Regional Center

 

 

1. Algebra I

 
  1. Reasoning about Numbers, Systems and Quantitative Situations (L1)
  2. Calculation, Algorithms, and Estimation (L2)
  3. Expressions, Equations, and Inequalities (A1)
  4. Functions (A2)
  5. Families of Functions (A3)
  6. Bivariate Data - Examining Relationships (S2)

 

Additional Links to General Mathematics Sites

5. Families of Functions (A3)

Students study the symbolic and graphical forms of each function family. By recognizing the unique characteristics of each family, they can use them as tools for solving problems or for modeling real-world situations.

High School

  1. A3.1 Lines and Linear Functions
    1. Beginning Algebra Tutorials
      This is a beginning algebra web tutorial.  It covers all areas of beginning algebra.  Could be used for students to access on their own or as a teacher presentation. Student and Teacher Resource.
    2. Direct and Partial Variations
      This site contains teacher lessons plans for direct and partial variations. The concepts of direct and partial variation are introduced and compared to each other.
    3. Function Evaluator and Grapher -
      Use of this system is pretty intuitive. Enter your function f(x) in graphing calculator format (press the "example" button to see some examples). Then specify some values of x, and press "Evaluate". To see a graph, enter a range of x-values (Xmin and xMax) and press "Graph." The graph will appear in a little window called "Your Graph."
    4. Function Flyer
      This site allows students in Algebra and Pre-calculus to graph equations using a java applet. Students may then observe what happens to the graph of a function when the constants are changed. The site provides printable grid sheets for "pencil and paper" activities as well as discussions on each graphing activity.
    5. Finite Mathematics
      Outstanding! This site provides students with interactive tutorials concerning functions and linear models. Specifically, functions from the numerical and algebraic viewpoints, functions from the graphical viewpoint, linear functions and models, linear regression, families of functions, and fitting functions to data. The site provides other on-line resources and the necessary math tools.
    6. Guessing Correlations
      This is an interactive site for students.  They are asked to look at a linear regression graph and decide an approximate value for the correlation coefficient.
    7. Maths Online Gallery: Functions 2
      Students match graphs to the functions they represent using and interactive applet. Types of functions include power, rational and trigonometric.
    8. Parallel and Perpendicular Lines
      Students are given an equation and either an x-int, y-int, or a point and have to find the equation for the new line that is either parallel or perpendicular to the given equation.
    9. Solving Linear Equations
      This is a self tutorial for solving linear equations.
    10. The Math Dude: Slope of a Line New
      See how cool math can be with The Math Dude. This video clip provides a fast paced, entertaining explanation of the slope of a line.
    11. Vertical Line Test
      An interactive site where a student can create a graph in a coordinate grid and use the vertical line test to identify if a graph is a function or not.
    12. The Yo-Yo Problem
      This site has a couple activities for students that a teacher can print that involve representing quantities with symbols and expressing their relationship with equations. In the Yo-Y-o problem, they must write and solve an equation. In the Penny Pattern, they explore another linear model with the calculator.
  2. A3.2 Exponential and Logarithmic Functions
    1. Exponentials/Logarithms
      Students can experiment with exponential or logarithmic graphs and compare them to each other. A lesson plan is provided for each activity.
    2. Exponential Growth and Decay
      Investigate compound interest as an application of exponential growth. Explore exponential growth and decay interactively with tables and bar graphs.This site allows the user to change the values of the principle amount as well as the rate and see how that affects the results.
    3. Function Evaluator and Grapher
      Use of this system is pretty intuitive. Enter your function f(x) in graphing calculator format (press the "example" button to see some examples). Then specify some values of x, and press "Evaluate". To see a graph, enter a range of x-values (Xmin and xMax) and press "Graph." The graph will appear in a little window called "Your Graph."
    4. "I Want a Credit Card -- or do I?"
      Outstanding - After using the Internet to research the cost of borrowing on credit cards, students will pretend to borrow money. They will calculate the cost of the credit based on different payment amounts, display results using a pie graph and use a spread sheet to display their computations and graph.
    5. Identify the Vertex of a Parabola
      Identify the vertex of a Parabola. Students work through problems finding the vertex of parabolas.
    6. Math is Fun
      Good step by step description of how compound interest works. Goes into detail on different terms and also explanation of APR, and has a compound interest calculator.
    7. Modeling Orbital Debris Problems
