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Algebra 2

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End-of-Course - Algebra II


Sites to help students practice skills needed for the Algebra II exam.


Links being verified 2/5/2015




Standards Number & Operations | Algebra | Geometry | Measurement | Data Analysis and Probability


Virginia Standards of Learning - Select Algebra II and 10, 20 or 40 questions - Repeat for a new set of questions
SOL Algebra I & II resources - posted by Rockingham County Public Schools
FCAT Sample Test Book - [2008] sample questions and test taking tips This is an Adobe Acrobat document This link includes something for the teacher to print
FCAT Sample Answer Book - [2008] sample questions and test taking tips This is an Adobe Acrobat document This link includes something for the teacher to print
Texas Released Tests
Virginia DOE index of released tests This is an Adobe Acrobat document

Standard 1 - Number and Operations
Students will recognize, represent, model, and apply real numbers and operations and will demonstrate an understanding of properties and operations of the complex number system.
Level 1

order a given set of real numbers

  1. Common Core Math Video 32 - [12:08] a You Tube video on comparing and ordering real numbers A video is available through this link
  2. Comparing and Ordering Real Numbers - An Adobe Acrobat document in .pdf format To determine which of two real numbers is greater, express each number as a decimal. Then compare the numbers
  3. Comparing and Ordering Real Numbers - An Adobe Acrobat document in .pdf format A lesson plan can be found at this site This link includes something for the teacher to print [4 pages] several sets of problems, each followed by answers
  4. Comparing Seven Digit Numbers - practice area followed by an interactive game This site is interactive and allows students to play a game or input or collect data
  5. Ordering Numbers - elementary level explanation with ten questions at the bottom of the page
  6. Ordering Real Numbers From Least To Greatest - [4:53] You Tube video A video is available through this link
  7. Properties of Real Numbers - intermediate algebra tutorial 5
  8. Rational and Irrational number review
identify the reciprocal of a real number
  1. Fractions: the Reciprocal - instructions followed by practice problems, reciprocal of real numbers practice is also available
  2. How do I find the reciprocal of a decimal mixed number? - an answer to a student's question
  3. Properties of Real Numbers - intermediate algebra tutorial 5 [provides practice with reciprocals
  4. Rational Number and its Reciprocal - a step-by-step examination of a problem by Dr. Math
  5. Reciprocal - explanation, examples, and review questions at the end [from Math is Fun]
  6. The Reciprocal of a Real Number - [37:25] You Tube video (caution: some users complained that the video was too long) A video is available through this link
  7. The Reciprocal of a Real Number - A PowerPoint show related to this standard [30 slides] PowerPoint show designed to teach about simplifying expressions involving reciprocals
  8. Reciprocal of a Real Number - [14 pages] lesson on the topic in the format of a slide show An Adobe Acrobat document in .pdf format
multiply two polynomials with each factor having no more than two terms.
  1. Factoring Trinomials - practice exercises at Math Pinball [This expired link is available through the Wayback Machine Internet Archive. If the page doesn't load quickly click on Impatient? at the bottom right of the page.] This site is interactive and allows students to play a game or input or collect data
  2. "FOIL": A Special (and Misleading) Case - a special method, useful ONLY for a two-term polynomial times another two-term polynomial
  3. General Polynomial Multiplication - switch over to vertical multiplication once the polynomials get big
  4. Interactive Algebra Review - Multiplying Algebraic Expressions [This expired link is available through the Wayback Machine Internet Archive. If the page doesn't load quickly click on Impatient? at the bottom right of the page.] This site is interactive and allows students to play a game or input or collect data
  5. Interactive Algebra Review - Solving Polynomial Equations (see also part B of this tutorial ) [This expired link is available through the Wayback Machine Internet Archive. If the page doesn't load quickly click on Impatient? at the bottom right of the page.] This site is interactive and allows students to play a game or input or collect data
  6. Multiply Polynomials - this two page .pdf document could be printed as a student handout An Adobe Acrobat document in .pdf format This link includes something for the teacher to print
  7. Multiply Polynomials - This WebMath page will show you how to multiply polynomials together
  8. Multiply Two Polynomials Using Algebra Tiles - multiple-choice question from IXL
  9. Multiplication of Polynomials - using the distributive property
  10. Multiplying Polynomials - this Math is Fun page has several animated explanations plus ten questions for students to check their understanding
  11. Multiplying Polynomials - a step-by-step explanation from PurpleMath
  12. Multiplying Polynomials - Beginning Algebra Tutorial 28 from West Texas A & M's Virtual Math Lab
  13. Multiplying Polynomials - following the explanation from Free Math Help you will find an interactive problem solver
  14. Multiplying Polynomials: an Example - video lesson from Khan Academy A video is available through this link
  15. Multiplying Polynomials Calculator - the Wolfram calculator includes input interpretation and possible intermediate steps This site is interactive and allows students to play a game or input or collect data
  16. Solving Polynomial Equations - In algebra you spend lots of time solving polynomial equations or factoring polynomials (which is the same thing). This paper ties them all together in a coherent whole.
  17. Steps Required for Multiplying Polynomials - five examples followed by a link to practice problems
Level 2

