Transcript Succeeding with the common core standards: ALGEBRA

SUCCEEDING WITH THE
COMMON CORE
STANDARDS(CCSS):
BEYOND ALGEBRA
PRESENTED SUMMER 2011
BY JUDITH T. BRENDEL, NJPSA/FEA
MATH SUPERVISOR, PASCACK VALLEY REGIONAL HS
BE PRO-ACTIVE
PREPARE 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
* 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
NJASK, HSPA*
2014-
New
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
FORMAT: COMMON CORE - HS
CONCEPTUAL 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 circle
Standards:
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-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)
Basic Level
Basic Algebra
gr.9
Regular Level Honors Level
Algebra
gr.9
Algebra
gr.8
Basic
Algebra
DISCUSS
REVIEW HS. CCSS STANDARDS
√ CCSS standards for ALL in appropriate course
(+) CCCS include as possible
Basic Level
Regular
Level
Honors Level
Hon.Geom
Gr.9
Basic Geom.
gr.10
Geometry
Gr.10
Hon. Alg.II
Gr. 10
Int.Algebra
Gr.11
Algebra II
Gr.11
Hon. PreCalc
Gr. 11
DISCUSS
Geometry
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
REASONING AND SENSE MAKING
1. INTERMEDIATE ALGEBRA:
Horseshoe in Flight - p.25
2. GEOMETRY: Bank Shot - p.27
3. 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?
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.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
these Projects?
of
What would you include on quarterly
assessments?
KEEP IN TOUCH
JUDITH T. BRENDEL
[email protected]
http://www.pascack.k12.nj.us