Number Patterns and Pattern Rules



There are three types of patterns:  repeating, growing, and shrinking.  

A pattern rule tells how to build a pattern.  You may be able to state a pattern rule in more than one way.   

The core of a pattern is the smallest part that repeats.



Repeating Patterns

In a repeating pattern, the numbers change in the same way each time.  The numbers can either be added or subtracted, as long as it is the same amount each time.

080410_75413_6.png

Repeating patterns may include operations other than addition.  See the examples below.


140410_102208_0.png
140410_102409_2.png


080410_75513_7.png





Growing Patterns

A growing pattern is a pattern in which the numbers increase, and the amount added changes each time in a predictable way.

For example,120, 121, 123, 126, 130, 135, 141, ...
The pattern rule is start at 120.  Add 1.  The amount you add increases by 1 each time.

Another example would be 870, 880, 889, 897, 904, 910...
The pattern rule is start at 870.  Add 10.  The amount you add decreases by 1 each time.

080410_75557_8.png

140410_102453_3.png

Note:  In some cases a number pattern can be classified as both a repeating pattern, and a growing pattern.

The pattern (4, 8, 16, 32, 64,...) can be identified as a repeating pattern because each time the previous number is multiplied by 2.  However, you can also see that you can add to each number, and because you would be adding by different amounts each time, the pattern can also be identified as growing.




Shrinking Patterns

A shrinking pattern is a pattern in which the numbers decrease, and the amount subtracted changes each time in a predictable way.

For example, 81, 72, 64, 57, 51, 46...
The pattern rule is start at 81.  Subtract 9.  The amount you subtract decreases by 1 each time.

Another example would be 537, 535, 531, 523, 507, 475...
The pattern rule is start at 537.  Subtract 2.  The amount you subtract doubles each time.





Core
The core of a pattern is the smallest part that repeats.

080410_74437_1.png

080410_74524_2.png


Key terms:   core, growing pattern, pattern rule, repeating, shrinking pattern,  

 A Maths Dictionary for Kids 2010 by Jenny Eather
 Harcourt Math Glossary
 Resource Room at Math Central

Links for review:

Hundred Square
This is a neat tool that you can use to create your own patterns and colour the numbers on the screen.  Play with it, and you'll see!

Interactive Hundred Chart
You can explore patterns using this hundred chart.  Choose different multiples to count by, then look at the chart to see what the patterns look like.

Sample Question:

1.  Extend these patterns and state the pattern rule.

a)  153, 157, 161, 165, ___, ___, ___
b)  940, 933, 926, 919, ___, ___, ___
c)  30, 31, 33, 36, 40, ___, ___, ___
d)  16, 32, 64, 128, ___, ___, ___
e)  81, 72, 64, 57, 51, ___, ___, ___

2.      a) Create a growing pattern     b) Create a shrinking pattern