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Mathematics 9
Unit: Algebraic Operations
Name:
Date:
Variables, Expressions
and Equations
Define: Variable, Coefficient, Term, Constant Term, Expression, Equation,
Monomial, Binomial, Trinomial, Polynomial, Degree
Remember:
Variable: letter that
represents an unknown value.
Coefficient: number that
multiplies the variable.
3 in 3x2 and 2 in 2x.
Degree: highest degree
(exponent) of a variable. Ex: 2
3x 2  2 x  5
Constant Term: term in
which the value remains
the same.
Term: numbers, variables or
the product/quotient of
numbers and variables. Terms
are separated by
addition/subtraction signs.
Class Example:
For each expression, identify the number of terms, the coefficient of the
first term, state whether the expression is a monomial, binomial, trinomial or
polynomial, the degree of the polynomial and any constant terms.
 5m  1  2m 2
3 terms; coefficient of first term is -5; trinomial;
degree 2; constant term is 1.
Try On Your Own:
 h 2  3  4h
Mathematics 9
Unit: Algebraic Operations
One Tiles
Name:
Variable Tiles
Date:
Variable Squared Tiles
Shaded tiles are positive; Clear are negative
Class Example:
Model the polynomial using algebra tiles.
 h 2  3  4h
Try On Your Own:
2b 2  b  4
Mathematics 9
Unit: Algebraic Operations
Mathematics
+
×
÷
=
x, a, q, t, p, y, z, n, d, g, etc.
7x
n+6
t-9
4x + 7
(x)(x) or x2
Name:
Date:
English Equivalent
plus, add, increase, greater than, larger,
augment
subtract, minus, negative, decrease, less than,
reduce, diminish
times, of, multiply
divided, goes into, a certain number of parts
equal, equal to, is, results in, gives you, makes
A number, an age, a quantity, a mass, a volume,
a certain amount, etc.
seven times a number, a number times seven
A number increased by six, six larger than a
number, etc.
A number decreased by nine, nine less than a
number, a number reduced by nine, etc.
Four times a number plus seven equals eight
A number times itself, a number squared
Class Example:
Write an English phrase for the mathematical phrase: 6 – n = 15
Answers may vary;
Six less a number is equal to fifteen.
Write a mathematical phrase for the English phrase: “ a number tripled is
divided by seven and then decreased by nine.”
3n ÷ 7 – 9
Try On Your Own:
Write an English phrase for the mathematical phrase: 7 + 2p = 18
Write a mathematical phrase for the English phrase: “fifteen less than onehalf a number.”