New York State Common Core Learning Standards

1. New York State Common Core Learning Standards Mathematics

2. Presented by Joyce Bernstein East Williston UFSD Elaine Zseller, Ph.D. Nassau BOCES

3. Why Common Core State Standards? • Preparation: The standards will help prepare students with the knowledge and skills they need to succeed in education and training after high school • Competition: The standards are internationally benchmarked • Equity: Expectations are consistent for all

4. Why Common Core State Standards? • Clarity: The standards are focused, coherent, and clear • Collaboration: The standards will create a foundation to work collaboratively across states and districts • pool resources and expertise • create curricular tools, professional development, assessments and other materials • compare policies and achievement across states and districts

5. Overview of New York State P-12 Common Core Learning Standards for Mathematics • Includes 450 College and Career Readiness Standards for all students • New York State added pre-kindergarten standards to the national common core to provide foundational support for kindergarten standards and beyond and two grade level standards, one at the kindergarten level and one at the first grade level • No new standards were added to the national common core for the rest of the grade levels (2-12)

6. Overview of CCLS for Mathematics • The CCLS for Mathematics are organized as: • Standards for Mathematical Practice • Standards for Mathematical Content

7. Overview of CCLS for Mathematics: Standards for Mathematical Practice • There are eight Standards for Mathematical Practice that are to be woven throughout the curriculum • taught in conjunction with content and procedures • correspond to NYS’s current Process Strands in mathematics • Unlike our experience with the current Process Strands, we are warned to take the Standards for Mathematical Process seriously.

8. Mathematical Practices 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. Students learn to monitor their solution path and change course if necessary. • Help student to build PERSEVERANCE and STAMINA!

9. Mathematical Practices 2 Reason abstractly and quantitatively. • Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects.

10. Mathematical Practices Construct viable arguments and critique the reasoning of others. • Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades

11. Mathematical Practices Model with mathematics. • In early grades, this might be as simple as writing an addition equation to describe a situation. Students should understand WHY they are learning mathematics.

12. Mathematical Practices Use appropriate tools strategically. These tools might include pencil and paper, concrete models, a ruler, a protractor, a calculator.

13. Mathematical Practices Attend to precision. • Mathematically proficient students try to communicate precisely to others. They try to use clear definitions in discussion with others and in their own reasoning. • In the elementary grades, students give carefully formulated explanations to each other. • Correct mathematical language is essential!

14. Mathematical Practices Look for and make use of structure. Young students, for example, might notice that three and seven more is the same amount as seven and three more, or they may sort a collection of shapes according to how many sides the shapes have. Later, students will see 7 × 8 equals the well remembered 7 × 5 + 7 × 3, in preparation for learning about the distributive property.

15. Mathematical Practices Look for and express regularity in repeated reasoning. For example: The rule “Add 3” results in a pattern of odd-even-odd-even-

16. How to Read the Common Core Learning Standards • Domain • Cluster • Standard • Be sure teachers are reading the examples. The standards are written on a level designed to be read by mathematicians. The examples clarify the content in terms of the past experience of the teacher.

17. Domain Progression

18. Mathematics Curriculum Mapping • Sequence content • There will be multiple lessons for one standard • Lessons should be logically sequenced to scaffold knowledge • Each math lesson should have one, maybe two, objectives, reflective of the standard to be covered. • Method – begin with CCLS • Break down into lessons • Find text lessons or other resources to match objective. • Don’t let your textbook series define your scope and sequence.

19. Shifts in Mathematics • 1. Focus Teachers must significantly narrow and deepen the scope of what they each. They must focus on content prioritized in the standards. They must let go of several topics they are currently teaching.

20. Spend Time on Important Mathematics Key topics demand that we slow down and devote more time to allow for reasoning/ thinking/ interactive discussion as well as the necessary drill and practice. e.g place value in K - 2 fractions in grades 3 – 5 We are moving away from the mile wide – inch deep pattern we learned as children and taught to this point.

