Virtual Laboratory

creative software environments

MathKit 6

dynamic mathematics software

We Offer
cooperation
What Can You Do
with the models we make
Sample Models
in new html5 format
More About MathKit
objects, tools, formats

TYPOLOGY OF OUR EDUCATIONAL MODELS

3. Construct

3.1. Compass-and-Ruler Constructions

One of the largest and most important classes of 1C:MathKit activities comprised of geometric construction problems. Any classical compass-and-ruler construction problem or a problem with a different set of drawing tools can be shaped into an interactive activity. A special feature of a dynamic construction is that it can be tested by varying its initial data both when it's finished or at any intermediate step. It may happen, for instance, that drawing a line through a previously constructed point, you hit a point that is very close, but not exactly the desired one. Such a drawing will seem to be correct, but it will fall apart as its initial objects are dragged. Data variation is also useful in experimental analysis of the number of solutions to the problem and their existence. In addition, construction activities can be supplied with automatic answer checking, as in the following model.

Reflecting a Point


Open screenshot

Download mkz-file

Start Java applet

3.2. Custom Toolbar

Another interesting feature of 1C:MathKit is the customizable toolbar. Firstly, the author can leave in the model only the tools that are actually needed in the given problem, considerably simplifying its interface. Secondly, the author can assign different sets of tools to the same problem, and this can dramatically change the idea of the solution, the required set of concepts and facts. Thus the same problem gives rise to a variety of activities. For example, a very simple problem 3.1 becomes much more interesting if we try to solve it with a straightedge alone.

Reflecting a Point by Straightedge Alone


Open screenshot

Download mkz-file

Start Java applet

3.3. Custom Tools

Custom tools are constructions carried out once to be stored and repeatedly reused later. They are available from the Toolroom menu together with the sample custom tools provided with the software; also, they can be put on the activity toolbar. For instance, the standard transformation commands in MathKit are confined to isometries and dilation; there is no tool for inversion. But such a tool can be created and is used in the model below. If you select the Inversion tool from the model’s toolbar and click successively on the center of the inversion circle, then on any point of the circle, and then on an arbitrary point X, you'll get the image Y of X under the inversion in this circle.

Inversion


Open screenshot

Download mkz-file

Start Java applet

3.4. 3D Constructions

Next is an example of a three-dimensional activity, in which students are to make a construction on a given rotating model of a solid. In fact, the same problem can be posed for an ordinary drawing and ordinary tools; not only that, the construction steps will basically be the same in both cases. What makes a great difference is the hidden rotating frame to which the solid in the drawing is attached. So in the course of construction students can choose the most convenient view of the figure which allows them to understand better the positional relationships of its elements, and, in general, to improve their spatial imagination. In a way, this kind of activities takes place between two and three dimensions.

Cutting the Cube


Open screenshot

Download mkz-file

Start Java applet

3.5. Transforming Function Graphs

Constructive activities involving function graphs do not boil down to plotting functions of one variable, i.e., graphs of equations y = f(x). It is possible to construct parametric curves, graphs of equations of the form F(x, y) = 0, tangents to curves, regions bounded by curves, etc. Much attention in the school course is given to construction of graphs by transformations, where the graph in question is obtained from a certain standard one by translations, dilations along axes, and reflections. MathKit has special tools for these transformations, and the next activity is based on these tools.

Transforming Parabolas


Open screenshot

Download mkz-file

Start Java applet

Previous page TYPOLOGY OF EDUCATIONAL MODELS Next page

© Virtual Laboratory LLC, 2009–2015 Contact us