DARTEF Hands-on Experimentation Devices

DARTEF designs and manufactures special devices for making tangible experiments at mathematics lessons. The table below shows devices that are currently available for testing in schools. If you wish to test any of these with your students – please contact us – we will send you a sample. For the best experience view table  on desktop computer, notebook or tablet.

Curriculum topic

Picture of manipulative device

Description of experiment

Teacher’ manual

Common fractions


This fully mechanical device visualizes the concept of common fraction. It explains how addition and subtraction work, why common denominator is necessary. It also explains multiplication and division of fractions. Students can manipulate device and predict its behaviour. In principle, experimentation with common fraction of any denominator is supported.

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Direct and reverse proportionality, functions and graphs

This device allows students to see and control physical representation of proportional or functional relations (only 1st quadrant of Cartesian coordinate plane) via controlling the intensity of the light bulb. Requires 5V (can be supplied via USB).

Functions and graphs

This device allows student to see and control physical representation of any real-valued function (all quadrants of Cartesian coordinate plane are supported) via controlling speed and direction of and air-flow. Requires 5V (can be supplied over USB).

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Linear slope (slope of linear function)

This fully mechanical device allow students to see physical representation of linear slope in action. Common misconception related to confusion of slope and intercept is addressed in this device. Both positive and negative slopes can be shown. The device supports parallel work with pen-and-paper.

Negative numbers (prototype)

This fully mechanical device explains basic characteristics of negative numbers via positive and negative weights. All basic operations (addition, subtraction, multiplication and division) are supported. The device demonstrates very well one of fundamental characteristics, that is “minus by minus gives plus”.

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Percentages

This fully mechanical device visualizes the concept of percentage. It allows to experiment with quantities and percentages, find percentage of a number and also find the number by given percentage.

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Proportional relations

This fully mechanical device allow students to construct deep knowledge about direct and reverse proportionality. The device facilitates acquisition of formal features of direct and reverse proportionalities (y/x or y*x=const).

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Trigonometry of acute angle

This fully mechanical device allows students to control main trigonometric ratios (sin, cos, tan) in tangible way. Device facilitates deep understanding of trigonometric ratios and explains its fundamental characteristics (e.g. why sin is decreasing while cos is increasing, etc.

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