Session 2 K-5 Mathematics

1. Common Core State Standards Session 2 K-5 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. “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. • 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. Building Foundation Ensuring Education • CCSSO Focus Aligned Daro Coherence Clarity Developmental Level 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

7. 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

8. Domains for K-12 A-Z

9. Cluster Headings Cluster Headings Cluster Headings Domain Domain Domain Domain Cluster Headings A-Z 9

10. Cluster Headings Standards Domain

11. Florida’s Numbering ofthe Common Core State Standards MACC.K.CC.2.5 Subject Grade Domain Cluster Standard A-Z

12. 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

13. Standards for Mathematical Practice Handout • Use appropriate tools strategically • Make sense of problems and persevere in solving them • 5 • 1 • Attend to precision • Reason abstractly and quantitatively • 6 • 2 • 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

14. 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 14 http://www.fldoe.org/bii/pdf/CCSS-ImplementationTimeline.pdf

15. 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 15

16. 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 16

17. Digital Task Handout 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….

18. Expectations • Students planning solution pathways, monitoring and evaluating their progress and asking “Does this make sense?” 1 • Students knowing and using different properties of operations and objects and creating a coherent representation of the problem at hand. 2 • Students understanding and using definitions. Students justifying and explaining their thinking and listening to arguments of others and deciding if they make sense.. 3 • Students applying and using mathematics to solve problems connected to real-life situations. Students using models to represent, analyze and interpret results. 4

19. Expectations Students communicating precisely to others. Students calculating accurately and efficiently, expressing numerical answers with a degree of precision appropriate for the problem context. 6 Students being able to look closely to discern a pattern or structure. Students being able to shift perspectives. 7 • Students evaluating the reasonableness of their results. Student Maintaining oversight of the process, while attending to the details. 8 Students being familiar with tools appropriate for their grade or course and using technology tools to explore and deepen their understanding of concepts. Students being able to make sound decisions about when each of these tools might be helpful. 5

20. http://www.wordle.net/show/wrdl/5360414/Mathematical_Practice_Actionshttp://www.wordle.net/show/wrdl/5360414/Mathematical_Practice_Actions

21. 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

22. 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.

23. 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 need more time. • Remember that ELLs from different countries may display mathematical functions in different ways.

24. K-5 Domains and Critical Areas Handout #2 A-Z

25. Two critical areas in Kindergarten In Kindergarten, instructional time should focus on two critical areas: • 1. • Representing, relating, and operating on whole numbers, initially with sets of objects Page 9 • 2. • Describing shapes and space More learning time in Kindergarten should be devoted to number than to other topics. http://www.corestandards.org/the-standards/mathematics/kindergarten/introduction/ 25

26. Identify the Kindergarten Critical Area #1 Numbers #1 Numbers #2 Shapes #1 Numbers #2 Shapes #1 Numbers #1 Numbers #2 Shapes #2 Shapes

27. Four critical areas in 1st Grade • 1. developing understanding of addition, subtraction, and strategies for addition and subtraction within 20 In Grade 1, instructional time should focus on four critical areas: • 2. developing understanding of whole number relationships and place value, including grouping in tens and ones Page 14 • 3. developing understanding of linear measurement and measuring lengths as iterating length units • 4. reasoning about attributes of, and composing and decomposing geometric shapes http://www.corestandards.org/the-standards/mathematics/grade-1/introduction/

28. Identify the 1st Grade Critical Areas #1 Operations #2 Base Ten #3 Measurement #1 Operations #3 Measurement #1 Operations #4 Geometry #2 Base Ten #3 Measurement #2 Base Ten #1 Operations

29. Four critical areas in 2nd Grade • 1. • extending understanding of base-ten notation In Grade 2, instructional time should focus on four critical areas: • 2. building fluency with addition and subtraction Page 17 • 3. • using standard units of measure • 4. describing and analyzing shapes http; ://www.corestandards.org/the-standards/mathematics/grade-2/introduction/ 29

30. Four critical areas in 3rd Grade • 1. developing understanding of multiplication and division and strategies for multiplication and division within 100 In Grade 3, instructional time should focus on four critical areas: • 2. developing understanding of fractions, especially unit fractions (fractions with numerator 1) Page 21 • 3. developing understanding of the structure of rectangular arrays and of area • 4. describing and analyzing two-dimensional shapes http; ://www.corestandards.org/the-standards/mathematics/grade-2/introduction/ 30

31. Mathematics Progressions Whole Numbers to Fractions in Grades 3-6 3-5 Number and Operations - Fractions Common Core Progressions Project http://youtu.be/w7h64xjN-PM http://commoncoretools.files.wordpress.com/2012/02/ccss_progression_nf_35_2011_08_12.pdf http://www.youtube.com/watch?v=w7h64xjN-PM&list=PLD7F4C7DE7CB3D2E6&index=7&feature=plpp_video

32. Three critical areas in 4th Grade • 1. developing understanding and fluency with multi-digit multiplication, and developing understanding of dividing to find quotients involving multi-digit dividends In Grade 4, instructional time should focus on three critical areas: • 2. developing an understanding of fraction equivalence, addition and subtraction of fractions with like denominators, and multiplication of fractions by whole numbers Page 27 • 3. understanding that geometric figures can be analyzed and classified based on their properties, such as having parallel sides, perpendicular sides, particular angle measures, and symmetry. http://www.corestandards.org/the-standards/mathematics/grade-4/introduction

33. Building Fluency Mathematics Fluency: A Balanced Approach (1:56) • http://www.youtube.com/watch?v=ZFUAV00bTwA&list=PLD7F4C7DE7CB3D2E6&index=13&feature=plpp_video • http://youtu.be/ZFUAV00bTwA

34. Key Fluencies Handout #3 A-Z

35. Three critical areas in 5th Grade • 1. developing fluency with addition and subtraction of fractions, and developing understanding of the multiplication of fractions and of division of fractions in limited cases (unit fractions divided by whole numbers and whole numbers divided by unit fractions) In Grade 5, instructional time should focus on three critical areas: • 2. extending division to 2-digit divisors, integrating decimal fractions into the place value system and developing understanding of operations with decimals to hundredths, and developing fluency with whole number and decimal operations Page 33 • 3. developing understanding of volume http://www.corestandards.org/the-standards/mathematics/grade-5/introduction

36. Mathematics Progressions Handout #4 Operations on Whole Number Progressions http://youtu.be/a-P9KQdhE0U http://www.youtube.com/watch?v=a-P9KQdhE0U&feature=BFa&list=PLD7F4C7DE7CB3D2E6

37. Mathematics Progressions Project • Kindergarten Counting and Cardinality • Number and Operations in Base Ten • Number and Operations—Fractions • K–5 Operations and Algebraic Thinking • Measurement and Data • Geometry Progression (coming soon!) • Expressions and Equations • Ratios and Proportional Relationships • Statistics and Probability, Grades 6–8 • http://commoncoretools.me/category/progressions/

38. Give me a lever long enough and a fulcrum to place it on, and I can move the world. ‐‐Archimedes

39. Reflective Thoughts Handout #5 • How will you use the Common Core Standards for Mathematical Practices to inform your curriculum and guide your instruction? • 1 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?