### ALGEBRA - Pascack Valley Regional School District

```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
2013-14 6-8
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 (NJASK, HSPA) in 2014-2015.
HS MATH IS DIVIDED INTO
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 (THINK, 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. (+) STEM: Use the special triangles to determine
geometrically the values of sine, cosine, …
DOMAIN:
INTERPRETING FUNCTIONS F-IF
CLUSTER: Understand the concept of
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
EXPONENTIAL MODELS
• Construct and compare linear,
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?
completing the square
x2 + 6x -9 = x2 + 6x + (3)2 -9 –(3)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. (X + 3)2 – 9
REVIEW ALGEBRA-I CCSS
√ CCSS standards experienced last year
standards that need to be added to
Geometry or Algebra-II (or Basic Geometry
or Intermediate Algebra)
Basic Level
Basic Algebra
gr.9
Regular Level Honors Level
Algebra
gr.9
Algebra
gr.8
Algebra
collab
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
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
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
THE QUESTION CHANGES!!!!
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
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
Here’s an extra problem to solve:
Plan a table tennis tournament for 7
players at a club with 4 tables, where
each player plays against each other
player.
Critique others’ plans!
SHARE MEANINGFUL PROJECTS
ALGEBRAS:
• Restaurant (Valley)
• Cell Phone (Valley: Doherty)
• Probability & Genetics (Valley: Doherty)
GEOMETRY: (see following slides)
ALGEBRA-II: (see following slides)
FST: – Chernobyl (Hills: Garruto)
SENIOR MATH: – Credit Cards (Hills: Curatola)
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?
SHARING RESOURCES
INTERMEDIATE ALGEBRA RR (a special-education resource room math
class): Word-Problem Wikki (Go to Ms. Curatola's Website
http://www.pascack.k12.nj.us/Page/610 and click on [Calendar] and see
Nov. 11, 2010 lesson) and then see the students' Wikki site for examples of
their work http://intalgwordproblems2010.wikispaces.com/.
SENIOR MATH Project (a special-education resource room math class):
http://www.pascack.k12.nj.us/Page/635
-Regression Project and Wikki See assignment (Dec. 6, 2010) and
student projects (Dec. 8, 2010).
-Money Budget Project: December 10, 2010
-Credit Card Project (Dec. 13, 2010) The project continues w/additional
links on Dec. 14-16; on Dec. 17 you can see a follow-up project dealing with
Websites recommended: from Algebra to Calculus
GEOMETRY RESOURCES
REPLACEMENT BASIC-GEOMETRY
Perimeter Worksheet (with numbers) 9/10/10 jb
Answer Key (Perimeter Numbers Worksheet) 9/10/10 jb
Perimeter Worksheet (with variables) 9/10/10 jb
Area Worksheet (with numbers) 9/10/10 jb
BASIC GEOMETRY:
Marking Period-1 project Find real-life pictures; create multimedia presentation (De Simone 10_15_08)
Marking Period-1 Webquest Polygon Webquest (Oct. 30, 08
De Simone)
Marking Period-1 project (Logical Reasoning: M.
Doherty 10_15_08)
HONORS GEOMETRY:
Marking Period-1 project Project fall 2008
Transformations: "Recreation Committee." Resources:
Facilitation Questions
Scaffold
Activity List
Web Sites
IDE Portal Resouces
1478 KB Word version Students collaborate to create a scaled
model of school grounds using traditional and indirect
measurement. They study ancient geometric methods developed
by Euclid and Eratosthenes to help with measurement of
irregular objects, such as trees.
Build a School90 KB PDF version Students use area and perimeter to create a
model of a new school. Then, they use map skills to show the
location of the school.
BASIC GEOMETRY (Glencoe Geometry text 2005) Chapter-1
resources from G. De Simone 10_08:
-PowerPoints: Points, Lines, & Planes, Key Words in Geometry,
Segments & Rays, Angles Pairs of Angles
-Glencoe Online Quiz, Glencoe Online Test
-Quia Quiz - Angles
-Quia Activities - Chapter 1 Vocabulary, Exploring Lines & Angles,
Distances & Midpoints
-Quia Quiz - Using the Distance Formula
-Classzone - Chapter 1 Animations
Can Do Project Document
Similarity: "The Golden Rectangle."
