Bell Work −3𝑥−7𝑥+8+𝑥+2 2) 𝑥+3 𝑥 2 +2 −3𝑥+ 𝑥 2 Simplify each expression by combining like terms when possible. −3𝑥−7𝑥+8+𝑥+2 2) 𝑥+3 𝑥 2 +2 −3𝑥+ 𝑥 2

In Algebra and in future mathematics courses, you will work with unknown quantities that can be represented using variables.  Today manipulatives called “algebra tiles” will be introduced to help you and your teammates answer some important questions, such as “What is a variable?” and “How can we use it?”

2-2. Draw a picture of each type of tile on your paper. The algebra tiles will be referred to by their areas.  Since the smallest square has a length of 1 unit, its area is 1 square unit.  Thus, the name for this tile is “one” or a “unit tile.”  Label your drawing of this tile with its side lengths and area. Tiles Can you use the unit tile to find the other lengths?  Why or why not? 

C. If you cannot use the unit tile to measure all of the other side lengths of the other tiles, how can you label them so that you can find their area?  Discuss this with your team and be prepared to share your ideas with the class.  D. Label your drawings and then name the other tiles using their areas.  Be sure to use what you know about the area of a rectangle and the area of a square.  

2-4.  Build each collection of tiles represented below.  Then name the collection using a simpler algebraic expression, if possible.  If it is not possible to simplify the expression, explain why not. A. 3x + 5 + x2 + y + 3x2 + 2 B. 2x2 + 1 + xy + x2 + 2xy + 5 C. 2 + x2 + 3x + y2 + 4y + xy D. 3y + 2 + 2xy + 4x + y2 + 4y + 1

While Lesson 2.1.1 focused on the area of algebra tiles, today’s lesson will focus on the perimeter.  What is perimeter?  How can you find it?  By the end of this lesson, you will be able to find the perimeter of complex shapes formed by collections of tiles. 

Is your expression as simplified as possible? Your class will also focus on several ways to find perimeter, recognizing that there are different ways to “see” or recognize perimeter.  Sometimes, with complex shapes, a convenient shortcut can help you find the perimeter more quickly.  Be sure to share any insight into finding perimeter with your teammates and with the whole class.  While working today, ask yourself and your teammates these focus questions: How did you see it? How can you write it? Is your expression as simplified as possible?

2-11.  Separate one of each shape and review its name (area).  Then find the perimeter of each tile.  Decide with your team how to write a simplified expression that represents the perimeter of each tile.  Be prepared to share the perimeters you find with the class.  

2-12. Each part of an expression that is separated by addition or subtraction signs is called a term.  If two terms contain the same variable(s), including the same exponents, if any, they are called like terms. Match the terms in the left column with the like terms that match them in the right column. A.  3x 1.  6y2 B.  –4y2 2.  7xy C.  6a4 3.  13 D.  10s 4.  –7c E. –8 5.  9a4 F.  6xy 6.  s G.  c 7.  5x

2-12 Continued Term--A term is a single number,  variable, or the product of numbers and variables.  In an expression, terms are separated by addition or subtraction signs.  For example, in the expression 1.2x − 45 + 3xy², the terms are 1.2x, − 45, and 3xy². Like terms--Two or more terms that contain the same variable(s), with corresponding variables raised to the same power.  For example, 5x and 2x are like terms. Combining like terms--Combining two or more like terms simplifies an expression by summing constants and summing those variable terms in which the same variables are raised to the same power.  For example, combining like terms in the expression 3x + 7 + 5x − 3 + 2x2 + 3y2 gives 8x + 4 + 2x2 + 3y2.  When working with algebra tiles, combining like terms involves putting together tiles with the same dimensions.

2-13.  For each of the shapes formed by algebra tiles: Use tiles to build the shape. Sketch and label the shape on your paper. Then write an expression that represents the perimeter. Simplify your perimeter expression as much as possible.  This process of writing the expression more simply by collecting together the parts of the expression that are the same is called combining like terms.  A. B. C. D.

Extra Practice –3y + 10z – 10y – 2 – 5y 1 + 3y + 8 + 10y 6 + 2p – 3t + 4t + p 2t + 6 + 6 + 8t 5 𝑏 2 – 9b + 2 – 4 𝑏 2 + 2