HS Geometry

1. “Teachers are thus free to provide students with whatever tools and knowledge their professional judgment and experience identify as most helpful for meeting the goals set out in the Standards.” ~ Introduction to the CCSS HS Geometry October 2012

2. Outcomes • Updates on Assessments • Use techniques to mitigate fluency gaps in HS Math • Share Instructional strategies for new and challenging topics • Create a plan to align HS Geometry

3. Quiz-Quiz-Share • Take a card, please don’t share with anyone what your card is. • Once we begin, ask your partner, they ask you, than exchange cards

4. Housekeeping • Dates: Feb 25 ISC-B • Computers • Available in Cart • Webpage

5. Identifying and rebuilding fluency • Factoring • Simplifying • Perfect Squares • Vocabulary

6. CCLS: High School

7. Share Instructional strategies for new and challenging topics • Understand independence and conditional probability and use them to interpret data.Link to data fromsimulations orexperiments S.CP.1, 2, 3, 4, 5 • Use the rules of probability to compute probabilities of compound events in uniform probability model. • Use probability to evaluate outcomes of decisions. (Introductory; apply counting rules (+) S.MD.6,7

8. Aligning Geometry • The pathways and courses are models, not mandates. • Units may also be considered “critical areas” or “big ideas” • Unit follows the order of the standards document in most case not the order in which they might be taught Modeling (defined by a * in the CCSS)

9. High School Functions A--‐REI.4. Solvequadraticequationsinonevariable.

10. High School Illustrative Sample Item Seeing Structure in a Quadratic Equation A--‐REI.4. Solvequadraticequationsinonevariable.

11. “Teachers are thus free to provide students with whatever tools and knowledge their professional judgment and experience identify as most helpful for meeting the goals set out in the Standards.” ~ Introduction to the CCSS Math Sprints Fluency in a minute

12. I • “On your mark, get set, GO!” • 1 minute, race against yourself, trying to answer as many as questions as possible. • Internal voice, “Faster, Faster, Faster!”

13. II • End of the minute: “Stop” • Calling out Answers • Students ‘choral’response “Yes” if they got it correct • If Wrong, circle and correct if time • Teacher continues calling until he doesn’t hear “Yes” • “Raise Hand if you got one or more right, 2,3,4… until winner(s) is determined. • Applause

14. III • Finish remainder of sprint • Cool down period • Let continue as long as most students are engaged • Students who are finished can distribute material for next sprint • Time constraints? Give one minute for step

15. IV • Fast exercise, happy hands. • Counting Forward and backward

16. V • Second Sprint, same as the first • Teacher calls out answers • Students Respond “Yes!”, until last “Yes” • “Raise hands if they got more than “2,3,4…” correct? • Recognize winner

17. Making a Sprint Sprint A Sprint B 3+1= 5+1= 7+1= 6+2= 16+5= • 2+1 • 4+1 • 6+1 • 7+2 • 17+4

18. What do Sprints look like? • K-1 • Start Untimed, no calling answers • Already mastered material • Use a watch (coach hat if wanted ) • Weakest should get 11 correct (min) • Strongest should not be able to finish • Take home next days sprint (for some.)

19. Math Sprint Construction • Rotate a minimum of 10 so they aren’t overly familiar. • Giving the same spring throughout the year is great for monitoring • Four Quadrants • Write your own to meet your kids where they are.

20. Multiplication Facts Gene Jordan’s work but I got the Idea from Gina King’s article:www.nctm.org teaching children mathematics • King, Fluency with Basic Addition, September 2011 p. 83

21. Math Sprints

22. Make your own

23. DRAFT New York State Assessment Transition PlanELA & Math Revised October 20, 2011 1 New ELA assessments in grades 9 and 10 will begin during the 2012-13 school year and will be aligned to the Common Core, pending funding. 2 The PARCC assessments are scheduled to be operational in 2014-15 and are subject to adoption by the New York State Board of Regents. The PARCC assessments are still in development and the role of PARCC assessments as Regents assessments will be determined. All PARCC assessments will be aligned to the Common Core. 3 The names of New York State’s Mathematics Regents exams are expected to change to reflect the new alignment of these assessments to the Common Core. For additional information about the upper-level mathematics course sequence and related standards, see the “Traditional Pathway” section of Common Core Mathematics Appendix A. 4 The timeline for Regents Math roll-out is under discussion. 5 New York State is a member of the NCSC national alternate assessments consortium that is engaged in research and development of new alternate assessments for alternate achievement standards. The NCSC assessments are scheduled to be operational in 2014-15 and are subject to adoption by the New York State Board of Regents.