Resources:
Golden Rectangle Project Document
Parallel Lines and Transversals: "Parallel
Line Project." Resources:
Parallel Line Project Document
Intro to Geometry: BrainPop (geometry basics - L, P)
http://www.brainpop.com/math/geometry/geometry/
Geometry Vocabulary: Math.com ( L, P)
http://www.math.com/school/subject3/lessons/S3U1L1GL.html
Coordinate Geometry: Math.com (points, lines, segments, rays L, P, E)
http://www.math.com/school/subject3/lessons/S3U1L2GL.html
Pairs of Lines: Math.com (parallel, perpendicular, skew - L, P, E)
http://www.math.com/school/subject3/lessons/S3U1L3GL.html
Lines in Art: Sasinschool Web Inquiry #106 (perspective drawing - A)
http://www.sasinschool.com/ProductEntrance/Launch/launch.jsp?unit=106
Investigating intersecting, parallel, and skew lines in a plane:
Explorelearning.com (A)
http://www.explorelearning.com/index.cfm?method=cResource.dspView&Res
ourceID=224
Lines and Planes: Regentsprep.org (easy-to-understand summary with
examples - L, P, E)
http://www.regentsprep.org/Regents/math/geometry/GG1/indexGG1.htm
Introducing Points, Segments, Rays, and Lines: Geometer's SketchPad
(introduces Geo basics and instructions on how-to-use GSP - A) [see
Discovering Geometry workbook]
Points, Lines, Planes Lesson: McDougal-Littel Teacher Resources
PowerPoint (powerpoint notes aligned to Geo textbook - L)
1.2 Points, Lines, Planes PPT
Constructing Congruent Segments and Angles:
Explorelearning.com (A)
http://www.explorelearning.com/index.cfm?met
hod=cResource.dspView&ResourceID=181
Emathlab.com (P)
http://emathlab.com/Geometry/Lines_and_Angl
DISTANCE AND MIDPOINT
Distance in 1, 2 & 3 dimensions: Sasinschool.com Interactivity #13
(A)
http://www.sasinschool.com/ProductEntrance/Launch/launch.jsp?uni
t=13
Midpoint of a Segment: Regentsprep.org (L, P)
http://www.regentsprep.org/Regents/math/geometry/GCG2/indexGCG
2.htm
Distance of a Line Segment: Regentsprep.org (L, P)
http://www.regentsprep.org/Regents/math/geometry/GCG3/indexGCG
3.htm
Distance & Midpoint: Emathlab.com (P)
http://emathlab.com/Geometry/Lines_and_Angles/DistMidPtGraf.php
Distance Formula: Explorelearning.com Activity A (A)
http://www.explorelearning.com/index.cfm?method=cR
esource.dspView&ResourceID=183
Distance Formula: Explorelearning.com Activity B (A)
http://www.explorelearning.com/index.cfm?method=cR
esource.dspView&ResourceID=64
Distance & Midpoint: Gomath.com (summary with
interactive example, links to lesson, worksheet - L, P,
E)
http://www.gomath.com/exercises2/DistanceMidpoint.p
hp
Measuring Angles: BrainPop.com (L, P)
http://www.brainpop.com/math/geometry/measuringangles/
Protractor: Keymath.com (interactive, how to use - A)
http://www.keymath.com/x19371.xml
Types of Angles: Keymath.com (A)
http://www.keymath.com/x19372.xml
Classifying Angles: Math.com (L, E, P)
http://www.math.com/school/subject3/lessons/S3U1L4GL.html
Angle Information: Regentsprep.org (L)
http://www.regentsprep.org/Regents/math/geometry/GP5/LAngles.htm
Angle Information: Regentsprep (P)
http://www.regentsprep.org/Regents/math/geometry/GP5/PAngles.htm
ANGLE PAIR RELATIONSHIPS
Classifying Angles/Special Angle Pairs: Sasinschool.com Web Inquiry #105 (A)
http://www.sasinschool.com/ProductEntrance/Launch/launch.jsp?unit=105
Angles and Intersecting Lines: Math.com (vertical, linear, adjacent, etc - L, E, P)
http://www.math.com/school/subject3/lessons/S3U1L5GL.html
Investigating Angle Theorems: Explorelearning.com - Activity A (complementary,
supplementary, vertical, and adjacent - A)
http://www.explorelearning.com/index.cfm?method=cResource.dspView&Resourc
eID=282
Investigating Angle Theorems: Explorelearning.com - Activity B (complementary,
supplementary, vertical, and adjacent - A)
http://www.explorelearning.com/index.cfm?method=cResource.dspView&Resourc
eID=185
Complementary and Supplementary Angles: Emathlab.com (P)
http://emathlab.com/Geometry/Lines_and_Angles/ComplSupplAngles.
