In a village there are three streets. All the streets are straight. One lamp-post is put up at each cross-roads.

What is the greatest number of lamp-posts that could be needed?

Now try for four streets and five streets, can you see a pattern?

[See also Rod Triangles]

Investigate further.....

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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.