1. SUCCEEDING WITH THE COMMON CORE STANDARDS(CCSS): BEYOND ALGEBRA PRESENTED SUMMER 2011 BY JUDITH T. BRENDEL, NJPSA/FEA MATH SUPERVISOR, PASCACK VALLEY REGIONAL HS

2. BE PRO-ACTIVE PREPARE FOR THE CHANGE Timeline: implementation & assessment What’s different? Transition Phase - Today’s Reality: LAST YEAR vs CCSS expectations Mathematical Practices Plan: Curriculum, Pacing, Assessments Align to texts OE Questions, Projects, Resources

3. TIMELINE Curriculum Assessments 2011-12 K-2 New 2012-13 3-5, HS New NJASK, HSPA* 2013-14 6-8 New NJASK, HSPA* 2014- NEW* from Algebra EOC test to quarterly benchmarks for all students * HSPA database but Only CCSS questions

4. Measure standards that are rigorous, globally competitive, and consistent across the states. New Jersey’s choice The assessment consortium PARCC (Partnership for Assessment of Readiness for College and Careers) New assessments will replace current state NCLB tests in 2014-2015. WHAT’S NEW

5. SIX CONCEPTUAL CATEGORIES Number and Quantity Algebra Functions Modeling Geometry Statistics and Probability

6. FORMAT: COMMON CORE - HS CONCEPTUAL CATEGORY DOMAIN CLUSTER Standards + STEM

7. CONCEPTUAL CATEGORY: FUNCTIONS (WHICH COURSE?) DOMAIN: F-TF Trigonometric Functions (p.71) Cluster: Extend the domain of trigonometric functions using the unit circle Standards: 1.Understand the radian measure of an angle as the length of the arc on the unit circle subtended by the angle. 2.Explain how the unit circle … 3.(+) Use the special triangles to determine geometrically the values of sine, cosine, …

8. DOMAIN: INTERPRETING FUNCTIONS F-IF CLUSTER: Understand the concept of a functions and use function notation. (p.69) Standards (F-IF.1, F-IF.2, F-IF.3) 2. Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. CLUSTER: Interpret functions that arise in applications in terms of the context (F-IF.4-6) CLUSTER: Analyze functions using different representations (F-IF.7a-9b)

9. BUILDING FUNCTIONS Build a function that models a relationship between two quantities Build new functions from existing functions

10. LINEAR, QUADRATIC, EXPONENTIAL MODELS Construct and compare linear, quadratic and exponential models and solve problems. Interpret expressions for functions in terms of the situation they model.

11. TRIGONOMETRIC FUNCTIONS Extend the domain of trigonometric functions using the unit circle Model periodic phenomena with trigonometric functions Prove and apply trigonometric identities

12. WHICH COURSE? QUADRATIC EQUATIONS in one variable completing the square x 2 + 6x -9 = x 2 + 6x + (3x) 2 -9 –(3x) 2 DOMAIN: Seeing Structure in Expressions A-SSE CLUSTER: Write expressions in equivalent forms to solve problems (p.64) Standards: 3b. Complete the square in a quadratic expression to reveal the maximum and minimum value of functions it defines.

13. REVIEW ALGEBRA-I CCSS √ CCSS standards experienced last year standards that need to be added to Geometry or Advanced Algebra (Intermediate or Algebra-II) Basic LevelRegular LevelHonors Level Basic Algebra gr.9 Algebra gr.9 Algebra gr.8

14. DISCUSS INTERMEDIATE ALGEBRA Basic Algebra

15. REVIEW HS. CCSS STANDARDS √ CCSS standards for ALL in appropriate course (+) CCCS include as possible Basic LevelRegular Level Honors Level Hon.Geom Gr.9 Basic Geom. gr.10 Geometry Gr.10 Hon. Alg.II Gr. 10 Int.Algebra Gr.11 Algebra II Gr.11 Hon. PreCalc Gr. 11

16. DISCUSS ALGEBRA - 2 Geometry

17. SMALL GROUP ACTIVITY CUT THE CAKE or FIND THE PERIMETER (Algebra Tiles: black=“x” yellow = “1”)

18. 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. MATHEMATICAL PRACTICES

19. REASONING AND SENSE MAKING

20. 1.INTERMEDIATE ALGEBRA: Horseshoe in Flight - p.25 2.GEOMETRY: Bank Shot - p.27 3.PROBABILITY AND STATISTICS: Two Hospitals - p.22 http://www.nctm.org

21. HORSESHOES IN FLIGHT INTERMEDIATE ALGEBRA P.26 As shown in the graph, the height of a thrown horseshoe depends on the time that has elapsed since its release. (Note that this graph of the horseshoe’s height is parabolic, but it is not the same as the graph of the horseshoe’s flight path.) 1 3/16 + 18t – 16t 2

22. 1 3/16 + 18T – 16T 2 1. Which expression is the most useful for finding the maximum height of the horseshoe, and why is it the most useful expression? a)1 3/16+18t–16t 2 c) 1/6(19-16t)(16t+1) b)-16(t-19/16)(t+1/16) d) -16(t-9/16) 2 +100/16 2. What information can you conclude about the horseshoe’s flight from other equivalent expressions? Explain your answers.

23. BANK SHOT – GEOMETRY P.27 Carom billiards refers to a collection of games typically played on a 5-by-10 foot “pocketless” table. In this game, a player scores points by striking a cue ball with a cue stick so that the cue ball hits each of two additional cue balls … before the cue ball comes to rest. (continued on handout) Answer questions 1, 2 and 3.

24. TWO HOSPITALS – PROBABILITY AND STATISTICS PAGE-22 Two hospitals keep track of the gender of the babies born each day. Hospital A is a large urban medical center. Hospital B is a small regional facility. Many more babies are born each day in the Hospital A than in Hospital B. Assume that for each birth, the probability that the baby is male is 0.5 and the probability that the baby is female is 0.5.

25. NEW EXPECTATIONS: MODELING Plan a table tennis tournament for 7 players at a club with 4 tables, where each player plays against each other player.

26. PROJECTS TO SHARE ALGEBRAS: RESTAURANT CELL PHONE PROBABILITY & GENETICS GEOMETRY: ALGEBRA-II: FST: – CERNOBYL SENIOR MATH: – CREDIT CARDS

27. PACING (QUARTERLY BENCHMARKS) Where would you include one of these NCTM Open-Ended Questions? Where would you include one of these Projects? What would you include on quarterly assessments?

28. KEEP IN TOUCH JUDITH T. BRENDEL jbrendel@pascack.k12.nj.us http://www.pascack.k12.nj.us