Using Algebra Tiles to Solve Equations, Combine Like Terms, and use the Distributive Property O B J E C T I V E : T O U N D E R S TA N D T H E D I F F E R E N T PA RT S O F A N E Q UAT I O N , A N D U S E A L G E B R A T I L E S T O H E L P U S S O LV E P R O B L E M S . 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 variabl e 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? Lets 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:
x2=3 x+3=7 7x=9 x5=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?
Lets 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 What does this tile represent? -x2 What do these tiles represent? x -x What do these tiles represent? 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
Lets 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!
2x + 3x + 5 +x 5x 1 2 2 x2 x2 x x x
1 1 1 1 Try these: 2x2+4x+2x2 x -1
x2 3x2 2x 1 3x2 2x 2 x2+2x+1 3x2 x 3x2 3x + x2 1 + 2x 3 1 3x2 2x + 4 Whats 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 Lets 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 xs 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 todays lesson. Switch problems with your partner and solve.