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Algebra
Algebra is a part of mathematics that uses
letters or symbols to represent changing or
unknown values.
Variable
Variable
• a letter used to represent a value that can
change or vary
• in 4x – 1, the letter x is a variable
Identify the variable:
2x
3y
-2x2
6a
Term
Term
• a number and a variable together or just a
number
• Examples: 4x
7
-3y
17w2
v
Give three other examples of a term
Numerical Coefficient
Numerical Coefficient
• The number in front of the variable.
• If no number is visible it is assumed to be 1.
• Examples: 5x has a numerical coefficient of 5
-3xyz has a numerical coefficient of -3
z has a numerical coefficient of 1.
What is the numerical coefficient of:
2y
-63f
w
-t
Literal Coefficient
Literal Coefficient
• The non-numeric factor of a term
• Examples: in 4x the literal coefficient is x
in 3x2, the literal coefficient is x2
What is the literal coefficient of:
3y
-8u
6ab
7x2y3z4
Expression
Expression
• Numbers and variables (terms), combined
by operations
• Examples: 2x + 3
two terms
x - y + z three terms
x - yz
two terms
How many terms are in the following?
3x + 7
4x – 5t + 2
6d – 7x2 + 3
Alge-Tiles
1
-1
x
-x
x2
- x2
We can represent a term or an expression
by drawing the number of tiles the term or
expression indicates:
3x means 3 groups of x
2x2 means 2 x2 tiles
-4 means 4 negative ones
5x + 2
3x2 – 6x + 3
Making Zero
Similar to integers, the positive and negative
Alge-Tiles combine to “make zero”.
Examples:
What expressions are represented
by the following groups of tiles?
1)
2)
3)
4)
5)
6)
7)
8)
9)
10)
11)
Draw tiles to represent the following expressions:
1) 5x + 2
2) -6x – 4
3) 4x2 – 3x + 6
4) -7x2 + 5x – 6
5) -2x2 – 3x – 11
6) 8x2 – 6x + 9
7) -3x + 4x
8) -5x + 12x
9) 10x2 + 6x2
10) 5x + 3x
11) -3x2 + 4x2
12) -3x – 5x
1) 5x + 2
2) -6x – 4
3) 4x2 – 3x + 6
4) -7x2 + 5x – 6
5) -2x2 – 3x – 11
6) 8x2 – 6x + 9
7) -3x + 4x
8) -5x + 12x
9) 10x2 + 6x2
10) 5x + 3x
11) -3x2 + 4x2
12) -3x – 5x