This is a general collection of math resources. It is a large collection, but you can use the fliters on the left side of the screen to filter down to the specific education level you are looking for. (You are encouraged to filter by education level, not grade.)
A web page and interactive applet showing the definition and properties of …
A web page and interactive applet showing the definition and properties of a trapezoid. The applet shows a trapezoid where the user can drag any vertex. The other points then move in such a way that the figure remains a trapezoid at all times. A control to hide the details allows a classroom discussion where students can try to infer what the properties are as it is reshaped by the discussion leader. Text on the page has the formal definition and properties of the trapezoid with links to related pages. A companion page is http://www.mathopenref.com/trapezoidarea.html showing the ways to calculate the area of a trapezoid 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 show the definition and …
An interactive applet and associated web page that show the definition and properties of a trapezoid in coordinate geometry. The applet has a trapezoid with draggable vertices. As the user re-sizes the trapezoid the applet continuously recalculates its altitude and median from the vertex coordinates. The trapezoid can be rotated on the plane to show the more complex cases. The grid, coordinates and calculations can be turned on and off for class problem solving. The applet can be printed in the state it appears on the screen to make handouts. The web page has a full definition of a trapezoid when the coordinates of the points defining it are known, 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 showing how to find the …
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 …
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 lesson applies the science and math of the rotation of a …
This lesson applies the science and math of the rotation of a sphere to water and wind movements on Earth. Students are introduced to convection, the Trade Winds and the Coriolis Force. Using an online visualizer, students generate trajectories and then analyze course patterns and latitudinal changes in strength. Note that this is lesson two of five on the Ocean Motion website. Each lesson investigates ocean surface circulation using satellite and model data and can be done independently. See Related URL's for links to the Ocean Motion Website that provide science background information, data resources, teacher material, student guides and a lesson matrix.
An interactive applet and associated web page that introduce the concept of …
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 …
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.
This task gives students a chance to explore several issues relating to …
This task gives students a chance to explore several issues relating to rigid motions of the plane and triangle congruence. As an instructional task, it can help students build up their understanding of the relationship between rigid motions and congruence.
A web page and interactive applet demonstrating the concept of the incenter …
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.
The purpose of this task is to emphasize the adjective "geometric" in …
The purpose of this task is to emphasize the adjective "geometric" in the "geometric" series, namely, that the algebraic notion of a common ratio between terms corresponds to the geometric notion of a repeated similarity transformation.
A web page and interactive applet demonstrating the concept of the centroid …
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 …
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 …
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 …
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 …
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 …
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) …
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.
Students learn about the fundamental strength of different shapes, illustrating why structural …
Students learn about the fundamental strength of different shapes, illustrating why structural engineers continue to use the triangle as the structural shape of choice. Examples from everyday life are introduced to show how this shape is consistently used for structural strength. Along with its associated activity, this lesson empowers students to explore the strength of trusses made with different triangular elements to evaluate the various structural properties.
An interactive applet and associated web page that demonstrate that in similar …
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.
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