Algebra tiles have
a variety of other names: algetiles, math tiles, and
virtual tiles. Algebra tiles can help you visualize
equivalent algebraic expressions and/or equations.
Many of the real tiles have a positive and a negative
side. The virtual algebra tiles activities will use
multi-coloured positive tiles. The reverse (negative)
side of each of these tiles is red. It helps to understand
that negative tiles have one positive and one negative
dimension.
Some algebra kits
use black tiles for positive areas and red for the flip
(negative) sides. Click the "Black/Red Tiles"
button for additional information.
The study of mathematics using letters.
The terms are the "words" of an algebraic expression or equation.
terms
-12, 5, -4x0, 15x0y0,
6x4,
5x3, 4x2y, -x2, x
Terms include numbers (numerical coefficients)
and letters (variables). Terms are connected by addition or subtraction.
constant ("to stand
firm") term
-12, 5, -4x0, 15x0y0
A term with unchanging value. The degree
of a constant term is 0.
variable
("changes") term
6x4, 5x3, 4x2y,
-x2, x
A variable is a letter or symbol representing
an unknown quantity(number). The value of a variable term changes depending on the
value of the variable.
The number
attached (by multiplication) to the variable(s). You can multiply by 1 without
changing the value, therefore the numerical coefficient of a variable term without a
number is 1.
monomial
("one term")
-12, 15x0y0, 6x4,
-x2, x
one term polynomial
= 3x
binomial
("two terms")
x2 + 3, 3y3 - 2x
two term polynomial
= 3x - 2
trinomial
("three terms")
5x3 + 2xy - 4
three term polynomial
= 2x2 + x - 1
polynomial ("many
terms")
15x0y0
x2 + 3
5x3 + 2xy - 4
-6x4 + 4x3 - 7xy - 9
Polynomial can be used to represent any
number of terms. Polynomial is often used to represent more than three terms.
polynomial degree
6x5 +
5x3 + 3
3x2y3
+ 3
The polynomial degree for both examples is
5. The degree is determined by the term with the greatest power. If there is
more than one variable in a term, add the exponents to get the degree.
like terms
2x, 3x, -6x
Like terms have the same
variable(s) and the same degree for each variable.
