5. Families and Functions (A3)
High School
- A3.2 Exponential and Logarithmic Functions
- Exponentials/Logarithms
Students can experiment with exponential or logarithmic graphs and compare them to each other. A lesson plan is provided for each activity. - Function Evaluator and GrapherUse 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."
- Jurassic Oil: Fuel BlendingStudents will convert statements to the language of mathematics by determining the optimal blend of gasoline that minimizes cost. The website is not interactive but contains worksheets, teacher notes and case studies.
- 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. - Shedding Light on the Subject: Function Models of Light DecayPresented 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.
- The Million $ Mission
Students can read story problems about exponential growth and calculate related values. Tables are also provided. - 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.
- Exponentials/Logarithms
- A3.6 Rational Functions
- Function FlyerThis 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.
- Using Rational Functions to Investigate the Behavior of Northwestern Crows
In this investigation students will explore possible reasons behind the observation that northwestern crows consistently drop a type of mollusk called a whelk from a height of 5 meters. - Variance and Covariance
This lesson uses Geometer's SketchPad notebooks and Microsoft Excel to explore variance and covariance. This lesson is intended for students 9-12 who are studying statistics.
- A3.7 Trigonometric Functions
- Basic Trigonometry NewThis site covers the basics of trigonometry, including the functions, special angles, and inverses. Many of the examples even give a video explanation of how to use the trig functions.
- Trigonometric functions and identities NewThis site gives definitions, values, and explains how to use the trig functions. It also provides an on-line quiz for the students to complete, or it can be printed as a worksheet. It covers functions, identities, and word problems.
- Volcano's Deadly WarningThis lesson integrates science and mathematics for the upper high school student. The math concepts are centered around sine waves and complex waves as they relate to the seismic signals from volcanoes.