1. BRENDA BRUSH, MATHEMATICS COORDINATOR DR. WILLIAM M C KERSIE, SUPERINTENDENT GREENWICH PUBLIC SCHOOLS LEADERSHIP INSTITUTE AUGUST 15, 2012 Common Core State Standards and Mathematics in the Greenwich Public Schools

2. Our Goals for Today Review the important changes and instructional shifts in Mathematics Provide a brief overview of the structure of the Content Standards Provide an overview the Standards for Mathematical Practice Begin to unpack one of the Standards for Mathematical Practice Next steps…

4. Instructional Shifts in Mathematics Shift 1: Focus  Narrow and deepen scope of how time and energy is spent in the classroom  Focus deeply on only the concepts that are prioritized in the standards  Allow students to reach strong foundational knowledge and deep conceptual understanding  Enable students to transfer mathematical skills and understanding across concepts and grade levels Shift 2: Coherence  Carefully connect learning within and across grades in order to build new understanding onto foundations built in previous years  Teachers can begin to count on a deep conceptual understanding of core content and build on it  Each standard is not a new event, but an extension of previous learning Adapted from EngageNY

5. Instructional Shifts in Mathematics Shift 3: Fluency  Students are expected to have speed and accuracy with simple calculations  Teachers structure class time and/or homework time to incorporate memorization through repetition  Allows students to be more able to understand and manipulate more complex concepts Shift 4: Deep Understanding  Support students’ ability to access concepts from a number of perspectives  Teach more than “how to get the answer”  Students demonstrate deep conceptual understanding of concepts by applying them to new situations, as well as writing and speaking about their understanding Adapted from EngageNY

6. Instructional Shifts in Mathematics Shift 5: Application  Students are expected to use math and choose the appropriate concept for application even when not prompted to do so  Provide opportunities at all grade levels to apply math concepts in “real world situations”  Teachers in content areas outside math (particularly science) ensure that students are using math to make meaning of and access content Shift 6: Dual Intensity  Students are both practicing and understanding with intensity  Create opportunities for both “drills” and making use of skills through extended application  The amount of time spent practicing and understanding learning is driven by the concept and varies throughout the school year Adapted from EngageNY

8. Structure of Content Standards Domains rather than strands – 11 total Clusters within each Domain Grade specific Standards Coherent Progression of domains across grade levels K-8 arranged by grade level 9-12 arranged by conceptual categories CT State Standards are 92% aligned with CCSS

9. Cluster Content Standards Domain Grade Level 2.NBT (code) Standard 2.NBT.1 (code) ClusterCluster HeadingsHeadings

10. Organized by Domains Rather than Strands

11. In Grade 2, instructional time should focus on four critical areas: (1) extending understanding of base-ten notation; (2) building fluency with addition and subtraction; (3) using standard units of measure; and (4) describing and analyzing shapes. (1) Students extend their understanding of the base-ten system. This includes ideas of counting in fives, tens, and multiples of hundreds, tens, and ones, as well as number relationships involving these units, including comparing. Students understand multi-digit numbers (up to 1000) written in base-ten notation, recognizing that the digits in each place represent amounts of thousands, hundreds, tens, or ones (e.g., 853 is 8 hundreds + 5 tens + 3 ones). (2) Students use their understanding of addition to develop fluency with addition and subtraction within 100. They solve problems within 1000 by applying their understanding of models for addition and subtraction, and they develop, discuss, and use efficient, accurate, and generalizable methods to compute sums and differences of whole numbers in base-ten notation, using their understanding of place value and the properties of operations. They select and accurately apply methods that are appropriate for the context and the numbers involved to mentally calculate sums and differences for numbers with only tens or only hundreds. (3) Students recognize the need for standard units of measure (centimeter and inch) and they use rulers and other measurement tools with the understanding that linear measure involves an iteration of units. They recognize that the smaller the unit, the more iterations they need to cover a given length. (4) Students describe and analyze shapes by examining their sides and angles. Students investigate, describe, and reason about decomposing and combining shapes to make other shapes. Through building, drawing, and analyzing two- and three- dimensional shapes, students develop a foundation for understanding area, volume, congruence, similarity, and symmetry in later grades. Grade Level Introduction Critical Area Grade Level Focus

12. Critical Areas There are two to four critical areas for instruction in the introduction for each grade level, model course or integrated pathway. They bring focus to the standards at each grade by providing the big ideas that educators can use to build their curriculum and to guide instruction.

14. Standards for Mathematical Practice Written for Grades K-12, encouraging coherence across grade levels “Habits of Mind” embodied by “mathematically proficient students” Many can be applied across content areas

15. Unpacking the Practice Standards What do these standards mean for teachers? What do the standards look like at each grade level? In other words, what are “mathematically proficient students” able to do? How can teachers support students in these “habits of mind”? What tasks can support students in learning and applying these practice standards?

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

18. Make Sense of Problems and Persevere in Solving Them If I have 10 ice cubes and you have 11 apples, how many pancakes will fit on the roof? Purple, because aliens don’t wear hats.

19. Unpacking the Practice Standards Standard 1: Make sense of problems and persevere in solving them.  Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, “Dose this make sense?” They can understand the approaches of others to solving complex problems and identify correspondences between different approaches.

20. Unpacking the Practice Standards Activity: Unpacking a Standard In your handout, look at the model standard that has already been unpacked for you. Let’s take a quick look…

22. Example - Grade K: Explain to themselves and others the meaning of a problem and look for ways to solve it. Determine if their thinking makes sense or if another strategy is needed. Solve number stories in various ways. As the teacher uses thoughtful questioning and provides opportunities for students to share thinking, kindergarten students begin to reason as they become more conscious of what they know and how to solve problems. What would students in my classroom be doing?

25. Unpacking the Practice Standards Activity: Unpacking a Standard In your group, work to begin “unpacking” Standard 2.  What are the key ideas found within the standard? (Think verbs and adjectives!)  What might “mathematically proficient students” might be doing in a classroom at different grade levels?  What types of tasks might help to support the development of this particular practice?

26. Reflections… 1. What do you feel was valuable about this exercise? 2. Did “unpacking” this standard help you to better understand what you might see in classrooms? 3. What more do you feel needs to be done in order to better help you understand and make sense of the Standards for Mathematical Practice?

27. Next Steps… Teachers  Professional learning through half-day workshop on 11/6 and Early Release days throughout the year  Embedded professional learning through coaching cycles  Introduction to performance tasks during Early Release day, implement and reflect using guiding questions in grade level teams Administrators  Support new learning and encourage teachers to “try out” the practice standards  Encourage sharing within and between grade level teams

29. Questions?