Saturday, December 17, 2016

#SwDMathChat From Patterns to Algebra (part 3)

I'm continuing to blog about my experiences with using the great ideas from the book From Patterns to Algebra.  In case you missed my first 2 blog posts, you can read the first one here and part 2 here.

So we worked on lesson 4: pattern building with composite rules this week.  The first pattern I showed them was the one on the right below with the yellow diamonds.  They were struggling a bit so I showed them the very first pattern we had worked with a few weeks ago (the one on the left without the yellow diamonds) and asked them what they noticed.  I started to hear some "ah-ha's".

My students are starting to get more flexible with this concept.  I can ask them different questions and they can apply what they know about the pattern rule to answer my questions.  For example, for the first few days, all I asked of them was to come up with the rule and what position 4 would look like.  Then I started asking them to show me position 0, or position 10, or how many tiles will there be in position 8, etc.

A few of my students can draw position 4, but are having a difficult time writing the rule independently; I have to prompt them with questions like "what's staying the same?" or "what's changing in each position?" for every pattern.  I have 8 students in this class and about 5 or 6 can come up with the correct rule and patterns for the positions I ask for fairly easily each day.  My big challenge going forward is to figure out how to help the last 2 or 3 make the connections needed to do this independently.

The last few days I really challenged them - I did not use 2 different colors, making it more difficult  for them to determine the constant.  About half of my students were able to identify it after a few minutes of productive struggle.  I love watching them all really thinking and talking about these patterns!

Here are the patterns we worked on this week:

I'm looking forward to the next lesson in which we work in reverse and I give each student a secret pattern rule and they must build what their positions 1, 2, and 3 look like.  Stay tuned...

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