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-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 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

* 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 (NJASK, HSPA) in 2014-2015.

WHAT’S NEW

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-IFCLUSTER: 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

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 + (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 Regular Level Honors Level

Basic Algebra gr.9

Algebra gr.9

Algebra gr.8

DISCUSS

Algebra-II collab

Algebra collab

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 - II

Geometry

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

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.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 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

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.

Share your plan! Defend your plan! 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 Real World Problems about compound interest including links to notes.

 

Websites recommended: from Algebra to Calculus

GEOMETRY RESOURCES

REPLACEMENT BASIC-GEOMETRYPerimeter Worksheet (with numbers) 9/10/10 jb      Answer Key (Perimeter Numbers Worksheet) 9/10/10 jbPerimeter Worksheet (with variables) 9/10/10 jbArea Worksheet (with numbers) 9/10/10 jb

BASIC GEOMETRY:Marking Period-1 project Find real-life pictures; create multi-media 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:

Task and Rubric

Facilitation Questions

Scaffold

Activity List

Web Sites

IDE Portal Resouces Shadow Games1478 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 School-90 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

 

Quadrilaterals: "Can-Do Packaging Project." Resources:

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&ResourceID=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?method=cResource.dspView&ResourceID=181

 

Segment Addition and Segment Bisectors: Emathlab.com (P)

http://emathlab.com/Geometry/Lines_and_Angles/SegAddBisect.php

DISTANCE AND MIDPOINT

 

Distance in 1, 2 & 3 dimensions: Sasinschool.com Interactivity #13 (A)

http://www.sasinschool.com/ProductEntrance/Launch/launch.jsp?unit=13

 

Midpoint of a Segment: Regentsprep.org (L, P)

http://www.regentsprep.org/Regents/math/geometry/GCG2/indexGCG2.htm

 

Distance of a Line Segment: Regentsprep.org (L, P)

http://www.regentsprep.org/Regents/math/geometry/GCG3/indexGCG3.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=cResource.dspView&ResourceID=183

 

Distance Formula: Explorelearning.com Activity B (A)

http://www.explorelearning.com/index.cfm?method=cResource.dspView&ResourceID=64

 

Distance & Midpoint: Gomath.com (summary with interactive example, links to lesson, worksheet - L, P, E)

http://www.gomath.com/exercises2/DistanceMidpoint.php

 

 

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&ResourceID=282

 

Investigating Angle Theorems: Explorelearning.com - Activity B (complementary, supplementary, vertical, and adjacent - A)

http://www.explorelearning.com/index.cfm?method=cResource.dspView&ResourceID=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.htm

 

Conditional Statements: Explorelearning.com (A)http://www.explorelearning.com/index.cfm?method=cResource.dspView&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.htm

 

Conditional Statements: Explorelearning.com (A)http://www.explorelearning.com/index.cfm?method=cResource.dspView&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.htm

 

Bi-Conditional Statements: Explorelearning.com (A)

http://www.explorelearning.com/index.cfm?method=cResource.dspView&ResourceID=173

  

DIRECT PROOF

Writing Proof: RegentsPrep.org (L, P)

http://www.regentsprep.org/Regents/math/geometry/GP3/indexGP3.htm

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

Additional Geometry resources will be added.

J. Brendel

August, 2012

HONORS ALGEBRA-II W/TRIGLinks to be updated!

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 Sketchpad) G. De Simone 10/14/08

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 RESOURCESAlgebra-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

RADICALS AND RATIONAL EXPONENTS:

Exponents  worksheet (SAT examples) (JB 11/2010)Exponents and Radicals (L, P)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)http://www.intmath.com/Exponents-radicals/5_Multiplication-division-radicals.php

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.intmath.com/Exponents-radicals/2_Fractional-exponent-laws.php

Radical Equations: Regentsprep.org (L, P) http://www.regentsprep.org/Regents/math/algtrig/ATE10/indexATE10.htm

Solving Radical Equations (using TI-84): MathBits (L, E)http://mathbits.com/MathBits/TISection/Algebra2/radicalequations.htm

ALG. 2 CONTINUED

FACTORING:Factoring ALL Polynomials: Coolmath.com (P)http://www.coolmath.com/algebra/algebra-practice-polynomials.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)

QUADRATIC EQUATIONS: Solving Quadratic Equations by Factoring (L) http://lgfl.skoool.co.uk/examcentre.aspx?id=302

Quadratics Review Plus: Coolmath.com (L, P, E)http://www.coolmath.com/algebra/Algebra2/index.html#Algebra_2:_Quadratics_Review_Plus

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)http://www.glencoe.com/sec/math/studytools/cgi-bin/msgQuiz.php4?isbn=0-07-827999-2&chapter=6&lesson=4&headerFile=10&state=nj

Quadratic Formula: SOS Math (L, E) http://www.sosmath.com/algebra/factor/fac08/fac08.html

Quadratic Functions & Equations: Quadratic Formula (L, P, E)http://my.hrw.com/math06_07/nsmedia/homework_help/alg1/alg1_ch09_09_homeworkhelp.html

Quadratic Equations, Discriminant, Quadratic Formula: Regentsprep.org (L, P)http://www.regentsprep.org/Regents/math/algtrig/ATE3/indexATE3.htm

Solving Quadratic Equations using the TI-84: Mathbits.com (L)http://www.mathbits.com/MathBits/TISection/Algebra2/quadraticequations.htm

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&ResourceID=99&ClassID=762341

Linear Inequalities Quiz: ClassZone.com (P)http://www.glencoe.com/sec/math/studytools/cgi-bin/msgQuiz.php4?isbn=0-07-827999-2&chapter=6&lesson=4&headerFile=10&state=nj

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&ResourceID=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=762326

