Transcript Introduction to Algebra

Introduction to Algebra
What do you think of when you hear
“algebra”?
We will…
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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:
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You use algebra with you cell phone plan!
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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: $35.00 +
$0.15x
Example:
2+[]=3+5
 What is the missing value?
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Example:
2+[]=3+5
 What is the missing value?
2+[]=3+5
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Example:
2+[]=3+5
 What is the missing value?
2+[]=3+5
2+[]=8
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Example:
2+[]=3+5
 What is the missing value?
2+[]=3+5
2+[]=8
2+6=8
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Example:
2+[]=3+5
 What is the missing value?
2+[]=3+5
2+[]=8
2+6=8
8=8
 So the missing value is 6!
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Vocabulary
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Algebraic Expression: a mathematical statement that
includes one or more variables and constants and at
least one mathematical operation (+, -, x, ÷).
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Algebraic Equation: a mathematical statement formed
by two algebraic expressions what are equal to each
other.
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Ex: 3x + 4
Ex: 3x + 4 = 2x + 6
Variable: a letter used to represent an unknown value
that can change or vary.
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Ex: x, y, z, n …
Vocabulary
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Constant: a value that does not change and is
represented by a number.
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Terms: parts of an algebraic expression.
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Ex: 7
Ex: the terms for 2x2 + 5x – 4 are 2x2, 5x, and -4.
Like Terms: terms that have the same non-numeric
factor
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Example:
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2x + 5x → 2x and 5x are like terms because x and x are the
same non-numeric factors in each term
2x + 5x2 → 2x and 5x2 are NOT like terms because x and x2 are
not the same
2x + 5y → 2x and 5y are NOT like terms because x and y are not
the same
Vocabulary
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Simplify: to simplify an algebraic expression, collect like terms
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Example: 3x + 4 – 1y + 2 – 5x + 3y = 3x – 5x – 1y + 3y + 2 + 4
= x (3 – 5) + y (-1 + 3) + (2 + 4)
= -2x + 2y + 6
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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.
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Ex: 2x + 1 and 3x2 – 8x + 2 are polynomials
Numerical Coefficient: the numeric factor in an algebraic term.
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Ex: for 6x the numerical coefficient is 6
Ex: for -2x2 the numerical coefficient is -2
Ex: for -x the numerical coefficient is -1
Vocabulary
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Algebra Tiles
x2
 y2
 x
 y
 unit (1)
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