perform basic operations using complex numbers (i.e., addition, subtraction, and multiplication)

  1. Basic Operations With Complex Numbers - topics covered are addition, multiplication and division, sample problems are given and answers are available
  2. Complex Number Operations - [9:56] a You Tube video A video is available through this link
  3. Complex Numbers - explanation, examples and review questions at the bottom of this Math is Fun page
  4. Complex Numbers - rules of complex arithmetic
  5. Complex Numbers - online algebra notes
  6. Complex Numbers Primer - algebra notes
  7. A concentration type game from Quia using algebraic expressions - If d = 2 match the algebraic expressions to the correct answers. This site includes questions for your students to check their understanding
  8. How To Perform Operations With Complex Numbers - explanation from the Dummies series
  9. Interactive Algebra Review - Rational Algebraic Expressions [This expired link is available through the Wayback Machine Internet Archive. If the page doesn't load quickly click on Impatient? at the bottom right of the page.] This site is interactive and allows students to play a game or input or collect data
  10. Operations on Complex Numbers - To simplify complex-valued expressions, you combine "like" terms and apply the various other methods you learned for working with polynomials.
  11. Operations With Complex Numbers - this Algebra Lab interactive page covers addition, multiplication and division and has sample problems for each operation
  12. Operations With Complex Numbers - [6:06] a You Tube video A video is available through this link
  13. Operations With Complex Numbers - this worksheet has two pages of problems and is followed by two pages of answers An Adobe Acrobat document in .pdf format This link includes something for the teacher to print
select a graph that represents an absolute value equation on a coordinate plane
  1. Absolute Value Inequalities - [5 pages] examples, exercises and a quiz An Adobe Acrobat document in .pdf format
  2. Absolute Value lesson - from Purple Math
  3. Coordinate Graphs - extensive explanation from Cliffs Notes
  4. Coordinate Planes and Graphs - explanation with quite a few examples
  5. Graphing Absolute Value Expressions - A PowerPoint show related to this standard [22 slides] several review questions for students included
  6. Graphing Absolute Value Functions - from the academic support center of Mercy High School in Michigan
  7. Graph Absolute Value Inequalities (Coordinate Plane) - [2:33] short video lesson A video is available through this link
  8. Graphing Absolute Value Inequalities on the Coordinate Plane - [5:43] video lesson A video is available through this link
  9. Graphing Inequalities - [8:04] video lesson from Khan Academy A video is available through this link
  10. Graphing Inequalities - from Tutor Vista
  11. How to Graph Absolute Value Inequalities on a Coordinate Plane - step by step from eHow
  12. Length of a Line Segment (Distance) - When working with Coordinate Geometry, there are many ways to find distances (lengths) of line segments on graph paper.
  13. Linear Inequalities - How to graph the equation of a linear inequality. [includes an interactive linear inequality] This site is interactive and allows students to play a game or input or collect data
  14. Popular Tutorials - topics in ordered pairs, relations, and the coordinate plane at Virtual Nerd
  15. Practice Problems - fifty-three practice problems, with solutions available from Hotmath
  16. Simplifying Basic Absolute Value Expressions - practice exercises at Math Pinball This site is interactive and allows students to play a game or input or collect data
  17. Solving Absolute Value Equations - a lesson from Purple Math
  18. Solving Absolute Value Equations and Inequalities - includes a short video A video is available through this link
identify the exponential form of a logarithmic expression and vice versa
  1. Changing from Exponential to Logarithmic Form - [4 pages] explanation, examples, and practice problems An Adobe Acrobat document in .pdf format
