This chapter discusses using algebra to represent and solve problems involving addition, subtraction, and finding patterns and rules. It includes the following key points: - Lesson 3-1 covers writing and evaluating expressions with variables and addition/subtraction. - Lesson 3-2 explains how to solve addition and subtraction equations mentally without using models. - Lesson 3-3 introduces identifying extra and missing information in word problems in order to write and solve the correct equations. - Lesson 3-4 teaches finding patterns in tables and writing rules as equations that can be used to determine future terms in the pattern.

1. Chapter 3
Algebra: Use Addition and Subtraction
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2. Algebra: Use Addition and Subtraction
3
Lesson 3-1 Addition and Subtraction
Expressions
Lesson 3-2 Solve Equations Mentally
Lesson 3-3 Problem-Solving Strategy: Missing
and Extra Information
Lesson 3-4 Algebra: Find a Rule
Lesson 3-5 Problem-Solving Investigation:
Choose a Strategy
Lesson 3-6 Balanced Equations

3. 3-1 Addition and Subtraction Expressions
Five-Minute Check (over Chapter 2)
Main Idea and Vocabulary
California Standards
Example 1
Example 2
Example 3

4. 3-1 Addition and Subtraction Expressions
• I will write and find the value of expressions.
• expression
• variable
• parentheses

5. 3-1 Addition and Subtraction Expressions
Standard 4AF1.1 Use letters, boxes, or other
symbols to stand for any number in simple
expressions or equations (e.g., demonstrate an
understanding and the use of the concept of a
variable).

6. 3-1 Addition and Subtraction Expressions
Mr. and Mrs. Presley and some of their children eat
apples in their lunches. Today, 3 of their children are
eating apples. What is the value of 2 + n if n = 3?
You need to find the value of 2 + n when n = 3.
2+n Write the expression.

7. 3-1 Addition and Subtraction Expressions
2 +3 Replace n with 3.
5 Add 2 and 3.

8. 3-1 Addition and Subtraction Expressions
What is the value of 4 + n if n = 7?
A. 7
B. 4
C. 11
D. 12

9. 3-1 Addition and Subtraction Expressions
Find the value of 15 + (h – 3) if h = 4.
15 + (h – 3) Write the expression.
15 + (4 – 3) Repleace h with 4.
15 + 1 Find (4 – 3) first.
16 Next, find 15 + 1.

10. 3-1 Addition and Subtraction Expressions
Find the value of (k + 2) – 1 if k = 6.
A. 6
B. 2
C. 1
D. 7

11. 3-1 Addition and Subtraction Expressions
Danielle ran 6 fewer miles than Martha last week.
Write an expression for the number of miles
Danielle ran.
Words Ran 6 fewer miles than Martha
Variable Define a variable. Let m represent the
miles that Martha ran.
Expression m–6
Answer: So Danielle ran m – 6 miles.

12. 3-1 Addition and Subtraction Expressions
Sven earned $10 more than Erin last month. Write
an expression for the amount of money Sven
earned.
A. a – 10
B. 10 – a
C. a + 10
D. a + 2b

14. 3-2 Solve Equations Mentally
Five-Minute Check (over Lesson 3-1)
Main Idea and Vocabulary
California Standards
Example 1
Example 2
Example 3
Addition and Subtraction Equations

15. 3-2 Solve Equations Mentally
• I will solve addition and subtraction equations
mentally.
• equation
• variable
• solve

16. 3-2 Solve Equations Mentally
Standard 4AF1.1 Use letters, boxes, or other
symbols to stand for any number in simple
expressions or equations (e.g., demonstrate
an understanding and the use of the concept
of a variable).

17. 3-2 Solve Equations Mentally
Misae baby-sat for 2 hours on Friday, and by the
end of the day on Saturday she had baby-sat 6
hours total. How many hour did she baby-sit on
Saturday?
In the previous Explore activity, you solved equations
using models. Equations can also be solved mentally.

18. 3-2 Solve Equations Mentally
One Way: Use Models
Step 1 Model the equation.
2+x=6

19. 3-2 Solve Equations Mentally
One Way: Use Models
Step 2 Find the value of x.

