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

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### Succeeding with thecommon core standards(CCSS): BEYONDALGEBRA

Presented SUMMER 2011

BY 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 vsCCSS expectations
- Mathematical Practices
- Plan: Curriculum, Pacing, Assessments
- Align to texts
- OE Questions, Projects, Resources

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

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 in 2014-2015.

six conceptual categories

- Number and Quantity
- Algebra
- Functions
- Modeling
- Geometry
- Statistics and Probability

Conceptual category: Functions(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 …
- (+) Use the special triangles to determine geometrically the values of sine, cosine, …

DOMAIN:Interpreting functions F-IF

- CLUSTER: 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)

Review HS. CCSS STANDARDS

- √ CCSS standards for ALL in appropriate course
- (+) CCCS include as possible

SMALL GROUP ACTIVITY

- CUT THE CAKE
- or
- FIND THE PERIMETER
- (Algebra Tiles: black=“x” yellow = “1”)

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.

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

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

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?
- 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.

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.

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: MODELING

- Plan a table tennis tournament for 7 players at a club with 4 tables, where each player plays against each other player.

PROJECTS to SHARE

- ALGEBRAS:
- RESTAURANT
- CELL PHONE
- PROBABILITY & GENETICS
- GEOMETRY:
- ALGEBRA-II:
- FST: – CERNOBYL
- SENIOR 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 TOUCH

- JUDITH T. BRENDEL
- [email protected]
- http://www.pascack.k12.nj.us

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