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5.18 Study Guide
Algebraic Expressions
Learning Goals
5.18
a)
b)
c)
d)
investigate and describe the concept of variable;
write an open sentence to represent a given mathematical relationship, using a variable;
model one-step linear equations in one variable, using addition and subtraction; and
create a problem situation based on a given open sentence, using a single variable.
Vocabulary
Variable Expression - mathematical phrase which can contain numbers, operators (add, subtract,
multiply, divide), and at least one variable. Expressions do not contain an =
sign. (Also known as algebraic expressions)
example: n + 7
Variable – a letter or symbol representing a varying quantity
example: n + 6 = 8
Open Sentence – a mathematical sentence which contains one or more variable and an = sign
n+7=9
Examples and Explanations
Problem Situation
Mike had some baseball cards and his brother
gave him four more
7 boxes each contained the same number of
apples
The cookies were split evenly among 3 friends
Problem Situation
Mike had six baseball cards, his brother gave
him four more, and now he has 18 cards.
7 boxes, each containing the same number of
apples, totaled 84 apples in all.
How many cookies were baked if four friends
each received three cookies?
Variable Expression
b+4
7a
c/4
Open Sentence
b + 4 = 18
7a = 84
c/4 = 3
Phrases can also be used to represent expressions
Phrase
four divided by a number
eight more than a number
seven less than a number
six times a number
Multiplication and Division
can be represented in
different forms
Multiplication
8x4
8∙4
8(4)
8n
Division
8÷4
8/4
8
4
Variable Expression
4÷n
t+8
k–7
6n
Practice at Home

Continue to practice basic addition, subtraction, multiplication and division facts. It is vital that
students know the basic facts in order to solve these equations.

Use simple phrases and real life problem situations to create open sentences or expressions.
Sample Questions
1. Which word describes the letter “p” in the expression below?
9xp
A
B
C
D
whole number
operation
algebra
variable
2. Which of these could be solved using the open sentence 7 – 2 = h?
A
B
C
D
Ryan had 7
now?
Ryan had 7
altogether?
Ryan had 7
in all?
Ryan had 7
hamsters. Each hamster had two babies. How many hamsters does Ryan have
hamsters. The bought two more at the pet store. How many does he have
hamsters. He gave each of them 2 treats? How many treats did he give them
hamsters. He gave 2 to a friend. How many does he have left?
3. Kathleen has three times as many seashells in her collections as her friend Gabby. Gabby has
15 seashells. Which number sentence could be used to find k, the number of seashells that
Kathleen has?
A
B
C
D
k = 15 - 3
k = 15 + 3
k = 15 x 3
k = 15/3
4. Which of the following phrases represents the phrase “4 less than a certain number”?
A
B
C
D
4
4
n
n
-n
+n
-4
+4