Calculus 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	Complex numbers	Complex plane - Plot complex numbers as points in the plane (rectangular and polar coordinates given. Perform various operations on the complex number.	2	2	3
	Complex numbers	Complex maps - "f(z)" - Input is a complex number and output is a complex number. Input is shown (in the plane) and output is shown (in another plane).	3	3	3

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	Functions	Function pages from NLVM - Each of the following six pages has interactive investigations on functions. Quite comprehensive. Each link has multiple pages. Introduction to Functions Definition of a Function Domain and Range Find the Function Applications of Functions Quiz	2	3	3
	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
		Geogebra - Great program for exploring functions, algebra, calculus, and geometry.	3	3	3
Represent and analyze mathematical situations and structures using algebraic symbols

Use mathematical models to represent and understand quantitative relationships	Derivatives	Surfing Derivatives - A man is riding on the surf. f(x) as the curve of the wave . Notice the slope of the surfboard. You may trace of the slope is the derivative of f(x). Real nice!	3	3	3
		Secant Line and Tangent Line - the classic diagram (tangent is the limit of the secant), but it is manipulatable with the mouse!	3	3	2
		SecantTangent Applet - show secant lines converging on a tangent line. Very nice!	3	3	3
		Geogebra - Great program for exploring functions, algebra, calculus, and geometry.	3	3	3
		Derivative Matching Game - Match the function and it's derivative. Click here to go directly to the game. Takes a few moments to load.	3	3	3
		Tangents Applet - This applet draws the graph of a function and its derivative. Similar to surfing derivatives, but you can use any function you wish. Click-and-drag on either graph. Very nice!	3	3	3
		Derivatives Applet - This applet draws the graph of a function and its derivative (similar to the applet above).	3	3	3
		One-sided derivative - This shows that the derivative does not exist when then left and right hand derivatives are different	3	3	1
		Differentiation 1 - has a number of real nice applets for looking at graphs of functions, derivative, and second derivatives. (part of Maths Online)	3	3	3	built in
		Estimating Slope of the Tangent Line - Pick point on curve and estimate the tangent line. Can zoom in on the point. By Daniel Heath.
		The Derivative Function - Similar to "surfing derivatives." Trace the curve and see the derivative graphed. By Daniel Heath.
	Derivative and Integral	Calculus Grapher - (no formulas) can drag points of function and show the Derivative and/or Integral AMAZING ! (from PhET).	3	3	3
		Function, Derivative and Integral - (no formulas) can drag points of function and show the Derivative and/or Integral (from cut-the-knot)	3	3	3
	Riemann Sums	Riemann Sums - Use rectangles to approximate the area under the curve.	3	3	2
		Riemann Sums - Use rectangles to approximate the area under the curve. (Similar to the applet above.)	3	3	2
		RiemannSums Applet - One more, similar to those above.	3	3	3
	Limit	Piecewise Functions, Limits, and Continuity - does left-hand, right-hand, and 2-sided limit.	3	3	3
		The d - e Definition of a Limit - Step-by-step process of choosing a, L, e, and (lastly) d to see if the limit exists (and is, in fact, L). By Daniel Heath.	3	2	3
		One-Variable Continuity Applet - d - e Definition of a Limit. You may type in any formula for f(x). You need to click the button to run the applet.	1	2	2

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
	Limits-Trig	Limit of sin(x)/x - Make arc approach 0 and see what happens.	2	3	3
Specify locations and describe spatial relationships using coordinate geometry and other representational systems	Solids of Revolution	Volume of Revolution - Shows the function and the solid of revolution. You can set f(x), a, b, and the axis of rotation.	2	2	3

Apply transformations and use symmetry to analyze mathematical situations

Use visualization, spatial reasoning, and geometric modeling to solve problems	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	Surface Area & Volume	Three Dimensional Box Applet: Working With Volume - Cut (equal) corners from a rectangular piece of cardboard and fold into a box.	3	3	3	Find the maximum volume

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

Feedback Form

About

Click here for the Index for >> Online Math Games, Demonstration/Exploration Tools, and Puzzles

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