Virtual and dynamic objects

Virtual manipulatives and applets are interactive, visual representations of dynamic objects that present opportunities for constructing mathematical knowledge, and help the students to have solid understanding of mathematical concepts. They can usually be manipulated with widgets in a GUI (Graphical User Interface), such as a slider, a checkbox or a button, and help to develop students’ visualization skills by connecting words, pictures and symbols simultaneously. With these tools, it is possible to simplify the tasks which can be difficult or impossible to do with the traditional educational tools. Virtual and dynamic objects can also be used to present pictorial proofs, puzzles, animations, simulations, and to generate unlimited questions.

You can find some examples below:

Factor trees

Sum of exterior angels of a polygon

Simplifying square roots


Perpendicular bisector of a line segment

System of two linear equations

Multiplication of fractions

Comparing values of fractions


First 5000 prime numbers

Finding your birthday in Pi number

Collatz Conjecture

Chaos Game

Minimum Spanning Tree

K-Means Clustering

Stem and leaf plot

Galton Board