Transcript Gr04_Ch_06 - Etiwanda E

Chapter 6
Algebra: Use Multiplication and Division
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6
Algebra: Use Multiplication and Division
Lesson 6-1
Multiplication and Division
Expressions
Lesson 6-2
Problem-Solving Strategy: Work
Backward
Lesson 6-3
Order of Operations
Lesson 6-4
Algebra: Solve Equations Mentally
Lesson 6-5
Problem-Solving Investigation:
Choose a Strategy
Lesson 6-6
Algebra: Find a Rule
Lesson 6-7
Balanced Equations
6-1
Multiplication and Division Expressions
Five-Minute Check (over Chapter 5)
Main Idea
California Standards
Example 1: Find the Value of an Expression
Example 2: Find the Value of an Expression
Example 3: Write an Expression
6-1
Multiplication and Division Expressions
• I will write and find the value of multiplication
and division expressions.
6-1
Multiplication and Division 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).
6-1
Multiplication and Division Expressions
Jake had 4 boxes of apples. There are 6 apples
in each box. Find the value of 4 × n if n = 6.
4×n
Write the expression.
6-1
Multiplication and Division Expressions
4×6
Replace n with 6.
24
Multiply 4 and 6.
Answer: So, the value of 4 × n is 24. Jake had
24 apples.
6-1
Multiplication and Division Expressions
Marian has 5 CD cases. Each CD case has 2 CDs
inside. Find the value of 5 × n if n = 2.
A. 7 CDs
B. 10 CDs
C. 5 CDs
D. 2 CDs
Multiplication and Division Expressions
6-1
Find the value of x ÷ (3 × 2) if x = 30.
x ÷ (3 × 2)
Write the expression.
30 ÷ (3 × 2)
Replace x with 30.
30 ÷ 6
Find (3 × 2) first.
5
Next, find 30 ÷ 6.
Answer: So, the value of x ÷ (3 × 2) if x = 30 is 5.
6-1
Multiplication and Division Expressions
Find the value of 45 ÷ (x × 1) if x = 5.
A. 9
B. 45
C. 5
D. 1
6-1
Multiplication and Division Expressions
Judy has d dollars to buy bottles of water that
cost $2 each. Write an expression for the number
of bottles of water she can buy.
Words
dollars
Variable
Expression
divided by
cost
Let d = dollars.
dollars
divided by
cost
d
÷
$7
Answer: So the number of bottles of water Judy can
buy is d ÷ 2.
6-1
Multiplication and Division Expressions
Toby has d dollars to spend on discounted books
that cost $3 a piece. Write an expression for the
number of books he can buy.
A. d ÷ 3
B. d – 3
C. d + 3
D. d × 3
6-2
Problem-Solving Strategy: Work Backward
Five-Minute Check (over Lesson 6-1)
Main Idea
California Standards
Example 1: Problem-Solving Strategy
6-2
Problem-Solving Strategy: Work Backward
• I will solve problems by working backward.
6-2
Problem-Solving Strategy: Work Backward
Standard 4MR1.1 Analyze problems by
identifying relationships, distinguishing relevant
from irrelevant information, sequencing and
prioritizing information, and observing patterns.
6-2
Problem-Solving Strategy: Work Backward
Standard 4NS3.0 Students solve problems
involving addition, subtraction, multiplication, and
division of whole numbers and understand the
relationships among the operations.
6-2
Problem-Solving Strategy: Work Backward
Currently, there are 25 students in the chess
club. Last October, 3 students joined. Two
months before that, in August, 8 students
joined. How many students were in the club
originally?
6-2
Problem-Solving Strategy: Work Backward
Understand
What facts do you know?
• Currently, there are 25 students in the club.
• 3 students joined in October.
• 8 students joined in August.
What do you need to find?
• The number of students that were in the club
originally.
6-2
Problem-Solving Strategy: Work Backward
Plan
Work backward to solve the problem.
6-2
Problem-Solving Strategy: Work Backward
Solve
Work backward and use inverse operations. Start
with the end result and subtract the students who
joined the club.
25
– 3
22
6-2
Problem-Solving Strategy: Work Backward
Solve
22
– 8
14
Answer: So, there were 14 students in the club
originally.
6-2
Problem-Solving Strategy: Work Backward
Check
Look back at the problem. A total of 3 + 8 or 11
students joined the club. So, if there were 14 students
originally, there would be 14 + 11 or 25 students in the
club now.
