Math chapter 4

Algebra: Operations and Equations

Chapter 4 Vocabulary
Algebraic expression – an expression that includes at
least one variable
Base – a number used as a repeated factor bª
Division Property of Equality – the property states
that if you divide both sides of an equation by the
same nonzero number, the sides remain equal
Evaluate – to find the value of a numerical or
algebraic expression
Exponent – a number that tells you how many times
the base is used as a factor bª

Vocabulary continued
Integers – the set of whole numbers and their
opposites {… -3, -2, -1, 0, 1, 2, 3 …}
Multiplication Property of Equality – the property
that states that if you multiply both sides of an
equation by the same number, the sides remain equal
Order of Operations – the process for evaluating
expressions (PEMDAS)
Subtraction Property of Equality – the property that
states that if you subtract the same number from
both sides of the equation, the sides remain equal

Chapter 4 Lesson 1
Exponents
bª exponent
Base

The base is the number used as the repeated factor
The exponent is the boss & tells how many times the
base is used as the factor.

Example: 10³ = 10 x 10 x 10 = 1000

Square Numbers
The product of a number and itself. A square number
can be represented using the repeated factor as the
base and 2 as the exponent.

b²

Complete the activity on page 126

 Explain how you can use multiplication to find the value of the
number 21².

Problem Solving pg. 128
Use the table to solve 17 - 19

17. A frog egg has split. Several splits later the egg has
128 cells. How many splits have there been?


18. A frog cell splits. How many cells would a frog egg
have after 9 splits? Write as the number of cells and
as an expression in exponent form.

Write Math - Journal
How do you use an exponent?

Chapter 4 Lesson 2
Order of Operations
Construct a “cheat sheet”
Parentheses ()
Exponents bª
Multiply x ·
Divide ÷ n/d
Addition +
Subtraction -

Algebraic Expressions pg. 130

In what order must operations be
evaluated to find a correct solution
to a problem?

Chapter 4 Lesson 3
Balance Equations
 With a partner complete Investigate
 Materials – balance & cubes

 What’s the error?

 Describe the error
Jill made.

Write Math – Journal
How can you use a pan balance to
solve an equation with a variable?

Chapter 4 Lesson 4
Addition Equations
Yara is going camping in the Everglades National
Park. Her backpack with camping gear weights 17
pounds. When she adds her camera gear, the total
weight of her backpack is 25 pounds. How much does
Yara’s gear weigh?
17 + c = 25
Use a model to solve.

Another Way pg. 138

Subtraction Property of Equality - the property that
states that if you subtract the same number from
both sides of the equation, the sides remain equal

Example: x + 4 = 7 check your work: x + 4 = 7
- 4 -4 3+4=7
x =3 7 =7

Try This!
Solve the equation. Check your answer

13 + d = 22

Can d in 13 + d = 22 have more than one value? Why
or why not?

Unlock the Problem 12 & 13-14

How can an equation with
addition be solved using
subtraction?

Chapter 4 Lesson 5
Subtraction Equations
 Addition Property of Equality – states that if you add the same
number to both sides of an operation, the two sides remain equal.
 Complete Activity on pg. 141
 Materials: balance, cubes

Example:
Addition Property of Equality
Kent has a collection of CDs. He gives 5 CDs to his
brother. Kent then has 8 CDs left in his collection.
How many CDs did Kent have before he gave some to
his brother?

Solve: c – 5 = 8 Check: c – 5 = 8
+ 5 +5 13 – 5 = 8
c = 13 8 =8

Use the bar graph to solve for 22 - 24

22. Taking a shower uses 13 gallons less water than
taking a bath. About how many gallons of water are
used for taking a bath?

Use the equation b – 13 = 23, where b is equal to the
number of gallons of water needed for a bath.


23. Washing the dishes uses about 29 gallons less water
than washing a load of laundry. How many gallons of
water are used to wash a load of laundry?

Use the equation l – 29 = 15, where l is equal to the
number of gallons of water needed for a load of
laundry.


24. You use 2 gallons less water to brush your teeth than
to wash your hands. Find how much water you use to
wash your hands.

Write an equation you can use to solve the problem.
Use h to represent the number of gallons of water
used to wash your hands.

