Making Sense Of The New Standards

1. Making SenseOf 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 21st Century Skills

3. Prior Knowlege • With your group discuss what you know about 21st 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 ELA 21st Century Skills

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

10. Connect action to a model for any choice (A set of all secret numbers)

18. 8th Grade Expectation 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. 7th Grade Common Core Standard Connection 7.EE.4. Use variables to represent quantities in a real-world or mathematical problem, and construct simpleequations and inequalities to solve problems by reasoning about the quantities.

23. Common Core Connections7 ------> 6 • 7th Grade (p. 31) 7.EE.4. Use variables to represent quantities in a real-world or mathematical problem, and construct simpleequations and inequalities to solve problems by reasoning about the quantities. • 6TH: (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 Back5—4—3—2—1—Kinder! Keep track of the standards you determine to be in the line from Kindergarten to 5th 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 • Make sense of problems and persevere in solving them. • Reason abstractly and quantitatively. • Construct viable arguments and critique the reasoning of others. • Model with mathematics. • Use appropriate tools strategically. • Attend to precision. • Look for and make use of structure. • 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. CCSS Requires Three Shifts in Mathematics • Focus: Focus strongly where the standards focus. • Coherence: Think across grades, and linkto major topics • Rigor: In major topics, pursue conceptual understanding, procedural skill and fluency,andapplication

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. Key Areas of Focus in Mathematics

32. Grade Shifts: Examples

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 • 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)

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

37. Required Fluencies in K-6

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.