Introduction to Algebra. What do you think of when you hear “algebra”?

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Presentation transcript:

Introduction to Algebra

What do you think of when you hear “algebra”?

We will… add and subtract algebraic terms concretely, pictorially, and symbolically to solve simple algebraic problems explore addition and subtraction of polynomial expressions concretely and pictorially demonstrate an understanding of multiplication of a polynomial by a scalar concretely, pictorially, and symbolically solve and verify simple linear equations algebraically

What is algebra? The basic idea of algebra is to solve for an unknown value or to express a situation mathematically with an unknown, changing value.

Real world example: You use algebra with you cell phone plan! You have your plan rate (your constant) plus your minutes cost (your variable) to get your bill. So if your plan rate is $35 per month and then your minutes cost 15 cents per minute you can come up with an algebraic expression for this: Let x be the number of minutes you use on your cell phone Your algebraic expression would be: $ $0.15x

Example: 2 + [ ] = What is the missing value?

Example: 2 + [ ] = What is the missing value? 2 + [ ] = 3 + 5

Example: 2 + [ ] = What is the missing value? 2 + [ ] = [ ] = 8

Example: 2 + [ ] = What is the missing value? 2 + [ ] = [ ] = = 8

Example: 2 + [ ] = What is the missing value? 2 + [ ] = [ ] = = 8 8 = 8 So the missing value is 6!

Vocabulary Algebraic Expression: a mathematical statement that includes one or more variables and constants and at least one mathematical operation (+, -, x, ÷). Ex: 3x + 4 Algebraic Equation: a mathematical statement formed by two algebraic expressions what are equal to each other. Ex: 3x + 4 = 2x + 6 Variable: a letter used to represent an unknown value that can change or vary. Ex: x, y, z, n …

Vocabulary Constant: a value that does not change and is represented by a number. Ex: 7 Terms: parts of an algebraic expression. Ex: the terms for 2x 2 + 5x – 4 are 2x 2, 5x, and -4. Like Terms: terms that have the same non-numeric factor Example: 2x + 5x → 2x and 5x are like terms because x and x are the same non-numeric factors in each term 2x + 5x 2 → 2x and 5x 2 are NOT like terms because x and x 2 are not the same 2x + 5y → 2x and 5y are NOT like terms because x and y are not the same

Vocabulary Simplify: to simplify an algebraic expression, collect like terms Example: 3x + 4 – 1y + 2 – 5x + 3y = 3x – 5x – 1y + 3y = x (3 – 5) + y (-1 + 3) + (2 + 4) = -2x + 2y + 6 Polynomial: an algebraic expression consisting of one or more terms separated by addition or subtraction signs with at least one variable that is raised to a non-negative whole number power. Ex: 2x + 1 and 3x 2 – 8x + 2 are polynomials Numerical Coefficient: the numeric factor in an algebraic term. Ex: for 6x the numerical coefficient is 6 Ex: for -2x 2 the numerical coefficient is -2 Ex: for -x the numerical coefficient is -1

Vocabulary Algebra Tiles x 2 y 2 x y unit (1)