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Street Sequences

Stage: 1 and 2 Challenge Level: Challenge Level:1

Street Sequences


Let's look at a street!
 
 
 
Real 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:

5Houses

Looking from above the numbers could appear as:
 

AA

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:

AB

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.
AC

Or:


B.
AD

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

AE

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:

AF

and some have fours:

AG

You can explore the addition of these groups too!
 

Why do this problem?

This problem is very useful when you want to give pupils opportunities to explore number patterns in their own way. There are various ways of exploring this activity with no particular 'right' way.

Possible approach

The way in which you introduce this activity will depend on the children you are working with.  It would be helpful to show the arrangement of numbers in the problem on a board (if a big group) or on paper (if a small group). 

Key questions

Some more experienced pupils may be asked "Why are these sequences like they are?"
Less experienced younger pupils can be asked simply "What do you notice about the answers we've got?"
Generally you can ask "What could you do now?"

Possible extension

An extension may be suitable for some pupils that comes from comparing the results from the sequences that we get when the houses are grouped.

Possible support

Some pupils may need number cards in front of them and calculators to free them up to think creatively.