Transcript Lesson 8-8

Chapter 8
Algebra: Ratios and Functions
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8
Algebra: Ratios and Functions
Lesson 8-1
Ratios and Rates
Lesson 8-2
Problem-Solving Strategy: Look
for a Pattern
Lesson 8-3
Ratio Tables
Lesson 8-4
Equivalent Ratios
Lesson 8-5
Problem-Solving Investigation:
Choose the Best Strategy
Lesson 8-6
Algebra: Ratios and Equations
Lesson 8-7
Algebra: Sequences and
Expressions
Lesson 8-8
Algebra: Equations and Graphs
8-1
Ratios and Rates
Five-Minute Check (over Chapter 7)
Main Idea and Vocabulary
California Standards
Example 1
Example 2
Example 3
Ratios and Tangrams
8-1
Ratios and Rates
• I will express ratios and rates in fraction form.
• ratio
• rate
• unit rate
8-1
Ratios and Rates
Preparation for Standard 6NS1.2 Interpret and
use ratios in different contexts (e.g., batting
averages, miles per hour) to show the relative
sizes of two quantities, using appropriate
notations
.
8-1
Ratios and Rates
Write the ratio in simplest form
that compares the number of
scooters to the number of
unicycles.
unicycles
scooters
4 = 2
10
5
8-1
Ratios and Rates
Answer: The ratio of unicycles to scooters is 2 ,
5
2 to 5, or 2:5. This means that for every
2 unicycles there are 5 scooters.
Ratios and Rates
8-1
Write the ratio in simplest form that compares
the number of singers in a duet to the number
in an octet.
A.
1
4
B.
2
8
C.
1
8
D.
2
4
8-1
Ratios and Rates
Several students were asked to name their favorite
kind of book. Write the ratio that compares the
number of people who chose sports books to the
total number of responses.
7 students preferred
sports out of a total of
7 + 9 + 4 + 5 or 25
responses.
8-1
Ratios and Rates
sports responses
total responses
7
25
Answer: The ratio in simplest form of the number of
students who chose sports to the total number
7
of responses is
, 7 to 25, or 7:25. So,
25
seven out of every 25 students preferred
sports.
8-1
Ratios and Rates
Several students were
asked to name their favorite
kind of movie. Choose the
ratio that compares the
number of people who
chose thriller movies to the
total number of responses
in simplest form.
A. 12:18
C.
2:5
B. 2:3
D.
12:30
8-1
Ratios and Rates
Find the cost per ounce of a 16-ounce jar of salsa
that costs $2.88.
$2.88
16 ounce
=
$0.18
1 ounce
Answer: So, the salsa costs $0.18 per ounce.
8-1
Ratios and Rates
A 4 pound package of ground beef costs $3.56.
What is the cost per pound?
A. $0.99
B. $0.88
C. $0.98
D. $0.89
8-2
Problem-Solving Strategy: Look for a Pattern
Five-Minute Check (over Lesson 8-1)
Main Idea
California Standards
Example 1: Problem-Solving Strategy
8-2
Problem-Solving Strategy: Look for a Pattern
• I will solve problems by looking for a pattern.
8-2
Problem-Solving Strategy: Look for a Pattern
Standard 5MR1.1 Analyze problems by
identifying relationships, distinguishing relevant
from irrelevant information, sequencing and
prioritizing information, and observing patterns.
Standard 5NS2.1 Add, subtract, multiply, and
divide with decimals; … and verify the
reasonableness of results.
8-2
Problem-Solving Strategy: Look for a Pattern
Emelia is waiting for her friend Casey to arrive. It
is 1:15 P.M. now, and Casey said that he would be
on the first bus to arrive after 6:00 P.M. Emelia
knows that buses arrive every 30 minutes,
starting at 1:45 P.M. How much longer will it be
before Casey arrives?
8-2
Problem-Solving Strategy: Look for a Pattern
Understand
What facts do you know?