21. Shifts in Mathematics • 2. Coherence • Teachers must connect learning within and across grades. Standards become extensions of prior learning. • The study of fractions in grades 3 – 6 is a wonderful example of coherence.

22. Coherence Write plans for a unit coherently: • Big Idea (Grant Wiggins UBD) • Essential Understanding • Interactive Learning • Articulated progressions and alignment of topics and performance. Your sequence of units should make sense.

23. The Number Line – K – 5(Coherence Starts Here) • Compare quantities, especially length • Compare by measuring: units • Add and subtract with ruler • Diagram of a ruler • Diagram of a number line • Arithmetic on the number line based on units • Representing time, money and other quantities with number lines

24. Fractions(Coherence Continues) • Understanding the arithmetic of fractions draws upon four areas introduced in prior grades: • equal partitioning, • understanding of a unit amount • number line • operations

25. Shifts in Mathematics • 3. Students are expected to have speed and accuracy with simple calculations. • Find fluencies by grade, beginning in Kindergarten. (engageny.org) • This is an important talking point with parents.

26. Shifts in Mathematics • 4. Deep Understanding • Students must have understanding beyond memorized procedures and mnemonics. • Students, even in early grades, must be able to apply the mathematics they know to new situations. • Relate to ELA – students must be able to speak and write about their mathematical understanding.

27. Mile deep: Operations:Algebraic Thinking Grade 3 Apply properties of operations as strategies to multiply and divide. • Commutative Property • Associative Property • Distributive Property

28. Mile deep: Operations:Algebraic Thinking Grade 3 • If 6 x 4 = 24 is known, then 4 x 6 = 24 is also known.(Commutative property of multiplication.) • 3 x 5 x 2 can be found by 3x 5 = 15, then 15x 2 = 30, or by 5 x 2 = 10, then 3 x 10 = 30. (Associativeproperty of multiplication.) • Knowing that 8 x 5 = 40 and 8 x 2 = 16, onecan find 8 x 7 as 8 x (5 + 2) = (8 x 5) + (8 x 2) = 40 + 16 = 56. (Distributiveproperty.)

29. Mile deep: Fractions Building Grades 3 to 5

30. Shifts in Mathematics • 5. Application • Link to the CCSS standards for modeling. Students must be able to choose an appropriate strategy, even when not prompted to do so. • Tie to real world experiences, including learning in science. • Students must be able to use the mathematics they are learning.

31. Mile deep: Connections to Prior Learning

32. Shifts in Mathematics • 6. Dual Intensity • Teachers have to create a fine balance between practice and understanding. • Students must be fluent. • Students must know how to use the math they are learning. • The balance is reset for every new topic.

33. Priorites (engageny.org)

34. Middle School Acceleration • Appendix A, p. 80 ff • Compacted courses for Grades 7 and 8 • Identifies specific standards to teach in each of these grades • Does not require acceleration earlier than Grade 7 • Accomplishes three years in two by removing redundancies

35. Algebra in 2012-13 This is a much more robust course, based upon a more rigorous middle school experience. Some topics are left to earlier grades:……..

36. What’s Out • Scientific notation • Percent • Permutations and Combinations • Line graphs, circle graphs

37. What’s Reduced • Simple linear equations for grades 5 – 8. • Some statistics

38. What’s New: Modeling, including domain constraints Slope in terms of instant rate of change Functional vertical shifts Cube root functions Derivation of the Quadratic Formula Recursion Standard Deviation Two-Way Frequency Tables

39. The Big Picture-Teacher Practice In order to be successful teaching the New York Learning Standards for Mathematics, teachers must: • Support the development of number sense. • Use multiple representations of mathematical entities. • Create language rich classroom routines. • Embed the mathematics in realistic, real-world contexts.

40. The Big Picture – Teacher Practice • Incorporate cumulative review by building coherent bridges within the curriculum. • Minimize what is no longer a priority • Make “Why?” and “How do you know?” routine responses to student answers. • Insist on holding all students responsible for mastering fluency.