Topic 7: Solving One-Step Equations
for use before
Bits and Pieces II
(
Investigation 1)
The relationships between addition and subtraction or multiplication and
division are called
inverse operations.
This concept of inverse operations and
undoing an operation is needed to solve algebraic equations.
A. Sue knows that her plant grows 2 inches each wee
k.
1. If
g
represents last week’s height of the plant in inches, write an
expression for the height of the plant this week.
2. Today the plant measures 16 inches in height. Set your expression
equal to 16.
3. How does subtracting 2 find the height of the plant last week?
4. How tall was the plant last week?
5. What would the expression 2
g
mean?
B. Patrick just bought a book for $9. He forgot how much money he had
when he entered the bookstore.
1. If
m
represents the amount of money he had before he bought the
book, write an expression for the amount of money he has now.
2. He counts his money and finds that he has $25 left after he bought the
book. Set your expression equal to 25.
3. Patrick wants to find the value of
m.
He does not know whether he
should add or subtract 9. Determine which operation is correct and
explain your decision.
4. How much money did Patrick have before he bought the book?
7 ? 3 ? 3 ? 7
12 ? 7 ? 7 ? 12
5 ? 4 ?
4 ? 5
16 ?
2 ? 2 ? 16
a
? 3 ? 3 ?
a
s
? 7 ? 7 ?
s
m
?
4 ? 4 ?
m
d
?
2 ? 2 ?
d
Arithmetic
Addition
Subtraction
Multiplication
Division
Algebra
Problem
7.1
C. Each student pays $4 to enter the school dance.
1. If
s
represents a student, write an expression for the amount of money
collected for the dance.
2. The money collected totals $168. Set your expression equal to 168.
Which operation do you need to solve for
s
?
3. How many students came to the dance?
D. Christopher is given sheets of paper to distribute to the class for a
project. He gives each student 5 sheets. He wants to know how many
sheets of paper he started with.
1. Determine whether this is a multiplication or a division situation.
2. If
p
represents the total number of sheets of paper, write an
expression for the number of students in the class.
3. There are 32 students in the class. Set your expression equal to 32.
4. How many sheets of paper did Christopher start with?
Exercises
For each Exercise 1–8, decide which operation is needed to isolate the
variable. Solve the equation.
1.
a
6
14
2.
b
– 39
3. 4
d
12
4.
7
+
t
15
5.
5
6.
6
7.
y
– 13
29
8. 11
h
132
9. Greg counted 11 people who get on the bus at the last stop. Now every
seat is filled. How many people were on the bus before the stop if the
bus has seats for 42 people?
10. There are four dozen daisies in a vase. If every person receives three
daisies until the daisies are gone, how many people will get daisies?
11. The bulletin board has 18 square feet of space. An announcement is
posted that takes up 2 square feet. How many of these announcements
could be placed on this bulletin board?
12. Becky wants to solve the equation 3
x
18. Becky says that 18 ? 3 ? 15,
so
x
5 15. Explain to Becky why her answer is incorrect.
5
55
5
n
59
x
2
55
15
5
Topic 7: Solving One-Step Equations
Guided Instruction
Mathematical Goals
• Use inverse operations to solve one-step equations.
Vocabulary
•
inverse operations
At a Glance
Introduce this topic by defining and supplying several examples of inverse
operations. Ask:
•
What do you get when you subtract 4 from 4?
(0)
•
What is the result of 5
?
5?
(0)
•
What would you subtract from 7 to get to 0?
(7)
•
What do you get when you divide 3 by 3?
(1)
•
Simplify
.
(1)
Once you are satisfied that the students understand the relationships
associated with identities and their inverses, begin to include variables into
the discussion. Use questions like:
•
What is the result of
b ?
5
?
5?
(
b
)
•
What is the result of 3
x ?
3?
(
x
)
•
When you are trying to change an expression from
b ?
6 to
b
, what
should you do?
(Add 6.)
•
When you are trying to change an expression from 7
b
to
b
, what should
you do?
(Divide by 7.)
The last developmental step to the topic is to place the expressions into
an equation. Use questions like these to introduce the problem.
•
What does it mean when you see an equal sign between two expressions?
(Both expressions have the same value.)
•
What happens when you add 3 to one of the expressions?
(The
expressions are no longer equal.)
•
What do you need to do to keep the expressions equal?
(Add 3 to the
other side as well.)
•
Why would you choose to add 3 to both sides of an equation?
(To get
the variable by itself.)
•
Give an example of an equation that could be solved by adding 3 to
both sides.
(Answers may vary. Sample:
t
? 3 ? 10.)
You will find additional work on solving equations in the grade 7 unit
Variables and Patterns.
12
12
PACING
1 day
ACE Assignment Guide
for Topic 7
Core
1–12
Answers to Topic 7
Problem 7.1
A. 1.
g
? 2
2.
g
? 2 ? 16
3.
Answers may vary. Sample: If you know
that the plant is 16 inches tall this week,
and that it grew 2 inches in the past week,
then subtracting 2 will allow you to work
back to the height last week.
4.
14 inches
5.
Answers may vary. Sample: The expression
2
g
would mean twice the height from last
week.
B. 1.
m
? 9
2.
m ? 9 ? 25
3.
Patrick needs to add in order to leave the
m
by itself and solve for the value of
m
.
4.
$34
C. 1.
4
s
2.
division
3.
42 students
D. 1.
Division; the whole was distributed 5 at a
time. We are trying to find the whole, or
total number of sheets.
2.
3.
? 32
4.
160 sheets
Exercises
1.
subtraction,
a
? 8
2.
addition,
b
? 12
3.
division,
d
? 3
4.
subtraction,
t
? 8
5.
multiplication,
x
? 10
6.
multiplication,
n
? 54
7.
addition,
y
? 42
8.
division,
h
? 12
9.
31 people
10.
16 people
11.
9 announcements
12.
Becky is trying to undo multiplication with
subtraction. To solve 3
x
? 18, she must divide
both sides by 3. The correct solution is
x
? 6.
She can check her work by substituting 6 into
the original equation. 3 ? 6 ? 18.
P
5
P
5