Formal Definition of Non-Traditional patterns
Non-traditional or Nonlinear patterns have varying rates of change and do not form straight
lines when graphed.
Example -
A nonlinear pattern: 1, 4, 9, 16,…
Common nonlinear patterns include patterns such as square numbers, cube numbers,
and growing patterns.
Kid Friendly Definition for Linear Patterns
Linear Patterns- Patterns repeat over and over. Patterns can be formed by objects, actions, or characteristics. Patterns can be arranged or occur naturally.
Examples-
A combination of repeated lines, colors, letters, numbers, shapes, forms, figures such as A B C A B C A B C
You can find many patterns in nature such as in leaves and snowflakes.
Formal Definition for Linear Patterns
Linear patterns have constant rates of change and form straight lines when
graphed.
Example – A linear pattern: The sequence 3, 5, 7, 9, 11, 13,… is a linear
pattern because each term increases by 2.
My definition for linear patterns emphasized the repetition that is found in a pattern as well as what elements can be contained in a linear pattern. The formal definition stresses the rate of change between the objects in a pattern and points out that graphing a pattern results in a straight line. As students begin to work with patterns, they look for the repetition within the pattern. By asking guiding questions, students can be focused on the rate of change and then introduced to the formal math vocabulary during discussions. Students can create their own simple patterns that can be graphed to show them how linear patterns form straight line graphs.
For example, the following data set can be studied and graphed.
The rate of change for this data set is y= 2x.
The graph that results from this data shows students that connecting the dots creates a straight line.
Combining this hands-on practice with the formal terms of the definition will help students internalize the definition without relying on memorization since they will have concrete experience with the rate of change and with a graph.
Credit:
http://www.mathsteacher.com.au/year8/ch15_graphs/02_linear/patterns.htm
