Tessellations

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 Generate an equilateral triangle a square a regular pentagon a regular hexagon a regular heptagon a regular octagon a regular nonagon a regular decagon a regular undecagon a regular dodecagon a parallelogram a trapezium a kite a right-angled triangle a scalene triangle an isosceles triangle a rectangle coloured select size then drag the shape you have generated onto the canvas below. Shapes which tessellate can completely cover a surface without overlapping. Which shapes tessellate? Drag the shapes to arrange them on the canvas so that they don't leave any gaps and don't overlap. Hold down the shift key or tick this while you drag to rotate the shape.

Tangram Template

Use the pieces of the tangram puzzle to fit into the outlines provided.

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Tetrominoes

Arrange the two sets of tetrominoes in the outline of a rectangle.

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Pentominoes

Arrange the twelve pentominoes in the outline of a rectangle.

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Investigations Home

A mathematical investigation is quite different to other mathematical activities. The best investigations are open ended and allow students to choose the way they work and how they record their findings. It is one of the few occasions when 'going off on a tangent' is not only acceptable but actively encouraged (within reason).

Students may ask for 'the answers' but this supposes that the activity is closed. Investigations can always be extended by varying the initial instructions or asking the question 'what if...?'. Sometimes students point out that the instructions are ambiguous and can be interpreted in different ways. This is fine and the students are encouraged to explain how they interpreted the instructions in their report.

Some students may benefit from a writing frame when producing the reports of their investigations. Teachers may suggest sections or headings such as Introduction, Interpretation, Research, Working and Conclusion or something similar.

Here are some other activities you may be interested in:

Bidmaze

Find your way through the maze encountering mathematical operations in the correct order to achieve the given total. This is an addictive challenge that begins easy but develops into quite a difficult puzzle.

Completing the Square

Practise this technique for solving quadratic equations and analysing graphs. So far this activity has been accessed 10802 times and 2224 people have earned a Transum Trophy for completing it.

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