      This is an excellent activity that students can do on the computer. They must use a spreadsheet program to enter data so they can make a scatter plot and get a best fit line. They can compare models they create to the actual data. They can also answer the questions with a word processor if they desire, or they can simply use a pencil and paper. Searching the Internet may be necessary to help them find answers to some of the questions. Students are exposed to linear, quadratic, and exponential function models. It also eludes to acceleration in terms of the changing rate of the deposit of orbital debris.
    8. Rhinos and M&M's® (Exponential Models)
      In activities that use paper folding and M&M’s, students will collect data, create scatterplots, and determine algebraic models that represent their functions. Students begin this lesson by collecting data within their groups. They fold a sheet of paper and determine the area of the smallest region after each fold. Next they draw a scatterplot of their data and determine by hand an algebraic model for it. After determining this algebraic model by hand, students collect exponential decay data using M&M’s and use the graphing calculator to determine a model for this data. Both investigations allow students to explore the patterns of exponential models in tables, graphs, and symbolic form. The final activity provides an opportunity for students to apply what they know about exponential models to future populations of African Rhinos.
    9. Shedding Light on the Subject: Function Models of Light Decay
      Presented by NCTM (Illuminations), this website provides the teacher with a four lesson unit on the decay of light as an exponential model. Teachers will appreciate the printer friendly lesson plans accompanied by student objectives, worksheets, and references. The site includes an interactive grapher and downloadable movie clips (quick time required) for students.
    10. The Math Dude: Exponential Functions New
      See how cool math can be with The Math Dude. This video clip provides a fast paced, entertaining explanation of exponential growth.
    11. The Million $ Mission
      Students can read story problems about exponential growth and calculate related values. Tables are also provided.
    12. The Normal Distribution
      This is an interactive site that allows students to change the standard deviation on a normal curve to see how it affects the graph.  It will also display a variety of histograms that could fit that curve.
  3. A3.3 Quadratic Functions
    1. Completing the Square
      Outstanding - User can guess at the correct answers when completing the square.
    2. Complete the Square: Solving Quadratic Equations
      Outstanding - user can go through a series of tutorials and then interactivly solve several progressivly difficult problems involving completing the square.
    3. Direct and Partial Variations
      This site contains teacher lessons plans for direct and partial variations. The concepts of direct and partial variation are introduced and compared to each other.
    4. Distance-Education-Quadratic Problems
      Several activities for quadratic problems including all the different ways to solve them. There are best practices and tips for teachers.
    5. Exploring Linear Functions
      This is a student activity that allows the student to explore how changes in the slope and y-intercept affect a linear graph. Also, what the effect would be if they are changed separately or simultaneously.
    6. Exploring Linear Functions: Representational Relationships
      This interactive web site explores linear functons.  An interactive model is included.  This interactive diagram shows the graph of f(x) = mx + b. Use the sliders to change the values of m and b, and observe how the graph changes.  Student interactive.
    7. Exponentials/Logarithms
      Students can experiment with exponential or logarithmic graphs and compare them to each other. A lesson plan is provided for each activity.
    8. Function Evaluator and Grapher
      Use of this system is pretty intuitive. Enter your function f(x) in graphing calculator format (press the "example" button to see some examples). Then specify some values of x, and press "Evaluate". To see a graph, enter a range of x-values (Xmin and xMax) and press "Graph." The graph will appear in a little window called "Your Graph."
    9. Function Flyer
      This site allows students in Algebra and Pre-calculus to graph equations using a java applet. Students may then observe what happens to the graph of a function when the constants are changed. The site provides printable grid sheets for "pencil and paper" activities as well as discussions on each graphing activity.
    10. Finite Mathematics
      Outstanding! This site provides students with interactive tutorials concerning functions and linear models. Specifically, functions from the numerical and algebraic viewpoints, functions from the graphical viewpoint, linear functions and models, linear regression, families of functions, and fitting functions to data. The site provides other on-line resources and the necessary math tools.
    11. Interactive Conic Flyer
      Applet that shows the changes of a parabola when the coefficients are changed. When you get to the site, you must go to the pull down menu and click on Vertical Parabola.
    12. Loan Calculator