Graphing Quadratic Functions: 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

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

Graphing Quadratic Inequalities: 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

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_group.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&ResourceID=131&ClassID=762326

Practice Quiz on Remainder & Factor Thms: Glencoe (P)http://www.glencoe.com/sec/math/studytools/cgi-bin/msgQuiz.php4?isbn=0-07-860861-9&chapter=4&lesson=3&quizType=1&headerFile=4&state=int

Remainder & Factor Theorems (L, E)http://www.intmath.com/Equations-of-Higher-Degree/2_Factor-Remainder-Theorems.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_Polynomial-Functions.php

Solving and Graphing Polynomial Equations: Regentsprep.org (L, P)http://www.regentsprep.org/Regents/math/algtrig/ATE13/indexATE13.htm

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)http://www.glencoe.com/sec/math/studytools/cgi-bin/msgQuiz.php4?isbn=0-07-877856-5&chapter=6&lesson=0&headerFile=7

RATIONAL FUNCTIONS:

Simplifying, Multiplying and Dividing Rational Expressions (P)http://my.hrw.com/math06_07/nsmedia/homework_help/alg2/alg2_ch08_02_homeworkhelp.html

Adding, Subtracting and Using LCM (P)http://my.hrw.com/math06_07/nsmedia/homework_help/alg2/alg2_ch08_03_homeworkhelp.html

Solving Rational Equations (P)http://my.hrw.com/math06_07/nsmedia/homework_help/alg2/alg2_ch08_05_homeworkhelp.html

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)http://www.wtamu.edu/academic/anns/mps/math/mathlab/int_algebra/int_alg_tut34_complex.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)http://www.wtamu.edu/academic/anns/mps/math/mathlab/col_algebra/col_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)http://www.glencoe.com/sec/math/studytools/cgi-bin/msgQuiz.php4?isbn=0-07-877856-5&chapter=9&lesson=0&headerFile=7

Workbook – Using Logarithmic Properties: Classzone.com (P)http://www.glencoe.com/sec/math/studytools/cgi-bin/msgQuiz.php4?isbn=0-07-877856-5&chapter=6&lesson=0&headerFile=7

Workbook – Solving Exponential and Logarithmic Equations: Classzone.com (P)http://www.glencoe.com/sec/math/studytools/cgi-bin/msgQuiz.php4?isbn=0-07-877856-5&chapter=6&lesson=0&headerFile=7

Exponential and Logarithmic Equations (E, P)http://www.intmath.com/Exponential-logarithmic-functions/6_Logarithm-exponential-eqns.php

TRIGONOMETRY:

Six Trigonometric Functions: Regentsprep.org (L, P)http://www.regentsprep.org/Regents/math/algtrig/ATT1/indexATT1.htm

Degrees, Radians, and Trig Angle Entries (TI-84): MathBits (L)http://mathbits.com/MathBits/TISection/Trig/degrees.htm

Trigonometric Functions with Geometer’s Sketchpad: Mathbits.com (A)http://www.mathbits.com/MathBits/GSP/TrigFunctions.htm

Trigonometric Functions (L, E)http://www.intmath.com/Trigonometric-functions/Trig-functions-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&ResourceID=161&ClassID=762341

Modeling Linear Systems – Activity A Gizmo: Explorelearning.com (A)http://www.explorelearning.com/index.cfm?method=cResource.dspView&ResourceID=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:_Systems_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=cResource.dspView&ResourceID=162&ClassID=762341

LINEAR PROGRAMMING:

Linear Programming – Activity A Gizmo: Explorelearning.com (A)http://www.explorelearning.com/index.cfm?method=cResource.dspView&ResourceID=143

Review Exercises for Linear Programming (P)http://people.hofstra.edu/Stefan_Waner/RealWorld/Finitequestlp.html

Self Quiz on Linear Programming: Glencoe.com (P)http://www.glencoe.com/sec/math/studytools/cgi-bin/msgQuiz.php4?isbn=0-07-860861-9&chapter=2&lesson=7&quizType=1&headerFile=4&state=int

MATRICES:

Introduction to Matrices: (L)http://www.tutor.ms.unimelb.edu.au/matrix/matrix_basics.html

Adding and Subtracting Matrices: Purplemath.com (L)http://www.purplemath.com/modules/mtrxadd.htm

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

will be added.

J. Brendel

August 2011

CALCULUS RESOURCESCALCULUS-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

Radian Measure:

Converting between degrees and radians and finding co-terminal angles in radians.

http://www.themathpage.com/aTrig/radian-measure.htm

Degrees and Radians:

This site includes a practice quiz. Take a peek - notice anything?

http://www.regentsprep.org/Regents/math/algtrig/ATM1/indexATM1.htm

CALCULUS CONTINUED

Arc Length and Radian Measure

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.

http://www.regentsprep.org/Regents/math/algtrig/ATM1/RadianPractice.htm

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 CONTINUEDhttp://www.regentsprep.org/Regents/math/algtrig/ATT3/referenceAngles.htm

Reference Angles

 

http://www.sparknotes.com/math/trigonometry/trigonometricfunctions/section4.rhtml

Reference Angles and Reference Triangles

 

http://www.regentsprep.org/Regents/math/algtrig/ATT3/referenceTriangles.htm

Practice with Reference Angles

 

http://www.regentsprep.org/Regents/math/algtrig/ATT3/PracReference.htm

Quadrantal Angles

 

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/students/ace.html

Definitions of the Derivative

The development of the definitions of the derivative.

CALCULUS CONTINUEDhttp://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 CONTINUEDhttp://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

jbrendel@pascack.k12.nj.us

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

[curriculum] [mathematics] [Workshop: Long Branch or CCSS Standards]