1. Lesson 4.1.1 and Lesson 4.1.2

2.  Rectangles Four-sided shape with two pairs of parallel sides and four 90 degree angle  Dimensions Length of each side of a shape, such as length and width of a rectangle  Completed area model Rectangle which we use to show that area as a product equals area as a sum  Diagonal Opposite rectangles within the completed area model  Algorithm Process or set of rules to be followed in calculations  Quadratic expressions Expression with a degree of two, meaning the highest exponent is two

3.  Students will review how to build rectangles using algebra tiles.  Students will identify patterns for determining the dimensions of a completed area model.  Students will identify that the products of the terms in each diagonal of an area model are equal.  Students will develop an algorithm to factor quadratic expressions without using algebra tiles. Clusters covered: A-SSE.B: Write expressions in equivalent forms to solve problems. (Quadratic and exponential)

4.  When coming up with the dimensions of a rectangle, write out the dimensions of each smaller rectangle.  6x is 6 “x” tiles lined up short side to short side  Think about numbers, 15 can be written as (3)(5), which are the factors of 15  So, the expression x 2 +5x+6 can be written as (x+3)(x+2), which are the factors of x 2 +5x+6  When forming rectangles from the sum, take out tiles for each term and only use those tiles to form a rectangle – What are the dimensions of the rectangle  Factor each term in the diagonal, so 3x 2 factors into 3x and x  Diamond problem  Top is multiplied (so diagonals multiplied)  Bottom is added (so middle term)  Have to figure out what numbers fit in the middle two diamonds  Then fill out the area model to find the dimensions (factors)