The document provides instructions and examples for writing algebraic expressions and equations to represent word problems and numeric relationships. It defines variables, shows how to relate variables in words and then write algebraic representations. Examples include writing expressions for phrases like "four times a number plus 20" and equations for word problems involving the number of tickets sold or dog treats eaten. Tables are used to show numeric relationships that can then be written as equations. The document emphasizes defining variables, relating variables in words, and then writing the appropriate expression or equation.

1. Agenda 9/8/10
Hand in any outstanding papers or show me your
covered book.
Any questions on Glyph or online book?
Ch. 1.1: Using variables
1
name
page 6 # 2 ­ 6, 14, 15, 18, 19, 21 ­ 26, 30, Green Trapezoids
31, 33 ­ 37, 40, 42, 43
9/8/10

2. The product of 6 and a A number increased by 16 A number decreased by 9
number is the same as 4 decreased
6x by 3 times the number k ­ 9
z + 16 = 4 ­ 3z
Four increased by a Seven increased by a Two less than a number
number is 20 number
n ­ 2
4 + x = 20 7 + n
Four more than a number 10 more than twice a A number decreased by 6
is the same as 3 times the number
sum of the number and 2
10 + 2r g ­ 6
c + 4 = 3(c + 2)
Eight decreased by 5 Four more than 5 times a Three times the sum of x
times a number is 18 number is the same as 3 and 4 is 21
times the number
8 ­ 5x = 18 3(x + 4) = 21
4 + 5x = 3x
Twelve decreased by 5 Five more than twice a Nine increased by a
times the sum of a number number
number and 7 5 + 2y
12 ­ 5(x + 7) 9 + w
The product of 6 and a A number increased by 16 A number decreased by 9
number is the same as 4 decreased
6x by 3 times the number k ­ 9
z + 16 = 4 ­ 3z
Four increased by a Seven increased by a Two less than a number
number is 20 number
4 + x = 20 7 + n n ­ 2
Four more than a number 10 more than twice a A number decreased by 6
is the same as 3 times the number
sum of the number and 2 g ­ 6
c + 4 = 3(c + 2) 10 + 2r
Eight decreased by 5 Four more than 5 times a Three times the sum of x
times a number is 18 number is the same as 3 and 4 is 21
8 ­ 5x = 18 times the number
3(x + 4) = 21
4 + 5x = 3x
Twelve decreased by 5 Five more than twice a Nine increased by a
times the sum of a number number
number and 7
12 ­ 5(x + 7) 5 + 2y 9 + w

3. 1.1 USING VARIABLES 9/8
a symbol used to represent an unspecified
Variable or unknown value
Factors quantities being multiplied
Product the result of multiplication
Quotient the result of division
Algebraic mathematical phrase that can include numbers,
Expression variables, and operation symbols
Equation a mathematical sentence with an
equal sign
Define a variable and write an algebraic expression for each phrase.
Example 1: 8 less than three times a number
Relate: 8 less than three times a number
Define: Let a = the number
Write: 3 a ­ 8
3a ­ 8

4. Define a variable and write an equation.
Example 2: Bob is three years older than twice his brother's age.
Relate: 2 times Bob's brother's age plus three equals Bob's age
Define: Let x = Bob's brother's age; Let y = Bob's age
Write: 2x + 3 = y
2x + 3 = y
How old is Bob when his brother is 12?
Why did we use x and y for variables?
What are good variables to use / not use and why?
Let's practice on your white boards:
the sum of n and 7 n + 7
the difference of n and 6 n ­ 6
the product of 5 and x 5x
the quotient of f and 10 f
10
the quotient of 20 and h 20
h

5. Write an algebraic expression for each
Four times a number plus 20 4x + 20
6 less than 10 times a number 10m ­ 6
The quotient of 8 and number 8
y
The product of 11 and a number 11n
A number divided by 20 w
20
The difference of twice a number and 9 2x ­ 9
Steps for writing an equation:
Relate: write the relationship of the variables
in words.
Define: write what variable each letter
represents
Write: write the equation

6. Example:
Write an equation to show the total income from
selling tickets to the school play for $5 each.
Relate:
total income = $5 times the number of tickets sold
Define:
t = total income
n = number of tickets sold
Write:
t = 5n
Now you try:
Sophia's Sounds sells CDs for $14 each. Write an
equation for the total cost of a given number of CDs.
Relate: total cost = $14 times number of CDs
Define: c = total cost
n = number of CDs
Write: c = 14n

7. "The total cost is the number of cans times $.70."
t = total cost, n = number of cans t = $.70n
We can make a table of this information, relating the
number of cans to the total cost:
Let's try another:
Oh, no!! Shaggy left the dog­treat box open.
Scooby Doo can eat 6 treats per minute.
Relate, define variables, write an equation
and create a table for this situation.

8. Relate: 6 times the number of minutes
equals the # of treats eaten
Let m = minutes
Define: Let t = # of treats eaten
Write: t = 6m
Number of
Treats Eaten
Table
One can also read a table, determine the relationship, define
variables, then write an equation to model the situation:

9. Relate: 2,000 times the number of minutes equals # of spins
Define: Let m = minutes and s = spins
Write: s = 2,000m
Please try to make an equation for each table.
(What must you do to "x" to get to "y"?)
Input (x) Output (y) Input (x) Output (y) Input (x) Output (y) Input (x) Output (y)
5 10 3 5 1 3 2 5
10 20 6 8 2 5 4 11
15 30 9 11 3 7 6 17
20 40 12 14 4 9 8 23
y = 2x y = x + 2 y = 2x + 1 y = 3x ­ 1

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