What is algebra? It is the language of mathematics It is a vehicle we use to condense large amounts of data into efficient mathematical statements It enables us to do three things: 1.Create mathematical models of a situation 2.Provides the mathematical structure necessary to use the model to solve problems 3.Links mathematical and graphical representations of data. Information from: Math Matters by Chapin & Johnson

What are the main ideas behind algebra? SymbolsVariablesStructureRepresentationPatternsGraphing Expressions & Equations Rules & Functions Information from: Math Matters by Chapin & Johnson

What is a variable? A letter such as n, that represents a number in an expression or an equation. What is a variables job? Represent specific unknown values in equations Varying quantities in functions (y=2x+1) Formulas (A=l x w) General Properties (a+b=b+a) Sets of numbers in inequalitie s (x<10) Does it matter what symbol I use? X, Y, and Z should represent an unknown Information from: Math Matters by Chapin & Johnson

Addition The joining together of two or more sets of objects Subtraction Removal of objects from a given set or the finding a missing part of a given set Multiplication Combining of several equal sized sets of objects Division The separation of a given amount of objects into equal sized sets

Group 9 Group 5 Group 1 Group 14 Group 10 Group 6 Group 2 Group 15 Group 11 Group 7 Group 3Group 4 Group 8 Group 12 Group 16Group 13

ExpressionTile ModelWritten Description of Procedure Mathematical Procedure (Algorithm) 2x + 3 4x – 2 2x x x x + 3 Simplifying Expressions using Algebra Tiles Names:_________________________________ Date_____________________ _________________________________ Adapted from:

ExpressionTile ModelWritten Description of Procedure Mathematical Procedure (Algorithm) 2x + 3 Two x tiles and three unit tiles were laid down. Could not be simplified 2x+3 4x – 2 Four x tiles and two negative units were laid down. Could not be simplified 4x-2 2x x + 2 Two x tiles and four unit tiles were laid down One x tile and two unit tiles were laid down. The expression was simplified by combining the x tiles to equal three x and the unit tiles to equal six 3x+6 - 3x x + 3 Three negative x tiles and one unit tile was laid down. One x tile and three unit tiles were laid down X terms were combined to equal negative two x. Unit tiles were combined to equal four -2x+4 Simplifying Expressions using Algebra Tiles Names:_________________________________ Date_____________________ _________________________________ ANSWER SHEET Adapted from:

If I had the equation: (-4x +4)+(2x + -2) How could I represent it? -4x 2x -2 4 How would I solve it? I would go with what I know, and cross out the Zero Pair. -4x 2x -2 4 Zero Pair cancel out. ANSWER: -2x+2

Group 9 Group 5 Group 1 Group 14 Group 10 Group 6 Group 2 Group 15 Group 11 Group 7 Group 3Group 4 Group 8 Group 12 Group 16Group 13

ExpressionTile ModelWritten Description of Procedure Mathematical Procedure (Algorithm) 2x = -8  One negative x is equal to 5  Take the opposite of each side of the equation  One x is equal to five negative units 3x = 2 + x -x 2x = 2 ÷2 ÷ 2 x = 1 Solving Equations using Algebra Tiles p.1 Names:_________________________________ Date_____________________ _________________________________ Adapted from:

ExpressionTile ModelWritten Description of Procedure Mathematical Procedure (Algorithm) 2x = -8 Two positive x’s are equal to negative eight Each x is worth four negative units 2x=-8 ÷2 ÷2 x=-4 3x=6 Three x is equal to six Evenly distribute units to each x. Each x is worth two units 3x = 6 ÷3 x= 2 -1x=5  One negative x is equal to 5  Take the opposite of each side of the equation  One x is equal to five negative units -1x= 5 ÷-1 ÷-1 x= -5 3x=2+x Three x is equal to two plus x. Find your zero pair, and cross out. Evenly distribute remaining units One x is equal to one unit. 3x = 2 + x -x 2x = 2 ÷2 ÷ 2 x = 1 Solving Equations using Algebra Tiles p.1 Names:_________________________________ Date_____________________ _________________________________ ANSWER SHEET Adapted from:

ExpressionTile ModelWritten Description of Procedure Mathematical Procedure (Algorithm) 2x + 1 = 5  Three negative x’s and two units are same as 5  Subtract two units from each side of the equation  Divide both sides of the equation into two equal groups  Flip both sides of the equation to make them opposites  One x is equal to one negative unit 2 x - 3 = 2 + x -x x – 3 = x = 5 Solving Equations using Algebra Tiles p.2 Names:_________________________________ Date_____________________ _________________________________ Adapted from:

