An interactive applet and associated web page showing how to find the area and perimeter of a trapezoid from the coordinates of its vertices. The trapezoid can be either parallel to the axes or rotated. The grid and coordinates can be turned on and off. The area and perimeter calculation can be turned off to permit class exercises and then turned back on the verify the answers. The applet can be printed as it appears on the screen to make handouts. The web page has a full description of the method for determining area and perimeter, a worked example and has links to other pages relating to coordinate geometry. Applet can be enlarged to full screen size for use with a classroom projector. This resource is a component of the Math Open Reference Interactive Geometry textbook project at http://www.mathopenref.com.

An interactive applet and associated web page that demonstrate the median line of a trapezoid (line linking midpoints of non-parallel sides). The applet shows a trapezoid with all vertices draggable. As you drag any vertex, the figure changes to remain trapezoid, and the median line id continually repositioned to remain correct. It can be seen visually that the median remains parallel to the bases and a formula shows that its length is the average of the bases. Applet can be enlarged to full screen size for use with a classroom projector. This resource is a component of the Math Open Reference Interactive Geometry textbook project at http://www.mathopenref.com.

This simulation is designed to provide students with a first hand, personal experience of the treaty making process. The insight they gain from this simulation will assist them in their understanding of treaty and its impact on the lives of First Nation peoples. This simulation is targeted at middle years to senior students.

An interactive applet and associated web page that introduce the concept of a triangle. The applet shows a triangle where the user can drag the vertices to reshape it. As it is being dragged a base and altitude are shown continuously changing. Demonstrates that the altitude may require the base to be extended. The text on the page lists the properties of a triangle and lists the various triangle types, with links to a definition of each. Applet can be enlarged to full screen size for use with a classroom projector. This resource is a component of the Math Open Reference Interactive Geometry textbook project at http://www.mathopenref.com.

The applet shows a triangle which the user can resize by dragging any of its vertices. It shows the three perpendicular bisectors of the sides and the point where they intersect - the circumcenter. These track the changes in the triangle in real time. It shows that the circumcenter may lie outside the triangle. The associated web page describes the properties of the circumcenter and points out that it the center of the triangle's circumcircle. Applet can be enlarged to full screen size for use with a classroom projector. This resource is a component of the Math Open Reference Interactive Geometry textbook project at http://www.mathopenref.com.

A web page and interactive applet demonstrating the concept of the incenter of a triangle. The applet shows a triangle where the user can drag the vertices around. The incenter and the angle bisector lines that generate it are continuously moved as the user drags the vertices. By experimentation the user can observe that the incenter always remains inside the triangle. The page text explains the definition of the incenter and how to find it. It describes how the incenter is also the center of the incircle of the triangle with a link to that page http://www.mathopenref.com/triangleincenter.html Applet can be enlarged to full screen size for use with a classroom projector. This resource is a component of the Math Open Reference Interactive Geometry textbook project at http://www.mathopenref.com.

A web page and interactive applet demonstrating the concept of the centroid of a triangle. The applet shows a triangle where the user can drag the vertices around. The centroid and the median lines that generate it are continuously moved as the user drags the vertices. By experimentation the user can observe that the centroid always remains inside the triangle. The page text explains the definition of the centroid and how to find it. It also shows that the centroid is the center of gravity of the triangle. Applet can be enlarged to full screen size for use with a classroom projector. This resource is a component of the Math Open Reference Interactive Geometry textbook project at http://www.mathopenref.com.

An interactive applet and associated web page that demonstrate the properties of the circumcircle of a triangle. The applet shows a triangle where the user can drag the vertices to reshape it. The circumcircle (the circle that passes through all vertices) is continuously updated as the triangle is resized. The center of the circle (circumcenter) is shown along with the three side bisectors that define it. Applet can be enlarged to full screen size for use with a classroom projector. This resource is a component of the Math Open Reference Interactive Geometry textbook project at http://www.mathopenref.com.

An interactive applet and associated web page that demonstrate the exterior angles of a triangle. The applet shows a triangle where the user can drag any vertex to reshape it. The exterior angles are shown and a running calculation shows that no matter how you change the triangle, the exterior angles always add up to 360 degrees An exterior angle is equal to the sum of the opposite interior angles Applet can be enlarged to full screen size for use with a classroom projector. This resource is a component of the Math Open Reference Interactive Geometry textbook project at http://www.mathopenref.com.

