Visual Technology for the Autonomous Learning of Mathematics
Downloadable Videos
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Title |
Description |
Screenshot |
English |
German |
isiXhosa |
| The Möbius Band | The Möbius Band, a curious one-sided surface, is explored. |  |
The Möbius Band - English - mp4 | The Möbius Band - Deutsch - mp4 | |
| Exponential Ducks | An exponential sequence (1 ; 2 ; 4 ; 8 ; ...) is generated and investigated through the process of doubling. |  |
Exponential Ducks - English - mp4 | | |
| Thale's Theorem Part 1 | When a semicircle is drawn such that its diameter is the hypotenuse of a right-angled triangle, the semicircle passes through all three vertices of the triangle. |  |
Thales' Theorem Part 1 - English - mp4 | Thales' Theorem Part 1 - Deutsch - mp4 | |
| Twin halves | Different ways of splitting a square array of blocks into two identical sections are explored. |  |
Twin halves - English - mp4 | Twin Halves - Deutsch - mp4 | |
| Traffic Lights | Different ways of stacking coloured blocks are investigated. |  |
Traffic Lights - English - mp4 | Traffic Lights - Deutsch - mp4 | |
| Equal Areas | Six different shapes are investigated in terms of their areas. The video clip concludes by showing why all six shapes have the same area. |  |
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| Matchstick Squares | A matchstick pattern based on a linear sequence is investigated. Different deconstructions of the pattern lead to different but algebraically equivalent expressions for the general term. |  |
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| Difference of two squares | A visual explanation is explored for the observation that 2²-1²=2+1; 3²-2²=3+2 etc. |  |
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| Sum of odd numbers | A visual explanation is explored for the observation that 1 + 3 + 5 + 7 + … for n terms equals n². |  |
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| Area of a trapezium | The formula for the area of a trapezium is explored through a series of different visualisations. |  |
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| A third minus a fifth | A visual approach is used for the subtraction of a smaller fraction from a larger one. The example used is a third minus a fifth. |  |
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| A third plus a quarter | A visual approach is used to support the conceptual understanding of the addition of two fractions. The example used is a third plus a quarter. |  |
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| Area of a rhombus | Two alternative formulae for determining the area of a rhombus are investigated. |  |
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| Angles of a polygon | The movement of a paperclip on the sides of a triangle points the way to the generation of a formula for the sum of the interior angles of a polygon. |  |
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| Rectangular products | This video clip makes use of geometric algebra to give elegant visual support for the distributive law. |  |
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| Visible faces | The general formula 4x+1 is modelled in terms of the number of faces visible when cubes are stacked on top of one another. |  |
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| The Theorem of Pythagoras #2 | A proposal is made for a visual proof of the Theorem of Pythagoras. The question is raised as to whether or not this constitutes a general proof. |  |
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| What's in the box? #2 | This video clip models the solving of simultaneous equations through a process of logical reasoning without the introduction of algebra. |  |
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| Interior angles of a triangle | This video clip investigates the sum of the interior angles of a triangle. A visually striking approach is used to show that these angles add up to 180 degrees. |  |
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| What's in the box? #3 | Building on from previous "What's in the box?" clips, variables are now introduced to represent unknown quantities. |  |
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| Tile patterns | This video clip explores the patterns and symmetry elements produced through tiling. |  |
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| The Theorem of Pythagoras #3 | Another striking visual approach is used to demonstrate the Theorem of Pythagoras. |  |
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| A quarter plus a third | A model of a rectangle is used to visualise the sum of two fractions, a quarter and a third. |  |
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| The Theorem of Pythagoras | A proposal is made for a visual proof of the Theorem of Pythagoras. The question is raised as to whether or not this constitutes a general proof. |  |
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| Discovering right-angled triangles | Squares are used to form the edges of triangles in order to discover Pythagorean triples. |  |
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| Palindromic sums | Visual aspects of palindromic sums such as 1+2+3+4+3+2+1 are investigated. |  |
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| Sums of cubes | This video clip illustrates the result that the sum of the first n cubes is the square of the nth triangular number. |  |
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| Viviani's Theorem | Visually illustrates that for a point inside an equilateral triangle, the sum of the perpendiculars from that point to the sides of the triangle equals the altitude of the triangle. |  |
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| What's in the box? | Matches and different coloured matchboxes are used to model the concept of variable. |  |
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| Hubcap geometry | Hubcaps are investigated in terms of their rotational and reflectional symmetry. |  |
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| Hidden faces | This video clip explores the number of faces which are hidden from view when cubes are stacked on top of each other. |  |
Hidden Faces - Deutsch - mp4 | ||
| Interior angles of a triangle #2 | A visually appealing approach is used to show that the interior angles of a triangle add up to 180 degrees. |  |
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| Sum of two squares | The following question is investigated: Is it possible to construct a third square whose area is the sum of two given squares? |  |
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| Ninety-nine |
The film suggests the following conjecture: If you take a two-digit number and subtract its reverse, and then take the answer and add its reverse, then the result is always 99 e.g. 42-24=18, 18+81=99 |
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| Winning with chance #1 | The film demonstrates a simple game based on the statistics of chance. The video clip makes use of specific activity sheets. |  |
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| Winning with chance #2 | The film suggests an extension to the video clip “Winning with chance #1”. |  |
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| Pythagorean triples | This video clip explores Pythagorean triples. |  |
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| Train Maths #1 | This video clip explores the drawing of scale diagrams through the use of model railway tracks. The clip is only available in German, and refers to specific activity sheets. |  |
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| Train Maths #2 | This video clip makes use of model railway tracks to explore basic algebra. The clip is only available in German, and refers to specific activity sheets. |  |
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| Train Maths #3 | This video clip is an extension of “Train Maths #2” and again explores simple algebra. The clip is only available in German, and refers to specific activity sheets. |  |
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| Train Maths #4 | This video clip is an extension of “Train Maths #3” and explores simple algebraic operations. The clip is only available in German, and refers to specific activity sheets. |  |
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