php
Vertical Angles: Emathlab.com (P)
http://emathlab.com/Geometry/Lines_and_Angles/VerticalAngles.php
Angle Pair Relationships: McDougal-Littel Teacher Resources
PowerPoint (powerpoint notes aligned to Geo textbook - L)
1.6 Angle Pair Relationships PPT
Conditional statements: RegentsPrep.org: Logic (L, P
)http://www.regentsprep.org/Regents/math/geometry/GP1/indexGP1.ht
m
Conditional Statements: Explorelearning.com
(A)http://www.explorelearning.com/index.cfm?method=cResource.dsp
View&ResourceID=178
Related Conditionals: RegentsPrep.org: (L,
P)http://www.regentsprep.org/Regents/math/geometry/GP2/indexGP2.
htm
Lewis Carroll Logic: Mathbits.com (Worksheet using Alice In
Wonderland to practice writing conditionals, inverse, contrapositive,
and converse –
A)http://mathbits.com/MathBits/MathMovies/LogicLewisCarroll.pdf
Conditional statements: RegentsPrep.org: Logic (L, P
)http://www.regentsprep.org/Regents/math/geometry/GP1/indexGP1.ht
m
Conditional Statements: Explorelearning.com
(A)http://www.explorelearning.com/index.cfm?method=cResource.dsp
View&ResourceID=178
Related Conditionals: RegentsPrep.org: (L,
P)http://www.regentsprep.org/Regents/math/geometry/GP2/indexGP2.
htm
Lewis Carroll Logic: Mathbits.com (Worksheet using Alice In
Wonderland to practice writing conditionals, inverse, contrapositive,
and converse –
A)http://mathbits.com/MathBits/MathMovies/LogicLewisCarroll.pdf
DEFINITIONS AND BICONDITIONAL STATEMENTS
Bi-conditional statements: RegentsPrep.org: Logic (L, P)
http://www.regentsprep.org/Regents/math/geometry/GP1/indexGP1.ht
m
Bi-Conditional Statements: Explorelearning.com (A)
http://www.explorelearning.com/index.cfm?method=cResource.dspVi
ew&ResourceID=173
DIRECT PROOF
Writing Proof: RegentsPrep.org (L, P)
http://www.regentsprep.org/Regents/math/geometry/GP3/indexGP3.ht
m
PARALLEL LINES AND TRANSVERSALS
Parallel Lines & Special Angles: Sasinschool.com Interactivity #15 (A)
http://www.sasinschool.com/ProductEntrance/Launch/launch.jsp?unit=15
Parallel Lines and Angles: RegentsPrep.org (L, P)
http://www.regentsprep.org/Regents/math/geometry/GP8/indexGP8.htm
Parallel Lines and Transversals: Emathlab.com (P)
http://emathlab.com/Geometry/Lines_and_Angles/ParallelLines.php
Proving Lines Parallel: Graphic Organizer: (R)
http://www.sw-georgia.resa.k12.ga.us/Math.html
Parallel Lines in our World (PROJECT - A)
Parallel Line Project
PARALLEL LINES AND TRANSVERSALS
Parallel Lines & Special Angles: Sasinschool.com Interactivity #15 (A)
http://www.sasinschool.com/ProductEntrance/Launch/launch.jsp?unit=15
Parallel Lines and Angles: RegentsPrep.org (L, P)
http://www.regentsprep.org/Regents/math/geometry/GP8/indexGP8.htm
Parallel Lines and Transversals: Emathlab.com (P)
http://emathlab.com/Geometry/Lines_and_Angles/ParallelLines.php
Proving Lines Parallel: Graphic Organizer: (R)
http://www.sw-georgia.resa.k12.ga.us/Math.html
Parallel Lines in our World (PROJECT - A)
Parallel Line Project
PARALLEL AND PERPENDICULAR LINES IN THE COORDINATE PLANE
Slope and Intercept: BrainPop (L, P)
http://www.brainpop.com/math/dataanalysisandprobability/slopeandintercept/
Slopes & Equations of Lines: RegentsPrep.org (L, P)
http://www.regentsprep.org/Regents/math/geometry/GCG1/indexGCG1.htm
