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Session 3 6-12 Mathematics

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. Handout #1

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Session 3 6-12 Mathematics

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  1. Common Core State Standards Session 3 6-12 Mathematics

  2. 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

  3. WELCOME Introductions 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 • June Campbell • ORTTTA • Nancy Kinard • Palm Beach • Michael Chase • Volusia County • Amy Coltharp • BFEP • Kim Wuellner • St. Johns • Martha Gioielli • DA

  4. “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)

  5. Expected Outcomes • Enhance knowledge base of the Common Core Standards for Mathematics. • 1 • 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 Understand how the critical areas bring focus to key mathematical concepts for students to learn at each grade level. • 4 • 5 Consider how the learning progressions can be used to inform curriculum and guide instruction.

  6. Digital Checkpoint Session 3 6-12 Mathematics

  7. Digital Checkpoint • Poll Everywhere • http://www.polleverywhere.com/

  8. How To Vote via Texting EXAMPLE Standard texting rates only (worst case US $0.20) We have no access to your phone number Capitalization doesn’t matter, but spaces and spelling do TIPS

  9. How to Vote via Web Response

  10. 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 Send to: 37607 Text Code # to respond Submit response at http://PollEV.com

  11. Virtual Parking Lot Send to: 37607 Text: 220274 plus your message Submit response at http://PollEV.com

  12. Digital Resources for the Common Core • Apple • http://itunes.apple.com/us/app/common-core-standards/id439424555 • Android • https://play.google.com/store/apps/details?id=com.edutater.corestandards • Common Core State Standards for Mathematics • http://www.corestandards.org/

  13. Building Foundation Ensuring Education • CCSSO Focus Aligned Daro Coherence Developmental Levels Clarity Evidenced-based Application Balanced Critical Areas Fluency Domains Clusters Habits of Mind Knowledge Guided by Principles Joint effort International Benchmarked Learner-focused Life-long skills IllustrativeMathematics McCallum Progressions Organized Robust, Relevant, Real-world National Focus NGA Quality Procedural fluency Opportunities Mathematical Practice Proficiency Research-based PARCC Rigor Teachers Whole Child Approach Standards Vision Sense-making Understanding Zimba X YOU Timeline

  14. Domains for K-12 A-Z

  15. 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. Cluster Headings Cluster Headings Cluster Headings Cluster Headings Domain Domain Domain Domain Domain Cluster Headings 16

  16. High School Conceptual Categories • Number and Quantity (N) • Algebra (A) • Functions (F) • Modeling (*) • Geometry (G) • Statistics and Probability (S) A-Z http://www.corestandards.org/assets/CCSSI_Math%20Standards.pdf

  17. Cluster Headings Cluster Headings Cluster Headings Domain Domain Domain Domain Cluster Headings A-Z

  18. Standards Cluster Headings Domain

  19. Florida’s Numbering ofthe Common Core State Standards MACC.7.EE.1.1 Subject Grade Domain Cluster Standard

  20. Florida’s Numbering ofthe Common Core State Standards MACC.912.N-RN.2.3 Subject Grade Category Domain Cluster Standard A-Z

  21. 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. 8 Standards for Mathematical Practice • Make sense of problems and persevere in solving them • Use appropriate tools strategically • 5 • 1 • Reason abstractly and quantitatively • Attend to precision • 2 • 6 • Look for and make sense of structure • Construct viable arguments and critique the reasoning of others • 7 • 3 • Look for and express regularity in repeated reasoning • Model with mathematics • 4 • 8 A-Z

  23. Florida’s Common Core State Standards Implementation Timeline 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 24 http://www.fldoe.org/bii/pdf/CCSS-ImplementationTimeline.pdf

  24. Standards for Mathematical Practice Session 3 6-12 Mathematics

  25. 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/ Don’t forget: You can copy-paste this slide into other presentations, and move or resize the poll.

  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 Seeing Structure and Generalizing 2. Reason abstractly and quantitatively 3. Construct viable arguments and critique the reasoning of others 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 27

  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 http://www.youtube.com/watch?v=9pKcO9E4Flw&feature=relmfu http://youtu.be/9pKcO9E4Flw A-Z 28

  28. 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

  29. 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 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: 37607 Text a CODE # to respond 31

  31. Mathematical Practice 1 - Make sense of problems and persevere in solving them. Submit responses at http://PollEV.com Text 130116 to 37607 Don’t forget: You can copy-paste this slide into other presentations, and move or resize the poll.

  32. Mathematical Practice 2 - Reason Abstractly and Quantitatively Submit responses at http://PollEV.com Text 50983 to 37607 Don’t forget: You can copy-paste this slide into other presentations, and move or resize the poll.

  33. Mathematical Practice 3 - Construct viable arguments and critique the reasoning of others. Submit responses at http://PollEV.com Text 71040 to 37607 Don’t forget: You can copy-paste this slide into other presentations, and move or resize the poll.

  34. Mathematical Practice 4 - Model with mathematics. Submit responses at http://PollEV.com Text 71234 to 37607 Don’t forget: You can copy-paste this slide into other presentations, and move or resize the poll.

  35. Mathematical Practice 5 - Use appropriate tools strategically. Submit responses at http://PollEV.com Text 71681 to 37607 Don’t forget: You can copy-paste this slide into other presentations, and move or resize the poll.

  36. Mathematical Practice 6 - Attend to precision. Submit responses at http://PollEV.com Text 71867 to 37607 Don’t forget: You can copy-paste this slide into other presentations, and move or resize the poll.

  37. Mathematical Practice 7 - Look for and make sense of structure. Submit responses at http://PollEV.com Text 72038 to 37607 Don’t forget: You can copy-paste this slide into other presentations, and move or resize the poll.

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

  39. http://www.wordle.net/show/wrdl/5360414/Mathematical_Practice_Actionshttp://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

  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. Critical Areas and Mathematics Progressions Session 3 6-12 Mathematics

  44. K-12 Domains and Critical Areas Handout #2

  45. 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 Page 39 • 3. • Writing, interpreting, and using expressions and equations • 4. Developing understanding of statistical thinking http://www.corestandards.org/the-standards/mathematics/grade-6/introduction/ 46

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

  47. 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 Page 46 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. • 4. Drawing inferences about populations based on samples http://www.corestandards.org/the-standards/mathematics/grade-7/introduction/

  48. Identify the 7th Grade Critical Areas 1-Proportions, 2-Rational 3-Geometry 2-Rational 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 Page 52 • 3. • Analyzing two- and three-dimensional space and figures using distance, angle, similarity, and congruence, and understanding and applying the Pythagorean Theorem http://www.corestandards.org/the-standards/mathematics/grade-8/introduction/ 50

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