Transcript Moving Straight Ahead - Day 1- Verbal Expressions

Moving Straight Ahead
The Study of Algebra
Algebra is the study of mathematics
that explores relationships between
variables. Let’s EXPLORE further!!!!
Vocabulary
A letter that represents a
number; something that
changes
A collection of variables,
numbers and symbols
( +, -, *, ÷)
A change that occurs in a
predictable way
A RULE; when you set an
expression equal to
something
The quantities separated by
a plus or minus sign
Number in front of a
variable
4e + 5
-2x + 400 = 244
40 + 3x = 8
•Is this an expression or an
equation?
•What is the variable?
•What are the terms?
•What is the coefficient?
•What is the constant term?
40 + 3x = 8
•This is an equation!
•The variables is x.
•The terms are 40, 3x
and 8
•The coefficients is 3.
•The constant term is 40
Moving Straight Ahead
Before you can solve
algebraic equations, you
must first be able to
translate them…
Translating Verbal Phrases
transfer
explain
interpret
decode
Writing Equations and
Expressions
The following common words and phrases indicate,
addition, subtraction, multiplication, and division.
Addition
Plus
The (sum) of
Increased by
Total
More than **
Added to
Subtraction
Minus
The (difference)
of
Decreased by
Fewer than
Less than **
Subtracted From
REMEMBER – “IS” means “equal to”
Multiplication
Division
Times
Divided by
The product of The quotient of
Multiplied by
Per
Of
Each
Determine what the phrase means…addition,
subtraction, multiplication, or division.
1. More than
Add
2. Divided by
Divide
3. The product of
Multiply
4. Multiplied by
Multiply
5. The difference of
Subtract
6. Increased by
Add
7. The quotient of
Divide
8. Fewer than
Subtract
Let’s translate these verbal
expressions together:
1. The sum of 5 and a number
5+n
2. The difference of 10 and some number, r
10 - r
3. The product of -3 and some number, s
-3s
4. The quotient of -25 and some number, j
-25 / j
Your turn!
1. The sum of 8 and a number is 12
2. The difference of 24 and a number
3. The product of 5 and a number is 45
4. The quotient of 5 and a number
5. 2/3 of a number is -8
Check your work!
 The sum of 8 and a number is 12 8 + n = 12
 The difference of 24 and a number 24 - n
 The product of 5 and a number is 45 5n = 45
 The quotient of 5 and a number 5/n
 2/3 of a number is -8 2/3n = -8
Understanding Linear
Equations
EQ: How do I take a word
problem and turn it into a
linear equation?
Linear Equation Vocabulary
 Equation: is a mathematical sentence that contains an
equal sign (=). If an equation contains at least one
variable, it is called an algebraic equation.
YOU MAY NEED TO WRITE ALGEBRAIC EQUATIONS
TO SOLVE WORD PROBLEMS.
 Linear Equation: is an equation where the variable or
variables are only raised to the first power.
Important Points when writing
equations
1. Write a short verbal model to represent the math problem
include operations
2. Substitute in the given numbers
1. Example: The Apollo 11 mission lasted about 195.5 hours.
The flight from Earth to the moon lasted about 103 hours,
and the flight from the moon back to Earth lasted about 71
hours. About how many hours did the Apollo 11 astronauts
spend on the moon? Write a verbal model. Let t represent
the number of hours the astronauts spent on the moon.
2.
Length of mission = length of flight to moon + time spent on moon + length of flight to earth.
3. 195.5 = 103 + x + 71
Let’s try one together
 You have 48 hours to visit a friend in Boston. Travel
time to Boston is 4.5 hours and the return trip is 5
hours. How long can you stay in Boston?
1. Write a verbal model that represents this problem.
Now another:
 A DVD contains 7.5 hours of bonus material, which is 3
times longer than the movie itself. Write and solve an
equation to find the length of the movie.
1. Write a verbal model that represents this problem.