Slope Equations: Emathlab.com: (P)
http://emathlab.com/Geometry/Slopes_and_Equations/SlopeEquations.php
Equations of Parallel & Perpendicular Lines: Emathlab.com (P)
http://emathlab.com/Geometry/Slopes_and_Equations/ParallelPerpendicular.php
do triangles and angles next
J. Brendel
August, 2012
HONORS ALGEBRA-II W/TRIG
Marking Period-I Chapter-I project
Objective: Use the distance, midpoint, and slope formulas to classify
triangles and quadrilaterals on the coordinate plane. (Geometer’s
Is Overpopulation Still a Problem?
129 KB Word version It wasn’t long ago that overpopulation was thought
to be one of the critical problems in our world. In recent years, concern
about overpopulation has fallen by the wayside. Still, the population of
the earth continues to grow. Should we be concerned? By examining
history, data and mathematical processes for examining that data,
students will assess the overpopulation problem and try to determine
whether or not it’s something about which we should still worry.
ALGEBRA-2 RESOURCES
Algebra-II (McDougal Littell 2006 text)
Chapter 1
• Properties of Numbers Quiz(Glencoe)Tutorial for Solving
Inequalities
Chapter 2 Technology Resources for Extra Practice
• Relations & Functions Quiz
• Linear Equations Quiz
• Slope Quiz
• Writing Linear Equations Quiz
• Using Scatter Plots Quiz
• Graphing Linear Inequalities Quiz
• Graphing Absolute Value Functions Quiz
Exponents worksheet (SAT examples) (JB 11/2010)
http://people.hofstra.edu/Stefan_Waner/RealWorld/tut_alg_review/framesA_2B.html
Using Exponent Rules: Coolmath.com (P)
http://www.coolmath.com/algebra/algebra-practice-polynomials.html
Multiplication and Division of Radicals (E)
Simplifying Square Roots II: Quia (P)
http://www.quia.com/rr/178420.html
Negative and Fractional Exponents: Regentsprep.org (L, P)
http://www.regentsprep.org/Regents/math/algtrig/ATO1/indexATO1.htm
Fractional Exponents (E)
http://www.regentsprep.org/Regents/math/algtrig/ATE10/indexATE10.htm
Solving Radical Equations (using TI-84): MathBits (L, E)
ALG. 2 CONTINUED
FACTORING:
Factoring ALL Polynomials: Coolmath.com (P)
http://www.coolmath.com/algebra/algebra-practicepolynomials.html
Review Factoring Polynomials: Regentsprep.org (L,P)
http://www.regentsprep.org/Regents/math/algtrig/ATV1/indexATV1
.htm
SCATTER PLOTS: (De Simone 10_08)
• 2.6 Draw Scatter Plots & Lines of Best Fit
• Explore Learning (class code W8SGPB3DW7)
• 2.6 Using Graphing Calculator for Scatter Plots (PPT)
Solving Quadratic Equations by Factoring (L) http://lgfl.skoool.co.uk/examcentre.aspx?id=302
Quadratics Review Plus: Coolmath.com (L, P, E)
Quadratic Functions & Equations: Completing the Square (L, P, E)
http://my.hrw.com/math06_07/nsmedia/homework_help/alg1/alg1_ch09_08_homeworkhelp.html
Completing the Square: HotMath (P) http://hotmath.com/help/gt/genericalg1/section_6_13.html
Completing the Square Self Quiz: Glencoe (P)
Quadratic Formula: SOS Math (L, E) http://www.sosmath.com/algebra/factor/fac08/fac08.html
http://my.hrw.com/math06_07/nsmedia/homework_help/alg1/alg1_ch09_09_homeworkhelp.html
http://www.regentsprep.org/Regents/math/algtrig/ATE3/indexATE3.htm
Solving Quadratic Equations using the TI-84: Mathbits.com (L)
COMPLEX NUMBERS:
Imaginary Numbers (L)
