7Simplifying Polynomials Students need to use the same idea of zero pairs with variables
8Simplifying Polynomials 1) 2x x + 2simplified: 3x + 62) -3x x + 3simplified: -2x + 4
9More Polynomials try: 3) 3x + 1 – 2x - 4 This process can be used with problems containing x2.(2x2 + 5x – 3) + (-x2 + 2x + 5)
10More Polynomials How would you show/demonstrate: 1) (3x + 5) – (2x + 2)?2 ) (2x2 – 2x + 3) – (3x2 + 3x – 2)?
11Substitution Using Algebra Tiles for evaluating expressions ; 6.EE.1; 6.EE.2
12Substitution Algebra tiles can be used to model substitution. Represent original expression with tiles.Then replace each rectangle with the appropriate tile value.Combine like terms.For example:3 + 2x let x = 4
13Substitution3 + 2x let x = 4Therefore when x=4,3 + 2x = 11
14Substitution Simplify Therefore when x=-4, 3 + 2x = -5 3 + 2x let x = -4SimplifyTherefore when x=-4,3 + 2x = -5
15Substitution How would you show/ demonstrate? 3 - 2x let x = 4
16Distributive Property Using Algebra Tiles to demonstrate the Distributive Property(numbers only); ; 6.EE.3
17Distributive Property Use the same concept that was applied with multiplication of integers, think of the first factor as the counter.The same rules apply.3(x+2)Three is the counter, so we need three rows of (x+2).
21Using Algebra Tiles to show the steps for solving equations
22Solving EquationsAlgebra tiles can be used to explain and justify the equation solving process. The development of the equation solving model is based on two ideas.Equations are unchanged if equivalent amounts are added to each side of the equation.Variables can be isolated by using zero pairs.
23Equations are unchanged if equivalent amounts are added to each side of the equation. x + 2 = 3Show using symbolsx + 2 = 3x = 1
33Dividing Polynomials Algebra tiles can be used to divide polynomials. Use tiles and frame to represent problem. Dividend should form array inside frame. Divisor will form one of the dimensions (one side) of the frame.Be prepared to use zero pairs in the dividend.
41Factoring Polynomials Algebra tiles can be used to factor polynomials. Use tiles and the frame to represent the problem.Use the tiles to fill in the array so as to form a rectangle inside the frame.3x + 32x – 6
42Factoring Polynomials x2 + 6x + 8We need to make a rectangle that uses all of the Algebra tiles