1. Committing to the Core Rethinking Mathematics for the 21 st Century Sara Good Heather Canzurlo Welcome to Session 2!

2. Take a FIRST BITE out of the Core! CHANGE 3 Locate each section underlined below in your binder. Read the summary for each section, and then the section itself. Change or add three words or phrases in the following summaries to better represent the important ideas of that section. Be ready to cite evidence from the text to justify your choices.

3. Common Core State Standards Initiative Standards-Setting Criteria The CCCS-M is organized by the guiding principles of RIGOR, CLARITY, COHERENCE, and FOCUS. These rigorous standards include high cognitive demand and ask students to demonstrate conceptual understanding through applying skills to new situations. They provide sufficient detail on how to teach and assess them. The big ideas and supporting concepts provide coherence that details a progression of learning, as well as focus that limits repetition across the grades.

4. Application to Students with Disabilities All students must have access to challenging academic standards within the general curriculum. Since SWD have difficulty benefiting from general education, how these standards are implemented are of utmost importance. Instruction must include such supports as IEP goals aligned to grade-level CCSS-M, trained personnel, multiple and engaging methods for demonstrating understanding, accommodations that do not change the grade-specific mathematics, and assistive technology.

5. Application of Common Core Standards for English Language Learners Language is an important resource for learning mathematics as it requires and develops both communication and reasoning skills. Math instruction should include class discourse and address academic vocabulary regularly, even as ELL students are learning English. Simple vocabulary instruction, including drill and practice, are not effective practices for developing language and mathematical understanding.

6. Key Takeaways from the CCSS Initiative in Mathematics The K-5 standards provide a solid foundation in applying understanding of whole numbers and operations. Kindergarten focuses on the number core: learning to correspond numbers to quantities, and how to put together and take apart numbers. K-5 standards help teachers navigate tough topics of fractions, negative numbers and geometry in a coherent manner. They also expect hands on learning in geometry (as well as algebra and probability and statistics in later grades).

7. Introduction: Common Core State Standards for Mathematics The CCSS-M is internationally benchmarked to provide greater focus and coherence. They draw from higher performing countries’ focus on number, measurement and geometry in early grades, with less emphasis on probability and algebra concepts. These countries devote about half the instructional time on number in grades 1-3, with almost all remaining time to geometry and measurement. The particulars of the content standards— i.e. meaning of whole numbers, math facts, procedures— must evolve to deeper structures of mathematics—i.e. properties of the rational number systems—in order to be coherent. Mathematical understanding and procedural skill are equally important, and are developed through rich tasks.

8. HELPING TEACHERS: COHERENCE & FOCUS http://www.ccsso.org/Resources/Digital_Resources/Common_Core_Implementation_Video_Series.html

9. Understand the structure and organization of the CCSS for math. Examine curriculum through the Common Core lens. Enrich mathematical content knowledge and pedagogy.

10. THE HANDSHAKE PROBLEM How many handshakes occur in a group of 8 people if each person shakes hands exactly one time with every other person?

11. THE HANDSHAKE PROBLEM

12. Standard for Mathematical Practice Evidence: What are students doing? 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and construct 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.

13. Domains larger groups of related standards Cluster Headings overview & quick summary of the mathematical ideas within a domain Clusters groups of related standards Standards define what students should understand and be able to do Organization of the CCSS Math Standards

14. Grade Level Introduction Critical Area of Focus Cross-cutting themes

15. Grade Level Overview Grade 4 Overview Operations and Algebraic Thinking Use the four operations with whole numbers to solve problems. Gain familiarity with factors and multiples. Generate and analyze patterns. Number and Operations in Base Ten Generalize place value understanding for multi-digit whole numbers. Use place value understanding and properties of operations to perform multi-digit arithmetic. Number and Operations—Fractions Extend understanding of fraction equivalence and ordering. Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers. Understand decimal notation for fractions, and compare decimal fractions. Measurement and Data Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit. Represent and interpret data. Geometric measurement: understand concepts of angle and measure angles. Geometry Draw and identify lines and angles, and classify shapes by properties of their lines and angles. Mathematical Practices 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

16. Organization of K-8 Standards Grade Level DomainDomain StandardStandard ClusterCluster

17. Grades K – 5 Counting and Cardinality CC Operations and Algebraic ThinkingOA Number and Operations in Base TenNBT Number and Operations – FractionsNF Measurement and DataMD Geometry G Cracking the Code

18. GRADE LEVEL DOMAIN: NUMBER AND OPERATIONS IN BASE TEN 1 ST STANDARD IN THE CLUSTER Number & Operations in Base Ten 3.NBT Use place value understanding and properties of operations to perform multi-digit arithmetic. 1.Use place value understanding to round whole numbers to the nearest 10 or 100. 3.NBT.1 Cracking the Code

19. Structure of K-8 Standards

20. The Importance of Mathematics Progressions http://www.ccsso.org/Resources/Digital_Resources/Common_Core_Implementation_Video_Series.html

21. Connecting Everyday Mathematics to the CCSS-M CRITICAL AREA #1: Extending understanding of base-ten notation CRITICAL AREA #2: Building fluency with addition and subtraction STANDARDS BEYOND CRITICAL AREAS OF FOCUS

22. GRADE LEVEL: 2 nd LESSON #11.3 LESSON TITLE: The Trade-First Subtraction Algorithm

23. Connecting Everyday Mathematics to the CCSS-M Identify the opportunities within the selected Everyday Mathematics lesson for students to engage in the Standards for Mathematical Practice. Record your findings in the chart below. Which practices lend themselves to the most emphasis within this particular lesson? Standard for Mathematical PracticeOpportunities within the Lesson 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and construct 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.

24. The Progressions Documents offer an in-depth expansion of the mathematics in each domain. Learning Progressions Documents Use the Say Something protocol to read and process K-5, Number and Operations in Base Ten with a partner.

25. Learning Progressions Documents ESSENTIAL QUESTIONSNOTES Read Overview, pp. 2-4. 1. Why is the base-ten number system so powerful? 2. What is the distinction between special strategies and general methods? Read Kindergarten section, page 5. 1. What common difficulty is associated with learning the numbers 11-19? 2. What models can support understanding of the teen numbers? Read Grade 1 section, pp.6-7. 1. How is the Grade 1 focus of “ten” different from Kindergarten? 2. What are first graders NOT expected to do? Read Grade 2 section, pp. 8-10. 1.How does base-ten understanding progress from earlier grades? 2.How can multiple representations support students in becoming fluent in addition and subtraction? SUMMARY How has this progression document improved my mathematical content knowledge? How does this progression document inform how I PLAN, ASSESS, and TEACH?

26. Reflect