http://mathforum.org/dr.math/faq/faq.imag.num.html
Complex Numbers: What Are They? - Coolmath.com (L)
http://www.coolmath.com/algebra/Algebra1/12Complex/01_whatarethey.htm
Factoring with i: Coolmath.com (L, P)
http://www.coolmath.com/algebra/Algebra1/12Complex/02_factoring.htm
Basic Operations with Complex Numbers (L)
http://www.intmath.com/Complex-numbers/2_Basic-operations.php
Complex Numbers: PurpleMath (L, E)
http://www.purplemath.com/modules/complex.htm
Complex Numbers: Regentsprep.org (L, P, A)
http://www.regentsprep.org/Regents/math/algtrig/ATO6/indexATO6.htm
Imagine That!: Quia (P)
http://www.quia.com/rr/178433.html
Complex Numbers with TI-84: Mathbits.com (R)
http://www.mathbits.com/MathBits/TISection/Algebra2/complexgc.htm
LINEAR INEQUALITIES:
Compound Inequalities Gizmo: Explorelearning.com (A, P)
http://www.explorelearning.com/index.cfm?method=cResource.dspView&R
esourceID=99&ClassID=762341
Linear Inequalities Quiz: ClassZone.com (P)
Graphing Inequalities: Regentsprep.org (L, P)
http://regentsprep.org/Regents/math/math-topic.cfm?TopicCode=Ginequal
Linear Inequalities in Two Variables – Activity A Gizmo:
Explorelearning.com (A, P)
http://www.explorelearning.com/index.cfm?method=cResource.dspView&R
esourceID=142&ClassID=762326
ABSOLUTE VALUE EQUATIONS/INEQUALITIES:
Absolute Value Equation: Regentsprep.org (L, P)
http://www.regentsprep.org/Regents/math/algtrig/ATE1/indexATE1.htm
Absolute Value Inequalities: Regentsprep.org (L, P)
http://www.regentsprep.org/Regents/math/algtrig/ATE2/indexATE2.htm
Absolute Value Equations and Inequalities: Quia.com (P)
http://www.quia.com/cb/255240.html
Absolute Value Equations & Inequalities (L, E, P)
http://www.themathpage.com/alg/absolute-value.htm
FUNCTIONS:
Vertical Line Test Link to a vertical line test applet (M.Doherty 10_08) (A)
http://www.mathwarehouse.com/algebra/relation/vertical-line-test.php
Relations and Functions: Regentsprep.org (L, P)
http://www.regentsprep.org/Regents/math/algtrig/ATP5/indexATP5.htm
Function Basics (L)
http://library.thinkquest.org/2647/algebra/funcbasc.htm
Functions: Coolmath.com (L, P)
http://www.coolmath.com/algebra/Algebra1/index.html#Algebra_1:_Functions
The Function Machine (A)
http://score.kings.k12.ca.us/lessons/functions/machine.html
Inverse Functions: Regentsprep.org (L, P)
http://www.regentsprep.org/Regents/math/algtrig/ATP8/indexATP8.htm
Inverse Functions: PurpleMath (L, E)
http://www.purplemath.com/modules/invrsfcn.htm
GRAPHS OF FUNCTIONS:
Families of Functions (L, E)
http://www.wmueller.com/precalculus/families/splash.html
Transformations with Functions: Regentsprep.org (L, P)
http://www.regentsprep.org/Regents/math/algtrig/ATP9/indexATP9.htm
Graphing Quadratic Functions – Activity A Gizmo: Explorelearning (P, A)
http://www.explorelearning.com/index.cfm?method=cResource.dspView&ResourceID=116&ClassID=7
62326
http://www.classzone.com/cz/books/algebra_2_2007_na/get_chapter_group.htm?cin=3&rg=animated_
math&at=animations&var=animations
Find the Maximum Value of Quadratic Function: Classzone.com (A)
http://www.classzone.com/cz/books/algebra_2_2007_na/get_chapter_group.htm?cin=3&rg=animated_
math&at=animations&var=animations
http://www.classzone.com/cz/books/algebra_2_2007_na/get_chapter_group.htm?cin=3&rg=animated_