  2. Convert Logarithms and Exponentials - explanation and examples
  3. Converting between Exponential and Logarithmic Equations - explanation including two graphs
  4. Exponential & Logarithmic Expressions - seventy-four question quiz This site includes questions for your students to check their understanding
  5. How Can Your Rewrite a Logarithm Expression - explanation, examples, and practice problems
  6. How Do You Convert From Logarithmic Form to Exponential Form? - [3:12] short video from Virtual Nerd A video is available through this link
  7. Logarithmic Expressions - explanation from the Regents Exam Prep Center
  8. Logarithm Worksheets - links to a large number of free worksheets, all in .pdf format
  9. Logarithms - In this section, you will learn a variety of properties and applications involving logarithms.
  10. Writing in Logarithmic and Exponential Form - [1:42] video lesson from Khan Academy A video is available through this link
simplify expressions with rational and negative exponents
  1. Converting Numbers to Scientific Notation - AAA Math lesson and practice problems This site is interactive and allows students to play a game or input or collect data & This site includes questions for your students to check their understanding
  2. Evaluating Exponents of Negative Numbers - AAA Math lesson and practice problems This site is interactive and allows students to play a game or input or collect data & This site includes questions for your students to check their understanding
  3. Exponent Practice - Try a workout of 10 problems. If you get at least 8 correct on your first attempt, then you're ready to move on. If not, review "In Depth" and try again. This site is interactive and allows students to play a game or input or collect data
  4. Exponents - Unit 3 from Ms. Glosser's Math Goodies
  5. Fractional Exponent Expressions - [2:02] video lesson from Khan Academy A video is available through this link
  6. How Do You Simplify an Expression With Negative Exponents? - [4:40] short video from Virtual Nerd A video is available through this link
  7. Interactive Algebra Review on Integer Exponents [This expired link is available through the Wayback Machine Internet Archive. If the page doesn't load quickly click on Impatient? at the bottom right of the page.] This site is interactive and allows students to play a game or input or collect data
  8. Negative Fractional Exponents Examples - video lesson from Khan Academy A video is available through this link
  9. Rational Expressions - lesson designed to help students convert radicals to expressions with rational exponents
  10. Rational Exponents - tutorial from the Virtual Math Lab at West Texas A & M University
  11. Scientific Notation - interactive practice This site is interactive and allows students to play a game or input or collect data
  12. Simplify Fraction Exponents - formula and examples of how to simplify fraction exponents
  13. Simplifying - Expressions that have had their like terms combined. Match each expression on the left with an expression on the right. Type the letter of the correct expression in the box. This site includes questions for your students to check their understanding
  14. Simplifying Expressions - examples of mathematical expressions from Tutor Vista
  15. Simplifying Expressions with Exponents - Demonstrates how to simplify exponent expressions, including fractional ones.
  16. Simplifying Expressions with Negative Exponents - several examples from Purple Math
  17. Use the Equation Calculator from Algebra Help This site is interactive and allows students to play a game or input or collect data
add, subtract, and multiply algebraic expressions.
  1. Add and Subtract Rational Expressions - [2:10] example followed by a short video A video is available through this link
  2. Add or Subtract Polynomials - This page will show you how to add and/or subtract polynomials. This site is interactive and allows students to play a game or input or collect data
  3. Adding and Subtracting Polynomials - examples, a short video animation and practice questions from Math is Fun
  4. Adding and Subtracting Rational Expressions - [8:15] video lesson from Khan Academy A video is available through this link
