Succeeding with the common core standards(CCSS): BEYOND ALGEBRA

1. Succeeding with thecommon core standards(CCSS): BEYONDALGEBRA Presented SUMMER 2011 BY judith t. brendel, njpsa/fea MATH SUPERVISOR, PASCACK VALLEY REGIONAL HS

2. Be Pro-activePrepare for the change • Timeline: implementation & assessment • What’s different? • Transition Phase - Today’s Reality: • LAST YEAR vsCCSS expectations • Mathematical Practices • Plan: Curriculum, Pacing, Assessments • Align to texts • OE Questions, Projects, Resources

3. TIMELINE *HSPA database but Only CCSS questions • 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

4. WHAT’S NEW 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 (NJASK, HSPA) in 2014-2015.

5. HS math is divided into 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(Think, WHICH COURSE?) • DOMAIN:F-TF Trigonometric Functions (p.71) • Cluster: Extend the domain of trigonometric functions using the unit circle • Standards: • Understand the radian measure of an angle as the length of the arc on the unit circle subtended by the angle. • Explain how the unit circle … • (+) STEM: Use the special triangles to determine geometrically the values of sine, cosine, …

8. DOMAIN:Interpreting functions F-IF • CLUSTER: Understand the concept of 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 • x2 + 6x -9 = x2 + 6x + (3)2-9 –(3)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. (X + 3)2 – 9

13. Review ALGEBRA-I CCSS • √ CCSS standards experienced last year • standards that need to be added to Geometry or Algebra-II (or Basic Geometry or Intermediate Algebra)

14. discuss Algebra-II collab Algebra collab

15. Review HS. CCSS STANDARDS • √ CCSS standards for ALL in appropriate course • (+) CCCS include as possible

16. discuss ALGEBRA - II Geometry

17. Review HS. CCSS STANDARDS • √ CCSS standards for ALL in appropriate course • (+) CCCS include as possible

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

19. MATHEMATICAL PRACTICES 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.

20. REASONING and SENSE MAKING

21. REASONING AND SENSE MAKING • INTERMEDIATE ALGEBRA: Horseshoe in Flight - p.25 • GEOMETRY: Bank Shot - p.27 • PROBABILITY AND STATISTICS: Two Hospitals - p.22 • http://www.nctm.org

22. 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 – 16t2

23. 1 3/16 + 18t – 16t2The Question changes!!!! • 1. Which expression is the most useful for finding the maximum height of the horseshoe, and why is it the most useful expression? • 1 3/16 + 18t – 16t2 c) 1/6(19-16t)(16t+1) • -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.

24. 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.

25. 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.

26. New expectations: MODELING • Here’s an extra problem to solve: • Plan a table tennis tournament for 7 players at a club with 4 tables, where each player plays against each other player. • Share your plan! Defend your plan! Critique others’ plans!

27. Share Meaningful projects • ALGEBRAS: • Restaurant (Valley) • Cell Phone (Valley: Doherty) • Probability & Genetics (Valley: Doherty) • GEOMETRY: (see following slides) • ALGEBRA-II: (see following slides) • FST: – Chernobyl (Hills: Garruto) • SENIOR MATH: – Credit Cards (Hills: Curatola)

28. 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?

29. SHARING RESOURCES • INTERMEDIATE ALGEBRA RR (a special-education resource room math class): Word-Problem Wikki(Go to Ms. Curatola's Website http://www.pascack.k12.nj.us/Page/610 and click on [Calendar] and see Nov. 11, 2010 lesson) and then see the students' Wikki site for examples of their work http://intalgwordproblems2010.wikispaces.com/. • SENIOR MATH Project (a special-education resource room math class): http://www.pascack.k12.nj.us/Page/635 • -Regression Project and WikkiSee assignment (Dec. 6, 2010) and student projects (Dec. 8, 2010). • -Money Budget Project: December 10, 2010 • -Credit Card Project (Dec. 13, 2010)The project continues w/additional links on Dec. 14-16; on Dec. 17 you can see a follow-up project dealing with Real World Problems about compound interest including links to notes. • Websitesrecommended: from Algebra to Calculus