• It is now 1:15 P.M.
• The first bus arrives at 1:45 P.M.
• Casey will be on the first bus after 6 P.M.
What do you need to find?
• How much longer will it be before Casey arrives?
8-2
Problem-Solving Strategy: Look for a Pattern
Plan
Start with the time the first bus arrives and look for
a pattern.
8-2
Problem-Solving Strategy: Look for a Pattern
Solve
Answer: So, the first bus to arrive after 6:00 P.M. is
the 6:15 P.M. bus. Since it is now 1:15 P.M.,
Casey will not arrive for another 5 hours.
8-2
Problem-Solving Strategy: Look for a Pattern
Check
Look back at the problem. Continue adding 30 minutes
to the previous arrival time until you reach 6:15 P.M.
Then add up the 30-minute periods.
8-3
Ratio Tables
Five-Minute Check (over Lesson 8-2)
Main Idea and Vocabulary
California Standards
Example 1
Example 2
Example 3
Example 4
8-3
Ratio Tables
• I will use ratio tables to represent and solve
problems involving equivalent ratios.
• ratio table
• equivalent ratio
• scaling
8-3
Ratio Tables
Standard 5MR2.3 Use a variety of methods,
such as words, numbers, symbols, charts,
graphs, tables, diagrams, and models, to explain
mathematical reasoning.
Preparation for Standard 5AF1.5 Solve
problems involving linear functions with integer
values; write the equation; and graph the resulting
ordered pairs of integers on a grid.
8-3
Ratio Tables
A recipe calls for 5 cups of water for each cup of
pinto beans. Use the ratio table to find how many
cups of water should be used for 4 cups of pinto
beans.
8-3
Ratio Tables
One Way: Find a pattern and extend it.
For 4 cups of beans, you would need a total of
5 + 5 + 5 + 5 or 20 cups of water.
2
3
10
15
20
8-3
Ratio Tables
Another Way: Multiply each quantity by the
same number.
20
Answer: So, for 4 cups of pinto beans, you will need
20 cups of water.
8-3
Ratio Tables
The recipe for rice calls for 3 cups of water for each
cup of rice. How many cups of water should be used
for 6 cups of rice?
A.
18 cups
B.
9 cups
C.
12 cups
D.
16 cups
8-3
Ratio Tables
There are over 50,000 species of spiders. Use
the ratio table below to find how many legs a
spider has.
2
8
16
Answer: So, a spider has 8 legs.
8-3
Ratio Tables
A marathon runner can run 24 miles in 3 hours.
How many miles can he run in 1 hour?
A.
16 miles
B.
8 miles
C.
12 miles
D.
4 miles
8-3
Ratio Tables
Coco used 12 yards of fabric to make 9 blouses.
Use the ratio table to find the number of blouses
she could make with 24 yards of fabric.
18
13.5
18
Answer: So, with 24 yards of fabric, Coco could make
18 blouses.
8-3
Ratio Tables
Mrs. Stine can grade 48 papers in 96 minutes. How
many can she grade in 24 minutes?
A. 6
B. 12
C. 24
D. 96
8-3
Ratio Tables
It takes a worker 70 minutes to pack 120 cartons of
books. The worker has 14 minutes of work left. Use
a ratio table to find how many cartons of books the
worker can pack in 14 minutes.
24
Answer: So, a worker can pack 24 cartons in 14
minutes.
8-3
Ratio Tables
It takes Sarah 60 minutes to walk 4 miles. How far
will she have walked after 30 minutes?
A.
1 mile
B.
2 miles
C.
3 miles
D.
4 miles
8-4
Equivalent Ratios
Five-Minute Check (over Lesson 8-3)
Main Idea
California Standards
Example 1
Example 2
Example 3
Example 4
Example 5
8-4
Equivalent Ratios
• I will determine if two quantities are equivalent.
8-4
Equivalent Ratios
Preparation for Standard 5AF1.5 Solve
problems involving linear functions with integer
values; write the equation; and graph the resulting
ordered pairs of integers on a grid.
