Vertical Alignment Professional Development

1. Vertical AlignmentProfessional Development February 8, 2012 Northern Vance High School

2. Where We’ve Been • Introduction to Common Core/NC Essential Standards • Mathematical Practices • CLOSE Reading Technique

3. What’s Next Today’s Purpose • To explore the format of the Common Core State Standards for Mathematics • To examine the vertical alignment of instruction and assessments to ensure that course expectations (2012-2013) are appropriately aligned to Common Core State Standards.

4. Key ideas • Common core state standards are research based. • The sequence of topics respects what is known about how children learn and develop over time. • The intent is for students to “understand”, not just do. • All students must have the opportunity to learn the same high standards.

5. Naming the standards What does 7.G.3 tell you? Grade level Standard number 7.G.3 Domain This is the third 7th grade Geometry standard.

6. High school standards (math 1) These standards have a slightly different naming convention. Conceptual category Standard number A-CED.3 Domain This standard is from the Algebra category and the Creating Equations domain. It is standard #3.

7. Accessing YOUR Standards • Go to the VCS Moodle site • Click on Instructional Technology from the Course Categories • Click on Common Core & NC Essential Standards • Select Common Core State Standards for Math from the Mathematics section

8. CLOSE Read • Closely read p. 5 of the CCSS, “How to read the grade level standards”. • List 3 key ideas from the page. • Share your ideas with others at your table. • Each table will report 2 ideas.

9. Key fact!!!! “These standards are not intended to be new names for old ways of doing business.” The standards for mathematical practice are crucial here.

10. Our standards are organized into FIVE Conceptual Categories: • Number and Quantity • Algebra • Functions • Geometry • Statistics and Probability • Modeling Standards Modeling is best interpreted not as a collection of isolated topics but rather in relation to other standards. Making mathematical models is a Standard for Mathematical Practice, and specific modeling standards appear the high school standards indicated by a star symbol (★).

11. A Close Look at the Knowing where to find information is just as important as knowing the information. Using the Common Core State Standards in Mathematics, search with others around you to navigate through the conceptual categories and answer the questions on the handout provided

12. A Close Look at the HIGH SCHOOL INTRODUCTION Approximately 5 mins.

13. High School Introduction p.57 1. What symbol indicates the mathematics that students need to take advanced courses? The symbol, “+” 2.  What does a * symbolize in the standards? Modeling standard  3. What does it mean if a cluster heading has a *? All standards in that cluster are modeling standards

14. A Close Look at the NUMBER AND QUANTITY Approximately 13 mins.

15. Number & Quantity p.58 – 59 4. …how will the numbers systems be extended for high school students? Imaginary and complex numbers are introduced 5. …what are the two ways that number systems remain the same? They all have communicative, associative, and distributive properties Their new meanings are consistent from before. 6. Read the subsection Quantities and explain the process of quantification. The analysis of attributes of interests by determining their quantity (value) as determined by the context of the problem.

16. Number & Quantity cont. p.58 – 59 7.

17. Number & Quantity p.58 – 59 8. List one standard or cluster that indicates a strong correlation to the MODELING standard. N-Q #1-3 (Quantities Cluster) Approximately 17 mins. ALGEBRA

18. Algebra pg. 62 – 63 9. What are the three subsections highlighted in the introduction? • Expressions • Equations & inequalities • Connections to Functions and Modeling

19. Algebra cont. pg. 62 – 63

20. Algebra cont. pg. 62 – 63 • 11. List one standard or cluster that indicates a strong • correlation to theMODELING standard. A-SSE #1, 3, & 4 A-CED #1-4 A-REI #11

21. FUNCTIONS Approximately 10 mins.

22. 12.

23. Functions cont. pg. 67 – 68 • 13. List one standard or cluster that indicates a strong correlation to the MODELING standard. • F – IF #4-7 • F – BF #1 & 2 • F – LE (all) • F – TF #5 & 7

24. MODELING Approximately 13 mins.

25. Modeling pg. 72 – 73 14. Complete the sentence from the first paragraph on pg. 72 Modeling is the process of CHOOSING _ and USING appropriate mathematics and statistics to analyze EMPIRICAL situations. 15. Complete the sentence from the second paragraph on pg. 72 Real-world situations are not ORGANIZED and LABELED for analysis; formulating tractable MODELS , representing such MODELS , and analyzing them is appropriately a CREATIVE process.

