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## 'Street Sequences' printed from http://nrich.maths.org/

Let's look at a street!

Most of the streets around here have their numbers going in order from one side of the street to the other - so that odds end up on one side and evens on the other.

So here's what is could be like:

Looking from above the numbers could appear as:

Well you can imagine walking down this street and adding the house numbers in various ways.

You could start with adding in pairs across the street:

and carry on as far as you can.

Explore the answers you get for these additions. What do you notice?

Can you explain why?

If you want to go a bit further with this you could change the grouping of houses in different ways. How about:

A.

Or:

B.

But maybe the houses are already grouped in some way - like all semi-detached:

Then one side of the street the totals are: 4, 12, 20, etc

and the other side are: 6, 14, 22 etc.

You could continue this and explore it further.

Some streets have terraces of three houses together:

and some have fours:

You can explore the addition of these groups too!