Precalculus Online Demonstration/Exploration Tools

Page Contents:

Number and Operations
Algebra
Geometry
Measurement
Data Analysis and Probability

Number and Operations

Broad Expectation*	Topic	Link to Applet and Description	How good for teacher demos (1-3)?	How easy for students (1-3)?	How good for exploration (1-3)?	Available activities
Understand numbers, ways of representing numbers, relationships among numbers, and number systems

Understand meanings of operations and how they relate to one another

Compute fluently and make reasonable estimate

Algebra

Broad Expectation*	Topic	Link to Applet and Description	How good for teacher demos (1-3)?	How easy for students (1-3)?	How good for exploration (1-3)?	Available activities
Understand patterns, relations, and functions	Function (general)	Function Flyer - one of the best applets on the web. Allows user to input function, manipulate x, and manipulate coefficients.	3	3	3
	Quadratic Functions	Quadratic Functions - Complete Square form f(x) = a(x-h)² + k. Manipulate a, h, and k.	2	3	3
		Quadratic Functions - General form. f(x) = ax² + bx + c. Manipulate a, b, and c. Calculates discriminant and shows axis of symmetry.	2	3	3
	Exponential Functions	Exponential Functions - y = ab^x.* Manipulate a and b, sliders or points on the graph.	2	3	3
	Translating Graphs	Translating Graphs of Functions - Manipulate h and k in y = f(x-h) + k.	3	3	3
	Expanding & Reflecting Graphs	Expanding, Compressing, or Reflecting Graphs of Functions - Manipulate a and b in y = af(bx)*.	2	3	3
	Inverse Functions	Inverse Functions - Graphs function and the inverse relation (6 function types, linear, cubic, etc.).	1	2	2
	Conic Sections	Conic Section Explorer - Actually cut the cone and see that the cross section is a circle, ellipse, paraboly, or hyperbola.	3	3	3	built in
		Conic Flyer - Manipulate h, k, r, etc. in the equation and see the resulting effects on the graph. (Shodor)	3	3	3
		Circles - Manipulate r, h, and k and manipulate the center (the point). (Blond)	3	3	3
		Circle Maker - Go from the equation to the graph. Click the center (on the graph) drag out to the radius. (Blond)	2	3	3	built in
		Ellipses and Hyperbolas - Manipulate a, b, h, and k. Does not show foci. (Blond)	2	3	3

Represent and analyze mathematical situations and structures using algebraic symbols

Use mathematical models to represent and understand quantitative relationships	Solving Polynomial Equations	Real & Complex Roots of a Polynomial - You may change the 5 coefficients in teh fourth degree polynomial (or make some zero). The graph of y = f(x) is shown and all the solutions are show in the complex plane. By Daniel Heath.	2	2	3

Analyze change in various contexts

Geometry

Broad Expectation*	Topic	Link to Applet and Description	How good for teacher demos (1-3)?	How easy for students (1-3)?	How good for exploration (1-3)?	Available activities
Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships	Trigonometry	Unit Circle - Pick modes from 4 to 24 points on the circle. Manipulate points on circle - Exact or Approximate.	2	3	3	Quickie
		Sine curve visualization tool - real basic. Manipulate point on the unit circle.	3	3	3
		Circular Sine Function - Shows unit circle and graph. Real basic.	5	3	2	Quickie
		Circular Functions - Sine, Cosine, and Tangent. Shows unit circle and graph. This would not be the first one I'd use. Has the feature of "solving" for a specific function value.	2	2	3
		Six Trigonometric Functions - Unit circle and angle of rotation. Uses color. (Does not show the graph.)	2	3	3	Quickie
		Vertical Transformations of Sine and Cosecant - Manipulate (only) amplitude and vertical shift. Vertical Transformations of Sine and Cosecant - Manipulate (only) b and c in y=sin(b[x-cπ]). Transformations of Sine and Cosine - Manipulate (all) a, b, h and k in y = asin(b[x-hπ]) + k. Transformation of Sine* - Here's another. It graphs y=a sin b(x-c). Shows original and new functions.	2 2 2 3	3 3 3 3	3 3 3 3

Specify locations and describe spatial relationships using coordinate geometry and other representational systems

Apply transformations and use symmetry to analyze mathematical situations

Use visualization, spatial reasoning, and geometric modeling to solve problems	Polyhedra	Platonic Solids - Investigate the solids (cube, tetrahedron, ...). Rotate the shape. Shift-click the edges, vertices, and the faces to color (and count them). V - E + F = ? Platonic Solid Duals - Investigate the solids and their duals.	3	2	3	Platonic Solids
	3D Points	3D Point Plotter - Enter ordered triples (x, y, z,). Very nice. Easy to manipulate.	3	3	3
	Spheres	Great Circle – Use a 3D globe to visualize and measure the shortest path between cities. Spherical geometry.	3	3	3

Measurement

Broad Expectation*	Topic	Link to Applet and Description	How good for teacher demos (1-3)?	How easy for students (1-3)?	How good for exploration (1-3)?	Available activities
Understand measurable attributes of objects and the units, systems, and processes of measurement

Apply appropriate techniques, tools, and formulas to determine measurements	Convert Units	Converting Units - Interactive. "Multiply by a form of 1" to convert.	3	3	3	built in

Data Analysis and Probability

Broad Expectation*	Topic	Link to Applet and Description	How good for teacher demos (1-3)?	How easy for students (1-3)?	How good for exploration (1-3)?	Available activities
Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them

Select and use appropriate statistical methods to analyze data

Develop and evaluate inferences and predictions that are based on data

Understand and apply basic concepts of probability

Index

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Explanation of Column Headings

(This page is organized using the five content areas in school mathematics, as articulated in the NCTM Principles and Standards, 2000.)

Broad Expectation - from NCTM Principles and Standards (2000) for each of the five NCTM Content Standards
Topic - Mathematical topic
Link to Applet and Description - A description of the applet and hyperlink to the page.
How good for teacher demonstrations (1-3)? - Is this applet good for the teacher to use in a class demonstration?

3=Excellent for class demonstrations of mathematics
2=Fair to Good for class demonstrations of mathematics
1=Not designed for class demonstrations of mathematics
How easy for students (1-3)? - How easy is the applet for students to use, without instruction?

3 = No advance instruction needed (very easy to use).
2 = Short demonstration helpful (pretty easy to use).
1 = Extensive demonstration needed (hard to use without an explanation).

How good for exploration (1-3)? - Is this applet designed for student exploration?

3=Excellent for student exploration of mathematics.
2=Fair to Good for student exploration of mathematics.
1=Not designed for student exploration of mathematics.
Available activities - Are there student activities already written to accompany this applet? If so, links are provided.

by: James R. Olsen, Western Illinois University
updated: December 14, 2011