1. Making Sense Of The New Standards K-12 Alliance Staff Developer Training January 25, 2013

2. New Opportunities for All Learners California Common Core State Standards (ELA and Math) Next Generation Science Standards 21 st Century Skills

3. Prior Knowlege With your group discuss what you know about 21 st Century Skills, CCSS, and NGSS What connections do you see? Chart your ideas. You will return to your thinking on Sunday.

4. In The Classroom Math Science 21 st Century Skills ELA

5. Activity Choose a secret number (don’t say it aloud) add 5 to that number double that sum subtract 4 from that product divide the results by 2 subtract your secret number from the quotient you have 3.

6. How Did That Happen? What is behind this trick? Is it foolproof? Discuss your thoughts at your table.

7. Explain this trick Use the tools at your table to explain what you think is happening. Remember: You may all have had different secret numbers. No matter what number you selected, you all ended up with 3.

8. Transfer to a Whiteboard Think about how to use the tools to demonstrate how the trick was done. Use the white board to depict your demonstration.

9. Connect action to a direct model with a specific “Secret #” choice InstructionsWhat I didMy model Choose a secret numberI chose 2 beans (2 beans) Add 5I added 5 more Double that sumI multiplied by two Subtract 4Subtracted 4 beans Divide by 2I pulled half away Subtract secret numberI pulled off 2 beans You have threeI was astonished!

10. Connect action to a model for any choice (A set of all secret numbers) InstructionsWhat I didMy model Choose a secret numberI chose a cup to represent “any” Cup Add 5I added 5 beansCup Double that sumI multiplied by twoCup Subtract 4Subtracted 4 beansCup Divide by 2I pulled half away Cup Subtract secret numberI pulled off the cup You have threeVoila!

11. WordsManipulativesAlgebra Expressions/Result Choose a secret numberCupn Add 5 Double that sum Subtract 4 Divide by 2 Subtract secret number You have three

12. WordsManipulativesAlgebra Expressions/Result Choose a secret numberCupn Add 5Cup N+5 Double that sum Subtract 4 Divide by 2 Subtract secret number You have three

13. WordsManipulativesAlgebra Expressions/Result Choose a secret numberCupn Add 5Cup N+5 Double that sumCup 2(n+5) = 2n + 10 Subtract 4 Divide by 2 Subtract secret number You have three

14. WordsManipulativesAlgebra Expressions/Result Choose a secret numberCupn Add 5Cup N+5 Double that sumCup 2(n+5) = 2n + 10 Subtract 4Cup 2n + 10 – 4= 2n+6 Divide by 2 Subtract secret number You have three

15. WordsManipulativesAlgebra Expressions/Result Choose a secret numberCupn Add 5Cup N+5 Double that sumCup 2(n+5) = 2n + 10 Subtract 4Cup 2n + 10 – 4= 2n+6 Divide by 2Cup(2n+6)/2 = n + 3 Subtract secret number You have three

16. WordsManipulativesAlgebra Expressions/Result Choose a secret numberCupn Add 5Cup N+5 Double that sumCup 2(n+5) = 2n + 10 Subtract 4Cup 2n + 10 – 4= 2n+6 Divide by 2Cup(2n+6)/2 = n + 3 Subtract secret numberN + 3 – n = 3 You have three

17. WordsManipulativesAlgebra Expressions/Result Choose a secret numberCupn Add 5Cup N+5 Double that sumCup 2(n+5) = 2n + 10 Subtract 4Cup 2n + 10 – 4= 2n+6 Divide by 2Cup(2n+6)/2 = n + 3 Subtract secret numberN + 3 – n = 3 You have threeYes, I do.3

18. 8 th Grade Expectation WordsResultsCumulative Expression Choose a secret numbernn Add 5N+5 Double that sum2(n+5) = 2n+102(n+5) Subtract 42n + 10 – 4 = 2n+62(n + 5) – 4 Divide by 2(2n+6)/2 = n + 3 2 Subtract secret numberN + 3 – n = 3 2 You have three 32(n + 5) – 4 -n = 3 2 2(n + 5) – 4 2(n + 5) – 4 -n

19. Language Of Doing Math Which of these words best describes what I asked you to do: Represent Solve Evaluate Simplify Determine Compare Find Explain

20. Instructional Words = implication for process Represent – To portray in another abstract way. Solve – Finding an unknown quantity or expression. Evaluate – To find the value of by substituting values in an expression or function. Simplify – To make a math expression simpler. Determine – Find or choose Compare – Relate values of 2 or more expressions Explain – Describe a process. Justify – Support the logic of a process or solution

21. Standards for Mathematical Content K-8 How the grade level standards are organized Standards Clusters Domains

22. 7 th Grade Common Core Standard Connection 7.EE.4. Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.

