HS GeometryOctober 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

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

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

Housekeeping Dates: Feb 25 ISC-B

Computers Available in Cart

Webpage

Identifying and rebuilding fluency Factoring

Simplifying

Perfect Squares

Vocabulary

CCLS: High School

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

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)

High School FunctionsA--‐REI.4. Solve quadratic equations in one variable.

High School Illustrative Sample Item

Seeing Structure in a Quadratic Equation

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A-- REI.4. Solve quadratic equations in one variable.‐

Math SprintsFluency 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

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!”

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

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

IV Fast exercise, happy hands. Counting Forward and backward

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

Making a SprintSprint A

1. 2+12. 4+13. 6+14. 7+25. 17+4

Sprint B1. 3+1=2. 5+1=3. 7+1=4. 6+2=5. 16+5=

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.)

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.

Very Easy (1-11) Moderate (23-33)Easy (11-22) Difficult (34-44)

Multiplication Facts X 1 2 3 4 5 6 7 8 9

1 1 x 1 1 x 2 1 x 3 1 x 4 1 x 5 1 x 6 1 x 7 1 x 8 1 x 9

2 2 x 1 2 x 2 2 x 3 2 x 4 2 x 5 2 x 6 2 x 7 2 x 8 2 x 9

3 3 x 1 3 x 2 3 x 3 3 x 4 3 x 5 3 x 6 3 x 7 3 x 8 3 x 9

4 4 x 1 4 x 2 4 x 3 4 x 4 4 x 5 4 x 6 4 x 7 4 x 8 4 x 9

5 5 x 1 5 x 2 5 x 3 5 x 4 5 x 5 5 x 6 5 x 7 5 x 8 5 x 9

6 6 x 1 6 x 2 6 x 3 6 x 4 6 x 5 6 x 6 6 x 7 6 x 8 6 x 9

7 7 x 1 7 x 2 7 x 3 7 x 4 7 x 5 7 x 6 7 x 7 7 x 8 7 x 9

8 8 x 1 8 x 2 8 x 3 8 x 4 8 x 5 8 x 6 8 x 7 8 x 8 8 x 9

9 9 x 1 9 x 2 9 x 3 9 x 4 9 x 5 9 x 6 9 x 7 9 x 8 9 x 9

CommutativeProperty

Identity Property

Doubles Squares(benchmark

)

Fives(benchmark)

Challenge

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

Math Sprints

Ready, Set, Go!

Sprint A

Review

Sprint A

Happy Hands

Sprint B

Review

Sprint B

Cool Down

Make your ownB Improvement ____ Correct ____Solve

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2  24  

3  25  

4  26  

5  27  

6  28  

7  29  

8  30  

9  31  

10   32  

New York State Assessment Transition PlanELA & Math

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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.

Assessment – Grade / Subject 2011-12 2012-13 2013-14 2014-15

ELA Grades 3-8 Aligned to 2005 Standards Grade 91 Grade 101

Aligned to the Common Core

Grade 11 Regents Aligned to 2005 Standards

PARCC2

Math

Grades 3-8 Aligned to 2005 Standards Aligned to the Common Core Algebra I3 Aligned to 2005 Standards Aligned to the Common Core Geometry3 Aligned to 2005 Standards Aligned to the Common Core4 Algebra II3 Aligned to 2005 Standards

PARCC2

Additional State Assessments NYSAA Aligned to the Common Core NCSC5 NYSESLAT Aligned to 2005 Standards Aligned to the Common Core

DRAFT

Accelerated Timeline2011-12 2012-13 13-14 14-15 15-16 16-17 17-18State Transition Plan Aligned 3-8 Aligned Alg & Geo Aligned Alg 2 Gr 5 Gr 6 Gr 7 Gr 8 Gr 9 Gr 10 Gr 11NA* 5th Gr Exam 6th Grade Exam 7th Grade Exam Algebra Geometry Algebra 2 Pre- Calculus Gr 6 Gr 7 Gr 8 Gr 9 Gr 10 Gr 11 Gr 12NA 6th Gr Exam 7th Grade Exam Algebra Geometry Algebra 2 Pre- Calculus Calculus Gr 7 Gr 8 Gr 9 Gr 10 Gr 11 Gr 12 NA 7th Gr Exam NA Algebra Geometry Algebra 2 Pre- Calculus Calculus Hybrid** Algebra Hybrid Geometry Hybrid Alg 2 Gr 8 Gr 9 Gr 10 Gr 11 Gr 12NA Algebra NA Geometry NA Algebra 2 Pre- Calculus Calculus(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.

Mainstream Math Students2011-12 2012-13 13-14 14-15 15-16 16-17 17-18

State Transistion Plan Aligned 3-8 Aligned Alg & Geo Aligned Alg 2

Gr 5 Gr 6 Gr 7 Gr 8 Gr 9 Gr 10 Gr 11

NA* 5th Gr Exam 6th Grade Exam 7th Grade Exam 8th Grade Exam Algebra Geometry Algebra 2

Gr 6 Gr 7 Gr 8 Gr 9 Gr 10 Gr 11 Gr 12

NA 6th Gr Exam 7th Grade Exam Grade 8 Exam Algebra Geometry Algebra 2 Pre-Calculus

Gr 7 Gr 8 Gr 9 Gr 10 Gr 11 Gr 12

NA 7th Gr Exam 8th Grade Exam Algebra Geometry Algebra 2 Pre-Calculus

Gr 8 Gr 9 Gr 10 Gr 11 Gr 12

NA 8th Grade Exam NA Algebra Geometry Algebra 2 Pre-Calculus

Hybrid Geometry Hybrid Algebra 2

Gr 9 Gr 9 Gr 10 Gr 11 Gr 12

NA Algebra NA Geometry NA Algebra 2 Pre Calculus Calculus

* 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.

Expanded Time Math Students2011-12 2012-13 13-14 14-15 15-16 16-17 17-18

State Transistion Plan Aligned 3-8 Aligned Alg & Geo Aligned Alg 2

Gr 5 Gr 6 Gr 7 Gr 8 Gr 9 Gr 10 Gr 11

NA* 5th Gr Exam 6th Grade Exam 7th Grade Exam 8th Grade Exam Pt 1 Algebra Pt 2 Algebra Geo Trig 1

Gr 6 Gr 7 Gr 8 Gr 9 Gr 10 Gr 11 Gr 12

NA 6th Gr Exam 7th Grade Exam Grade 8 Exam Pt 1 Algebra Pt Algebra Geo Trig 1 Geo Trig 2

Gr 7 Gr 8 Gr 9 Gr 10 Gr 11 Gr 12

NA 7th Gr Exam 8th Grade Exam Pt 1 Algebra Pt 2 Algebra Geo Trig 1 Geo Trig 2

Gr 8 Gr 9 Gr 10 Gr 11 Gr 12

NA 8th Grade Exam NA Pt 1 Algebra Pt 2 Algebra Geo Trig 1 Geo Trig 2

Hybrid Pt 1 Alg Hybrid Pt 2 Alg

Gr 9

NA Pt 1 Algebra NA Pt 2 Algebra Geo Trig 1 Geo 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.

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

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.

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

High School Illustrative Sample Item

Seeing Structure in a Quadratic Equation

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A-- SSE, Seeing Structure in Expressions‐

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 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).

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Aligns to the Standards and Reflects Good Practice

High School Illustrative Item Key Features and Assessment AdvancesThe 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.

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