSS fully implemented and assessed F L 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 A-Z

Session Mathematics Standards for Mathematical Practice

Poll Question Don’t forget: You can copy- paste this slide into other presentations, and move or resize the poll. How many Common Core Standards for Mathematical Practice are there? 26 Submit response at Send to: Text: plus your message

Standards for Mathematical Practice 27 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 them 6. Attend to precision 27

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 28 A-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

30 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….

Digital Task Text Numbers Practice #1 – code Practice #2 – code Practice #3 – code Practice #4 – code Practice #5 – code Practice #6 – code Practice #7 – code Practice #8 – code 6381 Submit responses at Send to: Text a CODE # to respond 31

Don’t forget: You can copy- paste this slide into other presentations, and move or resize the poll. Mathematical Practice 1 - Make sense of problems and persevere in solving them. Submit responses at Text to 37607

Don’t forget: You can copy- paste this slide into other presentations, and move or resize the poll. Mathematical Practice 2 - Reason Abstractly and Quantitatively Submit responses at Text to 37607

Don’t forget: You can copy- paste this slide into other presentations, and move or resize the poll. Mathematical Practice 3 - Construct viable arguments and critique the reasoning of others. Submit responses at Text to 37607

Don’t forget: You can copy- paste this slide into other presentations, and move or resize the poll. Mathematical Practice 4 - Model with mathematics. Submit responses at Text to 37607

Don’t forget: You can copy- paste this slide into other presentations, and move or resize the poll. Mathematical Practice 5 - Use appropriate tools strategically. Submit responses at Text to 37607

Don’t forget: You can copy- paste this slide into other presentations, and move or resize the poll. Mathematical Practice 6 - Attend to precision. Submit responses at Text to 37607

Don’t forget: You can copy- paste this slide into other presentations, and move or resize the poll. Mathematical Practice 7 - Look for and make sense of structure. Submit responses at Text to 37607

Don’t forget: You can copy- paste this slide into other presentations, and move or resize the poll. Mathematical Practice 8 - Look for and express regularity in repeated reasoning. Submit responses at Text 6381 to 37607

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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 41

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. 43

Session Mathematics Critical Areas and Mathematics Progressions

K-12 Domains and Critical Areas 45 6 th Grade Domains6 th 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. 7 th Grade Domains7 th 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. 8 th Grade Domains8 th 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 DomainsAlgebra 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 DomainsGeometry Critical Areas Handout #2 Handout #2

Four critical areas in 6 th Grade Connecting 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 equations 3. Developing understanding of statistical thinking standards/mathematics/grade-6/introduction/ Page 39

Identify the 6 th Grade Critical Area Cluster HeadingCritical 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 2-Rational # 1-Ratio 4-Statistics 3-Equations 2-Rational # Statistics 2-Rational #

Four critical areas in 7 th Grade 48 Page 46 standards/mathematics/grade- 7/introduction/ Developing understanding of and applying proportional relationships 1. 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 7 th Grade Critical Areas Cluster HeadingCritical 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 4-Statistics 3-Geometry 2-Rational, 3-Geometry 4-Statistics 2-Rational 49

Three critical areas in 8 th Grade 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 1. Grasping the concept of a function and using functions to describe quantitative relationships 2. Analyzing two- and three-dimensional space and figures using distance, angle, similarity, and congruence, and understanding and applying the Pythagorean Theorem standards/mathematics/grade- 8/introduction/ Page 52

Mathematics Progressions Ratio and Proportion in Grades 6-8: Connections to College and Career Skills Ratio and Proportion in Grades 6-8 Common Core Progressions Project w&feature=BFa&list=UUF0pa3nE3aZAfBMT8pq M5PA wordpress.com/2011/12/ccss _progression_sp_68_2011_12 _26_bis.pdf

Five critical areas in Algebra 1 Relationships Between Quantities and Reasoning with Equations 1. Linear and Exponential Relationships 2. Descriptive Statistics standards/mathematics/high-school- algebra/introduction/ Page 15 Expressions and Equations 4.4. Quadratic Functions and Modeling 5.5.

Six critical areas in Geometry Congruence, Proof, and Constructions 1. Similarity, Proof, and Trigonometry 2. Extending to Three Dimensions standards/mathematics/high-school- geometry/introduction/ Page 27 Connecting Algebra and Geometry Through Coordinates 4.4. Circles With and Without Coordinates 5.5. Applications of Probability 6.6.

Four critical areas in Algebra 2 54 Page 36 standards/mathematics/high- school-algebra/introduction/ Polynomial, Rational, and Radical Relationships 1. Trigonometric Functions 2. Modeling with Functions 3. Inferences and Conclusions from Data 4.

55 Building Fluency What is meant by fluency? CB3D2E6&index=13&feature=plpp_video Mathematics Fluency: A Balanced Approach (1:56)

GradeStandard Key Fluency KMACC.K.OA.1.5Add/subtract within 5 1MACC.1.OA.3.6Add/subtract within 10 2 MACC.2.OA.2.2 MACC.2.NBT.2.5 Add/subtract within 20 Add/subtract within 100 (pencil and paper) 3 MACC.3.NBT.1.2 MACC.3.OA.3.7 Add/subtract within 1,000 Multiply/divide within MACC Critical Area #1 Add/subtract within 1,000,000 Develop fluency with efficient procedures for multiplying whole numbers 5 MACC.5.NBT.2.5 Critical Area #1 Multi-digit multiplication Developing fluency with addition and subtraction of fractions 6 MACC.6.NS.2.2 MACC.6.NS.2.3 Multi-digit division Multi-digit decimal operations 7MACC.7.EE.2.4aSolve px + q = r, p(x + q) = r 8MACC.8.EE.3.8b Solve simple 2  2 systems by inspection Key Fluencies Handout #3 Handout #3 56 A-Z

Mathematics Progressions The Importance of Mathematics Progressions ZAfBMT8pqM5PA&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 58 High school Statistics and Probability

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 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? How will you use the Common Core Standards for Mathematical Practices to inform your curriculum and guide your instruction? Handout #5 Handout #5 60