Patterns

Yesterday during lunch duty I was talking about what I really want to teach one of my classes*.  I just introduced fractions last week and we did a lesson on ordering fractions last class.  It involved putting fractions in order and then making observations.  During the conversation I realized it is much more important to me that the students be able to recognize patterns and describe them, than to do anything more with fractions.  So, then and there I decided we would spend some time studying a variety of patterns.  Of course, I totally forgot until later that evening, but I asked twitter for ideas and they responded brilliantly to my request.  So much so that I want to share with you exactly what they said (grouped by conversation, some liberties taken with ordering).


7:16 pm: Tina asks twitter for help


@crstn85 What's your favorite pattern problem accessible to basic math kids? Decided at lunch today to study patterns tomorrow but forgot until now!

@jreulbach  Fibonacci. Or pascals triangle.
@crstn85  just searched the state test and they have pascals triangle but with 2 on the outside. We shall do both!


@Mythagon  1 11 21 1211 111221 312211 ...
@dandersod  thats a good one. Here's another: 3 3 5 4 4 3 5 5 4 3 6 ...
@johnberray Besides Fibonacci and @Mythagon's, I show harmonic sequence and perfect squares. Students find all sorts of patterns in squares.

@MathyMcMatherso Collatz Conjecture & Palindromic Numbers.  http://en.wikipedia.org/wiki/Collatz_conjecture & http://en.wikipedia.org/wiki/Lychrel_number
 @crstn85  simple but unsolved, what a cool thing to share!
@MathyMcMatherso  I know! That's why I love them

@crstn85  Thanks for all the awesome patterns! This is definitely going to be a unit not just a day before long weekend activity. You all rock.


@lmhenry9  Did someone give you the pattern with the perfect squares (1, 4, 9, 16, etc.)?
@crstn85 I'm doing that one with actual squares. I love the locker problem but one kid can't track a number line so it might be too hard...
@crstn85 oh! I just realized we could do it with pennies heads/tails. And maybe tally marks underneath? This has potential for next week.

10:01 PM : Tina goes to bed, but twitter never sleeps!


@lmhenry9  Cool! I'll be curious to hear how it turns out. I do like the locker problem as well.

@dandersod http://mathtest.idiotworld.com/
@MathyMcMatherso Bookmarked - soon to be used in math club.
@dandersod  it's a great site. Some brutal ones that high schoolers have no right getting.

@MathyMcMatherso  Just remembered: did patterns as a filler-thing to start school year. Here's the wkst I made:http://www.box.com/s/ec46ede0600ef8d1aa7f. hope it helps
@crstn85 excellent! I didn't get into visual patterns much so this is helpful.
@wahedahbug  I agree those visual patterns are GREAT!





By the time I went to bed I had Pattern Sheets A, B, C, D, E, F and G made.  The combined resources of the state test database (all the problems that I didn't type out) and online colleagues is rather astounding and I didn't use nearly all of their ideas yet!  The next morning I set up the locker problem sheet like I'd discussed with Lisa (during class, actually, when I needed a 5 minute break- they pulled it together since they knew I was mad and I calmed down and got to get the idea out of my head and onto paper where it couldn't bother me anymore).


The plan had been to give students the choice of any pattern sheet to start; everyone works at their own pace and we'd keep going until they were sick of patterns.  They had a different idea.  One person was excited about Pascal's triangle since it had a fun looking diagram, so everyone grabbed the same sheet.  Then we worked together, taking turns filling in parts on the smart board.  I was amazed that they happily spent an hour on just the first 7 rows of the triangle.  They noticed all sorts of patterns, then I had them color in multiples of 2, 3, 4 or 5 and we re-did the one on the smart board to reflect their coloring and found lots more patterns.  These are students who don't normally talk to each other so it was great to see them verbalizing so much of what they saw.  We even worked on taking jumbled ideas and forming coherent descriptions.  These kids awe me every class.   


*They're a group of 7 students who all have 'intensive' learning disabilities (a category between moderate and severe, they're in most - if not all - self-contained classes and have autism, pervasive developmental delay or some other significant cognitive impairment).  Each has a different background, but they all have had very little traditional math.  This is refreshing in some sense since I get to teach them everything: they haven't learned anything wrong and I know exactly what language to use to refresh their memory since it was my language!  But it's also overwhelming since I have to teach them everything (starting with multiples of two for some).  Two students have opted out of the state test (they're seniors) but the others have to take it even though they will never function at the level of their peers.  Administration is totally focused on passing the test, but as long as I assure them that we're studying MCAS topics (which we are!) I have pretty much free reign.  While the kids don't have a math background, these students are learning more than I thought possible, and much more than they thought they ever would.  On several occasions students have said to me "I get this!" or "I'm learning math!" or "I'm getting better at ___!" in total shock.  It gives the mantra of "high expectations" a whole new meaning.