Tuesday, November 29, 2016

#SwDMathChat From Patterns to Algebra

Image result for from patterns to algebraI recently discovered the book From Patterns to Algebra by Dr. Ruth Beatty and Dr. Catherine D. Bruce and thought it was perfect for my students to give them the hands-on and visual connections to linear equations and support their algebraic thinking.  As they say in the introduction, "Mathematics has been called 'the science of patterns'."  The lessons presented in the book are meant to be followed in the given sequence.   The first chapter of the book, which is where I am now with my students, has them playing "Guess My Rule" and pattern building.  I chose to purchase the DVD with the book which gave me access to video vingettes and Smart notebook files for each lesson.

In the first lesson, "Guess My Rule", I asked students to give me a random number between 2 and 9 (1 and 10 make it too easy), and then apply the rule I'm thinking of and write the answer.  As they figure out what the rule is (what I'm multiplying their input numbers by), they write it down on their whiteboards.  When I think everyone has figured it out, I take one more random number and have everyone write down the output number on their whiteboards to check.  Some of my students lack multiplication fact fluency, so this is good practice for them.  As the authors advise, don't have the input numbers in order because that leads to students looking for additive rules instead of multiplicative rules.

In the next lesson, I displayed various patterns with 'position number' cards underneath each iteration of the pattern.  The students must again figure out what the rule is.   The first day we did the patterns, I heard one student say "This is hard!"  I told her that once she sees how the first one is done, she will think they're a lot easier than she originally thought.  They were all overthinking it!  Once everyone figured out the rule and wrote it on their whiteboards, I had them draw what position number 4 would look like.  One student (the same student who thought this was hard) expressed the rule additively instead of multiplicatively at first (for the first example below she said you're adding 3 each time).  I asked her to try to see what the position number was being multiplied by instead of how the pattern was changing each time.

After doing the patterns for a few days, today I had them create the first 3 positions of their own patterns with color tiles.  After I checked their patterns, I had them rotate to someone else's pattern, write down the rule on the whiteboard, then try to build the 4th position themselves.  They really liked this activity!  I loved how engaged everyone was with creating their own patterns and figuring out each other's patterns.  Here's some of the patterns they created:

The lessons coming up next deal with composite rules.  I think this will be more difficult for my students because they have to see the two steps being done (multiplication and addition) instead of just one (multiplication).  I hope I'm pleasantly surprised and they pick this up very quickly.  I'll keep you updated on our progress!

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