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Math 84
Activity # 17
“Introduction to Variables and Expressions & Word Problems”
Your Name: ___________________ Team Member #1__________________
Team Member #2.______________ Team Member #3__________________
Task 1:
A variable is a letter used to represent a number (usually an unknown number). Before we can use
a variable in mathematics, we must define it.
We must specify what it represents. Such as, “g = Gunter’s secret number”
1. a) Everyone in your group should think of a number in between 1 – 20. Don’t forget
your number. Write it down on a scratch piece of paper if you have to but don’t
let anyone know what it is! It’s a secret!
b) Since we don’t know what the actual values are for each person’s number, we will
need to use variables to represent them. Use each person’s first letter in their first
name to assign variables. If your group has identical variables use the first letter in
their last name or middle name.
Person 1’s variable = _______
Person 2’s variable = _______
Person 3’s variable = ______
Person 4’s variable = ______
TASK 2:
An algebraic expression is a collection of numbers and variables connected by mathematical
operations. Some examples are:
x + 9,
r • t,
3 – y.
We can use variables in mathematical expressions the same way we use numbers because a
variable is really a number. We just don’t know what number it may be.
Let’s consider a sum of these secret values we made in Task 1. In this manner we can write an
algebraic expression to represent the sum of these secret numbers as a sum of variables.
1. a) Write an expression to represent the sum of these variables:
_____ + ______ + ______ + _______
b) What word in the above example told us to use addition? ________
2. a) Write an expression to represent the product of these variables.
________
________
________
_______
(variable 1) (variable 2)
(variable 3) (variable 4)
b) What operation did you use between the variables this time? _______
Why?
TASK 3:Fill in the chart below, by translating or converting the “English Expressions” into
“Algebraic Expressions.” This means, you will need to connect variables with other variables and
numbers using one of the mathematical operations ( + - • ÷ ).
English Expression
a) The sum of Person 1’s variable
and five
b) 8 more than Person 3’s variable
c) 4 minus Person 4’s variable
d) Seven less than Person 2’s
variable
e) Five times Person 1’s variable
f) Two-thirds of Person 4’s variable
g) The quotient of six and Person
3’s variable
h) Person 2’s variable divided by 2
Algebraic Expression
There are more English phrases that convert into mathematical operations, can you think of
some?
English words/phrases that mean
ADDITION
English words/phrases that mean
SUBTRACTION
English words/phrases that mean
MULTIPLICATION
English words/phrases that mean
DIVISION
(Now, check in your book, to make sure you found them all!)
TASK 4:
1. Write an algebraic expression that represents “7 increased by Person 3’s variable”
2. What is an equivalent algebraic expression for the expression above in #1. (What other
way can we write this expression?)
3. Why can we create two expressions for this?
4. Write an algebraic expression for:
a) 4 decreased by Person 2’s variable
b) 4 less than Person 2’s variable
5. The above expressions should be DIFFERENT, why are they not the same?
(You may want to double check your answer in Task 3 part d)
TASK 5
The next English Expressions involve more than one operation. Try these out!
English Expression
Algebraic Expression
Nine subtracted from the
product of 8 times Person 4’s
variable
Three times the sum of Person
3’s variable and six
The sum of twice Person 2’s
variable and seven
TASK 6
1. a) Write an algebraic expression for “8 more than Person 1’s variable”
_____ + 8
b) Now, rewrite the same expression below, and Person 1 fill in the answer without
telling what your secret number is:
_____ + 8 = ______
We have now created an ALGEBRAIC EQUATION
2. Describe in your own words how the algebraic expression in part (a) above, differs
from the algebraic equation in part (b) above.
3. Now, rewrite the equation created in #1b above, and solve for Person 1’s secret number.
_____ + 8 = ______
4. What is the value of Person 1’s secret number?
For #’s 5 – 7 below, let’s create our own algebraic equations using the variables that
represent our secret numbers. The Person who’s secret variable is in that problem will fill in
the answer, and then we will be able to solve and find out what our secret numbers are.
5. Person 2’s variable decreased by 3 is what? (Fill in the variable below, and Person 2 fill
in the answer)
______
-
3 = ______
Now, solve this equation.
Person 2’s variable is what value?
6. The product of 5 and Person 3’s variable is what? (Fill in the variable below, and Person
3 fill in the answer)
5 • ____ = ____
Now, solve this equation.
Person 3’s variable is what value?
7. The sum of four and twice Person 4’s variable is what? (Fill in the variable below, and
Person 4 fill in the answer)
4 + 2• ____ = ____
Now, solve this equation.
Person 4’s variable is what value?
TASK 7
Now that we have figured out the value of each person’s secret number, Let’s “evaluate” algebraic
expressions using the numbers.
1.
Below, write the expression that represents the sum of the secret numbers using
each person’s variable
_______ + _______ + _______ + _______
2.
Now, substitute these variables with the secret values they represent and find the
total.
_______ + _______ + _______ + _______ = ______
We just “evaluated” an algebraic expression!!!
3.
It is best to evaluate algebraic expressions by rewriting the expression and putting
parenthesis where the variables are, then substitute the values of each variable in
the parenthesis.
Example:
Evaluate x + 4y for x = 3 and y = 7
x + 4y
( ) + 4( ) =
4.
Evaluate: b – a for a = -2 and b = 5
Fill in the chart below, by translating or converting the “English Expressions” into an “Algebraic
Expressions.” (You already did these in TASK 3, so you can just copy from that)
And, in the third column, “evaluate” the expression by substituting the value for the variable.
English Expression
i)
j)
k)
l)
m)
n)
o)
p)
The sum of Person
1’s variable and five
8 more than Person
3’s variable
4 minus Person 4’s
variable
Seven less than
Person 2’s variable
Five times Person
1’s variable
Two-thirds of
Person 4’s variable
The quotient of six
and Person 3’s
variable
Person 2’s variable
divided by 2
Algebraic
Expression
Numerical Value of the Expression