The answer is correct.
6-3
Order of Operations
Five-Minute Check (over Lesson 6-2)
Main Idea and Vocabulary
California Standards
Key Concept: Order of Operations
Example 1: Use the Order of Operations
Example 2: Use the Order of Operations
6-3
Order of Operations
• I will use the order of operations to find the value
of expressions.
• order of operations
6-3
Order of Operations
Standard 4AF1.2 Interpret and evaluate
mathematical expressions that now use
parentheses.
Standard 4AF1.3 Use parentheses to
indicate which operation to perform first when
writing expressions containing more than two
terms and different operations.
6-3
Order of Operations
6-3
Order of Operations
Find the value of 12 – (4 + 2) ÷ 3.
12 – (4 + 2) ÷ 3
Write the expression.
12 –
Parentheses first. (2 + 4) = 6
12
÷3
6
–
10
2
Multiply and divide from left to right.
6÷3=2
Add and subtract from left to right.
12 – 2 = 10
6-3
Order of Operations
Find the value of 21 ÷ (3 + 4) + 5.
A. 16
B. 1
C. 8
D. 12
6-3
Order of Operations
Find the value of 4x + 3y ÷ 2, when x = 7 and y = 2.
Follow the order of operations.
4x + 3y ÷ 2 = 4 × 7 + 3 × 2 ÷ 2
= 28 +
= 28 +
=
Answer: 31
31
6
÷2
3
Replace x with 7 and
y with 2.
Multiply and divide
from left to right.
4 × 7 = 28, 3 × 2 = 6,
and 6 ÷ 2 = 3
Add.
6-3
Order of Operations
Find the value of 3x – 2y + 12 when x = 5 and y = 3.
A. 19
B. 11
C. 21
D. 12
6-4
Algebra: Solve Equations Mentally
Five-Minute Check (over Lesson 6-3)
Main Idea
California Standards
Example 1: Solve Multiplication Equations
Example 2: Solve Division Equations
Example 3: Write and Solve Equations
Multiplication and Division Equations
6-4
Algebra: Solve Equations Mentally
• I will solve multiplication and division equations
mentally.
6-4
Algebra: 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).
6-4
Algebra: Solve Equations Mentally
The All-Stars Used Car Lot has 8 rows of cars
with a total of 32 cars. Solve 8 × c = 32 to find
how many cars are in each row.
6-4
Algebra: Solve Equations Mentally
One Way: Use Models
Step 1 Model the
equation.
6-4
Algebra: Solve Equations Mentally
One Way: Use Models
Step 2 Find the value of c.
8 × c = 32
c=4
6-4
Algebra: Solve Equations Mentally
Another Way: Mental Math
8 × c = 32
8 × 4 = 32
You know that 8 × 4 = 32.
Answer: So, c = 4.
6-4
Algebra: Solve Equations Mentally
Kyung has just planted a garden. He has a total
of 49 vegetables with 7 vegetables in each row.
Solve 7 × v = 49 to find how many rows of
vegetables there are.
A. 6 rows
B. 7 rows
C. 8 rows
D. 49 rows
6-4
Algebra: Solve Equations Mentally
Solve 16 ÷ s = 8.
16 ÷ s = 8
16 ÷ 2 = 8
s=2
You know that 16 ÷ 2 = 8.
Answer: So, the value of s is 2.
6-4
Algebra: Solve Equations Mentally
Solve 36 ÷ p = 6.
A. 6
B. 7
C. 8
D. 9
6-4
Algebra: Solve Equations Mentally
Six friends went shopping. They each bought the
same number of T-shirts. A total of 24 T-shirts were
bought. Write and solve an equation to find out how
many T-shirts each person bought.
Write the equation.
Words
6 friends bought 24 T-shirts.
Variable
Let t = the number of T-shirts bought
per person.
Expression
6
×
t
=
24
6-4
Algebra: Solve Equations Mentally
Solve the equation.
6 × t = 24
6 × 4 = 24
t=4
Answer: So each person bought 4 T-shirts.
6-4
Algebra: Solve Equations Mentally
Six friends went to a driving range and hit a total of
54 golf balls. If they all hit the same number of golf
balls, how many did each one hit?
A. 7 golf balls
B. 8 golf balls
C. 9 golf balls
D. 10 golf balls
6-5
Problem-Solving Investigation: Choose a Strategy
Five-Minute Check (over Lesson 6-4)
Main Idea
California Standards
Example 1: Problem-Solving Investigation
6-5
Problem-Solving Investigation: Choose a Strategy
• I will choose the best strategy to solve a problem.