30. GEOMETRY RESOURCES • REPLACEMENT BASIC-GEOMETRYPerimeter Worksheet (with numbers) 9/10/10 jb      Answer Key (Perimeter Numbers Worksheet) 9/10/10 jbPerimeter Worksheet (with variables) 9/10/10 jbArea Worksheet (with numbers) 9/10/10 jb • BASIC GEOMETRY:Marking Period-1 project Find real-life pictures; create multi-media presentation (De Simone 10_15_08) • Marking Period-1 WebquestPolygon Webquest (Oct. 30, 08 De Simone)

31. Marking Period-1 project (Logical Reasoning: M. Doherty 10_15_08) • HONORS GEOMETRY:   Marking Period-1 project Project fall 2008 • Transformations: "Recreation Committee." Resources: • Task and Rubric • Facilitation Questions • Scaffold • Activity List • Web Sites

32. IDE Portal ResoucesShadow Games1478 KB Word version Students collaborate to create a scaled model of school grounds using traditional and indirect measurement. They study ancient geometric methods developed by Euclid and Eratosthenes to help with measurement of irregular objects, such as trees. Build a School-90 KB PDF version  Students use area and perimeter to create a model of a new school. Then, they use map skills to show the location of the school.

33. BASIC GEOMETRY (Glencoe Geometry text 2005) Chapter-1 resources from G. De Simone 10_08: • -PowerPoints: Points, Lines, & Planes, Key Words in Geometry, Segments & Rays, AnglesPairs of Angles • -Glencoe Online Quiz, Glencoe Online Test-Quia Quiz - Angles-Quia Activities - Chapter 1 Vocabulary, Exploring Lines & Angles, Distances & Midpoints-Quia Quiz - Using the Distance Formula-Classzone - Chapter 1 Animations • Quadrilaterals: "Can-Do Packaging Project." Resources: • Can Do Project Document

34. Similarity: "The Golden Rectangle." Resources: • Golden Rectangle Project Document • Parallel Lines and Transversals: "Parallel Line Project." Resources: • Parallel Line Project Document

35. Intro to Geometry: BrainPop (geometry basics - L, P) • http://www.brainpop.com/math/geometry/geometry/ • Geometry Vocabulary: Math.com ( L, P) • http://www.math.com/school/subject3/lessons/S3U1L1GL.html • Coordinate Geometry: Math.com (points, lines, segments, rays - L, P, E) http://www.math.com/school/subject3/lessons/S3U1L2GL.html • Pairs of Lines: Math.com (parallel, perpendicular, skew - L, P, E) http://www.math.com/school/subject3/lessons/S3U1L3GL.html

36. Lines in Art: Sasinschool Web Inquiry #106 (perspective drawing - A) http://www.sasinschool.com/ProductEntrance/Launch/launch.jsp?unit=106 • Investigating intersecting, parallel, and skew lines in a plane: Explorelearning.com (A) http://www.explorelearning.com/index.cfm?method=cResource.dspView&ResourceID=224 • Lines and Planes: Regentsprep.org (easy-to-understand summary with examples - L, P, E) http://www.regentsprep.org/Regents/math/geometry/GG1/indexGG1.htm • Introducing Points, Segments, Rays, and Lines: Geometer's SketchPad (introduces Geo basics and instructions on how-to-use GSP - A) [see Discovering Geometry workbook] • Points, Lines, Planes Lesson: McDougal-Littel Teacher Resources PowerPoint (powerpoint notes aligned to Geo textbook - L) • 1.2 Points, Lines, Planes PPT

37. Constructing Congruent Segments and Angles: Explorelearning.com (A) • http://www.explorelearning.com/index.cfm?method=cResource.dspView&ResourceID=181 • Segment Addition and Segment Bisectors: Emathlab.com (P) • http://emathlab.com/Geometry/Lines_and_Angles/SegAddBisect.php

