Virtual Manipulatives or Dynamic Web Explorations are interactive simulations of mathematical models. The user changes a variable and the model changes in numerical, graphical, and/or even symbolic form (equations). Through the use of numerical experimentation and "what if" questions, simulations offer a visual tool to help students understand even the most abstract math concept in a concrete way.

Use screencasting to capture your work or your students' work with manipulatives:
Adding Signed Numbers with
Color Chips - Addition
Geogebra Model:
Trig Function in the form
y = k + A sin (Bx + C)
From GeoGebra Tube:

Wolfram Alpha Demonstrations
Locus Definition of a Parabola

See an example of how I have used an applet (Dynamic Math Resource) in my Advanced Math Class:
It's all about asking good questions: What happens if I change the number here or make it negative? Helping students "see" the patterns and how they relate to the equations and to the graphs is a big part of making math meaningful.

Another example:
Explore the locus definition of a parabola:
Explore this version, too:
  • Move the focus point and see what happens.
  • Move the vertex and see what happens.
  • Move the point on the parabola and see what happens.
  • Move the directrix (interesting!)

For Joe, here is an exploration of the focus definition of ellipses and hyperbolas!

Extra Credit: Check out the General Form for Conic Sections and tell what happens when you change the letters.
Hint: start with

(this is the equation of a circle with center at (0,0) and radius of 2)

Textbook Connections – many textbook companies are putting computer activities in textbooks, but before these activities were related to specific software that schools may or may not be able to afford.

GeoGebra is similar to The Geometer’s Sketchpad and many of these activities can be adapted.
Tim Falberg - GeoGebra Wiki:
Geogebra tutorial:
John's Geogebra Tube:

‍Using Technology as Inquiry Tool
· Increased student motivation and engagement when every student can interact with the material
· Increased student problem-solving and "sense-making" by discovering concepts for themselves in "math lab" setting; students make conjectures and test out their ideas (much quicker on computer than through traditional pencil, compass, ruler constructions)
· No need for scissors, construction paper – quicker exploration that can be done during first fifteen minutes of class rather than take an entire class period or two through traditional means

More Dynamic Math Resources:
When searching for online dynamic simulations use the word "dynamic" in the search. Also, look for "standards-based" or NCTM because they will come with meaningful questions that will help students with "sense-making."

Note: Most applets are Java based and computers may need to update the Java in order for these to work. Check your applets on student computers to make sure they work!

GeoGebra - Download (free download)

NCTM - activities

Explore Learning - Gizmos (30 day free-trial)

National Library of Virtual Manipulatives



Another list, by topics

LONG List of math simulations (as well as other content areas) to check out:

Created by KLPost 2012