8-4
Equivalent Ratios
Determine if the pair of rates is equivalent.
Explain your reasoning.
42 people on 7 teams; 64 people on 8 teams
42 people
= 6 people per team
7 teams
64 people
= 8 people per team
8 teams
Answer: These rates are not equivalent since they are
not the same.
8-4
Equivalent Ratios
Determine if the pair of rates are equivalent.
2 chapters in one day; 18 chapters in 9 days
A.
Yes, both are 2:1.
B.
Yes, both are 18:9.
C.
No.
D.
not enough information to solve
8-4
Equivalent Ratios
Determine if the pair of rates is equivalent.
Explain your reasoning.
20 rolls for $5; 48 rolls for $12
20 rolls
$5
= $4 per roll
48 rolls
$12
= $4 per roll
Answer: These are equivalent because the rates are
the same.
8-4
Equivalent Ratios
Determine if the pair of rates is equivalent.
$12 for 3 hours; $15 for 5 hours
A.
Yes, both are $4 an hour.
B.
Yes, both are $5 an hour.
C.
No, they are not the same.
D.
not enough information
8-4
Equivalent Ratios
One day Jafar sold 21 pizzas in 3 hours. The next
day he sold 35 pizzas in 5 hours. Are these selling
rates equivalent? Explain your reasoning.
Write each rate as a fraction. Then find its unit rate.
8-4
Equivalent Ratios
21 pizzas
3 hours
35 pizzas
5 hours
=
7 pizzas
1 hour
=
7 pizzas
1 hour
Answer: Since the rates have the same unit rate, they
are equivalent. So, Jafar’s selling rates are
equivalent.
8-4
Equivalent Ratios
Paella sold 27 magazine subscriptions in 3 hours.
The next day she sold 32 magazine subscriptions in
4 hours. What are the selling rates for each day?
Are they equivalent?
A.
9, 9; yes
B.
9, 8; no
C.
8, 8; yes
D.
8, 9; no
8-4
Equivalent Ratios
Determine if the pair of ratios is equivalent.
Explain your reasoning.
5 laps swam in 8 minutes; 11 laps swam in 16 minutes
Write each ratio as a fraction.
5 laps
8 minutes
?
=
11 laps
16 minutes
The numerator and
denominator do not multiply
by the same number. So,
they are not equivalent.
Answer: Since the fractions are not equivalent the
ratios are not equivalent.
8-4
Equivalent Ratios
Determine if the pair of ratios is equivalent.
15 pages read in 30 minutes; 22 pages read
in 40 minutes
1
.
2
A.
Yes, they are both
B.
No.
C.
Yes, they are both 2 .
3
D.
not enough information
8-4
Equivalent Ratios
Determine if the pair of ratios is equivalent.
Explain your reasoning.
8 corrals with 56 horses; 4 corrals with 28 horses
Write each ratio as a fraction.
8 corrals
56 horses
?
=
1 corral
7 horses
8-4
Equivalent Ratios
4 corrals
28 horses
?
=
1 corral
7 horses
Answer: Since the fractions are equivalent, the rates
are equivalent.
8-4
Equivalent Ratios
Determine if the pair of ratios is equivalent.
7 barnyards with 49 cows; 9 barnyards with
63 cows
A.
Yes, both are 1 barnyard per 7 cows.
B.
Yes, both are 7 barnyards per 1 cow.
C.
Yes, both are 1 barnyard per 9 cows.
D.
No.
8-5
Problem-Solving Investigation: Choose the Best Strategy
Five-Minute Check (over Lesson 8-4)
Main Idea
California Standards
Example 1: Problem-Solving Investigation
8-5
Problem-Solving Investigation: Choose the Best Strategy
• I will choose the best strategy to solve a problem.