  5. Adding and Subtracting Rational Expressions - tutorial from the Virtual Math Lab at West Texas A & M University
  6. Adding and Subtracting Rational Expressions - just like with regular fractions, you'll have to convert to common denominators
  7. Adding and Subtracting Rational Expressions - free math help from Math Portal
  8. Adding and Subtracting Rational Expressions - examples worked out, step-by-step on this Cliffs Notes page
  9. Adding and Subtracting Rational (Fractional) Expressions - a Regents Prep site says the secret is to work slowly and show all of your work
  10. Addition and Subtraction of Algebraic Expressions - explanation followed by sample exercises, answers are available
  11. Adding, Subtracting, Multiplying and Dividing Algebraic Expressions - [5:07] a You Tube video lesson A video is available through this link
  12. Algebraic Expressions - explanations with a large number of examples, answers shown when you run your mouse pointer over the colored block
  13. Equations and Inequalities - solving addition and subtraction equations
  14. Evaluating Algebraic Expressions - tutorial from the Virtual Math Lab at West Texas A & M University
  15. How to Simplify Algebraic Expressions - [from Wiki How] Simplification allows a mathematician to change a complex, long, and/or awkward expression into a simpler or more convenient one that's equivalent
  16. Multiplying and Dividing Algebraic Terms - explanation followed by sample exercises, answers shown below the problems
  17. Simplifying Algebraic Expressions: Addition & Subtraction - a ten-slide presentation
Level 3
determine the conjugate of a complex number
  1. Complex Conjugate - one page handout for students An Adobe Acrobat document in .pdf format This link includes something for the teacher to print
  2. Complex Conjugate - definition from Math Words
  3. Complex Conjugate - definition and application from Hyper Physics
  4. Complex Conjugates - [8:03] a You Tube video lesson A video is available through this link
  5. Complex Conjugates and Dividing Complex Numbers - several step-by-step examples are given
  6. Complex Conjugates Example - [4:01] video lesson from Khan Academy A video is available through this link
  7. Complex or Imaginary Numbers - from The Math Page
  8. Conjugate and Modulus - a complex number primer from Paul's Online Math Notes
  9. Conjugate Complex Numbers - fairly advanced explanation
  10. Multiplying and Dividing Complex Numbers - [from Regents Prep] Multiplying two complex numbers is accomplished in a manner similar to multiplying two binomials
  11. Reciprocals, Conjugates, and Division - from Dave's Short Course on complex numbers
  12. Rules of Complex Arithmetic - basic rules from SOS Math
Sample Task
design and build a simple fractal from available materials
  1. Easy Fractal Generator - build your own
  2. Fractal Gallery - [from Cool Math] includes links to generators and a lesson explaining fractals
  3. Fractal Pack: Educator's Guide - Amazingly, fractals are extremely simple to make. A fractal is made by repeating a simple process again and again. An Adobe Acrobat document in .pdf format
  4. Fractals - a fractals unit for elementary and middle school students
  5. Fractals - step by step, how to create two famous fractals
  6. How to Make a Fractal - instructions on making a fractal by hand
  7. Kitchen Science Fractals - simple lab experiments
  8. Nico's Fractal Machine - fractal drawing site, students manipulate several variables This site is interactive and allows students to play a game or input or collect data
  9. Simple Fractals - move your mouse pointer over the fractals on this page to see them modified This site is interactive and allows students to play a game or input or collect data
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Standard 2 Algebra
Students will describe, extend, analyze, and create a wide variety of patterns and functions using appropriate materials and representations in real-world problem solving, and will demonstrate an understanding of the behavior of a variety of functions and their graphs.

