2010 Alabama Course of Study: Mathematics College- and Career-Ready Standards

1. 2010 Alabama Course of Study: MathematicsCollege- and Career-Ready Standards Domains of Study/Conceptual Categories Learning Progressions/Trajectories

2. CHARACTERISTICS • Aligned with college and work expectations • Written in a clear, understandable, and consistent format • Designed to include rigorous content and application of knowledge through high-order skills • Formulated upon strengths and lessons of current state standards • Informed by high-performing mathematics curricula in other countries to ensure all students are prepared to succeed in our global economy and society • Grounded on sound evidence-based research

3. 2010 Alabama Course of Study: Mathematics • Coherent • Rigorous • Well-Articulated • Enables Students to Make Connections

4. Coherence • Articulated progressions of topics and performances that are developmental and connected to other progressions. • Conceptual understanding and procedural skills stressed equally. • Real-world/Situational application expected.

5. FOCUS • Key ideas, understandings, and skills are identified. • Deep learning stressed.

6. Mathematical Content Format Grade Domain Cluster Standard Course Conceptual Category Domain Cluster Standard K-8 9-12

7. What’s the difference? • Domain • Cluster • Standards

8. What’s the difference? Domain:Overarching “big ideas” that connect content across the grade levels. Cluster:Group of related standards below a domain. Standards:Define what a student should know (understand) and do at the conclusion of a course or grade.

9. High School Conceptual Categories • Overarching big ideas that connect mathematics across high school • Illustrate progression of increasing complexity • May appear in all courses • Organize high school standards

10. High School Conceptual Categories Domains

11. High School Clusters • Multiple Courses • Illustrate Progression of Increasing Complexity from Grade to Grade

12. 9-12 Cluster

13. Content Standards • Content standards in this document contain minimum required content. • Each content standard completes the phrase “Students will.” • Reflect both mathematical understandings and skills, which are equally important.

14. High School Conceptual Categories

15. Modeling Algebra Geometry Statistics Number Functions Jigsaw Activity & & Quantity Probability

16. How many skills? • Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational. [N-RN3] • AI.3.1. Explain why the sum of two rational numbers is rational. • AI.3.2. Explain why the product of two rational numbers is rational. • AI.3.3. Explain that the sum of a rational number and an irrational number is irrational. • AI.3.4. Explain that the product of a nonzero rational number and an irrational number is irrational.

17. MathematicsDomains of Study by Grade

18. The Big Picture High School Functions, Statistics, Modeling and Proof K-2 Number and number sense. 3-5 Operations and Properties (Number and Geometry) Fractions 6-8 Algebraic and Geometric Thinking Data Analysis and using Properties

19. LearningProgressions/Trajectories Confrey (2007) “Developing sequenced obstacles and challenges for students…absent the insights about meaning that derive from careful study of learning, would be unfortunate and unwise.” CCSS, p. 4 “… the development of these Standards began with research-based learning progressions detailing what is known today about how students’ mathematical knowledge, skill, and understanding develop over time.”

20. Learning Progression Framework Starting Point Starting Point Ending Point Ending Point

21. Investigating the Domains/Conceptual Categories Domains provide common learning progressions. Curriculum and teaching methods are not dictated. Standards are not presented in a specific instructional order. Standards should be presented in a manner that is consistent with local collaboration.

22. Learning Progressions

23. Table Team Work • Beginning at the lowest grade examine the domain and conceptual category, cluster and standards at your grade level - identify how the use of numbers and number systems change from K- 12. • K-2 - Counting & Cardinality (CC) Number and Operations in Base Ten (NBT) • 3-5 - Number and Operations in Base Ten (NBT) Number and Operations – Fractions (NF) • 6 -8 - The Number System (NS) • 9-12 - Number and Quantity (N) • Look at the grade level above and grade level below (to see the context). • Make notes that reflect a logical progression, increasing complexity. • As a table group share a vertical progression (bottom–up or top-down) on chart paper.

24. What Goes On The Chart Paper? • Summary and/or representation of how the concept of the use of numbers grows throughout your grade band. • Easy for others to interpret or understand. • Visual large enough for all to see. • More than just the letters and numbers of the standards – include key words or phrases.

25. Banding Together for a Common Message • Display posters side-by-side and in order on the wall. • Begin at the grade band you studied. Read the posters for your grade band. • Discuss similarities and differences between the posters. • Establish a clear vision for your grade band.

26. Let’s Talk About It! • As a table group, consider your journey through the 2010 ACOS as you studied the concept of the use of numbers K-12. • What did you learn? • What surprised you? • What questions do you still have?

27. Value of Learning Progressions/Trajectories to Teachers • Know what to expect about students’ preparation. • More readily manage the range of preparation of students in your class. • Know what teachers in the next grade expect of your students. • Identify clusters of related concepts at grade level. • Clarity about the student thinking and discourse to focus on conceptual development. • Engage in rich uses of classroom assessment.

28. Review the Format

29. ?? Questions ??

30. Contact Information ALSDE Office of Student Learning Curriculum and Instruction Cindy Freeman, Mathematics Specialist • Phone: 334.353.5321 E-mail: cfreeman@alsde.edu