Algebra and concept circles

We are working on representing abstract concepts with concrete manipulatives to build conceptual understanding.  Today we used a concept circle where we can change the “a” (what is in the center of the circle) and we can represent all the other expressions in terms of “a”

We called this tile “1” to do some of our figuring.  We needed to do a bit more thinking when the tile in the center was the rectangular tile, representing “x”.

We saw that the rectangular tile is a variable, and so to show a variable squared we need the big square tile, and a variable cubed can be actually a cube! 

We took a summary note which covers the importance of noticing the brackets and following PEDMAS