20. 3-2 Solve Equations Mentally
Another Way: Mental Math
2+x=6
2+4=6
Answer: So, x = 4.

21. 3-2 Solve Equations Mentally
Adelina worked for 3 hours on Tuesday, and by
the end of Wednesday she had worked a total of
8 hours. How many hours did she work on
Wednesday?
A. 3
B. 8
C. 5
D. 11

22. 3-2 Solve Equations Mentally
Solve 19 – n = 12 mentally.
19 – n = 12 19 minus what number equals 12?
19 – 7 = 12 You know that 19 – 7 = 12.
n=7
Answer: So, the value of n is 7.

23. 3-2 Solve Equations Mentally
Solve 16 – y = 11 mentally.
A. 16
B. 5
C. 11
D. 6

24. 3-2 Solve Equations Mentally
Big Red had 7 puppies last spring. This spring she
had some more puppies and now has a total of 13
puppies. How many puppies did she have this
spring?
Write and solve an equation.
Words 7 puppies plus some more equals 13.
Variable Let p represent the additional puppies.
Expression 7 + p = 13

25. 3-2 Solve Equations Mentally
7 + p = 13 7 plus what number equals 13?
7 + 6 = 13 You know that 7 + 6 = 13.
p=6
Answer: So, Big Red had 6 more puppies this spring.

26. 3-2 Solve Equations Mentally
Write and solve an equation for the following
situation: 9 plus a number is 13.
A. 9 + x = 13; 4
B. 9 + x = 13; 3
C. 9 – x = 13; 3
D. 9 – x – 13; 4

28. 3-3 Problem-Solving Strategy: Missing and Extra Information
Five-Minute Check (over Lesson 3-2)
Main Idea
California Standards
Example 1: Problem-Solving Strategy

29. 3-3 Problem-Solving Strategy: Missing and Extra Information
• I will identify extra and missing information when
solving problems.

30. 3-3 Problem-Solving Strategy: Missing and Extra Information
Standard 4MR1.1 Analyze problems by
identifying relationships, distinguishing relevant
from irrelevant information, sequencing and
prioritizing information, and observing patterns.

31. 3-3 Problem-Solving Strategy: Missing and Extra Information
Standard 4AF1.1 Use letters, boxes, or other
symbols to stand for any number in simple
expressions or equations (e.g., demonstrate an
understanding and the use of the concept of a
variable).

32. 3-3 Problem-Solving Strategy: Missing and Extra Information
Trina is making friendship bracelets to sell for
$2 each. Last week, she sold 63 bracelets. Two
weeks ago, she sold 21 bracelets. How many
more bracelets did Trina sell last week than two
weeks ago?

33. 3-3 Problem-Solving Strategy: Missing and Extra Information
Understand
What facts do you know?
• Trina sells friendship bracelets for $2 each.
• She sold 63 bracelets last week.
• She sold 21 bracelets two weeks ago.
What do you need to find?
• Find how many more bracelets Trina sold last
week than two weeks ago.

34. 3-3 Problem-Solving Strategy: Missing and Extra Information
Plan
Once you identify the information needed to solve
the problem you can write a number sentence.
Look for any extra information.

35. 3-3 Problem-Solving Strategy: Missing and Extra Information
Solve
Subtract 21 from 63. You do not need to know how
much the bracelets cost. This is extra information.
last week two weeks ago
63 – 21 = n
63 – 21 = 42
Answer: So, Trina sold 42 more bracelets last
week than the week before.

36. 3-3 Problem-Solving Strategy: Missing and Extra Information
Check
Look back at the problem. You can check
subtraction with addition. 21 + 42 = 63. So, you
know the answer is correct.

38. 3-4 Algebra: Find a Rule
Five-Minute Check (over Lesson 3-3)
Main Idea
California Standards
Example 1

39. 3-4 Algebra: Find a Rule
• I will find a rule and use the rule to write an
equation.

40. 3-4 Algebra: Find a Rule
Standard 4AF1.5 Understand that an
equation such as y = 3x + 5 is a prescription
for determining a second number when a
first number is given.

