# House painting

The houses in Mathsland are all 3 storeys tall. Each storey is painted using one colour.

How many ways can the houses be painted if you have:

2 colours; 3 colours; 4 colours.......

[See also Cube Construction and Combinations and Permutations]

Investigate further.....

Investigations Home

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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.

## Here are some other activities you may be interested in:

#### Four Colour Theorem

This mathematical activity involves colouring in! That makes a change. Using the paint bucket tool can you flood fill the regions so that no two adjacent regions are the same colour?

#### Circle Equations

Recognise and use the equation of a circle with centre at the origin and the equation of a tangent to a circle. So far this activity has been accessed 56 times and it is ready for you to enjoy!

For Students:

For All:

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