ExpressionTile ModelWritten Description of Procedure Mathematical Procedure (Algorithm) 2x + 1 = 5 Two x and one unit is equal to five units. Find zero pair. Cancel Out Evenly distribute x to units. One x is equal to two units 2x + 1= x= 4 ÷2 ÷2 x=2 3x+4=-2 Three x and four units is equal to two negative units. Subtract four positive units from two negative units. Three x is equal to six negative units Evenly distribute x to units. One x is equal to two negative units. 3x+4 = x = -6 ÷3 ÷3 x= -2 -3x+2=5  Three negative x’s and two units are same as 5  Subtract two units from each side of the equation  Divide both sides of the equation into two equal groups  Flip both sides of the equation to make them opposites  One x is equal to one negative unit -3x + 2= x = 3 ÷-3 ÷-3 x= -1 2x-3=2+x Two x and negative three is equal to two and one x. Find zero pair and cancel out. Add negative three units to two units. Two x is equal to five. One x is equal to five 2 x - 3 = 2 + x -x x – 3 = x = 5 Solving Equations using Algebra Tiles p.2 Names:_________________________________ Date_____________________ _________________________________ ANSWER SHEET Adapted from:

Algebra Balance ntent/mesg/html/math6web/i ndex.html?page=lessons&less on=m6lessonshell11.swf

2x + 3 = 5 Solid means Multiply Dotted Line means Add part Whole 2 x x 3 5 part Whole

Group 9 Group 5 Group 1 Group 14 Group 10 Group 6 Group 2 Group 15 Group 11 Group 7 Group 3Group 4 Group 8 Group 12 Group 16Group 13

1.) - 2x + 7 = - 72.) 7x + 4 = ) 5 + 4x = 54.) 3 + 3x = 18 5.) 2x + 10 = 306.) - 5x + 2y = - 50 Names:_________________________________ Date_____________________ _________________________________

1.) - 2x + 7 = - 72.) 7x + 4 = ) 5 + 4x = 54.) 3 + 3x = 18 5.) 2x + 10 = 306.) - 5x + 2y = x 5 4x 10 2x y 2x x 7 -2 x -7-10

ExpressionTile ModelWritten Description of Procedure Mathematical Procedure (Algorithm) 1. 2x + 1 =  Three negative x’s and two units are same as 5  Subtract two units from each side of the equation  Divide both sides of the equation into two equal groups  Flip both sides of the equation to make them opposites  One x is equal to one negative unit 4. 2 x - 3 = 2 + x -x x – 3 = x = 5 Solving Equations using Algebra Tiles Names:_________________________________ Date_____________________ _________________________________ Adapted from:

ExpressionTile ModelWritten Description of Procedure Mathematical Procedure (Algorithm) 1. 2x + 1 = 5 Two x and one unit is equal to five units. Find zero pair. Cancel Out Evenly distribute x to units. One x is equal to two units 2x + 1= x= 4 ÷2 ÷2 x=2 3x+4=-2 Three x and four units is equal to two negative units. Subtract four positive units from two negative units. Three x is equal to six negative units Evenly distribute x to units. One x is equal to two negative units. 3x+4 = x = -6 ÷3 ÷3 x= -2 -3x+2=5  Three negative x’s and two units are same as 5  Subtract two units from each side of the equation  Divide both sides of the equation into two equal groups  Flip both sides of the equation to make them opposites  One x is equal to one negative unit -3x + 2= x = 3 ÷-3 ÷-3 x= -1 2x-3=2+x Two x and negative three is equal to two and one x. Find zero pair and cancel out. Add negative three units to two units. Two x is equal to five. One x is equal to five 2 x - 3 = 2 + x -x x – 3 = x = 5 Solving Equations using Algebra Tiles p.2 Names:_________________________________ Date_____________________ _________________________________ ANSWER SHEET Adapted from: p.1

5.) 6 - 3x = ) x = 56 7.) 3 - 5x = ) 9 - 7x = 16 Directions: Solve Equations using Algebra Map 9.) - 6x x = ) - 4x x = 2 Directions: Solve equations using algorithm. p.2

5.) 6 - 3x = ) x = 56 7.) 3 - 5x = ) 9 - 7x = 16 Directions: Solve Equations using Algebra Map 9.) - 6x x = x +4 = x= -24 ÷2 ÷2 x = ) - 4x x = 2 -4x -4x 2 + 2x= x=0 ÷2 ÷2 x=0 Directions: Solve equations using algorithm. p x x 3 -5 x 9 -7 x ANSWER SHEET

Variable Algebraic Expression Distributive Property Order of Operations CoefficientTerm ProductFactor

Algebraic Expression A mathematical phrase involving a variable or variables, numbers, and operations. Ex: n-2 Variable A letter such as n, that represents a number in an expression or an equation. Order of Operations The order in which operations are done in calculations. Work inside parentheses is done first. Then multiplication and division are done in order from left to right, and finally addition and subtraction are done in order from left to right. Distributive Property Multiplying a sum (or difference) by a number is the same as multiplying each number in the sum (or difference) by that number and adding the products. Example: 3x (10 + 4) = (3 x10) + (3x4) Term a part of a sum in an algebraic expression. Coefficient a constant that multiplies a variable. In Ax + By = C, A and B are coefficients of x and y. Factor one of two or more expressions that are multiplied together. Product the result of two numbers being multiplied. Answer Key

SumQuotient EquationInequality

Quotient the answer to a division problem. Sum the result of adding. Answer Key