41. 3-4 Algebra: Find a Rule
Write an equation that describes the pattern in the
table.
Pattern: 1 + 4 = 5
3+4=7
Rule: Add 4.
Equation: x + 4 = y

42. 3-4 Algebra: Find a Rule
Write an equation that describes the pattern in the
table.
A. x+1=y
B. x+9=y
C. x + 10 = y
D. x+8=y

43. 3-4 Algebra: Find a Rule
Use the equation to find the next three numbers.
9 11 13
Find the next three numbers when the input (x) is 5, 7, and 9.
x+4=y x+4=y x+4=y
5+4=9 7 + 4 = 11 9 + 4 = 13
Answer: So, the next three numbers in the pattern
are 9, 11, and 13.

44. 3-4 Algebra: Find a Rule
Use the equation, x + 5 = y, to find the last 2
numbers.
A. 10, 13
B. 15, 18
C. 17, 22
D. 9, 12

45. 3-4 Algebra: Find a Rule
The uniform store is offering a $5 discount for any
purchase of $20 or more. Use a rule to write an
equation to describe the pattern. Then use the
equation to find the next three prices.

46. 3-4 Algebra: Find a Rule
Identify the rule and write it as an equation.
Rule: Subtract 5.
Equation: x – $5 = y

47. 3-4 Algebra: Find a Rule
Find the next three numbers when the input (x) is
22, 23, and 24.
17 18 19
x–5=y x–5=y x–5=y
22 – 5 = 17 23 – 5 = 18 24 – 5 = 19
Answer: So, the next three amounts are
$17, $18, and $19.

48. 3-4 Algebra: Find a Rule
A shoe store is offering a discount of $7 for any
purchase of $15 or more. Use a rule to write an
equation to describe the pattern. Then use the
equation to find the next 2 prices.
A. x + y = 7; 11, 12
B. x + 7 = y; 18, 19
C. x + y = 8; 8, 9
D. x + 7 = y; 11, 12

50. 3-5 Problem-Solving Investigation: Choose a Strategy
Five-Minute Check (over Lesson 3-4)
Main Idea
California Standards
Example 1: Problem-Solving Investigation

51. 3-5 Problem-Solving Investigation: Choose a Strategy
• I will choose the best strategy to solve a problem.

52. 3-5 Problem-Solving Investigation: Choose a Strategy
Standard 4MR2.3 Use a variety of
methods, such as
words, numbers, symbols, charts, graphs, tabl
es, diagrams, and models, to explain
mathematical reasoning.

53. 3-5 Problem-Solving Investigation: Choose a Strategy
Standard 4NS3.0 Students solve problems
involving addition, subtraction, multiplication, and
division of whole numbers and understand the
relationships among the operations.

54. 3-5 Problem-Solving Investigation: Choose a Strategy
KAMILAH: My soccer team is raising
money by having a car wash. We earn
$36 each hour of washing cars.
YOUR MISSION: Find how much money
Kamilah’s soccer team will make in
5 hours.

55. 3-5 Problem-Solving Investigation: Choose a Strategy
Understand
What facts do you know?
• The soccer team earns $36 each hour.
What do you need to find?
• You need to find how much money the
team will make in 5 hours.

56. 3-5 Problem-Solving Investigation: Choose a Strategy
Plan
You can make a table that shows how much the
team will earn in 1, 2, 3, 4, and 5 hours.

57. 3-5 Problem-Solving Investigation: Choose a Strategy
Solve
The table shows how much money the team
earns in 1, 2, 3, 4, and 5 hours.
Answer: So, Kamilah’s soccer team will make $180.

58. 3-5 Problem-Solving Investigation: Choose a Strategy
Check
Look back at the problem. Start with $180.
Subtract $36 5 times.
$180 – $36 = $144
$144 – $36 = $108
$108 – $36 = $72
$72 – $36 = $36
$36 – $36 = $0
So, you know that the answer is correct.

60. 3-6 Balanced Equations
Five-Minute Check (over Lesson 3-5)
Main Idea and Vocabulary
California Standards
Example 1
Example 2
Example 3

61. 3-6 Balanced Equations
• I will balance addition and subtraction equations.
• balance

62. 3-6 Balanced Equations
Standard 4FS2.1 Know and understand that
equals added to equals are equal.

