A lot of my kiddos want to put the dot like a decimal...at 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.