8-5
Problem-Solving Investigation: Choose the Best Strategy
Standard 5MR2.3 Use a variety of methods, such
as words, numbers, symbols, charts, graphs, tables,
diagrams, and models, to explain mathematical
reasoning.
Standard 5SDAP1.1 Know the concepts of mean,
median, and mode; compute and compare simple
examples to show that they may differ.
8-5
Problem-Solving Investigation: Choose the Best Strategy
JUWAN: I took my dog to the
veterinarian’s office. While
waiting, I noticed that there were
more dogs than cats in the waiting
room. The vet said that for about
every 5 dogs he sees, he sees 2
cats.
YOUR MISSION: Find about how many
dogs the vet will see if 21 total
pets come into the office.
8-5
Problem-Solving Investigation: Choose the Best Strategy
Understand
What facts do you know?
• You know that the ratio of dogs to cats is
about 5:2.
What do you need to find?
• You need to find about how many dogs
the vet will see.
8-5
Problem-Solving Investigation: Choose the Best Strategy
Plan
Use counters to act out how many dogs the vet
will see.
8-5
Problem-Solving Investigation: Choose the Best Strategy
Solve
Use red counters to represent the dogs and
yellow counters to represent the cats. Since the
ratio of dogs to cats is 5:2, place 5 red counters
and 2 yellow counters in a group. Make groups
of 7 counters until you have 21 counters total.
8-5
Problem-Solving Investigation: Choose the Best Strategy
Solve
After three groups there are 21 counters, so
you can stop making groups. Find the number
of red counters to find how many dogs the vet
will see. 5 + 5 + 5 = 15.
Answer: So, if the vet sees 21 pets, about 15
of them will be dogs.
8-5
Problem-Solving Investigation: Choose the Best Strategy
Check
Find the ratio of red counters to yellow counters.
If the ratio is equivalent to the original ratio, 5:2,
then the answer is correct.
8-6
Algebra: Ratios and Equations
Five-Minute Check (over Lesson 8-5)
Main Idea
California Standards
Example 1
Example 2
Example 3
Example 4
Example 5
Example 6
8-6
Algebra: Ratios and Equations
• I will solve equations using equivalent fractions.
8-6
Algebra: Ratios and Equations
Standard 5AF1.1 Use information taken from a
graph or equation to answer questions about a
problem situation.
Standard 5AF1.2 Use a letter to represent
an unknown number; write and evaluate simple
algebraic expressions in one variable by substitution.
8-6
Algebra: Ratios and Equations
4 28
Solve =
.
5 x
4 28
=
5
x
Since 4 × 7 = 28, multiply the
numerator and denominator by 7.
4 28
=
5 35
5 × 7 = 35
Answer: So, x = 35.
8-6
Algebra: Ratios and Equations
5 20
Solve =
.
8 x
A.
x = 36
B.
x = 32
C.
x = 40
D.
x=2
8-6
Algebra: Ratios and Equations
b 16
Solve =
.
5 20
b 16
=
5 20
Since 5 × 4 = 20, multiply the
numerator and denominator by 4.
4 16
=
5 20
THINK What number multiplied
by 4 equals 16? The answer is 4.
Answer: So, b = 4.
8-6
Algebra: Ratios and Equations
Solve h = 6 .
6 36
A. h = 12
B. h = 5
C. h = 6
D. h = 1
8-6
Algebra: Ratios and Equations
Solve 19 = n .
38 22
Since 19 = 1 , then n = 11, which would make the
38 2
equation true because 11 is the same as 1 .
22
2
Answer: So, n = 11.
8-6
Algebra: Ratios and Equations
Solve
18 m
= .
45 5
A. m = 2
B. m = 9
C. m = 3
D. m = 7
8-6
Algebra: Ratios and Equations
7
Solve
= 28 .
t
60
7 28
=
t
60
Since 7 × 4 = 28, multiply the
numerator and denominator by 4.
7 28
=
15 60
THINK What number multiplied by
4 equals 60? The answer is 15.
