Quest of Nine

The Book

Investigating number patterns

ten marbles

Look at this pattern of 10 marbles

Each different coloured row makes a triangle. So you can make a triangle with 3, 6 and 10 marbles.

fifteen marbles

If you add another row of (5) marbles then there are 15 marbles in the next triangle

To build up the pattern we start with no marbles then add 1, then 2, then 3 then 4 and so on.

So the pattern is made up like this

0 - 1 - 3 -  6 - 10 - 15

From this you can see that the next number in the pattern can be worked out by adding 6 to 15 i.e. 6 + 15 = 21

A table like this one is a useful way to show how this pattern is made.

These numbers are sometimes called triangular numbers.

Can you see why?

ordernumberdifference
1st0
2nd11
3rd32
4th63
5th104
6th
7th
8th
squares of marbles

Look at this pattern of marbles.

Can you make any number patterns using this marble pattern?