Cubix

Introduction

The Cubix is aDALESTapplication. The main goal of Cubix is to find out (in any possible way) the volume and area of a structure built from unit-sized cubes. There are three sets of problems – for beginners, for advanced and for champions. Every set has 9 tasks in ascending order of difficulty. The sets and the tasks are described in an external text file, which can be modified, thus the end users can add their own problems.

When the cubix structure is displayed on the screen, the user can rotate it with the mouse. This is important for some cubix structure, especially those which contain "gaps", "holes" or "depressions". By default the cubes in the structure are colored in yellow. The user can ask the application to recolor each block of cubes in its own color. The application keeps track of users, the solved problems by each user and the time used by users for solving the problems

Activities

- Find the volume and area of a structure:
- by counting the number of cubes
- by calculating the number of cubes

- Find various methods/strategies for calculation of volume and area; determine the conditions when a specific method can be applied
- Practice "divide-and-conquer" method – split the structure into simpler substructures, examine them individually, and aggregate the final result
- Practice "symmetry" method – split the structure same-shaped substructures, examined in details only one of them, and aggregate the final result
- Practice "cuboids" method – use formulae to calculate the volume and area a structure which is parallelepiped; try to understand the meaning of the formulae
- Practice the "look around" method for calculation of area of non-concave structures
- Create new problems for others to solve and compare your result with the result of your opponent