Level 1

translate a verbal sentence into an algebraic equation and vice versa

  1. Expressions - SOL Quiz 7.13 An Adobe Acrobat document in .pdf format This link includes something for the teacher to print
  2. How Do You Turn a Longer Verbal Phrase Into an Algebraic Expression? - short video from Virtual Nerd A video is available through this link
  3. How to Translate an Equation Into a Sentence - [1:12] short video of homework help in math A video is available through this link
  4. The Language of Algebra - a four-step lesson from Math.com
  5. Learn to solve word problems - This is a collection of word problem solvers that solve your problems and help you understand the solutions. This site is interactive and allows students to play a game or input or collect data
  6. Ms. Lindquist: The Tutor - A free, web-delivered, intelligent tutoring system for tutoring students in writing expressions for algebra word problems. This site is sponsored by NSF. This site is interactive and allows students to play a game or input or collect data
  7. Solving Equations - illustrates the process of solving equations of various forms (from SOS Math)
  8. Translate Two-Step Verbal Sentences Into Algebraic Equations - index of resources available from a New York test prep site
  9. Translating Verbal Expressions to Algebraic Expressions - A PowerPoint show related to this standard [22 slides] a PowerPoint show
  10. Translating Verbal Expressions Into Algebraic Expressions - [8 page document] in this section you will study translating in more detail An Adobe Acrobat document in .pdf format
  11. Translating Verbal Phrases into Algebraic Expressions or Translating English into Math - short explanation from Algebra Lab
  12. Translating Verbal Sentence into Algebraic Equation - [7:20] a You Tube video lesson A video is available through this link
  13. Translating Word Problems - tutorial from Purple Math
  14. Verbal Phrases to Algebraic Expression - [24 page document] Objectives: translate verbal phrases into algebraic expressions, and solve word problems by translating sentences into equations. An Adobe Acrobat document in .pdf format
  15. Word Problems For Kids - This is a set of carefully selected problems (grade 5 to Grade 12) which can help you improve your problem solving skills. [This expired link is available through the Wayback Machine Internet Archive. If the page doesn't load quickly click on Impatient? at the bottom right of the page.]
select the algebraic equation that generalizes the pattern represented by data in a given table
  1. Chairs Around the Table - [an Illuminations lesson plan] Students investigate the number of chairs that can be placed around an arrangement of square tables. Three related problems in this lesson yield different linear relationships for students to discover. A lesson plan can be found at this site
  2. Graphic Representations of a Pattern - [designed for grade 7] review and practice
  3. How Do You Identify Exponential Behavior From a Pattern in the Data? - [7:16] short video from Virtual Nerd A video is available through this link
  4. Linear Patterns in Data - [13 page document] Use algebraic equations to represent patterns found in tables and charts. An Adobe Acrobat document in .pdf format A lesson plan can be found at this site
  5. Representing Patterns - Use tables and graphs to identify and represent patterns
  6. Scatterplot - a graphic tool used to display the relationship between two quantitative variables
solve multi-step (more than two steps) linear equations (one set of parentheses on each side of the equations and/or variables on both sides)
  1. How to Solve Multi-Step Linear Equations: Linear Algebra Education - [2:21] short video from You Tube A video is available through this link
  2. Multi-Step Equations - two-page worksheet, answers are on page 2 An Adobe Acrobat document in .pdf format This link includes something for the teacher to print
  3. Multi-Step Equations With Distribution - quiz from Khan Academy
  4. Solve Advanced Linear Equations - quiz at IXL This site includes questions for your students to check their understanding
  5. Solving Equations - examples from Regions Exam Prep Center
  6. Solving Equations - illustrates the process of solving equations of various forms (from SOS Math)
  7. Solving More Complicated Linear Equations with Integer Coefficients - practice exercises at Math Pinball [This expired link is available through the Wayback Machine Internet Archive. If the page doesn't load quickly click on Impatient? at the bottom right of the page.] This site is interactive and allows students to play a game or input or collect data
  8. Solving Multi-Step Equations - 47 practice problems at Hot Math, solutions are available
  9. Solving Multi-Step Equations - index of available tutorials from Virtual Nerd
  10. Solving Multi-Step Equations - Learning Objectives: Use properties of equality together to isolate variables and solve algebraic equations, and use the properties of equality and the distributive property to solve equations containing parentheses, fractions, and/or decimals. A lesson plan can be found at this site
  11. Solving Multi-Step Equations - from Algebra Lab
  12. Solving Multi-Step Linear Equations - most linear equations require more than one step for their solution [from Purple Math]
  13. Solving Simple Linear Equations with Integer Coefficients - practice exercises at Math Pinball This site is interactive and allows students to play a game or input or collect data [This expired link is available through the Wayback Machine Internet Archive. If the page doesn't load quickly click on Impatient? at the bottom right of the page.]
  14. Variables on Both Sides - [4:33] video lesson from Khan Academy A video is available through this link
select the graph that represents a given linear function expressed in slope-intercept form
  1. Algebra vs the Cockroaches - determine the slope of the line that cockroaches are crawling along to destroy them This site is interactive and allows students to play a game or input or collect data
  2. Equation of a Line: Slope-Intercept Form - An interactive applet that will help you visualize how changing the values for the slope, m, and the y-intercept, b, will affect the graph of the equation y = mx + b. [This expired link is available through the Wayback Machine Internet Archive. If the page doesn't load quickly click on Impatient? at the bottom right of the page.] This site is interactive and allows students to play a game or input or collect data
  3. The Slope-Intercept Form of a Linear Equation - explanation plus a short video A video is available through this link
  4. A PowerPoint show related to this standardSlope Intercept Jeopardy review game in the form of a PowerPoint show
select the graph that models a given real-world situation (i.e., linear and non-linear)  
identify the graphical representation of the solution to a one-variable inequality on a number line
  1. Number Line Bounce - use all the arrows to bounce back and forth along the number line to reach a target number This site is interactive and allows students to play a game or input or collect data
  2. Visualizing Numbers on an Interactive Number Line - instructions for using this activity are included This site is interactive and allows students to play a game or input or collect data
Level 2