Then solve the equation. Don’t forget to check your
work.

Chapter 4 Lesson 6
Write and Solve Equations
When writing equations it’s important to choose a
variable and know what that variable represents.
Choose the correct operation to solve the problem.

Underline what you are asked to find (in the word
problem)
Circle the word that tells you which operation to use
to write an equation.

Write and Solve Equations
The Panthers won the basketball game with a score of
73 points, which was 14 points greater than the score
of the other team, the Bears. How many points did
the Bears score?

What are you being asked to find?
What word tells you the operation used in the
equation?

Example pg. 146

In the championship game, the Panthers scored 13
points fewer than the Dolphins scored. If the
Panthers scored 54 points, how many points did the
Dolphins score?

What are you being asked to find?
What word tells you the operation used in the
equation?

Use the table to solve 8 – 10. Complete the table.

8. The Knights’ score was 15 points less than the Bulls’
score. What was the Bulls’ score?
Write & solve the equation.

9. The Tigers’ score was 17 points greater than the Cubs’
score. What was the Cubs’ score?
Write & solve the equation.

The Cougars scored 14 points in the first half of the
game. In the second half, the Cougars scored enough
points to beat the Hawks by 5 points. How many
points did the Cougars score in all? In the second half
of the game?
Write and solve the equations.

Chapter 4 Lesson 7
Solve a Simpler Problem – Function Tables
When creating and solving a function table you must
create a possible rule for the table to work correctly.

Example: Samantha is making a scarf using a pattern of equilateral
triangles. Each triangle has a perimeter of 6 inches. If Samantha adds
triangles from left to right, what is the perimeter of a scarf made from
15 triangles?

# of ‘s 1 2 4 6 8 10 12 15

Perimeter 6 8 12
 Continue the function table: what is the rule?

Unlock the Problem pg. 149

On an archaeological dig. Gabriel divides his dig site
into square sections that are 1 meter on each side. He
uses 4 meters of rope to rope of the first section. He
only needs 3 meters of rope for each additional
section. How many meters of rope will Gabriel need
for 10 sections?
Number of sections 1 2 3
Amount of rope (m) 4 7 10

Finish the table – what is the rule?

On Your Own pg. 152

4. Jane works as a limousine driver. Her base fee is $50,
and she makes $25 for every hour that she drives.
How much does Jane make if she works for 8 hours?
Complete the table.
Possible rule: ________________________

h 1 2 3 4 8
m $75 $100 ? ? ?

How can you solve a problem by
solving a simpler problem?

Chapter 4 Lesson 8
Multiplication Equations
Use a model.
At the movies, Jake bought 3 bags of popcorn for
himself and his friends Larry and Sal. Each bag of
popcorn was the same price. Jake paid $12 for the 3
bags. How much did each bag of popcorn cost?

Complete the model on pg. 155

So, 1 bag of popcorn cost $___.

Another Way pg. 156

Division Property of Equality – states that when you
divide both sides of an equation by the same non-
zero number, the two sides remain the same.

Solve: 3 x p = 12
3 3
p =4

Check: 3 x p = 12
3 x 4 = 12
12 = 12

Try This! Solve the equation
When solving an equation with two operations, use the
properties of equally twice to get the variable by itself on one
side of the equation. To get the variable by itself, the order
of operations is reversed so addition & subtraction is
undone first before multiplication & division.

6 x n + 3 = 27
-3 -3
6xn = 24
6 6
n =4


15. The drama club sees a movie. Each member of the
club buys one fruit snack. The club spends a total of
$76 on fruit snacks. How many members of the club
went to the movies? Solve the equation 4f = 76,
where f represents the number of fruit snacks bought.

On Friday, the snack bar made $992 selling buckets of
large popcorn. How many buckets of large popcorn
did the snack bar sell in Friday? Solve the equation
8p = 992, where p represents the number of buckets
of large popcorn sold.

18. Michaelsolves the equation 8y = 2 and
finds that y is equal to 16. Explain how
you know Michael’s solution is not
correct.

Chapter 4 Lesson 9
Division Equations
Multiplication Property of Equality – states that if you
multiply both sides of the equation by the same non-
zero number, the two sides remain equal.
Solve the equation & check your solution.
Unlock the Problem pg. 159


20.