math&at=animations&var=animations
Absolute Value Functions Gizmo: Explorelearning.com (A, P)
http://www.explorelearning.com/index.cfm?method=cResource.dspView&ResourceID=345
Piecewise Defined Functions (R)
http://archives.math.utk.edu/visual.calculus/0/functions.13/index.html
Piecewise Defined Functions (P)
http://my.hrw.com/math06_07/nsmedia/homework_help/alg2/alg2_ch09_02_homeworkhelp.html
VARIATION:
Direct and Inverse Variation: Regentsprep.org (L, P)
http://www.regentsprep.org/Regents/math/algtrig/ATE7/indexATE7.htm
Direct, Joint and Inverse Variation: Hotmath (P)
http://hotmath.com/help/gt/genericalg2/section_7_2.html
8.1 Compare Different Types of Variation: ClassZone (A)
http://www.classzone.com/cz/books/algebra_2_2007_na/get_chapter_g
roup.htm?cin=3&rg=animated_math&at=animations&var=animations
POLYNOMIAL FUNCTIONS: GRAPHS & ZEROS
Polynomial Division & Zeros: Hotmath (P)
http://hotmath.com/help/gt/genericalg2/section_6_8.html
Dividing Polynomials Using Synthetic Division Gizmo: Explorelearning.com
(A)
http://www.explorelearning.com/index.cfm?method=cResource.dspView&Re
sourceID=131&ClassID=762326
Practice Quiz on Remainder & Factor Thms: Glencoe (P)
Remainder & Factor Theorems (L, E)
http://www.intmath.com/Equations-of-Higher-Degree/2_Factor-RemainderTheorems.php
Zeros of Functions with TI-84: Mathbits.com (L)
http://www.mathbits.com/MathBits/TISection/Algebra2/zerofunctions.htm
Roots of Polynomials (L, E)
http://www.themathpage.com/aPreCalc/factor-theorem.htm
Descartes’ Rule of Signs: Purplemath (L)
http://www.purplemath.com/modules/drofsign.htm
Polynomial Functions: (R)
http://www.intmath.com/Equations-of-Higher-Degree/1_PolynomialFunctions.php
Solving and Graphing Polynomial Equations: Regentsprep.org (L, P)
http://www.regentsprep.org/Regents/math/algtrig/ATE13/indexATE13.ht
m
Graphing Fourth-Degree Polynomials – Activity A Gizmo:
Exploreleanring.com (A)
http://www.explorelearning.com/index.cfm?method=cResource.dspView
&ResourceID=136&ClassID=762326
Self Test – Polynomial Functions: Glencoe (P)
RATIONAL FUNCTIONS:
Simplifying, Multiplying and Dividing Rational Expressions (P)
http://my.hrw.com/math06_07/nsmedia/homework_help/alg2/alg2_ch08_02_homeworkhelp.ht
ml
Adding, Subtracting and Using LCM (P)
http://my.hrw.com/math06_07/nsmedia/homework_help/alg2/alg2_ch08_03_homeworkhelp.ht
ml
Solving Rational Equations (P)
http://my.hrw.com/math06_07/nsmedia/homework_help/alg2/alg2_ch08_05_homeworkhelp.ht
ml
Rational Equations and Inequalities: Regentsprep.org (L, P)
http://www.regentsprep.org/Regents/math/algtrig/ATE11/indexATE11.htm
Complex Fractions: Regentsprep.org (L, P)
http://www.regentsprep.org/Regents/math/algtrig/ATV2/indexATV2.htm
Complex Fractions (L)
htm
Simplifying Complex Fractions (E)
http://www.wisconline.org/objects/index_tj.asp?objID=TMH5005
**Definition of a Rational Function (R)
http://id.mind.net/~zona/mmts/functionInstitute/rationalFunctions/definition/definition.html
EXPONENTIAL AND LOGARITHMIC FUNCTIONS:
Logarithmic Expressions and Equations: Regentsprep.org (L, P)
http://www.regentsprep.org/Regents/math/algtrig/ATE9/indexATE9.htm
Logarithmic Functions: (L)
alg_tut43_logfun.htm
Working with Logarithms and the TI-84: Mathbits.com (E)