      Students can set the amount of the loan, the interest rate and the number of years to see how variations in these numbers can change amount of payment and interest paid over the course of the loan. They also can set the amount of the monthly payment and calculate the amount of time required to pay off the loan.
    13. Maths Online Gallery: Functions 2 -
      Students match graphs to the functions they represent using and interactive applet. Types of functions include power, rational and trigonometric.
    14. PhET: Equations Grapher New
      Interactive simulation that allows students to explore the characteristics of a parabola as the values of a, b, and c are changed. Teaching ideas with lesson plans and handouts are also available with this activity.
    15. Purplemath: CXmpleting the Square
      Step by step instructions on completing the square, leading up to the quadratic formula.
    16. Quadratic Equations Completing the Square
      Solving Quadratic Equations by completing the square. This site contains Interactive Worksheets for Algebra.
    17. Quadratic Equations Finding the Vertex
      Quadratic Equations: This site would be useful for whole class instruction and immediate student feedback for finding the vertex given the standard form and vertex form of a quadratic equation. Additional links allow students to practice finding the axis of symmetry.
    18. Quadratic Formula Rap
      Students sing a tune to help memorize the quadratic formula. Very engaging!
    19. Quadratics Formula Song (Crank that!!)
      Students sing a tune to help memorize the quadratic formula. Very engaging!
    20. Solving Quadratics by Completing the Square
      Students enter any quadratic equation and select the method by which to solve them. The steps are explained and the problem is solved using one of four methods.
    21. Solving Quadratic Equations
      Students enter any quadratic equation and select the method by which to solve them. The steps are explained and the problem is solved using one of four methods.
    22. The Math Dude: Graphing Parabolas New
      See how cool math can be with The Math Dude. This video clip provides a fast paced, entertaining explanation of graphing parabolas.
    23. Webmath: Completing the Square on a Polynomial
      Outstanding - User can input their polynomial and the site will show how the answer is found as well as the answer.
  4. A3.4 Power Functions (including roots, cubics, quartics, etc.)
    1. Compare Exponential and Power Functions
      User can compare the graphs of exponential and power functions.
    2. Direct and Partial Variations
      This site contains teacher lessons plans for direct and partial variations. The concepts of direct and partial variation are introduced and compared to each other.
    3. Function Flyer
      This site allows students in Algebra and Pre-calculus to graph equations using a java applet. Students may then observe what happens to the graph of a function when the constants are changed. The site provides printable grid sheets for "pencil and paper" activities as well as discussions on each graphing activity.
    4. Maths Online Gallery: Functions 2
      Students match graphs to the functions they represent using and interactive applet. Types of functions include power, rational and trigonometric.
    5. Power Functions
      User can scroll through successive power functions and root functions, which changes the respective graph.
    6. Power Functions
      Basic explanations of power functions with color graphics and interactive hint buttons.
    7. SOSMath
      Informational site consisting of the inverse and composition of functions.
  5. A3.5 Polynomial Functions
    1. Chapter 2 Polynomials!
      This site provides a series of lessons on Polynomial Functions.
    2. End Behavior of Polynomial Functions
      User can watch/use the downlaodable program to manipulate the coefficients to watch the end behavior.
    3. Equations
      Tutorial on solving equations.
    4. Function Flyer
      This site allows students in Algebra and Pre-calculus to graph equations using a java applet. Students may then observe what happens to the graph of a function when the constants are changed. The site provides printable grid sheets for "pencil and paper" activities as well as discussions on each graphing activity.
    5. Polynomial Functions
      Application where the user cab manipulate the coefficients of a degree 5 polynomial and watch how the graph changes.
    6. Polynomial Functions
      Site has the ability to graph functions with a certain degree (0 through 5th)where the user is also allowed to change the constants/coefficients.
    7. Polynomial Functions
      In this tutorial, we define polynomial functions. We investigate some properties of polynomials including the domain, range, roots and symmetry.
    8. Polynomial Functions
      Polynomial functions are nothing more than a sum of power functions. As a result, certain properties of polynomials are very "power-like." When many different power functions are added together, however, polynomials begin to take on unique behaviors.
    9. Polynomial Graphs: End Behavior
      Description of end behavior of even/odd polynomials with positive/negative leading coefficients.
    10. THE VOCABULARY OF POLYNOMIAL FUNCTIONS
      Functions can be categorized, and the simplest type is a polynomial function.

| Back | Next |