TC Name: _____________________________________
Period: _________ Pre-Algebra
Objective: to be able to write variable expressions
Variable – a letter that stands for a number (a,b,c)
Example:
m - miles per gallons
d - dollars
Algebraic expression – a mathematical phrase that uses variables, numerals, and operation symbols
Example: m + 3
3d – 5
In algebraic expression 4x, what is the variable?
Numerical expression – numbers only
3+5
Algebraic Expression - with variable
3x – 5
Numerical Expression or Algebraic Expression? a) 3b – 10
Word
Total
More than
Increased by
b) 14 + 2
c) x – 6
Writing Algebraic Expressions
Vocabulary Tip
Symbol
Word
Symbol
Difference
Fewer than
Less than
Decreased by
Product
Times
Multiply
Twice
Trice
Quotient
Divided by
Split
STEPS:
1) Underline the important vocabulary/words and
numbers.
2) Write in symbols under it, assign a variable and Check
if you need to change the order of the expression.
Change the order if:
More than
“than” – switch
Less than
a) 5 more than m
fewer than
b) 4 less than 3x
Write in symbols:
1) A number z times three
2) A number a divided by 12
3) 5 times the quantity 4 plus a number c
4) 10 less than 2c
5) 2x more than 3
6) x fewer than 7
7) Nine more than a number y
8) 4 less than a number n
9) the sum of nine and eight
RECALL: Identify the operation:
1) More than _____
2) decreased by _____
5) quotient
6) Times _______
_____
3) product _______
4) less than _______
7) divided by _______
8) added by ______
9) Split _____
10) fewer than ______
11) multiply _______
13) twice
14) sum _______
15) fewer than _____
_____
Opposite of a number:
Ex.
4
-9
a) The product of d and the opposite of 5.
12) increased by _____
12
b) The sum of g and the opposite of -2.
Quantity: parenthesis ( )
Ex.
c) five times the quantity of a sum of 3 and “b”
d) 10 divided by the quantity of “h” and 4
B. Write in symbols the following expressions:
1) The value in cents of 5 quarters
2) The number of days in k years
3) 16 more than m
4)10 fewer than j
5) n divided by 3
6) the product of c and 3
7) d dozen of eggs
8) The value in cents of q quarters
9) The difference of y and 9.
10) Eight multiply by b.
11) Nine less than four times a number
12) Nine minus the product of four and a number
13) The product of a number and opposite of four.
14) Four less nine times a number
15) “x” divided by 3 plus the opposite of 10
16) the sum of nine and eight
17) fourteen decreased by a number p
18) the product of a number and 6
19) seven less than a number t
20) seven divided by twice a number
21) the product of 9 and a number n
22) thirty-two divided by a number y
SC Name: _____________________________________
Period: _________ Pre-Algebra
Objective: to be able to _______________________________________________
Variable – a _________ that stands for a number (a,b,c)
Example:
m - miles per gallons
d - dollars
Algebraic expression – a mathematical phrase ____________________________________________________
Example: m + 3
3d – 5
In algebraic expression 4x, what is the variable?
Numerical expression – numbers only
3+5
Algebraic Expression - with variable
3x – 5
Numerical Expression or Algebraic Expression? a) 3b – 10
Word
Total
More than
Increased by
b) 14 + 2
c) x – 6
Writing Algebraic Expressions
Vocabulary Tip
Symbol
Word
Symbol
Difference
Fewer than
Less than
Decreased by
Product
Times
Multiply
Twice
Trice
Quotient
Divided by
Split
STEPS:
3) _______________ the important
vocabulary/_______and ______________
4) ________________________ under it, assign a variable
and _____________ if you need to change the order of
the expression.
Change the order if:
More than
“than” – switch
Less than
a) 5 more than m
fewer than
b) 4 less than 3x
Write in symbols:
1) A number z times three
2) A number a divided by 12
3) 5 times the quantity 4 plus a number c
4) 10 less than 2c
5) 2x more than 3
6) x fewer than 7
7) Nine more than a number y
8) 4 less than a number n
9) the sum of nine and eight
RECALL: Identify the operation:
1) More than _____
2) decreased by _____
5) quotient
6) Times _______
_____
3) product _______
4) less than _______
7) divided by _______
8) added by ______
9) Split _____
10) fewer than ______
11) multiply _______
13) twice
14) sum _______
15) fewer than _____
_____
Opposite of a number:
Ex.
4
-9
a) The product of d and the opposite of 5.
12) increased by _____
12
b) The sum of g and the opposite of -2.
Quantity: ________________________________
Ex.
c) five times the quantity of a sum of 3 and “b”
d) 10 divided by the quantity of “h” and 4
B. Write in symbols the following expressions:
1) The value in cents of 5 quarters
2) The number of days in k years
3) 16 more than m
4) fewer than j
5) n divided by 3
6) the product of c and 3
7) d dozen of eggs
8) The value in cents of q quarters
9) The difference of y and 9.
10) Eight multiply by b.
11) Nine less than four times a number
12) Nine minus the product of four and a number
13) The product of a number and opposite of four.
14) Four less nine times a number
15) “x” divided by 3 plus the opposite of 10
16) the sum of nine and eight
17) fourteen decreased by a number p
18) the product of a number and 6
19) seven less than a number t
20) seven divided by twice a number
21) the product of 9 and a number n
22) thirty-two divided by a number y
TC Name: _____________________________________
Period: _________ Pre-Algebra
Objective: to be able to write algebraic equations in symbols
Algebraic Equation – mathematical statement of equality between algebraic expressions
Ex.
