Mathematical Investigation

Odd Dice

Take three dice. How many ways can they be turned so that they show only odd numbers on top?

Dice Dice Dice

[See also Combinations and Permutations]

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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.

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Move the pieces of the tower from one place to another in the minimum number of moves. This puzzle was invented in 1883 but is still as captivating today as it was all those years ago.

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Remainder Race

A game involving chance and choice requiring an ability to calculate the remainder when a two digit number is divided by a single digit number.

The short web address is:

Transum.org/go/?to=remainder

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Two-Step Percentages

Two-Step Percentages

An exercise in which each problem requires two percentage calculations to find the solution. So far this activity has been accessed 89 times and 4 Transum Trophies have been awarded for completing it.

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