succeeding with the common core standards(ccss): beyond algebra

SUCCEEDING WITH THE COMMON CORE

STANDARDS(CCSS): BEYOND ALGEBRA

PRESENTED SUMMER 2011BY JUDITH T. BRENDEL, NJPSA/FEA

MATH SUPERVISOR, PASCACK VALLEY REGIONAL HS

BE PRO-ACTIVEPREPARE 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

TIMELINE Curriculum Assessments

2011-12 K-2 New2012-13 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

Measure standards that are rigorous, globally competitive, and consistent across the states.

New Jersey’s choiceThe 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

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

FORMAT: COMMON CORE - HSCONCEPTUAL CATEGORY

• DOMAIN• CLUSTER

• Standards

+ STEM

CONCEPTUAL CATEGORY: FUNCTIONS (WHICH COURSE?)

DOMAIN: F-TF Trigonometric Functions (p.71)Cluster: Extend the domain of trigonometric functions using the unit circleStandards: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, …

DOMAIN:INTERPRETING FUNCTIONS F-IFCLUSTER: 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)

BUILDING FUNCTIONS• Build a function that models a

relationship between two quantities• Build new functions from existing

functions

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.

TRIGONOMETRIC FUNCTIONS• Extend the domain of trigonometric

functions using the unit circle• Model periodic phenomena with

trigonometric functions• Prove and apply trigonometric

identities

WHICH COURSE?QUADRATIC EQUATIONS in one variable

completing the square

x2 + 6x -9 = x2 + 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.

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 Level Regular Level Honors Level

Basic Algebra gr.9

Algebra gr.9

Algebra gr.8

DISCUSS

INTERMEDIATE ALGEBRA

Basic Algebra

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

Basic Level Regular Level

Honors LevelHon.Geom

Gr.9

Basic Geom. gr.10

Geometry Gr.10

Hon. Alg.IIGr. 10

Int.AlgebraGr.11

Algebra IIGr.11

Hon. PreCalcGr. 11

DISCUSS

ALGEBRA - 2

Geometry

SMALL GROUP ACTIVITY

CUT THE CAKE or

FIND THE PERIMETER(Algebra Tiles: black=“x” yellow = “1”)

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 precision7. Look for and make use of structure.8. Look for and express regularity in repeated reasoning.

MATHEMATICAL PRACTICES

REASONING AND SENSE MAKING

REASONING AND SENSE MAKING

1. INTERMEDIATE ALGEBRA: Horseshoe in Flight - p.25

2. GEOMETRY: Bank Shot - p.273. PROBABILITY AND STATISTICS:

Two Hospitals - p.22

http://www.nctm.org

HORSESHOES IN FLIGHT INTERMEDIATE ALGEBRA P.26As 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’sflight path.)

1 3/16 + 18t – 16t2

1 3/16 + 18T – 16T2

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–16t2 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.

BANK SHOT – GEOMETRY P.27Carom 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.

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.

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

PROJECTS TO SHAREALGEBRAS:• RESTAURANT• CELL PHONE• PROBABILITY & GENETICS

GEOMETRY:ALGEBRA-II: FST: – CERNOBYLSENIOR MATH: – CREDIT CARDS

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?

KEEP IN TOUCHJUDITH T. BRENDELjbrendel@pascack.k12.nj.us

http://www.pascack.k12.nj.us