select functional notation to generalize a given numeric pattern

  1. Calculating the nth Term - how to develop a formula that can be used to calculate these terms

  2. Multiple-Choice Questions ? twenty (20) questions on?Patterns & Functions This site includes questions for your students to check their understanding
solve one-variable linear equations with rational expressions
  1. Solving Simple Linear Equations with Integer Coefficients - practice exercises at Math Pinball This site is interactive and allows students to play a game or input or collect data [This expired link is available through the Wayback Machine Internet Archive. If the page doesn't load quickly click on Impatient? at the bottom right of the page.]
  2. Solving More Complicated Linear Equations with Integer Coefficients - practice exercises at Math Pinball [This expired link is available through the Wayback Machine Internet Archive. If the page doesn't load quickly click on Impatient? at the bottom right of the page.] This site is interactive and allows students to play a game or input or collect data
select the graph of a two-variable inequality  
determine the domain of polynomial, rational, square root, exponential and logarithmic functions
  1. Simplifying Radical Expressions - Intermediate Algebra tutorial
  2. Simplifying Radicals - explanation and practice problems
determine the range of a wide variety of functions given a graph  
solve a system of linear equations with 2 variables (e.g. substitution, elimination, Cramer?s Rule, and graphing)  
apply properties of logarithms to simplify a logarithmic expression
  1. Properties of Logarithms from SOS Math
  2. College Algebra - a tutorial on Logarithmic Properties with several examples and practice problems
  3. Basic Log Rules from Purple Math
identify matrices that model given real-world situations

 

Level 3

determine the inverse of a logarithmic function given its graph

  1. Exponential functions - a review of logarithms from SOS Math
  2. Inverse, Exponential and Logarithmic functions - five practice problems from Spark Notes
Sample Task
examine patterns found in Pascal?s Triangle  
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Standard 3 Geometry
Students will investigate, model, and apply geometric properties and relationships
Level 1

apply the given Pythagorean Theorem to real-world problems

  1. Animated Proof of the Pythagorean Theorem
  2. Demonstrate the Pythagorean Theorem - from NOVA This site is interactive and allows students to play a game or input or collect data
  3. Interactive Proof of Pythagoras' theorem - This Java applet was written by Jim Morey. It won grand prize in Sun Microsystem's Java programming contest in the Summer of 1995. This site is interactive and allows students to play a game or input or collect data
  4. Nineteen Pythagorean Theorem applets This site is interactive and allows students to play a game or input or collect data
  5. Pythagorean theorem - In this session, you will look at a few proofs and several applications of one of the most famous theorems in mathematics A lesson plan can be found at this site
  6. Proof of the theorem is demonstrated through a Quicktime animation
  7. Pythagorean Theorem - a java applet that allows students to investigate this theorem This site is interactive and allows students to play a game or input or collect data
  8. Pythagorean Theorem and its many proofs (43 to be precise)
  9. The Pythagorean Theorem, Distance Formula and Intro to Trigonometry - other practice activities
  10. Using the Pythagorean Theorem Once you know the equation a 2 + b 2 = c 2 is true, then you can use it to solve all kinds of problems. Try the Pythagorean theorem with two other examples given on this page
Level 2

predict the graphical transformation that occurs when coefficients and/or constants of given function are changed (no trigonometric or logarithmic functions)

 
apply proportion and the concepts of similar triangles to solve real world problems
  1. Geometry Java Applets - Similar Figures This site is interactive and allows students to play a game or input or collect data
  2. A Mathematical Droodle - Two Triples of Similar Triangles This site is interactive and allows students to play a game or input or collect data
  3. Percent and Proportion - unit 10 from Ms. Glosser's Math Goodies
  4. Plane Math - Nine activities involving aviation and mathematic This site is interactive and allows students to play a game or input or collect data
  5. Proportional Thinking and Probability - here you will find the Customizable Proportion Problems and much more
  6. Ratio and Proportion - four stage lesson includes examples and a set of workout problems
Level 3

describe the transformation that has changed a ?parent function? to the given related function (e.g., right shift of 3 units, reflection in the x-axis)

