Virtual+Manipulatives

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: @http://nlvm.usu.edu/en/nav/topic_t_1.html || **Geogebra Model:** From GeoGebra Tube: @http://www.geogebratube.org/student/m5477 ||
 * **NLVM**
 * Adding Signed Numbers with**
 * Color Chips - Addition**
 * Trig Function in the form**
 * y = k + A sin (Bx + C)**
 * media type="custom" key="13508478" || media type="custom" key="13508480" ||

@http://demonstrations.wolfram.com/LocusOfPointsDefinitionOfAnEllipseHyperbolaParabolaAndOvalOf/ ||  ||
 * **Wolfram Alpha Demonstrations**
 * Locus Definition of a Parabola**
 * media type="custom" key="13508486" ||  ||

See an **//example//** of how I have used an applet (Dynamic Math Resource) in my Advanced Math Class: http://the-wiki-post.wikispaces.com/Trig+Curves 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.

Tim Falberg - GeoGebra Wiki: http://geogebrawiki.wikispaces.com/ Geogebra tutorial: [] John's Geogebra Tube: []
 * GeoGebra** is similar to The Geometer’s Sketchpad and many of these activities can be adapted.

· 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
 * ‍Using Technology as Inquiry Tool**

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."
 * More Dynamic Math Resources:**

//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) @http://www.geogebra.org/cms/
 * Resources:**

NCTM - activities @http://illuminations.nctm.org/

Explore Learning - Gizmos (30 day free-trial) []

National Library of Virtual Manipulatives @http://nlvm.usu.edu/en/nav/vlibrary.html

InterActivate @http://www.shodor.org/interactivate/activities/

Wolfram @http://demonstrations.wolfram.com/index.html

Another list, by topics @http://jc-schools.net/dynamic/math/mathresources.htm

LONG List of math simulations (as well as other content areas) to check out: @http://www.techtrekers.com/sim.htm

Created by KLPost 2012