Videos | German

The total number of different pathways that a marble can move through a square array is explored. Extension activities are suggested.

A game of probability involving balls and cubes of two different colours is described. A winning strategy is sought, and an extension exercise is proposed.

The two-player strategy game "Domino Challenge" is introduced. A conjecture is made regarding a winning strategy.

Hexagon Dissections

A regular hexagon is dissected by cutting along a number of its diagonals. The resulting pieces are used to create different combinations of polygons. Extension activities are suggested.

Exploring Hexagons

Two students discuss and explore the following investigation: "Dissect a regular hexagon by cutting along some of the diagonals and investigate what polygons can be formed from the resulting pieces."

Domino Challenge Revisited

The two-player strategy game "Domino Challenge" is revisited. A winning strategy for the player who plays second is hinted at.

Geoboard Rectangles

A geoboard is used to explore "hollow rectangles" - i.e. rectangles containing no inner nails. A formula based on the number of border nails is proposed to calculate the area of such rectangles.

Reflecting on Pick's Theorem

Pick's theorem is used to calculate the area of polygons on a geoboard. An explanation is proposed for how Pick's theorem can be used to prove that all rectangles created on a geoboard have whole number areas.

Transforming Primitive Triangles

The notion of a "primitive triangle" on a geoboard is introduced. An interesting transformation is proposed that suggests that all primitive triangles have an area of half a unit square.

Shapes are built from four matches, the matches being oriented end-to-end either vertically or horizontally. A question is posed regarding the number of "different" shapes that can be made in this way.

The game of "Sprouts" is introduced. The rules of the game are demonstrated and a conjecture is proposed with respect to the starting conditions.

The density of a stone is determined by investigating its mass in relation to the volume of water it displaces.

Acute, right and obtuse angles are introduced. Different combinations of acute angles are explored in terms of forming right angles, acute angles and obtuse angles.

Pathways are created by placing four matchsticks end to end on a grid. An investigation is proposed regarding the endpoints of all possible pathways based on given conditions.

The Möbius Band, a curious one-sided surface, is explored.

An exponential sequence (1 ; 2 ; 4 ; 8 ; ...) is generated and investigated through the process of doubling.

Thales' 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.

Different ways of splitting a square array of blocks into two identical sections are explored.

Different ways of stacking coloured blocks are investigated.

Six different shapes are investigated in terms of their areas. The video clip concludes by showing why all six shapes have the same area.

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.

Difference of two squares

A visual explanation is explored for the observation that 2²-1²=2+1; 3²-2²=3+2 etc.

Sum of odd numbers

A visual explanation is explored for the observation that 1 + 3 + 5 + 7 + … for n terms equals n².

Area of a trapezium

The formula for the area of a trapezium is explored through a series of different visualisations.

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.

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.

Two alternative formulae for determining the area of a rhombus are investigated.

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.

Rectangular products

This video clip makes use of geometric algebra to give elegant visual support for the distributive law.

The general formula 4x+1 is modelled in terms of the number of faces visible when cubes are stacked on top of one another.

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.

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.

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.

What's in the box? #3

Building on from previous "What's in the box?" clips, variables are now introduced to represent unknown quantities.

This video clip explores the patterns and symmetry elements produced through tiling.

The Theorem of Pythagoras #3

Another striking visual approach is used to demonstrate the Theorem of Pythagoras.

A quarter plus a third

A model of a rectangle is used to visualise the sum of two fractions, a quarter and a third.

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.

Discovering right-angled triangles

Squares are used to form the edges of triangles in order to discover Pythagorean triples.

Visual aspects of palindromic sums such as 1+2+3+4+3+2+1 are investigated.

This video clip illustrates the result that the sum of the first n cubes is the square of the nth triangular number.

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.

What's in the box?

Matches and different coloured matchboxes are used to model the concept of variable.

Hubcaps are investigated in terms of their rotational and reflectional symmetry.

This video clip explores the number of faces which are hidden from view when cubes are stacked on top of each other.

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.

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?

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.

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.

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.

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.

Winning with chance #2

The film suggests an extension to the video clip “Winning with chance #1”.

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.

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. VITALmaths

The VITALmaths and VITALmathsLIC site consists of a databank of short and funky video clips that specifically interrogate the conceptual aspects of a mathematical idea, process or concept. Some of the video clips contain strategic dialogues to encourage appropriate mathematical talk and conversation.

You are here SANDBOXmaths

SANDBOXmaths is a collection of more experimental video clips done by students in their mathematics teacher-training classes and researchers wishing to use specific video clips in their teaching and research. APPLETmaths

The APPLETmaths site consists of a selection of GeoGebra applets that were developed by students and researchers for their research projects.