26. Modeling pg. 72 – 73 16. 17. Compare descriptive modeling and analytic modeling as described on page 73 Descriptive – describes or summarizes existing phenomena Analytic – explain data based on theoretical ideas with parameters based on the situational model. VALIDATE REPORT PROBLEM FORMULATE COMPUTE INTERPRET

27. DELING GEOMETRY Approximately 10 mins.

28. 20.

29. Geometry cont. pg. 74 – 75 • List one standard or cluster that indicates a strong correlation to the MODELING standard. • G – SRT #8 • G – GPE #7 • G – GMD #3 • G – MG #1-3

30. DELING STATISTICS & PROBABILITY Approximately 7 mins.

31. 21 • Why is there a star (*) in the title of this strand on page 79? ALL STATISTICS AND PROBABILITY STANDARDS ARE ALSO MODELING STANDARDS

32. FINAL SUMMATION TIME!

33. The Current Dilemma Inch-deep coverage Lengthy review Re-teaching at next level Definition of insanity

35. The Solution VERTICAL ALIGNMENT Establishing and/or recognizing the scope and sequence of course content to ensure… DAILY instructional activities/lessons are aligned to state standards An appropriate amount of time is devoted to instruction Unnecessary repetitions are removed Gaps are indentified Assessments are appropriate (Cohen, 1987; English & Steffy, 2001; Moss-Mitchell, 1998; Neidermeyer & Yelon, 1981; Porter et al., 1994; Porter & Smithson, 2001; Price-Braugh, 1997; Wishnick, 1989)

36. Activity: Building a Map • In two separate groups, • remove the content of the • envelope and place them • on the table so that all • members can read its statements • Discuss what statements should be learned and/or mastered at each grade band (K-2, 3-5, 6-8 and 9-12) in regards to the Geometry Domain

37. Activity: Building a Map • Have one group member keep notes of the conversations and/or questions that arise • Once a group consensus has been made, arrange them on the table under the appropriate grade band • Make note of how one statement may contribute to the understanding of another

38. Activity: Building a Map • Have a group member share out the group’s progression map and discussions with the whole group

39. Compare your maps to the Common Core State Standards for Mathematics 1.G.3 Partition circles and rectangles into two and four equal shares, describethe shares using the words halves, fourths, and quarters, and use the phrases half of, fourth of, and quarter of. 2.G.2 Partition a rectangle into rows and columns of same-size squares and count to find the total number of them. K.G.2 Correctly name shapes regardless of their orientations or overall size. K-2 Standards

40. 3-5 Standards 5.G.2 Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation 4.G.1 Draw points, lines, line segments, rays, angles 3.G.1 Understand that shapes in different categories

41. 6-8 Standards 7.G.5 Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations foran unknown angle in a figure. 8.G.4 Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; 6.G.3 Draw polygons in the coordinate plane given coordinates for thevertices

42. 9-12 Standards G.GPE.5 Prove the slope criteria for parallel and perpendicular lines and usethem to solve geometric problems G.CO.3 Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself. G.C.1 Prove that all circles are similar.

43. HOW DID YOUR GROUP DO? Discuss your reactions and any misconceptions that you/your group may have had.

44. Where We’re Going • On next/last early release session will be on Wednesday, March 21 at Northern • We will begin Unit/Assessment Planning and Locating Resources • There will be two days of Common Core/NC Essential Standards training for core teachers this summer – Dates TBA

45. Before you GO… • To submit an evaluation on today’s professional development session: • Return to the 1:1 Professional Development VCS Moodle http://moodle.vcs.k12.nc/moodle • Under the EVALUATION topic, select “Professional Development (Feb. 8, 2012) EVALUATION” *Hard copies are available for those without laptops/internet connection