## Videos | English

### Card Flip Solitaire

The game ‘Card Flip Solitaire’ is described and explored. Possible strategies and considerations are subtly alluded to.

### Round and Round

A game involving six numbered cards is described and illustrated. A number of scenarios are proposed for exploration.

### Heidi’s Discovery

Through folding the sides of an acute-angled triangle, Heidi discovers some interesting properties and wonders about their generality to other triangles.

### Euclidean Algorithm

A visual analogue of the Euclidean Algorithm for determining the greatest common divisor of two whole numbers is explored.

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.

### Domino Challenge

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.

### Planes of Symmetry

Four cubes are arranged asmmetrically. By adding either one or two additional cubes, different structures can be created, some of which have vertical planes of symmetry. wo examples are shown, and extension activities are suggested.

### Geoboard Areas

A geoboard is used to create a number of irregular shapes. The area of a particular shape is then calculated by sub-dividing it into smaller shapes. A number of different sub-divisions are explored.

### Billiards

On a simplified billiards board, with a ball moving diagonally at 45 degrees, a relationship is explored between the number of rebounds the ball makes before landing in a corner pocket and the dimensions of the board.

### 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.

### Four Matches

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.

### Sprouts

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

### Density

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

### Angles

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.

### Train Tracks

The concept of parallel lines is explored through the use of train tracks.

### Pathways

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

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

### Exponential Ducks

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.

### Twin halves

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

### Traffic Lights

Different ways of stacking coloured blocks are investigated.

### 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.

### 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.

### Area of a rhombus

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

### Rectangular products

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

### 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.

### 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.

### Tile patterns

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

### 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.

### Palindromic sums

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

### 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.

### Hubcap geometry

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

### 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?

### Ninety-nine

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.

### 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.