Well I wonder how often you have noticed that there are numbers around the
place that follow one after another 1, 2, 3 ... etc.? Sometimes they
appear in reverse order when a countdown is happening for a launch of a rocket.
But usually they happen in an order going up, like when you read through a book
and notice the page numbers. These kinds of numbers are called consecutive
numbers, you may have heard of the word before - it simply means that they are
whole numbers that follow one after another.
This investigation uses the idea of consecutive numbers and gives us other
numbers to explore. You may very well discover things that NO ONE else
has discovered or written about before, and that's GREAT!
So this is how it starts. You need to choose any four consecutive
numbers and place them in a row with a bit of a space between them, like this:
When you've chosen your consecutive numbers, stick with those same ones for
quite a while, exploring ideas before you change them in any way. Now place
4 + 5 - 6
+ 7
4 - 5 + 6
+ 7
and so on until you have found all the possibilities. Are you sure you've got
them all? You should include one using all
Now work out the answers to all your calculations (e.g. 4 - 5 + 6 + 7 = 12 and
so on).
Now try other sets of four consecutive numbers and look carefully at the sets
of answers that you get each time.
Are you surprised by anything you notice?
It is probably a good idea to write down your 'noticings'.
This can lead you to test some ideas out by starting with new sets of
consecutive numbers and seeing if the same things happen in the same way.
You might now be doing some predictions that you can test out...
FINALLY, it is good to ask the question "I wonder what would happen if I ... ?"
You may have thought up your own questions to explore further. Here are some we
thought of:
"What would happen if I took the consecutive numbers in an order going
down, instead of up?"
"What would happen if I only used sets of three consecutive numbers?"
"What would happen if I used more consecutive numbers?"
"What would happen if I changed the rule and allowed consecutive numbers
to include fractions or decimals?"
"What would happen if I allowed a