38. DISTANCE AND MIDPOINT • Distance in 1, 2 & 3 dimensions: Sasinschool.com Interactivity #13 (A) • http://www.sasinschool.com/ProductEntrance/Launch/launch.jsp?unit=13 • Midpoint of a Segment: Regentsprep.org (L, P) • http://www.regentsprep.org/Regents/math/geometry/GCG2/indexGCG2.htm • Distance of a Line Segment: Regentsprep.org (L, P) • http://www.regentsprep.org/Regents/math/geometry/GCG3/indexGCG3.htm • Distance & Midpoint: Emathlab.com (P) • http://emathlab.com/Geometry/Lines_and_Angles/DistMidPtGraf.php

39. Distance Formula: Explorelearning.com Activity A (A) • http://www.explorelearning.com/index.cfm?method=cResource.dspView&ResourceID=183 • Distance Formula: Explorelearning.com Activity B (A) • http://www.explorelearning.com/index.cfm?method=cResource.dspView&ResourceID=64 • Distance & Midpoint: Gomath.com (summary with interactive example, links to lesson, worksheet - L, P, E) • http://www.gomath.com/exercises2/DistanceMidpoint.php

40. Measuring Angles: BrainPop.com (L, P) • http://www.brainpop.com/math/geometry/measuringangles/ • Protractor: Keymath.com (interactive, how to use - A) • http://www.keymath.com/x19371.xml • Types of Angles: Keymath.com (A) • http://www.keymath.com/x19372.xml • Classifying Angles: Math.com (L, E, P) • http://www.math.com/school/subject3/lessons/S3U1L4GL.html • Angle Information: Regentsprep.org (L) • http://www.regentsprep.org/Regents/math/geometry/GP5/LAngles.htm • Angle Information: Regentsprep (P) • http://www.regentsprep.org/Regents/math/geometry/GP5/PAngles.htm

41.  ANGLE PAIR RELATIONSHIPS • Classifying Angles/Special Angle Pairs: Sasinschool.com Web Inquiry #105 (A) • http://www.sasinschool.com/ProductEntrance/Launch/launch.jsp?unit=105 • Angles and Intersecting Lines: Math.com (vertical, linear, adjacent, etc - L, E, P) • http://www.math.com/school/subject3/lessons/S3U1L5GL.html • Investigating Angle Theorems: Explorelearning.com - Activity A (complementary, supplementary, vertical, and adjacent - A) • http://www.explorelearning.com/index.cfm?method=cResource.dspView&ResourceID=282 • Investigating Angle Theorems: Explorelearning.com - Activity B (complementary, supplementary, vertical, and adjacent - A) • http://www.explorelearning.com/index.cfm?method=cResource.dspView&ResourceID=185

42. Complementary and Supplementary Angles: Emathlab.com (P) • http://emathlab.com/Geometry/Lines_and_Angles/ComplSupplAngles.php • Vertical Angles: Emathlab.com (P) • http://emathlab.com/Geometry/Lines_and_Angles/VerticalAngles.php • Angle Pair Relationships: McDougal-Littel Teacher Resources PowerPoint (powerpoint notes aligned to Geo textbook - L) • 1.6 Angle Pair Relationships PPT

43. Conditional statements: RegentsPrep.org: Logic (L, P )http://www.regentsprep.org/Regents/math/geometry/GP1/indexGP1.htm • Conditional Statements: Explorelearning.com (A)http://www.explorelearning.com/index.cfm?method=cResource.dspView&ResourceID=178 • Related Conditionals: RegentsPrep.org: (L, P)http://www.regentsprep.org/Regents/math/geometry/GP2/indexGP2.htm • Lewis Carroll Logic: Mathbits.com (Worksheet using Alice In Wonderland to practice writing conditionals, inverse, contrapositive, and converse –A)http://mathbits.com/MathBits/MathMovies/LogicLewisCarroll.pdf