6-5
Problem-Solving Investigation: Choose a Strategy
Standard 4MR1.1 Analyze problems by
identifying relationships, distinguishing relevant
from irrelevant information, sequencing and
prioritizing information, and observing patterns.
6-5
Problem-Solving Investigation: Choose a Strategy
4NS3.0 Students solve problems involving
addition, subtraction, multiplication, and division
of whole numbers and understand the
relationships among the operations.
6-5
Problem-Solving Investigation: Choose a Strategy
MATT: I take 30-minute guitar
lessons two times a week. How
many minutes do I have guitar
lessons in six weeks?
YOUR MISSION: Find how many
minutes Matt has guitar lessons
in six weeks.
6-5
Problem-Solving Investigation: Choose a Strategy
Understand
What facts do you know?
• Each lesson Matt takes is 30 minutes long.
• He takes lessons two times a week.
What do you need to find?
• Find how many minutes Matt has guitar
lessons in six weeks.
6-5
Problem-Solving Investigation: Choose a Strategy
Plan
You can use a table to help you solve the
problem.
6-5
Problem-Solving Investigation: Choose a Strategy
Solve
Find how many minutes Matt has lessons each
week.
30 lesson 1
+ 30 lesson 2
60 minutes per week
6-5
Problem-Solving Investigation: Choose a Strategy
Solve
Find how many minutes Matt has lessons in
six weeks.
60
120 180 240 300 360
Answer: So, Matt has lessons 360 minutes
in six weeks.
6-5
Problem-Solving Investigation: Choose a Strategy
Check
Look back at the problem.
Subtract 60 from 360 six times.
The result is 0.
So, the answer is correct.
6-6
Algebra: Find a Rule
Five-Minute Check (over Lesson 6-5)
Main Idea
California Standards
Example 1: Find a Multiplication Rule
Example 2: Find a Multiplication Rule
Example 3: Find a Division Rule
Example 4: Find a Division Rule
6-6
Algebra: Find a Rule
• I will find and use a rule to write an equation.
6-6
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.
6-6
Algebra: Find a Rule
Mike earns $10 when he
babysits for 2 hours. He
earns $20 when he babysits
for 4 hours. If he babysits for
6 hours, he earns $30. Write
an equation that describes
the money Mike earns.
Put the information in a table.
Then look for a pattern to
describe the rule.
6-6
Algebra: Find a Rule
Pattern:
2 × 5 = 10
4 × 5 = 20
6 × 5 = 30
Rule:
Multiply by 5.
Equation:
x × 5
=
y
6-6
Algebra: Find a Rule
Answer: The equation x × 5 = y describes the money
Mike earns from babysitting.
6-6
Algebra: Find a Rule
Ricardo earns $16 dollars when he mows 2 lawns
of grass. He earns $32 when he mows 4 lawns, and
$48 when he mows 6 lawns. Write an equation that
describes the money Ricardo earns.
A.
8x = y
B.
x+y=8
C.
2x + 8 = y
D.
x×8=y
6-6
Algebra: Find a Rule
Use the equation x × 5 = y to
find how much money Mike
earns for babysitting for 8, 9,
or 10 hours.
6-6
Algebra: Find a Rule
x×5=y
8 × 5 = $40
x×5=y
9 × 5 = $45
x×5=y
10 × 5 = $50
40
45
50
6-6
Algebra: Find a Rule
Answer: So, Mike will earn $40, $45, or $50 if he
babysits for 8, 9, or 10 hours.
6-6
Algebra: Find a Rule
Use the equation x × 8 = y to find how much
money Ricardo earns for mowing 7 or 8 lawns.
A.
$49, $64
B.
$15, $16
C.
$56, $64
D.
$63, $72
6-6
Algebra: Find a Rule
The cost of admission
into a water park is shown
in the table at the right.
Write an equation that
describes the number
pattern.
6-6
Algebra: Find a Rule
Pattern:
6÷6=1
12 ÷ 6 = 2
18 ÷ 6 = 3
Rule:
Divide by 6.
Equation:
c
÷ 6
=
n
6-6
Algebra: Find a Rule
Answer: The equation c ÷ 6 = n describes the cost of
admission into the water park.
6-6
Algebra: Find a Rule
The cost of admission into a basketball game is
shown in the table below. Write an equation that
describes the number pattern.
