Learning Mathematical Modeling
Using Graphs and Matrices enables students to model realworld situations in order to understand the world around them. Matrices provide a powerful mathematical tool to help model situations such as airline or car routes, cooperation and competition, traffic patterns, and population problems. Most real situations are complex. Mathematical Modeling helps students learn the uses and limitations of modeling. Mathematical Modeling provides that opportunity.
Make connections
Using graphs and matrices together, students use this educational software to interpret situations both visually and numerically. Many students have had some exposure to maps and distance tables. Now, with Mathematical Modeling, they can interpret and manipulate the data to better understand the connection between the visual and numerical representations.

Users can make connections on a picture like this one representing airline routes on a world map, while the program builds a matrix interpreting those connections.

Multiple views of the same problem
This educational software allows students to manipulate the data in the models to see how changes can affect the entire system. Students can also explore mathematical concepts such as connectivity, central position, and diameter of graphs. These can be studied from a purely mathematical viewpoint or through practical applications like trip routing or city planning.

Students can easily change variables to see the effect on the problem; multiple representations give students insight into their relationships and significance.

Reproducible worksheets
Over 15 scenarios are included in this software and are correlated to reproducible Student Worksheets in the Teacher’s Guide. The software is openended so students can create and study their own unique scenarios. Pictures can be imported to assist in graph creation and to add realism.
Using Mathematical Modeling, students can create a graph and watch as the matrix is automatically built on the screen. Students can also begin with a matrix and observe the associated graph, which is created by the program. This interaction helps students see the association between the visual and numeric representations of a given scenario.

The CDROM contains over 15 realworld problems correlated to the lessons and reproducible student worksheets in the Teacher’s Guide.

The creators of Mathematical Modeling
Mathematical Modeling was designed by the Freudenthal Institute, Utrecht, The Netherlands.