44. Conditional statements: RegentsPrep.org: Logic (L, P )http://www.regentsprep.org/Regents/math/geometry/GP1/indexGP1.htm • Conditional Statements: Explorelearning.com (A)http://www.explorelearning.com/index.cfm?method=cResource.dspView&ResourceID=178 • Related Conditionals: RegentsPrep.org: (L, P)http://www.regentsprep.org/Regents/math/geometry/GP2/indexGP2.htm • Lewis Carroll Logic: Mathbits.com (Worksheet using Alice In Wonderland to practice writing conditionals, inverse, contrapositive, and converse –A)http://mathbits.com/MathBits/MathMovies/LogicLewisCarroll.pdf

45. DEFINITIONS AND BICONDITIONAL STATEMENTS • Bi-conditional statements: RegentsPrep.org: Logic (L, P) • http://www.regentsprep.org/Regents/math/geometry/GP1/indexGP1.htm • Bi-Conditional Statements: Explorelearning.com (A) • http://www.explorelearning.com/index.cfm?method=cResource.dspView&ResourceID=173 • DIRECT PROOF • Writing Proof: RegentsPrep.org (L, P) • http://www.regentsprep.org/Regents/math/geometry/GP3/indexGP3.htm

46. PARALLEL LINES AND TRANSVERSALS • Parallel Lines & Special Angles: Sasinschool.com Interactivity #15 (A) • http://www.sasinschool.com/ProductEntrance/Launch/launch.jsp?unit=15 • Parallel Lines and Angles: RegentsPrep.org (L, P) • http://www.regentsprep.org/Regents/math/geometry/GP8/indexGP8.htm • Parallel Lines and Transversals: Emathlab.com (P) • http://emathlab.com/Geometry/Lines_and_Angles/ParallelLines.php • Proving Lines Parallel: Graphic Organizer: (R) • http://www.sw-georgia.resa.k12.ga.us/Math.html • Parallel Lines in our World (PROJECT - A) • Parallel Line Project

47. PARALLEL LINES AND TRANSVERSALS • Parallel Lines & Special Angles: Sasinschool.com Interactivity #15 (A) • http://www.sasinschool.com/ProductEntrance/Launch/launch.jsp?unit=15 • Parallel Lines and Angles: RegentsPrep.org (L, P) • http://www.regentsprep.org/Regents/math/geometry/GP8/indexGP8.htm • Parallel Lines and Transversals: Emathlab.com (P) • http://emathlab.com/Geometry/Lines_and_Angles/ParallelLines.php • Proving Lines Parallel: Graphic Organizer: (R) • http://www.sw-georgia.resa.k12.ga.us/Math.html • Parallel Lines in our World (PROJECT - A) • Parallel Line Project

48. PARALLEL AND PERPENDICULAR LINES IN THE COORDINATE PLANE • Slope and Intercept: BrainPop (L, P) • http://www.brainpop.com/math/dataanalysisandprobability/slopeandintercept/ • Slopes & Equations of Lines: RegentsPrep.org (L, P) • http://www.regentsprep.org/Regents/math/geometry/GCG1/indexGCG1.htm • Slope Equations: Emathlab.com: (P) • http://emathlab.com/Geometry/Slopes_and_Equations/SlopeEquations.php • Equations of Parallel & Perpendicular Lines: Emathlab.com (P) • http://emathlab.com/Geometry/Slopes_and_Equations/ParallelPerpendicular.php • do triangles and angles next

49. Additional Geometry resources will be added. • J. Brendel • August, 2012

50. Honors Algebra-II w/Trig • Links to be updated! • Marking Period-I Chapter-I project • Objective: Use the distance, midpoint, and slope formulas to classify • triangles and quadrilaterals on the coordinate plane. (Geometer’s Sketchpad) G. De Simone 10/14/08 • Is Overpopulation Still a Problem?129 KB Word version It wasn’t long ago that overpopulation was thought to be one of the critical problems in our world. In recent years, concern about overpopulation has fallen by the wayside. Still, the population of the earth continues to grow. Should we be concerned? By examining history, data and mathematical processes for examining that data, students will assess the overpopulation problem and try to determine whether or not it’s something about which we should still worry.