23. Common Core Connections 7 ------> 6 7 th Grade (p. 31) 7.EE.4. Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. 6 TH : (P. 26) 6.EE.6. Use variables to represent numbers and write expressions when solving a real- world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.

24. Follow the Standard Back 5—4—3—2—1—Kinder! Keep track of the standards you determine to be in the line from Kindergarten to 5 th grade and on to Middle school. Remember the key idea is representing (modeling) a mathematical idea in a manner chosen by the student.

25. Common Core Standards for Mathematics Two Types of Standards Mathematical Practice (recurring throughout the grades) Mathematical Content (different at each grade level)

26. 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 Which of These Describe your work on the “Trick”?

27. Common Core Math Standards

28. 1997 CA. Math Standards

29. 29 CCSS Requires Three Shifts in Mathematics 1.Focus: Focus strongly where the standards focus. 2.Coherence: Think across grades, and link to major topics 3.Rigor: In major topics, pursue conceptual understanding, procedural skill and fluency, and application

30. 30 Shift #1: Focus Strongly where the Standards Focus Significantly narrow the scope of content and deepen how time and energy is spent in the math classroom. Focus deeply on what is emphasized in the standards, so that students gain strong foundations.

31. 31 Grade Focus Areas in Support of Rich Instruction and Expectations of Fluency and Conceptual Understanding K–2 Addition and subtraction - concepts, skills, and problem solving and place value 3–5 Multiplication and division of whole numbers and fractions – concepts, skills, and problem solving 6 Ratios and proportional reasoning; early expressions and equations 7 Ratios and proportional reasoning; arithmetic of rational numbers 8 Linear algebra Key Areas of Focus in Mathematics

32. Grade Shifts: Examples Concept 1997 Standards CCSS Compose simple shapes to form larger shapes (e.g., 2 triangles to form a rectangle) Grade 2 K Introduction to Probability Grade 3 Grade 7 Introduction of fractions as numbers Grade 2 Grade 3 Add and subtract simple fractions Grade 3 Grade 4

33. 33 Shift #2: Coherence: Think Across Grades, and Link to Major Math Topics Within Grades Carefully connect the learning within and across grades so that students can build new understanding on foundations built in previous years. Begin to count on solid conceptual understanding of core content and build on it. Each standard is not a new event, but an extension of previous learning.

34. Shift #3: Rigor: Expect fluency, deep understanding, and application 34 The CCSSM require a balance of:  Solid conceptual understanding  Procedural skill and fluency  Application of skills in problem solving situations Pursuit of all threes requires equal intensity in time, activities, and resources.

35. Solid Conceptual Understanding Teach more than “how to get the answer” and instead support students’ ability to access concepts from a number of perspectives Students are able to see math as more than a set of mnemonics or discrete procedures Conceptual understanding supports the other aspects of rigor (fluency and application ) 35

36. Fluency The standards require speed and accuracy in calculation. Teachers structure class time and/or homework time for students to practice core functions such as single-digit multiplication so that they are more able to understand and manipulate more complex concepts 36

37. 37 Required Fluencies in K-6 GradeStandardRequired Fluency KK.OA.5Add/subtract within 5 11.OA.6Add/subtract within 10 2 2.OA.2 2.NBT.5 Add/subtract within 20 (know single-digit sums from memory) Add/subtract within 100 3 3.OA.7 3.NBT.2 Multiply/divide within 100 (know single-digit products from memory) Add/subtract within 1000 44.NBT.4Add/subtract within 1,000,000 55.NBT.5Multi-digit multiplication 66.NS.2,3 Multi-digit division Multi-digit decimal operations

38. Application Students can use appropriate concepts and procedures for application even when not prompted to do so. Teachers provide opportunities at all grade levels for students to apply math concepts in “real world” situations, recognizing this means different things in K-5, 6-8, and HS. Teachers in content areas outside of math, particularly science, ensure that students are using grade-level- appropriate math to make meaning of and access science content. 38