Answer: So, t = 15.
8-6
Algebra: Ratios and Equations
4
Solve
= 64 .
y
80
A. y = 3
B. y = 6
C. y = 5
D. y = 4
8-6
Algebra: Ratios and Equations
Out of the 40 students in a gym class, 12 say
soccer is their favorite sport. Based on this
result, predict how many of the 4,200 students
in the community would rate soccer as their
favorite sport.
Write and solve an equation. Let s represent the number
of students who can be expected to prefer soccer.
8-6
Algebra: Ratios and Equations
School
Class
prefer soccer
total students
s
12
=
4200
40
prefer soccer
total students
The denominators 40 and 4,200 are not easily related
by multiplication, so simplify the ratio 12 out of 40.
Then solve using equivalent fractions.
8-6
Algebra: Ratios and Equations
12
s
3
=
=
40
4200
10
Since 10 × 420 = 4,200,
multiply the numerator
and denominator by 420.
Answer: So, about 1,260 out of 4,200 students in
the school can be expected to prefer
soccer.
8-6
Algebra: Ratios and Equations
Out of the 30 kids in Mrs. Ankrum’s class, 12
are girls. Based on this result, predict how may
of the 660 students in the school are girls.
A. 264 girls
B. 300 girls
C. 260 girls
D. 284 girls
8-6
Algebra: Ratios and Equations
Cedric earned $184 for 8 hours of work. At this
rate, how much will he earn for 15 hours of work?
Step 1 Set up the equation. Let a represent the
amount of money to be earned.
184 dollars
8 hours
=
a dollars
15 hours
8-6
Algebra: Ratios and Equations
Step 2 Find the unit rate.
184 dollars
8 hours
=
23
1
=
$345
15 hours
Answer: So, Cedric will earn $345 for working for
15 hours.
8-6
Algebra: Ratios and Equations
Julio earned $145 for mowing 5 lawns. At this
rate, how much will he earn for 30 lawns?
A. $174
B. $870
C. $850
D. $445
8-7
Algebra: Sequences and Expressions
Five-Minute Check (over Lesson 8-6)
Main Idea and Vocabulary
California Standards
Example 1
Example 2
Example 3
Example 4
8-7
Algebra: Sequences and Expressions
• I will extend and describe arithmetic sequences
using algebraic expressions.
• sequence
• term
• arithmetic sequence
8-7
Algebra: Sequences and Expressions
Standard 5AF1.2 Use a letter to represent
an unknown number; write and evaluate
simple algebraic expressions in one variable
by substitution.
Standard 5AF1.5 Solve problems involving
linear functions with integer values; write the
equation; and graph the resulting ordered pairs of
integers on a grid.
8-7
Algebra: Sequences and Expressions
Use the words and symbols to describe the value
of each term as a function of its position. Then find
the value of the tenth term in the sequence.
Notice that the value of each term is 7 times its
position number. So the value of the term in position
n is 7n.
8-7
Algebra: Sequences and Expressions
Now find the
value of the tenth
term.
7n = 7 × 10
= 70
Replace n with 10.
Multiply.
Answer: So, the value of the tenth term in the
sequence is 70.
8-7
Algebra: Sequences and Expressions
Use the words and symbols to describe the value
of each term as a function of its position. Then find
the value of the fifth term in the sequence.
A. 7 times its position number; 7n, 35
B. 6 times its position number; 6 + n, 11
C. 6 times its position number; 6n, 30
D. 3 times its position number; 3n, 15
8-7
Algebra: Sequences and Expressions
Use the words and symbols to describe the value
of each term as a function of its position. Then find
the value of the tenth term in the sequence.
Notice that the value of each term is 2 more than its
position number, so the rule is n + 2.
8-7
Algebra: Sequences and Expressions
Now find the value
of the tenth term.
n + 2 = 10 + 2
= 12
Replace n with 10.
Add.
Answer: So, the value of the tenth term in the
sequence is 12.
