Street Sequences

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:



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.



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!