Sunday, September 28, 2014

repeating-patterns

Here are a few tips on teaching repeating patterns with kindergarten and first grade children.  Before I get started, here's a short story that might interest you:

"It's October and first year teacher Miss Larson prepares a math lesson on repeating patterns with her kindergarten class.  The evening before the lesson, she carefully counts out 8 purple and blue cubes and she puts them in a sandwich bag.  She repeats this procedure 19 more times.  All 20 of her kindergartners will have their own bag of manipulatives to work with at their tables.  Miss Larson is confident that her upcoming lesson will be a success.  During the entire month of September she has used the a-b-a-b-a-b pattern on the September calendar by alternating apples with leaves.  She had pointed out the red and white stripes on the American flag and discussed the repeating pattern.  The week before her lesson she had a "Show and Tell" day in which the children came to school in striped clothing to demonstrate alternating color patterns.  She was sure that EVERYONE would easily master a-b-a-b-a-b patterning during her lesson.  Much to her surprise, a little guy in her class named Jerry randomly places the purple and blue cubes (in no particular order) in a neat row.  No repeating pattern!  Miss Larson is stumped.  Jerry was the calendar helper during the last week of September and demonstrated the a-b-a-b-a-b pattern sequence with the apples and leaves without hesitation.  Miss Larson does not realize that Jerry has CVD!  (aka:  "colorblindness")  If only she had known.  She would have used a different medium (something other than color) to teach and assess Jerry's understanding of the concept of repeating patterns."

*If you care to know more about CVD, click here.
Using color as the medium to teach patterning concepts may not be the best choice.


In Virginia, one of our kindergarten math standards deals with repeating patterns.  It falls under the Patterns, Functions, and Algebra strand.  Some of the key skills require the children to create and extend repeating patterns.  Luckily for Jerry, several kinds of mediums can be used to teach this!
Using size as the medium might be a better choice than color.  The picture above shows the a-b-a-b-a-b pattern with big and small buttons.  A perceptive child might also notice that the small buttons have two holes and the big ones have four.

What other mediums can be used to create repeating patterns?  LOTS!  Size, texture, sound, movement with their bodies, and quantity are a few examples.  Using a variety of media AND manipulatives, may foster growth in their modalities of learning as well.  It's best to start patterning with two objects that are VERY DIFFERENT from each other.
Using two, very different mediums will avoid common misconceptions.  These misconceptions are unrelated to the concept at hand which is to repeat and extend a pattern.  The wooden cubes and the aquarium decor shown above, are two, very different types of materials. 


Virginia kindergarten students also need to identify the core in a repeating pattern.  Another word for the core is the unit pattern.  The core is where the pattern starts and ends before it is duplicated.  In the pattern ABBABBABB, the core would be ABB.  It's best to make sure that children have mastery of the a-b-a-b-a-b pattern before introducing new patterns (such as the a-b-c-a-b-c-a-b-c and a-a-b-b-a-a-b-b).
This is an "a-b-a-b-a-b" pattern.  The pattern is expressed with position of the milk caps . . . "cap up-cap down-cap up-cap down . . . "

One way to cause a little "disequilibrium" for students that are becoming competent in their patterning concepts is to give them just one type of material.  Then ask them to create an "a-b-a-b-a-b" pattern from it.  At first they might be confused until they realize that position or quantity can be used as the medium.  The photo above is an "a-b-a-b-a-b" pattern.  The position of the milk caps is utilized as the expression of the pattern.

The children's patterning days aren't over when they enter first grade either.  In addition to using what they learned about patterning in kindergarten, they also need to TRANSFER a pattern from one form to another.

They need to transfer a pattern from one form to another.  Get this freebie sheet by clicking here!

First graders also need to create GROWING patterns . . . and there is a difference between a repeating pattern and a growing pattern.  It's important to use manipulatives and visuals when introducing growing patterns.  A written numeric form of a pattern such as:  "5, 8, 11 . . . "  Can be very confusing to young children and therefore is not the best method of teaching the concept of a growing pattern.
This is a simple, growing pattern.
The photo above shows a growing pattern.  It is a "Plus One" pattern which shows the numbers 1, 2, 3, 4, 5, and 6. Later on, a child might be able to show a sequence with a stack of 3 cubes, then 7 cubes, then 10, then 13, and so forth to show an increasing pattern of "Plus 3". 
The pattern shown above is a-b-a-b-a-b. It could be stated as:  "one-two-one-three-one-four-one-five".
Sometimes patterns can express both a repeating and growing sequences.  The photo shown above is one such pattern which is a higher level of complexity than simple, repeating patterns.

I'm excited to tell you about a little resource I've created to help your students with patterning.  The packet is solely for the a-b-a-b-a-b pattern.  Perfect for kindergartners in the month of October!  My little fellow is testing out the product.  He already has mastered simple, repeating patterns but was willing to try out my activities.
First he has to continue the pattern by drawing more candy corn and pumpkins.  
In row two, he'll need to draw the candy corn upside down.

The medium in row three is about size.  So he'll make big and little candy corn.

Since "thinking about thinking" (or meta-cognition) is so important in order to make a concept stick, it's necessary that THEY create their OWN patterns.  In the first worksheet, the pattern was already made up for him.  All he needed to do was extend it!  Now he has to CREATE the a-b-a-b-a-b pattern.  The medium is color.  He has to "program" the candy corn that gets cut out as well, using  the appropriate colors.  (The color medium is fine for him because he does not have "colorblindness".  It's always a good thing to know your students!)

I think at this point, he had a plan to take a short cut.  It was faster for him to keep the same color in his hand and skip the uncolored images.

Then he went back and colored the rest of the candy corn in the row.


He chose, what looked like, two shades of orange for the final row.  Go figure!
I really liked that HE got to choose the colors for his candy corn math instead of being told what colors to use.  This makes the activity a little more open-ended instead of having a "cookie-cutter" look displayed for student work.

I used square shapes for the cut-outs which is much easier to cut than any other shape.  There's no point in frustrating kindergartners with their "cut and paste" activities.  He was so focused on the cutting that he didn't even pay attention to the paper falling off the dining room table!
 Then we glued the "programmed" pieces.

The finished work!
The packet also has a few photos that are sized for pocket charts. They're photos of candy corn and the pumpkin variety of candy corn. 
We have shown you just three of the items included in this packet.  There's more!  Some of the pages have a color version for laminating.  These could be added to your fall themed math centers.  The image below shows a little more of what's included.  The "Petrified Patterns" page is an introduction to the core pattern concept.  It is intended for exposure and not a practice of the skill.  Right now I am selling this for just a dollar.  Click the image below to view this packet at my Teachers Pay Teachers shop.  

https://www.teacherspayteachers.com/Product/repeating-patterns-925274

Lessons by Molly © 2014  All rights reserved.

Teacher Treasure Hunter hosted a giveaway to celebrate her "follower" milestones.  There were a number of different categories.  While the giveaway has ended, you can still purchase the products shown below!  Read more about the "Fabulous Fall Friends Giveaway".  Just click the image below.
http://teachertreasurehunter.blogspot.com/2014/09/fabulous-fall-friends-giveaway-and-fall.html