http://www.mathbits.com/MathBits/TISection/Algebra2/logarithms.htm
Properties of Logarithms: Purplemath.com (L, E)
http://www.purplemath.com/modules/logrules.htm#changeofbase
Properties of Logarithms: (L, E)
http://www.helpalgebra.com/articles/propertiesoflogarithms.htm
Self Test – Exponential and Logarithmic Relations: Glencoe (P)
Workbook – Using Logarithmic Properties: Classzone.com
(P)
Workbook – Solving Exponential and Logarithmic
Equations: Classzone.com (P)
Exponential and Logarithmic Equations (E, P)
http://www.intmath.com/Exponential-logarithmicfunctions/6_Logarithm-exponential-eqns.php
TRIGONOMETRY:
Six Trigonometric Functions: Regentsprep.org (L, P)
http://www.regentsprep.org/Regents/math/algtrig/ATT1/inde
xATT1.htm
Degrees, Radians, and Trig Angle Entries (TI-84): MathBits
(L)
http://mathbits.com/MathBits/TISection/Trig/degrees.htm
Mathbits.com (A)
http://www.mathbits.com/MathBits/GSP/TrigFunctions.htm
Trigonometric Functions (L, E)
http://www.intmath.com/Trigonometric-functions/Trigfunctions-intro.php
SYSTEMS OF EQUATIONS:
Systems of Linear Equations; Activity A Gizmo: Explorelearning.com (A, P)
http://www.explorelearning.com/index.cfm?method=cResource.dspView&R
esourceID=161&ClassID=762341
Modeling Linear Systems – Activity A Gizmo: Explorelearning.com (A)
http://www.explorelearning.com/index.cfm?method=cResource.dspView&R
esourceID=278&ClassID=762326
Systems of Equations (2x2): Coolmath.com (P)
http://www.coolmath.com/algebra/cruncher/system2x2.htm
Systems of Equations: Coolmath.com (L, P)
http://www.coolmath.com/algebra/Algebra2/index.html#Algebra_2:_System
s_of_Equations
SYSTEMS OF INEQUALITIES:
System of Inequalities: Coolmath.com (L)
http://www.coolmath.com/algebra/Algebra2/07Systems3x3/
09_inequalities.htm
System of Inequalities – Activity A Gizmo:
Explorelearning.com (A)
http://www.explorelearning.com/index.cfm?method=cResou
rce.dspView&ResourceID=162&ClassID=762341
LINEAR PROGRAMMING:
Linear Programming – Activity A Gizmo:
Explorelearning.com (A)
http://www.explorelearning.com/index.cfm?method=cResour
ce.dspView&ResourceID=143
Review Exercises for Linear Programming (P)
http://people.hofstra.edu/Stefan_Waner/RealWorld/Finitequ
estlp.html
Self Quiz on Linear Programming: Glencoe.com (P)
nt
MATRICES:
Introduction to Matrices: (L)
http://www.tutor.ms.unimelb.edu.au/matrix/matrix_basics.html
Adding and Subtracting Matrices: Purplemath.com (L)
Adding and Subtracting Matrices: Purplemath.com (L, P)
http://www.ucl.ac.uk/Mathematics/geomath/level2/mat/mat4.html
Matrices: Definition(R)
http://www.mrc-cbu.cam.ac.uk/Imaging/Common/matrices.pdf
Working with Matrices on the TI-84: Mathbits.com (L)
http://www.mathbits.com/MathBits/TISection/Precalculus/matrices.htm
Working with Determinants of Matrices on the TI-84: Mathbits.com (L)
http://www.mathbits.com/MathBits/TISection/Precalculus/determinants.htm
Matrices and Determinants (L, E)
http://www.intmath.com/Matrices-determinants/Matrix-determinant-intro.php
PRE-CALCULUS RESOURCES
PRE-CALCULUS RESOURCES
J. Brendel
August 2011
CALCULUS RESOURCES
CALCULUS-BC Resources (from M. Hinrichsen's Web page Oct. 31, 08)
Measurements of Angles:
Graphing angles with degree measure and co-terminal angles.