63. 3-6 Balanced Equations
Show that the equality of 7 + 9 = 16 does not
change when 3 is added to each side of the
equation.
7 + 9 = 16 Write the equation.
7 + 9 + 3 = 16 + 3 Add 3 to each side.
19 = 19 19 = 19
So, when you add 3 to each side, the equality does
not change.

64. 3-6 Balanced Equations
Show that they equality 1 + 2 = 3 does not change
when 6 is added to each side of the equation.
A. 1 + 2 + 6 = 3 + 6; 9 = 9
B. 1+2+3=3+6=6=9
C. 1 + 2 = 3 + 6; 3 = 9
D. 1 + 2 + 6 = 3 + 6; 6 = 6

65. 3-6 Balanced Equations
Show that the equality of 12 + 5 = 17 does not
change when 6 is subtracted from each side of the
equation.
12 + 5 = 17 Write the equation.
12 + 5 – 6 = 17 – 6 Subtract 6 from each side.
11 = 11 11 = 11
So, when you subtract 6 from each side, the equality
does not change.

66. 3-6 Balanced Equations
Show that the equality of 10 + 9 = 19 does not
change when 4 is subtracted from each side of the
equation.
A. 10 + 9 = 19 – 4; 19 = 15
B. 10 + 9 = 19; 15 = 15
C. 10 + 9 – 4 = 19 – 4; 15 = 15
D. 10 + 9 – 4 = 19 – 4; 15 = 19

67. 3-6 Balanced Equations
Find the missing number in 27 – 11 = 9 + 3 + ___ .
27 – 11 = 9 + 3 + Write the equation.
27 – 11 = 9 + 3 + You know that 27– 11 = 16.
To keep the equation balanced, a number must
be added to 9 + 3 that will give the result of 16.
9 + 3 + 4 = 16.
Answer: So, the missing number is 4.

68. 3-6 Balanced Equations
Find the missing number in 24 + 2 = 12 + 12 + ___.
A. 12
B. 2
C. 24
D. 10

70. Algebra: Use Addition and Subtraction
3
Five-Minute Checks
Addition and Subtraction Equations

71. Algebra: Use Addition and Subtraction
3
Lesson 3-1 (over Chapter 2)
Lesson 3-2 (over Lesson 3-1)
Lesson 3-3 (over Lesson 3-2)
Lesson 3-4 (over Lesson 3-3)
Lesson 3-5 (over Lesson 3-4)
Lesson 3-6 (over Lesson 3-5)

72. Algebra: Use Addition and Subtraction
3
(over Chapter 2)
Find each difference.
200 – 189
A. 10
B. 121
C. 11
D. 21

73. Algebra: Use Addition and Subtraction
3
(over Chapter 2)
Find each difference.
$3.00 – $1.67
A. $2.43
B. $1.33
C. $4.67
D. $1.43

74. Algebra: Use Addition and Subtraction
3
(over Chapter 2)
Find each difference.
5,500 – 1,254
A. 4,356
B. 6,754
C. 3,256
D. 4,246

75. Algebra: Use Addition and Subtraction
3
(over Chapter 2)
Find each difference.
6,000 – 5,454
A. 546
B. 1,546
C. 456
D. 1,656

76. Algebra: Use Addition and Subtraction
3
(over Chapter 2)
Find each difference.
$70.00 – $22.17
A. $57.83
B. $58.93
C. $47.83
D. $37.83

77. Algebra: Use Addition and Subtraction
3
(over Lesson 3-1)
Find the value of each expression if x = 3 and a = 4.
(9 – a) + 7
A. 13
B. 12
C. 6
D. 11

78. Algebra: Use Addition and Subtraction
3
(over Lesson 3-1)
Find the value of each expression if x = 3 and a = 4.
x + (3 – 2)
A. 4
B. 5
C. 9
D. 8

79. Algebra: Use Addition and Subtraction
3
(over Lesson 3-1)
Find the value of each expression if x = 3 and a = 4.
8 + (15 – x)
A. 19
B. 18
C. 11
D. 20

80. Algebra: Use Addition and Subtraction
3
(over Lesson 3-1)
Find the value of each expression if x = 3 and a = 4.
4 + (a + 5)
A. 12
B. 13
C. 5
D. 4

