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HS Geometry October 2012 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

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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

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Quiz-Quiz-Share Take a card, please dont share with anyone what your card is. Once we begin, ask your partner, they ask you, than exchange cards

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

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Identifying and rebuilding fluency Factoring Simplifying Perfect Squares Vocabulary

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CCLS: High School

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Share Instructional strategies for new and challenging topics Understand independence and conditional probability and use them to interpret data. Link to data from simulations or experiments 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

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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)

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High School Functions A-- REI.4. Solve quadratic equations in one variable.

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High School Illustrative Sample Item Seeing Structure in a Quadratic Equation 10 A--REI.4. Solve quadratic equations in one variable.

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Math Sprints Fluency in a minute 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

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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!

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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 doesnt hear Yes Raise Hand if you got one or more right, 2,3,4 until winner(s) is determined. Applause

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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

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IV Fast exercise, happy hands. Counting Forward and backward

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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

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

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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.)

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Math Sprint Construction Rotate a minimum of 10 so they arent 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. Very Easy (1-11)Moderate (23-33) Easy (11-22)Difficult (34-44)

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Multiplication Facts X123456789 11 x 11 x 21 x 31 x 41 x 51 x 61 x 71 x 81 x 9 22 x 12 x 22 x 32 x 42 x 52 x 62 x 72 x 82 x 9 33 x 13 x 23 x 33 x 43 x 53 x 63 x 73 x 83 x 9 44 x 14 x 24 x 34 x 44 x 54 x 64 x 74 x 84 x 9 55 x 15 x 25 x 35 x 45 x 55 x 65 x 75 x 85 x 9 66 x 16 x 26 x 36 x 46 x 56 x 66 x 76 x 86 x 9 77 x 17 x 27 x 37 x 47 x 57 x 67 x 77 x 87 x 9 88 x 18 x 28 x 38 x 48 x 58 x 68 x 78 x 88 x 9 99 x 19 x 29 x 39 x 49 x 59 x 69 x 79 x 89 x 9 Commutative Property Identity Property DoublesSquares (benchmark) Fives (benchmark) Challenge Gene Jordans work but I got the Idea from Gina Kings article:www.nctm.org teaching children mathematics King, Fluency with Basic Addition, September 2011 p. 83

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Math Sprints Ready, Set, Go! Sprint A Review Sprint A Happy Hands Sprint B Review Sprint B Cool Down

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Make your own B Improvement ____Correct ____ Solve 1 23 2 24 3 25 4 26 5 27 6 28 7 29 8 30 9 31 10 32

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23 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 States 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. DRAFT

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2011-122012-1313-1414-1515-1616-1717-18 State Transition PlanAligned 3-8Aligned Alg & GeoAligned Alg 2 Gr 5Gr 6Gr 7Gr 8Gr 9Gr 10Gr 11 NA* 5th Gr Exam6th Grade Exam7th Grade ExamAlgebraGeometryAlgebra 2Pre- Calculus Gr 6Gr 7Gr 8Gr 9Gr 10Gr 11Gr 12 NA 6th Gr Exam7th Grade ExamAlgebraGeometryAlgebra 2Pre- CalculusCalculus Gr 7Gr 8Gr 9Gr 10Gr 11Gr 12 NA 7th Gr ExamNA Algebra GeometryAlgebra 2Pre- CalculusCalculus Hybrid** AlgebraHybrid GeometryHybrid Alg 2 Gr 8Gr 9Gr 10Gr 11Gr 12 NA AlgebraNA Geometry NA Algebra 2Pre- CalculusCalculus (8th Grade Exam) * NA= Non Aligned to the CCLS ** A Hybrid course might be a temporary change to a curriculum that helps fill in the gaps because there is no transistion period. *** This brief overview doesn't account for expanded courses.

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2011-122012-1313-1414-1515-1616-1717-18 State Transistion PlanAligned 3-8Aligned Alg & GeoAligned Alg 2 Gr 5Gr 6Gr 7Gr 8Gr 9Gr 10Gr 11 NA* 5th Gr Exam6th Grade Exam7th Grade Exam8th Grade ExamAlgebraGeometryAlgebra 2 Gr 6Gr 7Gr 8Gr 9Gr 10Gr 11Gr 12 NA 6th Gr Exam7th Grade ExamGrade 8 ExamAlgebraGeometryAlgebra 2Pre-Calculus Gr 7Gr 8Gr 9Gr 10Gr 11Gr 12 NA 7th Gr Exam8th Grade ExamAlgebraGeometryAlgebra 2Pre-Calculus Gr 8Gr 9Gr 10Gr 11Gr 12 NA 8th Grade ExamNA AlgebraGeometryAlgebra 2Pre-Calculus Hybrid GeometryHybrid Algebra 2 Gr 9 Gr 10Gr 11Gr 12 NA AlgebraNA GeometryNA Algebra 2Pre CalculusCalculus * NA= Non Aligned to the CCLS ** A Hybrid course might be a temporary change to a curriculum that helps fill in the gaps because there is no transistion period.

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2011-122012-1313-1414-1515-1616-1717-18 State Transistion PlanAligned 3-8Aligned Alg & GeoAligned Alg 2 Gr 5Gr 6Gr 7Gr 8Gr 9Gr 10Gr 11 NA* 5th Gr Exam6th Grade Exam7th Grade Exam8th Grade ExamPt 1 AlgebraPt 2 AlgebraGeo Trig 1 Gr 6Gr 7Gr 8Gr 9Gr 10Gr 11Gr 12 NA 6th Gr Exam7th Grade ExamGrade 8 ExamPt 1 AlgebraPt AlgebraGeo Trig 1Geo Trig 2 Gr 7Gr 8Gr 9Gr 10Gr 11Gr 12 NA 7th Gr Exam8th Grade ExamPt 1 AlgebraPt 2 AlgebraGeo Trig 1Geo Trig 2 Gr 8Gr 9Gr 10Gr 11Gr 12 NA 8th Grade ExamNA Pt 1 AlgebraPt 2 AlgebraGeo Trig 1Geo Trig 2 Hybrid Pt 1 AlgHybrid Pt 2 Alg Gr 9 NA Pt 1 AlgebraNA Pt 2 AlgebraGeo Trig 1Geo Trig 2 * NA= Non Aligned to the CCLS ** A Hybrid course might be a temporary change to a curriculum that helps fill in the gaps because there is no transistion period.

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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 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

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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.

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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

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

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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. a)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. b)Solve quadratic equations by inspection (e.g., for x 2 = 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). 32

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Aligns to the Standards and Reflects Good Practice 33