This document provides examples of translating verbal phrases and word problems into algebraic expressions and equations. It begins by defining key terms like variable, expression, and equation. It then gives examples of evaluating expressions by substituting values for variables. The document shows how to write expressions and equations to represent verbal phrases and solve word problems about population changes, waterfall heights, and spending money on movies and games. It emphasizes setting up and solving equations to find unknown values based on given information.

1. Day 1: Translating Verbal Phrases
Variable
Algebra A letter that is used
Day 1 to represent one or
Translating Verbal Phrases
and sentences
more numbers.
Example
In the expression m+5,
the letter m is the variable
Evaluate a variable
expression
Equation
Substituting a value for each A mathematical sentence
variable in the expression and formed by setting two
simplifying the resulting numerical
expression expressions equal
Example Example
Evaluating 2x+3y when 3x6=18
x=1 and y=4 x+7
gives 2(1)+3(4)
are equations
2+12=14
Solution of an
equation
Finding all solutions of the equation
by using mental math of the
properties of equality
Example
The solution of the
equation n-3=4 is 7

2. Day 1: Translating Verbal Phrases
Homework
Homework
the product of 6 and w is 42 6w = 42
the product of 6 and w is 42 X =
The sum of n and 8 n+8
The sum of n and 8
+
1/3 of y 1/3y
1/3 of y X
12 decreased by the quotient of x and 2
12 decreased by the quotient of x and 2 - 12 - (x/2)
Homework
Homework
twice a number 2n
twice a number x
3 times x equals 12 3x = 12
3 times x equals 12 x =
the difference of c and 11 will be 22 c - 11 = 22
the difference of c and 11 will be 22 - =
seven equals n less than 13
7 = 13 - n
seven equals n less than 13 = -
Writing Expressions Wednesdays Homework
The sum of 8 and twice a number 8 + 2x
A number increased by 5
2/3 of a number decreased by 14 2/3x - 14
7 less than a number
-8 increased by the quotient of 13 and a number -8 + (13/x)
3 more than twice a number The difference of -2 and a number equals 15 -2 - y = 15
4 decreased by the quotient The sum of twice a number and 14 is -8 2y + 14 = -8
of a number and 7
3/4 of a number decreased by -2 is 24 3/4y - (-2) = 24
2x + 3 x + 5 x - 7 4 - x/7

3. Day 1: Translating Verbal Phrases
Writing Equations Word Problem
16 increased by a number is 27 The population of Alexandria,
Virginia increased by 17,000
The product of 1/2 and a number
is 36 people from 1990 to 2000. In
The difference of twice a number
2000, the population of Alexandria
and 3 equals -4 was 128,000 people. Write an
-3 is equal to twice the sum of a equation to find the population of
number and 2 Alexandria in 1990.
16 + y = 27 1/2y = 36 -3 = 2(y + 2) 2y - 3 = -4
Word Problem Word Problem
The population of Alexandria, Lake Ontario, which has a
Virginia increased by 17,000 depth of about 800 feet,
people from 1990 to 2000. In
is four times as deep as
2000, the population of Alexandria
Lake Erie. Write an
was 128,000 people. Write an
equation to find the population of equation to find the depth
Alexandria in 1990. of Lake Erie.
Word Problem Word Problem
Lake Ontario, which has a Pennsylvania, the second state
to enter the Union, was
depth of about 800 feet, admitted 172 years before
is four times as deep as Alaska. Alaska was admitted
Lake Erie. Write an to the Union in 1959. Write
equation to find the depth an equation to determine when
Pennsylvania was admitted to
of Lake Erie.
the Union.

4. Day 1: Translating Verbal Phrases
Word Problem Word Problem
Pennsylvania, the second state Dunanda Falls and Union Falls
to enter the Union, was are two waterfalls in Yellowstone
admitted 172 years before National Park. The difference
Alaska. Alaska was admitted
between the heights of Union
to the Union in 1959. Write
Falls and the height of Dunanda
an equation to determine when
Falls is 100 feet. Dununda Falls
Pennsylvania was admitted to
the Union. is 150 feet tall. How tall is
Union Falls.
Word Problem
Word Problem
Dunanda Falls and Union Falls are
two waterfalls in Yellowstone You rent two movies from a video store for
$6.95 each and g video games for $2.95
National Park. The difference each. You have $25 to spend on the movies
between the height of Union Falls and the video games. Write an equation that
and the height of Dunanda Falls is represents the situation.
100 feet. Dununda Falls is 150
feet tall. How tall is Union Falls.
Word Problem
You rent two movies from a video store for
$6.95 each and g video games for $2.95
each. You have $25 to spend on the movies
and the video games. Write an equation that
represents the situation.
2($6.95) + $2.95g = $25