http://www.themathpage.com/aTrig/measure-angles.htm
Converting between degrees and radians and finding co-terminal angles in
This site includes a practice quiz. Take a peek - notice anything?
http://www.regentsprep.org/Regents/math/algtrig/ATM1/indexATM1.htm
CALCULUS CONTINUED
The relationship between angles in radians and arc length.
http://www.regentsprep.org/Regents/math/algtrig/ATM1/arclengthlesson.htm
Practice with Radian Measure and Arc Length
Practice converting angle measurements between degrees and radians and applying
to arc length.
Arc Length
http://www.themathpage.com/aTrig/arc-length.htm
Angles in Standard Position and Reference Angles
http://www.regentsprep.org/Regents/math/algtrig/ATT3/referenceAngles.htm
CALCULUS CONTINUED
http://www.regentsprep.org/Regents/math/algtrig/ATT3/referenceAngles.htm
Reference Angles
http://www.sparknotes.com/math/trigonometry/trigonometricfunctions/section
4.rhtml
Reference Angles and Reference Triangles
http://www.regentsprep.org/Regents/math/algtrig/ATT3/referenceTriangles.ht
m
Practice with Reference Angles
http://www.regentsprep.org/Regents/math/algtrig/ATT3/PracReference.htm
CALCULUS CONTINUED
http://www.themathpage.com/aTrig/unit-circle.htm
Calculus Presentations - What Is.....
http://www.calculus-help.com/funstuff/phobe.html
Chapter Resources - Quizzes
http://www.college.hmco.com/mathematics/larson/calculus_analytic/7e/st
udents/ace.html
Definitions of the Derivative
The development of the definitions of the derivative.
CALCULUS CONTINUED
http://www.archive.org/details/AP_Calculus_BC_Lesson_19
Differentiability and Continuity
http://ia300143.us.archive.org/0/items/AP_Calculus_BC_Lesson_25/Container.
html
Basic Differentiation Rules
Basic rules - power, product, quotient, etc.
http://ia300136.us.archive.org/1/items/AP_Calculus_BC_Lesson_20/Container.
html
The Chain Rule
http://ia300143.us.archive.org/2/items/AP_Calculus_BC_Lesson_21/Container.
html
Implicit Derivatives
Implicit derivatives - lesson and practice.
CALCULUS CONTINUED
http://www.archive.org/details/AP_Calculus_BC_Lesson_26
Paramateric Equations and Conic Sections
http://www.archive.org/details/AP_Calculus_BC_Lesson_11
Parametric Derivatives
http://www.archive.org/details/AP_Calculus_BC_Lesson_28
Derivatives of Inverse Functions
http://www.archive.org/details/AP_Calculus_BC_Lesson_24
Derivatives of Exponential Functions
CALCULUS (LAST SLIDE)
http://www.archive.org/details/AP_Calculus_BC_Lesson_22
Derivatives of Logarithmic Functions
http://www.archive.org/details/AP_Calculus_BC_Lesson_23
Logarithmic Differentiation
http://www.archive.org/details/AP_Calculus_BC_Lesson_27
Tutorial: Extrema and Critical Numbers
KEEP IN TOUCH
JUDITH T. BRENDEL
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http://www.pascack.k12.nj.us
[curriculum] [mathematics] [Workshop:
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