 

Sample Task
use properties of similar triangles to determine the height of objects that are difficult to measure
  1. Determining The Height Of A Waterfall - In research on waterfalls often the most confusing aspect has been determining the true height of a waterfall.
  2. How to use the distance formula to find distances between (x,y) points
  3. Object Height Calculator - Use the SCSA Object Height Calculator to calculate the height of tall shadow-casters, e.g., buildings, flagpoles, utility poles, trees, etc. This site is interactive and allows students to play a game or input or collect data
  4. Out of the Shadows: The Problem of Slopes - Knowing the sun's elevation is not enough to determine the height of an object from the length of its shadow; the slope of the surface on which the shadow is being cast must also be known.
  5. Measured Altitude of a Model Rocket - a simple way to determine the maximum altitude the rocket reaches at the end of the coasting flight
  6. Measured Altitude of a Kite - a simple way to determine the altitude of a flying kite
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Standard 4 Measurement
The student will understand and be able to apply the units, systems and processes of measurement.
Level 1

select the area representation for a given product of two binomials

 
Level 2
apply the given formula to find area and circumference of circles, area and perimeter of polygons, and volume of regular solids
  1. Lesson on Circumference of a Circle - a quiz is included at the bottom of the page
  2. Lesson on the Area of a Circle This site is interactive and allows students to play a game or input or collect data
  3. Circle, Sphere & Cylinder Calculator This site is interactive and allows students to play a game or input or collect data
Level 3

solve real world problems given logarithmic and exponential formulas (e.g. Ph scale, Richter scale.)

 

Sample Task

Students construct designs using basic geometric constructions. Then they transfer the design to a piece of 8" X 11" pane of plexiglas and paint the pane to create a ?stained glass.? Students construct one of the? regular 3-dimensional solid and compute the volume and surface area.

 
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Standard 5 Data Analysis and Probability
The student will collect, organize, represent, and interpret data; make and evaluate inferences and predictions; present and evaluate arguments based on data analysis; and model situations to determine theoretical and experimental probabilities.
Level 1

make a prediction from the graph of a real-world data set

  1. Graphs and charts - four different graphs and charts for you to consider This site is interactive and allows students to play a game or input or collect data
  2. Math in Daily Life: How do numbers affect everyday decisions? - A unit from Annenberg CPB which includes several hands-on activities. A lesson plan can be found at this site
  3. Plane Math - Nine activities involving aviation and mathematic This site is interactive and allows students to play a game or input or collect data
  4. Using Data and Statistics - good graphs, however they are not interactive
  5. Fun and Sun Rent-a-Car - students use tables, graphs, linear functions to solve a real-world problem A lesson plan can be found at this site
  6. Hand Squeeze - (a data collection and analysis class experiment) - Pass a "hand squeeze" around a circle and measure the amount of time that it takes for the hand squeeze to complete the circle. A lesson plan can be found at this site
  7. What Percentage of your Class is Right or Left Handed? - a data collection and analysis class experiment A lesson plan can be found at this site
  8. What are Your Chances - What many people refer to as 'good luck' can actually be explained by a little knowledge about probability and statistics. Our dice game allows you to see how increasing or decreasing the number of dice rolls effects an outcome. This site is interactive and allows students to play a game or input or collect data
determine the measures of central tendency for a given set of real-world data
  1. Central Tendency - explanation of this concept and related concepts
  2. Measures of Central Tendency - tutorial and examples
  3. Running and Weighted Averages - tutorial and examples
choose the matching linear graph when given a set of ordered pairs representing real-world data

 

Level 2

categorize the correlation of a scatter plot using real-world data (i.e., positive, negative, strong, or weak)