24. Accelerated Timeline

25. Mainstream Math Students

26. Expanded Time Math Students

27. The CCLS offer very specific examples for us • The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak. (6.RP.1) • For every vote candidate A received, candidate C received nearly three votes. (6.RP.2) • This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is ¾ cup of flour for each cup of sugar. (6.RP.2) • We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger. • If it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns mowed? (6.RP.3b) http://www.p12.nysed.gov/apda/sam/math/mathei-sam-11.pdf

28. PARCC Framework: Key Progressions • K-8 • Geometric Measures • Length, area, volume, angle, surface area, and circumference • HS Geometry uses these in tandem with others to model tasks • Grade 8 • Rotation, Reflection, and Translation • Learning Pythagorean Theorem (distances on a coordinate plane) • Connecting equations with the graphs of circles • Algebra 1 • Simplifying and transforming square roots • Solving distance, area and problems involving the Pythagorean theorem • The algebraic techniques developed in Algebra I can be applied to study analytic geometry. Geometric objects can be analyzed by the algebraic equations that give rise to them. Some basic geometric theorems in the Cartesian plane can be proven using algebra.

29. PARCC Framework: Fluency Recommendations • Fluency with the triangle congruence and similarity criteria will help students throughout their investigations of triangles, quadrilaterals, circles, parallelism and trigonometric ratios. These criteria are necessary tools in many geometric modeling tasks. • G-SRT.5 ) Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures. • Fluency with the use of coordinates to establish geometric results, calculate length and angle, and use geometric representations as a modeling tool are some of the most valuable tools in mathematics and related fields. • G-GPE.4, 5, 7 • Fluency with the use of construction tools, physical and computational, helps students draft a model of a geometric phenomenon and can lead to conjectures and proofs. • G-CO.12 Page 55 in PARCC Framework October 2011

31. High School Illustrative Sample Item Seeing Structure in a Quadratic Equation A--‐SSE, SeeingStructureinExpressions

32. Aligns to the Standards and Reflects Good Practice High School Sample Illustrative Item: Seeing Structure in a Quadratic Equation Task Type I: Tasks assessing concepts, skills and procedures Alignment: Most Relevant Content Standard(s) A-REI.4. Solve quadratic equations in one variable. Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x – p)2 = q that has the same solutions. Derive the quadratic formula from this form. Solve quadratic equations by inspection (e.g., for x2 = 49), taking square roots, completing the square, the quadratic formula, and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as abi for real numbers a and b. Alignment: Most Relevant Mathematical Practice(s) Students taking a brute-force approach to this task will need considerable symbolic fluency to obtain the solutions. In this sense, the task rewards looking for and making use of structure (MP.7).

33. Aligns to the Standards and Reflects Good Practice High School Illustrative Item Key Features and Assessment Advances The given equation is quadratic equation with two solutions. The task does not clue the student that the equation is quadratic or that it has two solutions; students must recognize the nature of the equation from its structure. Notice that the terms 6x – 4 and 3x – 2 differ only by an overall factor of two. So the given equation has the structure where Q is 3x – 2. The equation Q2 - 2Q is easily solved by factoring as Q(Q-2) = 0, hence Q = 0 or Q = 2. Remembering that Q is 3x – 2, we have . These two equations yield the solutions and .  Unlike traditional multiple-choice tests, the technology in this task prevents guessing and working backwards. The format somewhat resembles the Japanese University Entrance Examinations format (see innovations in ITN Appendix F). A further enhancement is that the item format does not immediately indicate the number of solutions.