81. Algebra: Use Addition and Subtraction
3
(over Lesson 3-1)
Find the value of each expression if x = 3 and a = 4.
(a + 4) – 3
A. 4
B. 11
C. 5
D. 6

82. Algebra: Use Addition and Subtraction
3
(over Lesson 3-2)
Solve each equation mentally.
6 + n = 13
A. n = 8
B. n = 6
C. n = 7
D. n = 5

83. Algebra: Use Addition and Subtraction
3
(over Lesson 3-2)
Solve each equation mentally.
k–2=7
A. k = 9
B. k = 8
C. k = 10
D. k = 5

84. Algebra: Use Addition and Subtraction
3
(over Lesson 3-2)
Solve each equation mentally.
8–g=3
A. g = 3
B. g = 5
C. g = 6
D. g = 4

85. Algebra: Use Addition and Subtraction
3
(over Lesson 3-2)
Solve each equation mentally.
x + 4 = 15
A. x = 10
B. x = 9
C. x = 12
D. x = 11

86. Algebra: Use Addition and Subtraction
3
(over Lesson 3-3)
Identify any missing or extra information. Then
solve if possible. An express train leaves Grand
Terminal at 5:05 P.M. The train arrives at the first
stop at 5:21 P.M., the second stop at 5:46 P.M., and
the last stop at 6:04 P.M. How long is the train ride?
A. missing information: what time the train arrives
at the last stop; can not solve the problem
B. extra information: the times of the first and
second stops; 59 minutes

87. Algebra: Use Addition and Subtraction
3
(over Lesson 3-3)
Identify any missing or extra information. Then
solve if possible. An express train leaves Grand
Terminal at 5:05 P.M. The train arrives at the first
stop at 5:21 P.M., the second stop at 5:46 P.M., and
the last stop at 6:04 P.M. How long is the train ride?
C. extra information: the time of the first stop:
41 minutes
D. extra information: the times of the first and
second stop; 1 hour

88. Algebra: Use Addition and Subtraction
3
(over Lesson 3-3)
Identify any missing or extra information. Then
solve if possible. An express train leaves Grand
Terminal at 5:05 P.M. The train arrives at the first
stop at 5:21 P.M., the second stop at 5:46 P.M., and
the last stop at 6:04 P.M. How long is the train ride?
B. extra information: the times of the first and
second stops; 59 minutes

89. Algebra: Use Addition and Subtraction
3
(over Lesson 3-4)
Use a rule to write an equation to describe the
pattern. Then use the equation to find the next
three numbers in the pattern.
A. x + 3 = y; 11, 14, 17
B. 3x = y; 24, 33, 42
C. x + 4 = y; 12, 15, 18
D. 5 + x = y; 13, 16, 19

90. Algebra: Use Addition and Subtraction
3
(over Lesson 3-5)
Identify any missing or extra information. Use the
Four-Step Plan in this problem; solve if possible.
Viviana is taking a late train from home to visit her
cousins. The train leaves Savannah at 11 A.M. and
arrives in Charleston at 1:30 P.M. on July 13. How
long is Viviana’s trip?
A. 2 hours and 30 minutes; extra information: July
13, visiting her cousins, late train
B. 10 hours and 10 minutes; no extra information

91. Algebra: Use Addition and Subtraction
3
(over Lesson 3-5)
Identify any missing or extra information. Use the
Four-Step Plan in this problem; solve if possible.
Viviana is taking a late train from home to visit her
cousins. The train leaves Savannah at 11 A.M. and
arrives in Charleston at 1:30 P.M. on July 13. How
long is Viviana’s trip?
C. 1 hour and 30 minutes; extra information: July
13, visiting her cousins, late train
D. 2 hours and 30 minutes; missing information:
why she is visiting her cousins

92. Algebra: Use Addition and Subtraction
3
(over Lesson 3-5)
Identify any missing or extra information. Use the
Four-Step Plan in this problem; solve if possible.
Viviana is taking a late train from home to visit her
cousins. The train leaves Savannah at 11 A.M. and
arrives in Charleston at 1:30 P.M. on July 13. How
long is Viviana’s trip?
A. 2 hours and 30 minutes; extra information: July
13, visiting her cousins, late train

93. This slide is intentionally blank.