A.
c÷9=n
B.
c+9=n
C.
c+n=9
D.
c–9=n
6-6
Algebra: Find a Rule
Use the equation c ÷ 6 = n
to find how many people
will be admitted to the park
for $24, $30, and $36.
6-6
Algebra: Find a Rule
c÷6=n
24 ÷ 6 = 4
c÷6=n
c÷6=n
30 ÷ 6 = 5
36 ÷ 6 = 6
4
5
6
6-6
Algebra: Find a Rule
Answer: So, $24, $30, and $36 will buy tickets for
4, 5, and 6 people.
6-6
Algebra: Find a Rule
Use the equation c ÷ 9 = n to find how many
people will be admitted to the basketball game
for $45 and $63.
A.
4 people, 5 people
B.
5 people, 6 people
C.
7 people, 8 people
D.
5 people, 7 people
6-7
Balanced Equations
Five-Minute Check (over Lesson 6-6)
Main Idea
California Standards
Example 1: Balanced Equations
Example 2: Balanced Equations
Example 3: Find Missing Numbers
Example 4: Find Missing Numbers
6-7
Balanced Equations
• I will balance multiplication and division equations.
6-7
Balanced Equations
Standard 4AF2.2 Know and understand
that equals multiplied by equals are equal.
6-7
Balanced Equations
Show that the equality of 6r = 24 does not change
when each side of the equation is divided by 6.
6r = 24
6r ÷ 6 = 24 ÷ 6
r=4
Answer: So, r = 4.
Write the equation.
Divide each side by 6.
6-7
Balanced Equations
Check
6r = 24
6 × 4 = 24
24 = 24
Replace r with 4.
6-7
Balanced Equations
Show that the equality of 3y = 9 does not change
when each side of the equation is divided by 3.
A.
3y ÷ 3 = 9 ÷ 3; 6 = 6
B.
3y ÷ 3 = 9 ÷ 3; 3 = 3
C.
3y ÷ 3 = 9; 9 = 9
D.
3y = 9 ÷ 3; 3 = 9
6-7
Balanced Equations
Show that the equality of q ÷ 7 = 4 does not change
when each side of the equation is multiplied by 7.
q÷7=4
q÷7×7=4×7
q = 28
Answer: So, q = 28.
Write the equation.
Multiply each side by 7.
6-7
Balanced Equations
Check
q÷7=4
28 ÷ 7 = 4
4=4
Replace q with 28.
6-7
Balanced Equations
Show that the equality v ÷ 5 = 5 does not change
when each side of the equation is multiplied by 5.
A. v ÷ 5 × 5 = 5; 10 = 10
B. v ÷ 5 × 5 = 5 × 5; 25 = 25
C. v ÷ 5 = 5; 5 = 5
D. v ÷ 5 × 5 = 5 × 5; 10 = 10
6-7
Balanced Equations
Find the missing number in 5 × 10 × 4 = 50 ×
.
5 × 10 × 4 = 50 ×
Write the equation.
5 × 10 × 4 = 50 ×
You know that 5 × 10 = 50.
Each side of the equation must be multiplied by
the same number to keep the equation balanced.
Answer: So, the missing number is 4.
6-7
Balanced Equations
Find the missing number in 8 × 5 × 3 = 40 ×
A. 8
B. 5
C. 3
D. 40
.
6-7
Balanced Equations
Find the missing number in 2 × 12 ÷ 4 = 24 ÷
.
2 × 12 ÷ 4 = 24 ÷
Write the equation.
2 × 12 ÷ 4 = 24 ÷
You know that 2 × 12 = 24.
Each side of the equation must be divided by the
same number to keep the equation balanced.
Answer: So, the missing number is 4.
6-7
Balanced Equations
Find the missing number in 4 × 11 ÷ 2 = 44 ÷
A. 4
B. 11
C. 44
D. 2
.
6
Algebra: Use Multiplication and Division
Five-Minute Checks
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Multiplication and Division Equations
6
Algebra: Use Multiplication and Division
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6
Algebra: Use Multiplication and Division
6
Algebra: Use Multiplication and Division
6
Algebra: Use Multiplication and Division
6
Algebra: Use Multiplication and Division
6
Algebra: Use Multiplication and Division
Lesson 6-1
(over Chapter 5)
Lesson 6-2
(over Lesson 6-1)
Lesson 6-3
(over Lesson 6-2)
Lesson 6-4
(over Lesson 6-3)
Lesson 6-5
(over Lesson 6-4)
Lesson 6-6
(over Lesson 6-5)
Lesson 6-7
(over Lesson 6-6)
6
Algebra: Use Multiplication and Division
(over Chapter 5)
Tell whether 13 is composite, prime, or neither.
