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Using Algebra Tiles to Solve Equations, Combine Like Terms, and use the Distributive Property OBJECTIVE: TO UNDERSTAND THE DIFFERENT PARTS OF AN EQUATION, AND USE ALGEBRA TILES TO HELP US SOLVE PROBLEMS. Important Vocabulary! • Equation – An equation is a mathematical statement that uses an equal sign to show that two expressions have the same value. • To solve an equation that contains a variable, find the value of the variable that makes the equation true. This value of the variable is called the solution of the equation. • Term – the parts of an expression that are added or subtracted. • Like Term – Two or more terms that have the same variable raised to the same power. • Coefficient – The number that is multiplied by a variable in an algebraic expression. • Constant – A value that does not change. • Equivalent Expression – Equivalent expressions have the same value for all values of the variables. Parts of an Equations! Like Terms 5x + 4x + 5 = 50 constant coefficient variable Your Turn… 6y + 5x + 2y = 42 • Coefficients? • Variables? • Like Terms? • Constant? Discovery • What do you think the different tiles stand for? Why? Algebra Tiles What do these stand for? Why? Let’s Try It • Represent the following equations on your tile mat. Compare your answer with a neighbor. Assist each other as needed. 5+x=2 5 – 5x = -1 2x – 5 = 9 Build this equation 5+x=2 On your own: • x–2=3 • x+3=7 • 7–x=9 • x–5=1 • 2 = -x – 4 Build this equation 2x = 6 • -3x = 15 • -12 = -4x • 3x = 12 • 6x = 3 • 5 = 5x To solve for the variable, you must do the inverse operation. With tiles, in order to divide, you must create even groups of x tiles and unit tiles. x=3 When should we NOT use tiles? • Let’s say this piece of paper represents our whole x. • How many sections are there on the paper? • How many positive tiles will go in each section? • Using the visual, what is the value of x? Build this equation • This can stand for x/5 (5) (5) To solve for the variable, you must do the inverse operation. With tiles, you must isolate x first, then you can figure out what x equals. x = 50 Activity… Use your algebra tile mat and algebra tiles, to solve the following equations. 2x – 3 = 9 5 – 5x = -1 Zero pairs 3x – 1 = 8 7 = 5x + 2 2x + 3 = 3x 4x – 2 = 3x + 6 Make even groups with each x x=6 Summary! • How will algebra tiles be useful to you in solving equations and combining like terms? Combining Like Terms What does this tile represent? x2 -x2 What does this tile represent? What do these tiles represent? What do these tiles represent? x -x 1 -1 Combining Like Terms 4x + 5 These are NOT the same shape Can these be combined? Explain your reasoning. 4x + 5x Can these be added together? Explain your reasoning. Let’s Try It! Represent the following expressions on your tile mat. Compare your answer with a neighbor. Assist each other as needed. 3x + 4 – 2x 3x + 5 2x2 – 6x +2 x2 – 2x – 3 3x2 + 3x – 5x Combining Like Terms: Build It! 2x2 + 3x + 5 +x2 – 5x – 1 x2 x2 x x x 1 1 1 1 1 Try these: 2x2+4x+2x2 – x 3x2 – 2x – 1 – 3x2 -1 – 2x – 2 x2 x2+2x+1 – 3x2 – x 3x2 – 3x + x2 – 1 + 2x – 3 3x2 – 2x + 4 What’s left?? -x -x -x -x -x Summary • Write 2 – 3 sentences explaining how you use algebra tiles to combine like terms. Pretend you are teaching this concept to a 4th grader. Distributive Property • Using algebra tiles, we will use Distributive Property to help us combine like terms and solve equations. • Distributive Property - The property that states that if you multiply a sum by a number, you will get the same result if you multiply each addend by that number and then add the products. How does it work? Represent the following expression using algebra tiles: 3 (x + 2) 3 groups of x plus 2 When we group our like tiles, what expression do we have? 3 (x + 2) = 3x + 6 Let’s Practice! Simplify the following expressions: 2(x – 4) 2 groups of x – 4 On your own: (2x + 1)4 6(-x – 2) + 3 = 2x – 8 (3 – 2x)3 + x After grouping like tiles, what do we have? Distributive Property and Equations Use distributive property to solve the following equations! 2(x + 3) = 10 You try: (-x – 4)3 = 3 2 + 2(2x – 3) = 8 4 = 3x – (-x + 3)2 x=2 After making zero pairs, we are left with 2 x’s And 4 unit tiles. What does x equal? Summary • Pair up with a partner. Each partner will make up a problem that uses the concepts learned in today’s lesson. Switch problems with your partner and solve.