8-7
Algebra: Sequences and Expressions
Use the words and symbols to describe the value
of each term as a function of its position. Then find
the value of the tenth term in the sequence.
A. 2 less than its position number; 2 – n, 8
B. 2 less than its position number; n – 2, 8
C. 3 less than its position number; 3 – n, 7
D. 3 less than its position number; n – 3, 7
8-7
Algebra: Sequences and Expressions
MEASUREMENT There
are 60 seconds in 1
minute. It takes Panya 9
minutes to walk to school.
Make a table, and then
write an algebraic
expression relating the
number of seconds to the
number of minutes. Find
how many seconds it
takes Panya to walk to
school.
8-7
Algebra: Sequences and Expressions
Notice that the number of seconds is 60 times the
number of minutes.
8-7
Algebra: Sequences and Expressions
Now find the ninth term.
60n = 60 × 9
= 540
Replace n with 9.
Multiply.
Answer: So, it will take Panya 540 seconds to
walk to school.
8-7
Algebra: Sequences and Expressions
There are 60 minutes in an hour. It takes Mr.
Daugherty 5 hours each week to grade all of his
fifth graders’ papers. Choose an expression and
correct answer that represents the amount of
minutes Mr. Daugherty spends grading papers
each week.
A. 60h; 300
C. 60 – h; 55
B. 60 ; 12
h
D. 60 = h; 5
8-7
Algebra: Sequences and Expressions
The table to the right
shows the number of
plants in a garden,
based on the number of
rows. Write an
expression to find the
number of plants in n
rows.
8-7
Algebra: Sequences and Expressions
The number of plants increases by 3, so the rule
contains 3n. If the rule were simply 3n, then the value
for 1 row would be 3.
Notice that adding 1
to the number of rows
multiplied by 3 gives
the number of plants.
Answer: So, 3n + 1 gives the number of flowers in
n rows.
8-7
Algebra: Sequences and Expressions
Choose the expression
to find the number of
cars in each row.
A. n + 7
B. n × 8
C. 3n × 8
D. 6n + 2
8-8
Algebra: Equations and Graphs
Five-Minute Check (over Lesson 8-7)
Main Idea
California Standards
Example 1
Example 2
Example 3
Example 4
Example 5
Example 6
8-8
Algebra: Equations and Graphs
• I will write an equation to describe a linear
situation.
8-8
Algebra: Equations and Graphs
Standard 5AF1.1 Use the information taken from
a graph or an equation to answer questions about
a problem situation.
Standard 5AF1.5 Solve problems involving
linear functions with integer values; write the
equation; and graph the resulting ordered pairs
of integers on a grid.
8-8
Algebra: Equations and Graphs
Write an equation to represent the function
displayed in the table.
Each output y is equal to 5 times the input x.
8-8
Algebra: Equations and Graphs
Answer: So, the equation that represents the
function is y = 5x.
8-8
Algebra: Equations and Graphs
Choose the equation that represents the function
displayed in the table.
A. x = 6y
B. y = 3y + 3
C. y = 6x
D. y = x + 6
8-8
Algebra: Equations and Graphs
Javier sells handmade notebooks. He charges
$25 for each book. Make a table to show the
relationship between the number of b books
sold and the total amount Javier earns t.
The total earned
(output) is equal
to $25 times the
number of books
made (input).
8-8
Algebra: Equations and Graphs
Jean sells dream catchers. She charges $15 for each
one. Which table correctly shows the relationship
between the number of b dream catchers and the
total amount Jean earned?
A.
8-8
Algebra: Equations and Graphs
Jean sells dream catchers. She charges $15 for each
one. Which table correctly shows the relationship
between the number of b dream catchers and the
total amount Jean earned?
B.
8-8
Algebra: Equations and Graphs
Jean sells dream catchers. She charges $15 for each
one. Which table correctly shows the relationship
between the number of b dream catchers and the
total amount Jean earned?
C.
