ONE STEP EQUATIONS – ADD AND SUBTRACT
INTRODUCTION
The objective for this lesson on One Step Equations – Add and Subtract is, the student will solve
one-step equations with addition and subtraction in mathematical and real-world situations.
The skills students should have in order to help them in this lesson include, writing and
evaluating expressions.
We will have three essential questions that will be guiding our lesson. Number One, why do we
use variables in solving equations? Number Two, what are the goals when solving equations?
And Number Three, in an addition equation, how do we isolate the variable?
Begin by completing the warm-up on problems with addition and subtraction to prepare for the
lesson on one-step equations with addition and subtraction.
SOLVE PROBLEM – INTRODUCTION
The SOLVE problem for this lesson is, Maria’s mother is planning to help her buy a new pair of
jeans. They are on sale. The total cost of the jeans, including tax, is seventeen dollars. Her
mother gave her fourteen dollars and fifty cents. How much more money does Maria need to
purchase the jeans?
In Step S, we Study the Problem. First we need to identify where the question is located within
the problem and underline the question. The question for this problem is, how much more
money does Maria need to purchase the jeans?
Now that we have identified the question we need to put this question in our own words in the
form of a statement. This problem is asking me to find the amount of money Maria needs.
During this lesson we will learn how to solve one-step equations with addition and subtraction in
order to complete this SOLVE problem at the end of the lesson.
ADDITION EQUATIONS – CONCRETE MODELS
Place one yellow unit tile on the left side of the scale.
Identify the value of one yellow tile. One
Is the scale balanced? Explain your thinking. No, because the value on one side is positive one
and the value on the other side is zero.
What can we do to balance the scale? Place a yellow unit tile on the right side.
What does it mean for the scale to be balanced? Both sides need to be equal in value.
Place two yellow tiles on the left side of the scale.
What is the value of the two tiles? Two
Is the scale balanced? No
What can we do to balance the scale? Place two yellow tiles on the right side of the scale.
What does it mean for the scale to be balanced? Both sides need to be equal in value.
When modeling equations there are two things that we must focus on.
The first is to isolate the variable. What does it mean to be isolated? To be alone or by yourself.
Let’s look at the equation c plus two equals three.
What is the variable in the equation? C
Explain the meaning of the word variable. A variable is a symbol that represents an unknown
value or number. Variables are usually written as letters.
The second focus is to balance the equation.
What does the equal sign mean? If two things are equal, they have the same value.
In other words, whatever is on one side of the equation (in this case, c plus two) must equal what
is on the other side (in this case, three).
Place cup on the scale on the left. The cup represents our variable c.
How can we model adding two? Place two yellow tiles on the left side of the balance scale.
What needs to be placed on the right side of the scale to represent the three? Three yellow tiles
What are the two goals when working with equations? Isolate the variable and balance the
equation; whatever you do to one side you must do to the other.
How can we isolate the variable? How could you use the idea of opposite operations to isolate
the variable? To isolate the variable, we perform the opposite operation or inverse operation.
What type of equation do we have? Addition
What operation can we use to isolate the variable? Explain. We can use subtraction because it is
the opposite of addition.
Let’s subtract, or take away, the two yellow tiles by removing them from the scale.
Is the variable now isolated, or alone? Yes
Is the equation still balanced? Explain your thinking. No, because the same operation must be
performed on both sides.
How can we balance the equation? Take away two yellow tiles from the right side.
Is the equation balanced now? Justify your answer. Yes, because we have performed the same
operation to both sides of the equation.
What is the value of c? c equals one
Let’s check the problem using tiles.
Go back to the original equation.
c plus two equals three
What is the value of c? one
Substitute one yellow tile for the c.
What is the value on the left? Three yellow tiles
What is the value on the right? Three yellow tiles
Is the equation balanced? Is our answer correct? Yes, because three yellows equals three
yellows, the equation is balanced and we know the answer is correct.
Let’s look at the next equation, c plus four equals six.
Place a cup on the scale on the left to represent our variable c.
How can we model adding four? Place four yellow tiles on the left side of the balance scale.
What needs to be placed on the right side of the scale to represent the six? Six yellow tiles
What are the two goals when working with equations? Isolate the variable and balance the
equation; whatever you do to one side you must do to the other.
How could we isolate the variable? How could you use the idea of opposite operations to isolate
the variable? To isolate the variable, we perform the opposite operation or inverse operation.
What type of equation do we have? Addition
What operation can we use to isolate the variable? Explain. We can use subtraction because it is
the opposite of addition.
Let’s subtract, or take away, the four yellow tiles by removing them from the scale.
Is the variable now isolated, or alone? Yes
Is the equation still balanced? Explain your thinking. No, because the same operation must be
performed on both sides.
How can we balance the equation? Take away four yellow tiles from the right side.
Is the equation balanced now? Justify your answer. Yes, because we have performed the same
operation to both sides of the equation.
What is the value of c? c is equal to two
Let’s check the problem using tiles. Go back to the original equation. c plus four equals six.
What is the value of c? Two
Substitute two yellow tiles for the c.
What is the value on the left? Six yellow tiles
What is the value on the right? Six yellow tiles
Is the equation balanced? Is our answer correct? Yes, because six yellows equal six yellows, the
equation is balanced and we know the answer is correct.
ADDITION EQUATIONS – PICTORIAL
What letter do we use to represent the cup? c
What letter do we use to represent the positive two? The y
c plus two y equals three y
What is our first step in solving the equation? Isolate the variable
How can we isolate the variable? We can subtract the two ys by crossing them out.
Have we isolated the variable? yes
Is the equation balanced? Explain your answer. No, because we only subtracted the positive two
from one side.
