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 		 Exploring whole numbers ( Number Operations & Number Theory )
Term    : 1 
Module : 1 - Capturing Data 
Unit 1      : Numbers Made Easy (  Whole Numbers ) -
                            Number Sequence & Patterns
                      Other Patterns - Pascal's Triangle		  
Patterns
in
The Pascal's Triangle
 

We can think of a pattern as a design or picture which repeats itself at regular intervals.

The Pascal's Triangle shown below is built up by using a special pattern.

 * To build up each row start with one and end with one.
 * The numbers in between are made up by adding the adjacent numbers above.
  (eg. The 2 in the green box + the 1 in the blue box = the 3 in the yellow box below.)

Now notice the interesting patterns formed by adding the numbers of each row:
 * Totals : {1, 2, 4, 8, 16, 32, 64, 128, 256 }

 * Each number is the previous number multiplied by two.

 * Or 2 to the power (0,1,2,3,4,5,6,7,8)  

 Find the sequence of numbers within the triangle which are triangular numbers.
 (visit number theory to find out about triangular numbers)
 

  
The Pascal's Triangle

 

Observe The
Patterns

  
Reading
Grids
 		 The diagram below consists of a grid which is made up of squares, between a horizontal x axis, and a vertical y axis. We can plot points on this grid by checking (circling) where the x axis meet (intersect) the y axis.

Now observe the points plotted in the graph below, and also observe the number patterns (eg (x + 1).

{(1,2) x=1, y=2}; {(2,2) x=1+1, y=2}; {(3,2) x=2+1, y=2} ...		  
Grid

Observe The
Patterns

  
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