8-8
Algebra: Equations and Graphs
Jean sells dream catchers. She charges $15 for each
one. Which table correctly shows the relationship
between the number of b dream catchers and the
total amount Jean earned?
D.
8-8
Algebra: Equations and Graphs
Jean sells dream catchers. She charges $15 for each
one. Which table correctly shows the relationship
between the number of b dream catchers and the
total amount Jean earned?
A.
8-8
Algebra: Equations and Graphs
Write an equation to find the total amount earned
t for selling b books.
Study the table.
8-8
Algebra: Equations and Graphs
The total earned equals $25 times the number of
books Javier sells.
Answer: So, the equation is t = 25b.
8-8
Algebra: Equations and Graphs
Choose the equation to find the total amount t
Jean earned.
A. 15t = b
C. t + 15 = b
B. 15 = b
t
D. 15 × 5 = b
8-8
Algebra: Equations and Graphs
How much will Javier earn if he sells 7 books
using the equation t = 25b?
t = 25b
Write the equation.
t = 25(7)
Replace b with 7.
t = 175
Simplify.
Answer: So, Javier will earn $175.
8-8
Algebra: Equations and Graphs
How much will Jean earn if she sells 9 dream
catchers? Use the equation t = 15b.
A. $140
B. $135
C. $160
D. $155
8-8
Algebra: Equations and Graphs
The table below shows
the amount that a kennel
charges for grooming a
dog. Write a sentence
and an equation to
describe the data. Then
find the total cost of
grooming 11 dogs, 12
dogs, and 13 dogs.
8-8
Algebra: Equations and Graphs
The cost of getting a dog groomed is $12 for each
dog. The total cost t is $12 times the number of dogs
d. Therefore, t = 12d.
8-8
Algebra: Equations and Graphs
The table below shows the amount that a Girl
Scout troop charges for a box of cookies.
Choose the correct equation to describe the
data. Then find the total cost for 12, 13, and 14
boxes of cookies.
8-8
Algebra: Equations and Graphs
A. 3t = c; $30, $40, $50
B. 3c = t; $30, $40, $50
C. c + 3 = t; $36, $39, $42
D. 3c = t; $36, $39, $42
8-8
Algebra: Equations and Graphs
Graph the results from Example 5 on a
coordinate plane.
8-8
Algebra: Equations and Graphs
Step 1 Make a
coordinate place
with the d values
along the x-axis
and the t values
along the y-axis.
Step 2 Using the (d, t)
values from
Example 5, plot
the coordinate
plane.
8-8
Algebra: Equations and Graphs
Use the information in
the table to make a
graph on a separate
sheet of paper. Choose
the best description of
the line that is formed.
A. curved, descending line
B. steep, straight, upward line
C. straight, horizontal line
D. “u” shaped line
8
Algebra: Ratios and Functions
Five-Minute Checks
Ratios and Tangrams
8
Algebra: Ratios and Functions
Lesson 8-1
(over Chapter 7)
Lesson 8-2
(over Lesson 8-1)
Lesson 8-3
(over Lesson 8-2)
Lesson 8-4
(over Lesson 8-3)
Lesson 8-5
(over Lesson 8-4)
Lesson 8-6
(over Lesson 8-5)
Lesson 8-7
(over Lesson 8-6)
Lesson 8-8
(over Lesson 8-7)
8
Algebra: Ratios and Functions
(over Chapter 7)
Solve 8p = 56.
A. 8
B. 7
C. 12
D. 9
8
Algebra: Ratios and Functions
(over Chapter 7)
Solve 30 = 3f.
A. 10
B. 3
C. 12
D. 15
8
Algebra: Ratios and Functions
(over Chapter 7)
Solve –15v = –45.
A. 5
B. 4
C. 3
D. 6
8
Algebra: Ratios and Functions
(over Chapter 7)
Solve 7y = –70.
A.
–7
B.
10
C.
7
D.