A web page and interactive applet demonstrating the concept of the incircle of a triangle - the largest circle the will fit inside a triangle. The applet shows a triangle where the user can drag the vertices around. The incircle is continuously adjusted as the user drags the vertices. By experimentation the user can observe that the three sides of the triangle are always tangents to the incircle. The page text explains the definition of the incircle and how to draw it. It describes how the incenter is the center of the incircle of the triangle with a link to that page http://www.mathopenref.com/triangleincircle.html Applet can be enlarged to full screen size for use with a classroom projector. This resource is a component of the Math Open Reference Interactive Geometry textbook project at http://www.mathopenref.com.

An interactive applet and associated web page that demonstrate the concept of triangle inequality. The applet shows a triangle where the vertices can be dragged to reshape the triangle It shows that no matter what you do, the longest side is always shorter than the sum of the other two. Applet can be enlarged to full screen size for use with a classroom projector. This resource is a component of the Math Open Reference Interactive Geometry textbook project at http://www.mathopenref.com.

An interactive applet and associated web page that demonstrate the properties of the interior angles of a triangle. The applet shows a triangle where the user can drag the vertices to reshape it. As it is being changed, the angles are continually updated, along with an expression showing that they always add to 180 degrees Applet can be enlarged to full screen size for use with a classroom projector. This resource is a component of the Math Open Reference Interactive Geometry textbook project at http://www.mathopenref.com.

An interactive applet and associated web page that demonstrates the midsegment (midline) of a triangle. A triangle is shown that the user can reshape by dragging any vertex. As it is being dragged, the midline changes accordingly. From this can be seen that the midsegment is always parallel to the base and half it's length. Applet can be enlarged to full screen size for use with a classroom projector. This resource is a component of the Math Open Reference Interactive Geometry textbook project at http://www.mathopenref.com.

An interactive applet and associated web page that demonstrate that in similar triangles, the ratio of their areas is the square of the ratio of the sides. As you drag one triangle to resize it, it remains similar to another and the ratios of sides and areas is calculated as you drag. One can be seen to be the square of the other at all times. A slight 'snap-to' effect allows easy selection of integer ratios (2:4 etc). Applet can be enlarged to full screen size for use with a classroom projector. This resource is a component of the Math Open Reference interactive geometry reference book project at http://www.mathopenref.com.

An interactive applet and associated web page that demonstrate that in similar triangles, ten items are always in the same ratio to each other (perimeter, three sides, three altitudes, three medians). As you drag one triangle to resize it, it remains similar to another and the ratios of sides and medians is calculated as you drag. They can be seen to be the same at all times. Applet can be enlarged to full screen size for use with a classroom projector. This resource is a component of the Math Open Reference Interactive Geometry textbook project at http://www.mathopenref.com.

An interactive applet and associated web page that illustrate the triangles that can be drawn inside a polygon. The applet has a pentagon with the triangles drawn. The user can change the number of sides, and switch between regular / irregular. The vertices are draggable. The text on the page discusses the uses of these triangles. Applet can be enlarged to full screen size for use with a classroom projector. This resource is a component of the Math Open Reference Interactive Geometry textbook project at http://www.mathopenref.com.

Courtesy of Comox Valley Schools (SD71) in B.C., an archived site with a series of excellent kits for middle-grade Core French units that carefully structure and encourage oral communication:

Ma vie... c'est moi! (My Life... It's Me!)
La nourriture (Food)
Les vêtements (Clothing)
Les activités (Activities)

The units target participation, starting with whole-class activities and moving through rotating stations, each with visual support and follow-up activities.

A web page and interactive applet illustrating the properties of an undecagon (11 sided polygon). The applet shows an undecagon where the user can drag any vertex to reshape it. User can see that the interior and exterior angles are constant in a regular undecagon, but vary in an irregular version. Controls allow the display or hiding of the diagonals, and triangles within the undecagon. The web page lists the properties of the undecagon including interior angles, exterior angles, sum of exterior angles, area, number of diagonals and number of internal triangles. Links to pages with generalized properties of all polygons. Applet can be enlarged to full screen size for use with a classroom projector. This resource is a component of the Math Open Reference Interactive Geometry textbook project at http://www.mathopenref.com.

Here is a group of Java programs which were designed to help undergraduate engineering students. These programs cover the basics of aerodynamics and propulsion. The icon at the top of each section will take you to a web page which contains a simulator or calculator for an aerodynamics problem. The web page assumes that you understand the problem and contains only the applet and a couple of hyperlinks to additional pages which describe the science and math behind each problem and some additional instructions on the program operation. The linked pages will take a little longer to load into your browser. If you follow the instructions given below, you can download a copy of each program to your computer and you can then run the programs off-line.

A simulation to help understand the difference between a physical and chemical change.