There is an equal sign “=”
a = 5 3x + 5= 24
𝑏
2
=5
“is” means equal
Steps:
1) Highlight “is” and put = under it
2) Highlight the other operation and put the sign under it
3) Look for variable and numbers and write the equation
A) Write the following statements as an equation.
1)
2) opposite of 2 less than a number is 4
3)
4) Four more than 3 times a number is equal to 13.
5) A number increased by nine is fifteen
6) Twice a number is eighteen.
7) Four less than a number is twenty.
8) A number divided by six is eight.
9) Twice a number, decreased by twenty-nine, is seven.
B)
10) Thirty-two is twice a number increased by eight.
SC Name: _____________________________________
Period: _________ Pre-Algebra
Objective: to be able to ______________________________________________________ in symbols
Algebraic Equation – mathematical ________________________________________ between algebraic expressions
Ex.
There is an ___________________________
a = 5 3x + 5= 24
𝑏
2
=5
“is” means equal
Steps:
1) Highlight “_______” and __________ under it
2) Highlight the other _________________and put the ___________ under it
3) Look for______________________________________ and write the equation
A) Write the following statements as an equation.
1)
2) opposite of 2 less than a number is 4
3)
4) Four more than 3 times a number is equal to 13.
5) A number increased by nine is fifteen
6) Twice a number is eighteen.
7) Four less than a number is twenty.
8) A number divided by six is eight.
9) Twice a number, decreased by twenty-nine, is seven.
10) Thirty-two is twice a number increased by eight.
11) Jessie had 100 coins. He gave n coins to his friend. What expression should the number of coins Jessie has left?
B)
The product of nine and a number, decreased by six
Thirty divided by seven times a number
seven divided by twice a number
Jenny earns $30 a day working part time at a supermarket. Write an algebraic expression to
represent the amount of money she will earn in d days.
#___________Name: ____________________________________ Pre-Algebra
Objective:
Steps:
Equation
NOTE:
“is”
1) A number increased by nine is fifteen
1) Highlight “is” and put = under it
2) Highlight the other operation and put the sign under it
3) Look for variable and numbers to complete the equation
2) Twice a number is eighteen.
3) Four less than a number is twenty.
4) A number divided by six is eight.
5) Twice a number, decreased by twenty-nine, is seven.
6) Thirty-two is twice a number increased by eight.
7) The quotient of fifty and five more than a number is ten. 8) Twelve is sixteen less than four times a number.
#___________Name: ____________________________________ Pre-Algebra
Objective:
Steps:
Equation
NOTE:
“is”
1) Highlight “is” and put = under it
2) Highlight the other operation and put the sign under it
3) Look for variable and numbers to complete the equation
1) A number increased by nine is fifteen
2) Twice a number is eighteen.
3) Four less than a number is twenty.
4) A number divided by six is eight.
5) Twice a number, decreased by twenty-nine, is seven.
6) Thirty-two is twice a number increased by eight.
7) The quotient of fifty and five more than a number is ten. 8) Twelve is sixteen less than four times a number.
9) Twice a number is twenty-eight.
10) The quotient of thirty-nine and a number is three
11) Five less than three times a number is forty-six.
number and five.
12) Three is twenty-one, divided by the sum of a
9) Twice a number is twenty-eight.
10) The quotient of thirty-nine and a number is three
11) Five less than three times a number is forty-six.
number and five.
12) Three is twenty-one, divided by the sum of a
Name: _____________________________________
Period: _________ Pre-Algebra
Objective: to be able to determine if the given values are solutions for given equations
Equation – a mathematical sentence with an equal sign (=) (a sentence)
Example:
3x =12
9+2 = 11
Open sentence – an equation with one or more variables
Example: 3x = 12
CFU: Give an example of an equation
x+7
x + 7 = 37
Which is an open sentence? A. 4+5 = 9
B) 4 +x = 15
An equation could be True or False or an open sentence.
Tell whether the equation is true, false or an open sentence.
I do:
You do:
We do:
1) 6 + 12 = 18
6) 5 + 9 = 14
10) 9 ∙3 = 21
2) 6 = 4+ 3
7) 4x – 8 = 25
11) 4 + d = 6
3) 8 + x = 2
4) 3 – 7 = 4 + (-8)
8) 20 = 2∙10
12) 3+ (-7) = 10
9) x- 10 = 22 - x
5) -2 (5-3) = 6 (-1)
CHALLENGE:
Write an equation for the given sentence and state whether the equation is true or false.
1)
2)
3)
4)
Three times the opposite of -4 is -12.
Eight times the absolute value of -6 is 40.
Negative two times the opposite of 8 is -16.
Nine times the absolute value of -4 is -36.
Name: _____________________________________
Period: _________ Pre-Algebra
Objective: to be able to determine if the given values are solutions for given equations
Solution of an Equation -a number is a solution of an equation if it makes the equation true (correct)
Example: 9 – m =3; 6
Not a solution:
c+5=3;2
24 = c + 29; -2
CFU: What is a solution of an equation?
Is the given number a solution of the equation?
I do:
We do:
You do:
1) 24 = c + 29 ; -2
3) 8 = a + 3 ; 10
5) 175 – x = 150; 25
2) 20 – c = 12; 8
4) 120 + x = 75
6) -6k ÷ 8 = 3 ; -4