  1. Creating an Excel XY (Scatter) Plot - simple explanation
  2. Creating a Scatter Plot in Excel - two elaborate examples of scatter plots; Beer's law scatter plot and linear regression, and creating a scatter plot of titration data
  3. Explanation of Scatter Plot s from the Engineering Statistics Handbook
  4. Scatter Plot Applet - This applet draws a scatter plot of points (a,b), where the data is taken from an input table. The table is on the left side of the applet and can be edited by the user. This site is interactive and allows students to play a game or input or collect data
  5. Using Excel to create a Scatter Plot - an Internet4Classrooms module
  6. Weather and Spreadsheets - Java applet which allows you to enter data and display a scatter plot or a column chart of the data entered This site is interactive and allows students to play a game or input or collect data
determine the number of possible outcomes for a given experiment (i.e. the multiplication counting principle, permutations, or combinations)

 

determine the theoretical probability of a simple event for a given situation
  1. Probabilistic Situations - a short slide show on the topic
  2. Coin Flipping - Flip the coin and calculate the probability of flipping heads or tails. This site is interactive and allows students to play a game or input or collect data
  3. Ken White's Coin Flipping page - flip up to 100 coins and see the total number of heads and tails. Excellent for teaching about probability. This site is interactive and allows students to play a game or input or collect data
  4. Interactive Probability Tutorials: Sample Spaces and Events , Estimated Probability , Empirical Probability , Abstract Probability and Conditional Probability and Independence This site is interactive and allows students to play a game or input or collect data
  5. What are Your Chances - What many people refer to as 'good luck' can actually be explained by a little knowledge about probability and statistics. Our dice game allows you to see how increasing or decreasing the number of dice rolls effects an outcome. This site is interactive and allows students to play a game or input or collect data
determine the theoretical probability of a compound event (i.e., dependent or independent, union and intersection)

 

Level 3
find the equation for the line of best fit given a scatter plot depicting real-world data
  1. see a list above
Sample Task
Students analyze real-world data collected from the newspaper and explore and report the uses, misuses, and abuses of reported statistical data.? Students search the internet to collect age and market value of a selected vehicle over a specific period of time.? They use a graphing calculator to create a scatter plot and construct a line of best fit to predict the depreciation of the vehicle.
  1. Finding Data on the Internet - You'll soon be checking facts and downloading reputable data on everything from public safety to education to agriculture to crime to economics ... you name it. This site is intended as a resource for journalists, but why not make this a source for projects. Your students can find raw data related to: aviation, demographics, weather, energy, health, immigration and more.
  2. List of Data Sources on the Internet4Classrooms Project page
  3. Review of tables, charts and graphs - an index of topics
  4. Using Graphs, Equations, and Tables to Investigate the Elimination of Medicine from the Body - This three-part example illustrates the use of iteration, recursion, and algebra to model and analyze the changing amount of medicine in an athlete's body. A lesson plan can be found at this site




A resource for the teacher to use in planning their lessons site for teachers | A PowerPoint show related to this standard PowerPoint show | An Adobe Acrobat document in .pdf format Acrobat document | A Microsoft Word document to be downloaded Word document | This interactive site would work well on an interactive whiteboard whiteboard resource | This resource includes voice instructions for students sound | A video is available through this link video format | This site is interactive and allows students to play a game or input or collect data interactive lesson | This site includes questions for your students to check their understanding a quiz | A lesson plan can be found at this site lesson plan | This link includes something for the teacher to print to print

 


Multiple
Review
Activities
  1. SOS Mathematics - Algebra lessons
  2. AAA Math offers a large number of math review topics , each one supported by an interactive practice page (8th grade level)
  3. Interactive online End of Course Algebra Review - [This expired link is available through the Wayback Machine Internet Archive. If the page doesn't load quickly click on Impatient? at the bottom right of the page.]
  4. Practical Algebra Lessons from PurpleMath - The lessons give practical tips, hints, and examples, and point out common mistakes.
  5. Practice Tests from Virginia State Standards of Learning - Select Algebra I or II , and then select 10, 20, or 40 questions. This site is interactive and allows students to play a game or input or collect data
  6. Algebra Help - in-depth algebra help through algebra history, an online textbook, and various articles covering everything from basic algebra fundamentals to the latest-and-greatest algebra software help available
  7. National Library of Virtual Manipulatives - Virtual manipulatives related to the NCTM Number & Operations standard.

Internet4classrooms is a collaborative effort by Susan Brooks and Bill Byles.
 

  

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