1. Domains of Study/Conceptual Categories Learning Progressions/Trajectories

2.  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.  Coherent  Rigorous  Well-Articulated  Enables Students to Make Connections

4.  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.  Key ideas, understandings, and skills are identified.  Deep learning stressed.

6. K-89-12 Grade Domain Cluster Standard Course Conceptual Category Domain Cluster Standard

7.  Domain  Cluster  Standards

8. 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.  Illustrate progression of increasing complexity from grade to grade.  Organize standards within each grade. Note: Domains typically span a few grades.

11.  May appear in multiple grades.  Illustrate progression of increasing complexity from grade to grade.

12. Grade 1 Grade 2 Add and subtract within 20. 5.Relate counting to addition and subtraction (e.g., by counting on 2 to add 2). [1-OA5] 6.Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 – 4 = 13 – 3 – 1 = 10 – 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 – 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13). [1-OA6] Add and subtract within 20. 2.Fluently add and subtract within 20 using mental strategies. (See standard 6, Grade 1, for a list of mental strategies.) By end of Grade 2, know from memory all sums of two one-digit numbers. [2-OA2]

13.  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.  Turn to the Mathematics standards for your grade.  Domain by Domain, read the cluster headings and count the number of standards within each cluster.  Write the number of standards that corresponds to each cluster heading in the boxes provided.

15. 7.Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and, =, and < symbols to record the results of comparisons. [4-NBT2] 4.7.1.Read multi-digit whole numbers using base-ten numerals. 4.7.2.Read multi-digit whole numbers using number names. 4.7.3.Read multi-digit whole numbers using expanded form. 4.7.4.Write multi-digit whole numbers using base-ten numerals. 4.7.5.Write multi-digit whole numbers using number names. 4.7.6.Write multi-digit whole numbers using expanded form 4.7.7.Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.

16. Critical Area Grade Level Focus

18.  Identify Two to Four Areas of Concentrated Study.  Bring Focus to the Standards.  Provide the Big Ideas for Building Curriculum and Guiding Instruction.

19.  In groups of 2-4, select one of the critical areas for your grade.  Read your critical area and underline the key words that help summarize this area.  Discuss with your table partners the key words you underlined for your grade and how they will help guide the focus of your instruction.

20.  In grade-level groups, analyze the critical areas for your grade.  Underline the key words and phrases that help summarize this area.  Design a poster that describes the focus of your grade level.

21. 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 High School Functions, Statistics, Modeling and Proo f

23. Read the excerpt from Learning Trajectories in Mathematics: A Foundation for Standards, Curriculum, Assessment, and Instruction  Identify 3 ideas that you are willing to talk about with colleagues.  Highlight the location in the text where these ideas appear.

24. 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.”

25.  Designate a facilitator and timekeeper.  A volunteer begins by reading the sentence(s) from the text that embody one of his/her selected ideas. The speaker does not comment on the text at this point.  The individual to right of first speaker takes up to one minute to comment on the selected text.  The next two individuals also take up to one minute to comment on the initial speaker’s idea.  The individual selecting the idea has up to 1 minutes to react to colleagues’ ideas and to talk about why she or he thought this was important.  Another group member introduces one idea, and the group follows the same protocol. Continue until all members have shared or until time is called.

26. Learning Trajectories – sometimes called learning progressions – are sequences of learning experiences hypothesized and designed to build a deep and increasingly sophisticated understanding of core concepts and practices within various disciplines. The trajectories are based on empirical evidence of how students’ understanding actually develops in response to instruction and where it might break down. Daro, Mosher, & Corcoran, 2011

27. Starting Point Ending Point Starting Point Ending Point K12345678HS Counting and Cardinality Number and Operations in Base TenRatios and Proportional Relationships Number and Quantity Number and Operations – Fractions The Number System Operations and Algebraic Thinking Expressions and Equations Algebra Functions Geometry Measurement and DataStatistics and Probability

28. 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.

29.  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. ◦ Counting & Cardinality (CC) – K only ◦ Number and Operations in Base Ten (NBT) – K-5 ◦ Number and Operations – Fractions (NF)– 3-5 ◦ The Number System (NS)– 6-8  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.

30.  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.

31.  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.

32.  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?

33. K12345678HS Counting and Cardinality Number and Operations in Base TenRatios and Proportional Relationships Number and Quantity Number and Operations – Fractions The Number System

34.  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.

35. 2003 ACOS2010 ACOS Contains bulletsDoes not contain bullets Does not contain a glossaryContains a glossary............

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