Patterning

I had a great lesson today with my students on patterning.  Why this is such a difficult concept for children I'll never know.  Every year when we analyze our previous year's scores, our students always seem to be low in analyze a geometric or numeric pattern.  Hopefully the lessons we've gone over these past few days will have cleared up any misconceptions my students may have had.  My teaching partner and I were discussing today how we never really understood patterning when we were children.  We just don't remember being taught how to find the pattern.  I definitely hated questions that asked me to find the a certain number of shapes in the pattern ie., find the seventh shape if the pattern continues.  Hated that! I never understood the concept of the unit.  Students must find the unit, or repeating sequence, in order to determine what shape comes next.  Eventually I think I figured that much out, but until now I didn't realize there was a number pattern that would help me.  Our problem we worked on today was from Pearson's Investigations Unit 6.  It was titled Find the Greens.  We were given a cube train consisting of red, blue, green, red, blue, green, red, blue, green, up to 12 cubes.  The goal was for students to realize that we can find the number of any green cube by skip counting by three's since the green cube was in the last position.  We made an input/output table to check our work.  By figuring out what number each green cube fell on, we can now figure out the number of any of the other cubes in our basic unit sequence.  For example, I know that the 4th green in my pattern is the twelfth cube in my train.  I can now figure out the 4th blue also because it is just one less than the 4th green.  This will work for any number in the pattern.  What would the 20th cube in the pattern be?  I know that the 7th green is the 21st cube so the 20th cube will be blue. If students make a table listing all of the greens they can then add in what each blue and red should be.  This lesson is great for hitting a large majority of the mathematical practice standards.