A. composite
B. prime
C. neither
6
Algebra: Use Multiplication and Division
(over Chapter 5)
Tell whether 26 is composite, prime, or neither.
A. composite
B. prime
C. neither
6
Algebra: Use Multiplication and Division
(over Chapter 5)
Tell whether 37 is composite, prime, or neither.
A. composite
B. prime
C. neither
6
Algebra: Use Multiplication and Division
(over Chapter 5)
Tell whether 1 is composite, prime, or neither.
A. composite
B. prime
C. neither
6
Algebra: Use Multiplication and Division
(over Chapter 5)
Tell whether 21 is composite, prime, or neither.
A. composite
B. prime
C. neither
6
Algebra: Use Multiplication and Division
(over Lesson 6-1)
Find the value of the expression if m = 4.
m × 10
A. 18
B. 14
C. 40
D. 80
6
Algebra: Use Multiplication and Division
(over Lesson 6-1)
Find the value of the expression if m = 4 and n = 8.
3 × (n ÷ m)
A. 1.5
B. 6
C. 12
D. 36
6
Algebra: Use Multiplication and Division
(over Lesson 6-1)
Find the value of the expression if m = 4 and n = 8.
(12 ÷ m) × n
A. 6
B. 16
C. 24
D. 64
6
Algebra: Use Multiplication and Division
(over Lesson 6-1)
Find the value of the expression if m = 4 and n = 8.
(n × m) ÷ 2
A. 6
B. 16
C. 30
D. 64
6
Algebra: Use Multiplication and Division
(over Lesson 6-2)
Work backward to solve the problem. Lance had
4 granola bars left from his weekend hike. On
Saturday, he ate 2 bars. Before he left for the trip
on Friday, his mother added 5 bars to what he
had. How many bars did he have to start with?
A. 7 bars
B. 5 bars
C. 3 bars
D. 1 bar
6
Algebra: Use Multiplication and Division
(over Lesson 6-3)
Find the value of the expression.
4 + (5 × 2) – 1
A. 6
B. 11
C. 13
D. 14
6
Algebra: Use Multiplication and Division
(over Lesson 6-3)
Find the value of the expression.
6+6×3
A. 12
B. 15
C. 24
D. 36
6
Algebra: Use Multiplication and Division
(over Lesson 6-3)
Find the value of the expression.
(17 – 3) – (2 × 4)
A. 6
B. 7
C. 8
D. 22
6
Algebra: Use Multiplication and Division
(over Lesson 6-3)
Find the value of the expression.
(21 ÷ 3) + 3
A. 9
B. 10
C. 21
D. 22
6
Algebra: Use Multiplication and Division
(over Lesson 6-4)
Solve 5 × x = 25 mentally.
A. 4
B. 20
C. 5
D. 6
6
Algebra: Use Multiplication and Division
(over Lesson 6-4)
Solve 56 ÷ m = 8 mentally.
A. 8
B. 48
C. 49
D. 7
6
Algebra: Use Multiplication and Division
(over Lesson 6-4)
Solve r ÷ 7 = 3 mentally.
A. 21
B. 3
C. 24
D. 7
6
Algebra: Use Multiplication and Division
(over Lesson 6-4)
Solve k × 9 = 36 mentally.
A. 3
B. 45
C. 4
D. 36
6
Algebra: Use Multiplication and Division
(over Lesson 6-5)
Use any strategy to solve. Jacobo is 6 years old
and his brother is 2 years old. How old will each of
them be when Jacobo is twice his brother’s age?
A. Jacobo will be 12 and his brother will be 6.
B. Jacobo will be 8 and his brother will be 4.
C. Jacobo will be 7 and his brother will be 3.
D. Jacobo will be 10 and his brother will be 6.
6
Algebra: Use Multiplication and Division
(over Lesson 6-6)
Find a rule and equation that describes the pattern.
Then use the equation to find the missing number.
A. Multiply by 4; x × 4 = y;
18
B. Add 8; x + 8 = y; 14
C. Multiply by 3; x × 3 = y;
18
D. Multiply by 3; y × 3 = x;
18
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