Wednesday, March 26, 2014

Algebraic Expressions-Multiplying

Moving from the X to the dot for multiplication--mind blowing for a lot of students.  This is the first part of our learning about how to multiply algebraic expressions.  We talk about how this is no longer "baby math" and now this is the BIG LEAGUES.  They buy into it and feel excited because they are doing 'fancy math.' 
A lot of my kiddos want to put the dot like a the bottom of a number.  We referencing where to put the dot, we talk about putting it in the middle, like you would wear a belt, not at the bottom like a pair of shoes.  Since this analogy, we have not had a SINGLE mis-placed dot!  YAY :)

I am all about the conceptual learning before getting into the abstract learning.  It takes time, but the pay-off is huge!  It gives kids a point of reference for their work, and they are more engaged.  Algebra is no different.
I start by providing an algebraic expression to the class.  We discuss how many "d's" we have in this case.  This tells us that we have 3 d's.  From our work with adding and subtracting expressions (post to come), students know that the variable is represented with a little bathroom cup.  In this case, 3d tells us that we need 3 cups.  The important information "d=6" tells  us that each cup is worth 6 blocks (I use base-10 unit blocks).


Now the job is to figure out how many blocks we have in all.  I teach students with learning disabilities, so they need to physically count the blocks.  So, we dump them out of the cups..
and into a pile.  Then, we bridge the concrete representation with the symbolic representation by using substitution.

Here's my sixers working on the expressions.


They did SOOOO good with this!  I was so super excited with how well they learned the content and retained it :)  Day 2 we worked on the representational (pictures) and symbolic (numbers) forms to evaluate the expressions.  I didn't snap any pictures, but you can pick up the FREEBIE here.





Alison Rose said...

Love that you put the "dot" where you would buckle your belt. I will need to try that out with my students. I remember the first time they were introduced to the "dot"....they thought I was nuts!
Rockin' and Lovin' Learnin'

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