Equations and Expressions
The Pool Tiles Problem
Here were two ways of seeing the rectangle problem on the front of the "Patterns HW"
Here are 4 ways that people saw the fountains problem on the back of the Patterns HW.
Here is what was decided worked for y = x*x+1 versus what worked for y = x(x+1)
Here are different diagrams students made to match b = 7n
Here are different diagrams students used to match b = 4n+3n (notice how they are the same or similar to b = 7n above)
Here are diagrams students used to match b = 3 + 4n
FACTORED FORM - area of the whole rectangle, with at least one side cut into smaller lengths.
EXPANDED FORM - the sum of the areas of the smaller rectangles to find the area of the larger rectangle.
SIMPLIFIED FORM - the simplest way to express the area of a rectangle.
(Students have models for the definitions above in their vocabulary and classwork sections of their binders).