1. Patterns
2. Variability and Change

Additional Links to General Mathematics Sites

• Mathematics Games and Student Activities
• Mathematics Lessons Plans
• Interactive Learning and Problem Solving Activities
• Word Searches and Puzzles in Mathematics
• Miscellaneous Sites

High School

1. Benchmark 1. "Identify and describe the nature of change and begin to use the more formal language such as rate of change, continuity, limit, distribution and deviation."
   1. Bottles and Divers - Variability and Change (I.2.HS.1)
      This site is a good resource for teachers to help lay down the foundation for calculus by connecting the concept of slope to rates of change. This site contains a couple of different problems: Graphically Speaking (Bottles), The Bungee Jumper, The Diver Problem, and The Fish Population. The activities require a prior understanding of how to find a slope, and scatter plot calculator skills would be helpful. One problem includes a calculation involving a trigonometric function. These activities could be done by precalculus students or as a good review for calculus students.
   2. Finite Mathematics - Variability and Change (I.2.HS.1,2,3,4,5&6)
      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.
   3. Pascal's Triangle - Variability and Change (I.2.HS.1,2,3&6)
      Outstanding - This site gives Standards, Lessons, and Links for students in K-4, 5-8, and 9-12 and references for Pascal's Triangle. It emphasizes the concept of patterns and this site is for all grade levels. If you have geometer sketchpad there are some interactive activities to do.
   4. The Normal Distribution - Variability and Change (I.2.HS.1)
      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.
2. Benchmark 2. "Develop a mathematical concept of function and recognize that functions display characteristic patterns of change (e.g., linear, quadratic, exponential).
   1. Exploring Linear Functions: Representational Relationships - Variability and Change  (I.2.HS.2)
      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.
   2. Exponentials/Logarithms - Variability and Change (I.2.HS.2)
      Students can experiment with exponential or logarithmic graphs and compare them to each other. A lesson plan is provided for each activity.
   3. Finite Mathematics - Variability and Change (I.2.HS.1,2,3,4,5&6)
      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.

      Function Evaluator and Grapher - Variability and Change (I.2.HS.2,3,4&5)

      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."

      Loan Calculator - Variability and Change (I.2.HS.2&6)

      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.

      Pascal's Triangle - Variability and Change (I.2.HS.1,2,3&6)
      Outstanding - This site gives Standards, Lessons, and Links for students in K-4, 5-8, and 9-12 and references for Pascal's Triangle. It emphasizes the concept of patterns and this site is for all grade levels. If you have geometer sketchpad there are some interactive activities to do.

      Savings Calculator - Variability and Change (I.2.HS.2&6)

      Students can use the savings calculator and see how changing the amount deposited, frequency of deposits, interest rate, time, and method of compounding interest affects their total.
3. Benchmark 3. "Expand their understanding of function to include non-linear functions, composition of functions, inverses of functions, and piecewise- and recursively-defined functions."
   1. Finite Mathematics - Variability and Change (I.2.HS.1,2,3,4,5&6)
      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.
   2. Function Evaluator and Grapher - Variability and Change (I.2.HS.2,3,4&5)
      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."
   3. Function Notation; f(x) - Variability and Change (I.2.HS.3&4)
      This site allows students to work problems in the f(x) notation step by step.
   4. Pascal's Triangle - Variability and Change (I.2.HS.1,2,3&6)
      Outstanding - This site gives Standards, Lessons, and Links for students in K-4, 5-8, and 9-12 and references for Pascal's Triangle. It emphasizes the concept of patterns and this site is for all grade levels. If you have geometer sketchpad there are some interactive activities to do.
   5. SOSMath - Variability and Change (I.2.HS.3)
      Informational site consisting of the inverse and composition of functions.
   6. Vertical Line Test - Variability and Change (I.2.HS.3)
      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.
4. Benchmark 4. "Represent functions using symbolism such as matrices, vectors and functional representation (f(x))."
   1. Finite Mathematics - Variability and Change (I.2.HS.1,2,3,4,5&6)
      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.
   2. Function Evaluator and Grapher - Variability and Change (I.2.HS.2,3,4&5)
      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."
   3. Function Notation; f(x) - Variability and Change (I.2.HS.3&4)
      This site allows students to work problems in the f(x) notation step by step.
   4. Maths Online Gallery: Functions 2 - Variability and Change (I.2.HS.4,5&6)
      Students match graphs to the functions they represent using and interactive applet. Types of functions include power, rational and trigonometric.
5. Benchmark 5. "Differentiate and analyze classes of functions including linear, power, quadratic, exponential, circular and trigonometric functions, and realize that many different situations can be modeled by a particular type of function."
   1. Direct and Partial Variations - Variability and Change (I.2.HS.5)
      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.
   2. Function Evaluator and Grapher - Variability and Change (I.2.HS.2,3,4&5)
      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."
   3. Finite Mathematics - Variability and Change (I.2.HS.1,2,3,4,5&6)
      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.
   4. Maths Online Gallery: Functions 2 - Variability and Change (I.2.HS.4,5&6)
      Students match graphs to the functions they represent using and interactive applet. Types of functions include power, rational and trigonometric.
6. Benchmark 6 . "Increase their use of functions and mathematical models to solve problems in context."
   1. Finite Mathematics - Variability and Change (I.2.HS.1,2,3,4,5&6)
      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.
   2. Function Evaluator and Grapher - Variability and Change (I.2.HS.2,3,4&5)
      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."
   3. Loan Calculator - Variability and Change (I.2.HS.2&6)
      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.
   4. Pascal's Triangle - Variability and Change (I.2.HS.1,2,3&6)
      Outstanding - This site gives Standards, Lessons, and Links for students in K-4, 5-8, and 9-12 and references for Pascal's Triangle. It emphasizes the concept of patterns and this site is for all grade levels. If you have geometer sketchpad there are some interactive activities to do.
   5. Real World Situations with Functions - Variability and Change (I.2.HS.6)
      This site is from NASA and provides 6 different real world activities.
   6. Savings Calculator - Variability and Change (I.2.HS.2&6)
      Students can use the savings calculator and see how changing the amount deposited, frequency of deposits, interest rate, time, and method of compounding interest affects their total.
   7. Maths Online Gallery: Functions 2 - Variability and Change (I.2.HS.4,5&6)
      Students match graphs to the functions they represent using and interactive applet. Types of functions include power, rational and trigonometric.