How Do I Love Thee: Patterning

Patterning:
Patterns are one of the first mathematical concepts covered in elementary school due to their presence in most every learning domain.  First grade students are encouraged to seek out and apply patterns to better understand a variety of content including addition.

Counting in itself is addition since you are adding 1 to the first number to arrive at the second number in a number sequence.  If starting at 0, 0+1=1 and so forth.  First grade students master counting by 1s followed by 10s, 5s, and 2s.  This is often called skip counting, otherwise known as adding on, or the beginning stages of multiplication (repeated addition).  These counting patterns can be easily seen on a number grid with the help of a little color...

• Counting by 10s can be connected to a color and students begin to recognize that all of the numbers have commonalities.  There is a 0 in the ones place and the tens place is counting by 1s.  Students can connect this with addition and subtraction.  One hop straight down will add ten to any number, or hoping up will do the opposite, subtraction.  
• Counting by 5s with the addition of color is a back and forth motion on the number grid.  Students are encouraged to notice the overlay of 10s and 5s.  In doing so, students recognize the number pattern of 5, 0, 5, 0 in the ones place with the tens place counting by 1s yet again. 
• Counting by 2s on the number grid is a reaffirmation of place value patterns with additional connections to both the tens and the ones place.  Students also gain a better understanding of even and odd numbers as well as the addition of evens and odds.  
• Adding on with different numbers becomes exciting as students discover new patterns.  They look for new number grid designs that can be found when adding on by 3s, 6s, 12s and so on.  Students also notice what numbers are most frequently used in patterns, and those that are often left uncolored.  

Patterns on the number grid initially help cement learning and provide a resource for students to independently check their work while adding on.  However, this knowledge also provides a short cut that can be used ineffectively if a student is not secure in his or her foundation of number sense.  Those who try to fill out a number grid with strictly the pattern in mind often end up skipping rows and losing their place.  Other students absentmindedly memorize patterns without the understanding of how the patterns are formed by adding on the same numbers over and over again.  Furthermore, these patterns on the number grid will only help those when adding numbers from 1 to 100 (or as high as the number grid will go).  The limitations of the number grid can be harmful if students do not have other foundations in mind such as place value.  Adding together 2,o46 to 15,334 will take quite awhile on a number grid.  These misunderstandings can be dangerous and cause a large amount of reteaching.

Re-patterning: 
Patterns are a repetitive form or plan (Bernstein, Sparks of Genius).  They are discovered when understandings are layered to build new connections.

First grade students are originally guided to discover number patterns with adding on, or skip counting. This usually becomes a rote memory procedure with a sing-song rhythm.  Young children are taught to drag out the numbers before the new group of tens so that they will later recognize these stand out patterns.  When given a number grid, the oral counting is transfered to the written numbers.  This is when students recognize the visual similarities in the numbers they have been singing all along.  New patterns can be found when students color counts by 10s, 5s, and 2s.  This provides students with a visual representation of repeatedly adding on by the same number.  It is important that students take ownership of these patterns so that the number grids do not hold limitations.  Students who know how to count to 100 by 1s, 2s, 5s, 10s, and so forth should be able to count on and on, or backwards for that matter.

Later in first grade the number grid is deconstructed and put back together to support patterns of addition.  The numbers are no longer in order, but connected on a grid by combinations from 1 through 10.  The numbers on the top of the grid can be traced down while the numbers on the left side of the grid can be traced over.  The answer can be found to an addition problem by tracing rows and columns until they intersect at the answer.  (For example, by placing your right hand on the top 2, your left hand on the side 5, and tracing down and over until the lines intersect will bring you to 7.  2+5=7!)  The color coding on this new tool further supports patterns in addition and helps students recognize new ways to combine numbers.  (For example, 9+2=11 but one more over is 12, so 9+3=12.)

http://bte2.wikispaces.com/Addition+Timed+Tests

This impacts the topic of addition and the learning process.  Different students learn in very different ways.  Some students find it useful to organize information with pictures, words, colors, numbers and more.  This new representation of a number grid to support addition is simply another resource that will reach students on a new level of organization and pattern building.  However, it is important that the understanding of patterns within addition continues beyond the visual representation.  Such visual enlightenment should only be used to cement pattern recognition and inspire future pattern seeking as well as pattern creating.