22. Asher wants to buy a handheld video game console.
In order to save the money needed to buy it, he
divides the cost to see how much he needs to save
every month for 5 months. He finds that he must
save $37 a month. Write and solve a division equation
with a variable that describes the problem.

***Don’t forget to check your solution.***

23. Jasmine says that x = 348 is the solution to
x ÷ 12 = 29. Explain how you can justify Jasmine’s
solution.

Chapter 4 Lesson 10
Use Substitution
 Underline what you are asked to find.
 Circle the information you will use.
 Use a Model.

Erik knows that 1 cube weighs 2 ounces and that 9
cubes weigh the same as 3 bouncy balls. Use this
information to find the weight of 1 bouncy ball.

Another Way pg. 164
Use the Substitution Property of Equality
 Substitution Property of Equality – states that if you know that one quantity is equal to another, you
can substitute that quantity for the other in an equation.
Erik remembers that 1 cube weighs 2 ounces and that 9 cubes weigh the
same as 3 bouncy balls. How can Erik use this information in another way
to recall the weight of 1 bouncy ball?
Step 1: Write an equation for the information given in the problem.
1 cube = 2 ounces 1c = 2 or (c=2)
9 cubes -= 3 bouncy balls 9c = 3b
Step 2: Use the Substitution Property of Equality
Substitute c=2 9(2) = 3b
Multiply 18 = 3b
Step 3: Solve the equation
Use the Division Property of Equality 18 = 3b
3 3
6=b

Use the pan balances to solve 12 - 14

12. The weight of 6 blocks is shown on the first pan
balance. What is the weight of one block? If one
green cylinder on the second pan balance has the
same weight as 4 blocks what is the weight of the
cylinder?

Step 1: Write an equation
Step 2: Use the Substitution Property of Equality
Step 3: Solve the equation
Step 4: Check your work

Use the pan balances to solve 12 - 14
14. Using the two pan balances shown, what if the
weight on the right side of the first pan balance
weighed 90 ounces, and a green cylinder weighed the
same as 3 blocks? What is the weight of the block?
What is the weight of one green cylinder?

Step 1: write an equation
Step 2: use the substitution property of equality
Step 3: solve the equation
Step 4: check your work

13. Using the information from Problem 12, what is the
weight of one triangle? Explain how you know.

Don’t forget to follow the steps to solve a substitution
problem.

Chapter 4 Lesson 11
Understand Integers
Integers – the set of whole numbers and their
opposites. For example: +8 and -8 are opposites

Positive Integers – any integer greater than 0. For
example: +19 is read positive 19

Negative Integers – any integer less than 0. For
example: -47 is read negative 47

Name the integer for each situation
The highest point in Florida, Britton Hill, is 345 feet
above sea level.
Larry withdraws $30 from his bank account.
The lowest recorded temperature in Florida was 2
degrees below zero in Tallahassee in 1899.
A team loses 10 yards in a football game.
Larry deposits $300 into a bank account.
Tiger Woods hit 7 under par.

Opposite Numbers & Graphing
Opposite integers are the same distance from zero on
a number line in opposite directions.

Complete Try This!

Example pg. 168
Use a vertical number line


17. Miriam goes scuba diving. She dives to a depth of 25
meters below sea level. What integer represents her
dive?

18. Neil earns $17. He owes his brother $23. What
integers represent the amount Neil earns and the
amount he owes?

20. Which integer represents 7 days before now if today
is Day 0?

What real-world situations can be
described using positive and
negative numbers?

Chapter 4 Lesson 12
Compare & Order Integers

One Way & Another Way pg. 172

Use the table for 15 - 17

15. Which is greater, the average temperature of Earth
or the average temperature of Mars?
Explain how you know.
16.The average temperature of the planetoid Pluto is
-393°F. Is that greater than or less than the average
temperature of Mercury? Is it greater than or less
than the average temperature of Neptune?
19. At 7:00 A.M. the temperature was -4°C. At 10:00 A.M. the
temperature was +6°C. By how many degrees Celsius
did the temperature change?

How do you compare and order
integers?

Math chapter 4

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