What do we need to do to balance the equation? Subtract two y from the right side of the
equation because whatever operation you do to one side, you must do to the other.
What is the value of c? c is equal to y or one yellow
Let’s check the equation by substituting the value of c, which is y, into the original equation. Y
plus two Ys equal three Ys. Three Ys are equal to three Ys.
Is the equation balanced? Yes, because three Ys equal three Ys.
Let’s look at the next equation. C plus four Ys are equal six Ys.
What is our first goal? Isolate the variable. We can subtract the four Ys by crossing them out.
Is the variable now by itself? Yes
Is the equation balanced? Explain your answer. No
What do we need to do to balance the equation? Subtract four Ys from the right side of the
equation because whatever operation you do to one side, you must do to the other.
What is the value of c? c equals two Ys or two yellows.
Let’s check the equation by substituting the value of c which is two Ys into the original equation.
Two Ys plus four Ys is equal to six Ys. Six Ys are equal to six Ys.
Is the equation balanced? Yes, because six Ys are equal to six Ys.
ADDITION EQUATIONS
C plus two equals three.
What is the first step in solving an equation? Isolate the variable.
Explain how to isolate the variable. Perform the opposite operation.
What operation will we use in an addition equation to isolate the variable? Subtracting a two.
Subtract two from the left side of the equation.
Is the equation now balanced? No.
What do we need to do to balance the equation? Subtract two from the right side of the equation
because whatever operation you do to one side, you must do to the other.
What is the value of c? C is equal to one.
Substitute the value of c back into the original problem to check. C plus two is equal to three.
When we substitute the value of one in for c, one plus two is equal to three, and we have the
value of three is equal to three.
SUBTRACTION EQUATIONS
What are the two goals in solving any type of equation? Isolate the variable and balance the
equation.
What operation did we use to isolate the variable in the addition equations? Subtraction, which
is the opposite, or inverse, of addition.
What operation should we use to isolate the variable in a subtraction equation? Addition, which
is the opposite, or inverse, of subtraction.
Let’s look at the equation c minus three equals five.
What does the equation mean? Subtract three from a number to get a difference of five.
Let’s draw a pictorial representation of this equation.
How can we isolate the variable in this equation? By adding a value to both sides of the
equation, because the opposite of subtraction is addition.
What number is being subtracted from the variable c? Three
How can we model adding three to the left side of the equation? Add three Ys.
Is the equation now balanced? No
What do we need to do to balance the equation? Add three Y’s to the right side of the equation,
because what you do to one side, you must do to the other.
What is the value of c? c is equal to eight Y.
How can we check the equation? Substitute the value of c, which is eight Y’s, into the original
equation.
Is the equation balanced? Yes, because five Ys equal five Ys.
Write the equation c minus three equals five in the “Solve the equation” box.
What is our first goal? Isolate the variable.
How can we isolate the variable? Use the opposite or inverse operation.
What operation will help us to isolate the variable? Addition
Because this is a subtraction equation, we can isolate the variable by adding three to both sides.
Add three to the left side of the equation.
Is the equation now balanced? No
What do we need to do to balance the equation? Add three to the right side of the equation
because whatever operation you do to one side, you must do to the other.
What is the value of c? c equals eight
Substitute the value of c back into the original equation to check. c minus three equals five. c is
equal to eight, eight minus three is equal to five. And five is equal to five.
SOLVE CLOSURE
Now let’s go back to the SOLVE problem from the beginning of the lesson. Maria’s mother is
planning to help her buy a new pair of jeans. They are on sale. The total cost of the jeans,
including tax, is seventeen dollars. Her mother gave her fourteen dollars and fifty cents. How
much more money does Maria need to purchase the jeans?
In the S Step, we Study the Problem. First, underline the question, then complete this statement.
This problem is asking me to find, the amount of money Maria needs.
In the O Step, we Organize the Facts. First we Identify the Facts. Maria’s mother is planning to
help her buy a new pair of jeans./ They are on sale./ The total cost of the jeans, including tax, is
seventeen dollars./ Her mother gave her fourteen dollars and fifty cents./
After we Identify the Facts, then we go back and Eliminate the unnecessary facts. A fact is
unnecessary, if it does not have information in it to help us determine the amount of money
Maria needs to purchase the jeans. We delete Maria’s mother is planning to help her buy a new
pair of jeans and they are on sale.
Then we list the necessary facts. Jeans cost seventeen dollars. Mother gave her fourteen dollars
and fifteen cents.
In the L Step, we Line Up a Plan. Write in words what your plan of action will be. Write an
equation that we can use to solve the problem and then solve the equation.
Choose an operation or operations. Subtraction.
V, Verify Your Plan with Action. First, estimate your answer. Our estimate here is about two
dollars. Then carry out your plan. X plus fourteen dollars and fifty cents is equal to seventeen
dollars. We solve with subtraction to isolate the variable. We keep our equation balanced by
subtracting fourteen dollars and fifty cents from each side of the equation. We find the value of
our unknown, which is x, which is two dollars and fifty cents.
E, Examine Your Results. Does your answer make sense? Compare you answer to the question.
Yes, because we were looking for the amount of money Maria needs.
Is your answer reasonable? Compare your answer to the estimate. Yes, because it is close to the
estimate of two dollars.
Is your answer accurate? Check your work. Yes.
Write your answer in a complete sentence. Maria still needs two dollars and fifty cents to buy
jeans.
CLOSURE
Now let’s go back and discuss the essential questions from this lesson.
Our first question was, why do we use variables in solving equations? Variables take the place
of unknown values in equations.
Number Two, what are the goals when solving equations? Isolate the variable and balance the
equation.
Number Three, in an addition equation, how do we isolate the variable? In an addition equation,
we use subtraction to isolate the variable.