–10
8
Algebra: Ratios and Functions
(over Lesson 8-1)
Write the ratio as a fraction in simplest form.
16 apples out of 24 pieces of fruit
4
A.
6
2
B.
8
2
C. 3
D.
8
6
8
Algebra: Ratios and Functions
(over Lesson 8-1)
Write the ratio as a fraction in simplest form.
18 dogs out of 90 pets
4
A.
5
8
B.
10
1
C. 5
D.
9
10
8
Algebra: Ratios and Functions
(over Lesson 8-1)
Write the following as a unit rate.
$5 for 10 folders
A. $0.50/1 folder
B. $0.10/1 folder
C. $5.00/1 folder
D. $2.00/1 folder
8
Algebra: Ratios and Functions
(over Lesson 8-1)
Write the following as a unit rate.
48 chairs for 3 rows
A. 12 chairs/1 row
B. 8 chairs/1 row
C. 16 chairs/1 row
D. 15 chairs/1 row
8
Algebra: Ratios and Functions
(over Lesson 8-2)
Solve. Luis saw the numbers below in a science
report. Describe the pattern. Then find the next 3
numbers in the pattern.
6, 18, 54, 162, 486, __, __, __
A. multiply by 3; 1,548; 4,747; 13,122
B. multiply by 3; 1,458; 4,374; 13,122
C. multiply by 3; 972, 1,844; 3,688
8
Algebra: Ratios and Functions
(over Lesson 8-3)
Use the ratio table to solve the problem. A dozen
roses sell for $18. How much will 16 roses cost?
A. $26
B. $32
C. $20
D. $24
8
Algebra: Ratios and Functions
(over Lesson 8-3)
Use the ratio table to solve the problem. How much
will 24 roses cost?
A. $30
B. $36
C. $12
D. $18
8
Algebra: Ratios and Functions
(over Lesson 8-4)
Determine if each pair of ratios or rates are
equivalent.
$18 in 3 days; $42 in 6 days
A. No
B. Yes
8
Algebra: Ratios and Functions
(over Lesson 8-4)
Determine if each pair of ratios or rates are
equivalent.
50 desks in 2 rooms; 75 desks in 3 rooms
A. No
B. Yes
8
Algebra: Ratios and Functions
(over Lesson 8-4)
Determine if each pair of ratios or rates are
equivalent.
8 fruit drinks for $20; 9 fruit drinks for $24
A. No
B. Yes
8
Algebra: Ratios and Functions
(over Lesson 8-4)
Determine if each pair of ratios or rates are
equivalent.
12 dogs out of 18 pets; 10 dogs out of 15 pets
A. No
B. Yes
8
Algebra: Ratios and Functions
(over Lesson 8-5)
Solve. Tell what strategy you used. Maria is building
chains. She uses 1 ring on the first chain, 6 rings on
the second, 11 rings on the third, and 16 rings on the
fourth. If she continues the pattern, how many rings
will be on the next chain?
A. 35 rings
B. 19 rings
C. 34 rings
D. 21 rings
8
Algebra: Ratios and Functions
(over Lesson 8-6)
Solve.
w
5
=
40
8
A. 15
B. 25
C. 100
D. 30
8
Algebra: Ratios and Functions
(over Lesson 8-6)
Solve.
A. 18
B. 20
C. 15
D. 25
6
n
=
11
33
8
Algebra: Ratios and Functions
(over Lesson 8-6)
Solve.
A. 18
B. 22
C. 60
D. 15
50
300
=
a
3
8
Algebra: Ratios and Functions
(over Lesson 8-6)
Solve.
A. 90
B. 88
C. 15
D. 45
x
15
=
66
11
8
Algebra: Ratios and Functions
(over Lesson 8-7)
Use words and symbols to describe the value of
each term as a function of its position. Then find
the value of the ninth term in the sequence.
A. 5n + 5; 45
B. 15n + 5; 60
C. 15n + 10; 80
This slide is intentionally blank.