UNIT 1
Number and
Operations
Additional Resources
Personal
Math Trainer
my.hrw.com
Online
Assessment and
Intervention
Assessment Resources
• Leveled Unit Tests: A, B, C, D
• Performance Assessment
Study Guide Review
Vocabulary Development
Integrating the ELPS
Encourage English learners to refer to their notes and the illustrated, bilingual glossary as
they review the unit content.
c.4.E Read linguistically accommodated content area material with a decreasing need for linguistic
accommodations as more English is learned.
MODULE 1 Rational Numbers
7.2, 7.3.A, 7.3.B
Key Concepts
• A number that can be written as a terminating decimal or a repeating decimal is a rational
number. (Lesson 1.1)
• A subset is a set of numbers contained in a larger set. (Lesson 1.2)
• To subtract a number, add its opposite. (Lesson 1.4)
• The product of two numbers with different signs is negative. The product of two numbers
with the same signs is positive. (Lesson 1.5)
• The quotient of two numbers with different signs is negative. The quotient of two
numbers with the same signs is positive. (Lesson 1.6)
49
Unit 1
UNIT 1
Study Guide
MODULE
?
1
Review
Rational Numbers
EXAMPLE 3
1 - __
2 .
Find the product: 3(- __
6 )( 5 )
Key Vocabulary
ESSENTIAL QUESTION
How can you use rational numbers to solve real-world problems?
rational number (número
racional)
repeating decimal
(decimal periódico)
3(- _16 ) = - _12
Find the product of the first two factors. One is
positive and one is negative, so the product is negative.
- _12(- _25 ) = _15
Multiply the result by the third factor. Both are
negative, so the product is positive.
3(- _16 )(- _25 ) = _15
set (conjunto)
EXAMPLE 1
Eddie walked 1_23 miles on a hiking trail. Write 1_23 as a decimal.
Use the decimal to classify 1_23 by naming the set or sets to
which it belongs.
subset (subconjunto)
terminating decimal
(decimal cerrado)
EXAMPLE 4
15.2
Find the quotient: ____
.
−2
15.2
____
= -7.6
-2
1.66
⎯
The quotient is negative because the signs are different.
3⟌ 5.00
1_23 = _53
-3
20
-1 8
20
-18
2
2
Write 1__
as an improper
3
fraction.
EXERCISES
Write each mixed number as a whole number or decimal. Classify
each number by naming the set or sets to which it belongs: rational
numbers, integers, or whole numbers. (Lessons 1.1, 1.2) 4; whole number, integer,
Divide the numerator by
the denominator.
1. _34
_
The decimal equivalent of 1_23 is 1.66…, or 1.6. It is a repeating decimal, and
therefore can be classified as a rational number.
0.75; rational number
11 3.66…,
3. __
3
rational number
2. _82
rational number
4. _52
2.5, rational number
Find each sum or difference. (Lessons 1.3, 1.4)
EXAMPLE 2
Find each sum or difference.
4.5
5. -5 + 9.5
A. -2 + 4.5
5
8. -3 - (-8)
-_23
6. _16 + (- _56 )
9. 5.6 - (-3.1)
-9
7. -0.5 + (-8.5)
8.7
10. 3_12 - 2_14
1_14
0
13. -8 × 8
-64
© Houghton Mifflin Harcourt Publishing Company
0 1 2 3 4 5
45
11. -9 × (-5)
-56
14. ____
8
Start at -2 and move 4.5 units to the right. -2 + 4.5 = 2.5
-7
17. - _25 (- _12 )(- _56 )
B. - _25 - (- _45 )
12. 0 × (-7)
-130
15. _____
-5
-_16
26
18.
34.5
16. ____
1.5
(_15 )(- _57 )(_34 )
23
3
-__
28
19. Lei withdrew $50 from her bank account every day for a week. What
was the change in her account in that week?
-1
0
© Houghton Mifflin Harcourt Publishing Company
Find each product or quotient. (Lessons 1.5, 1.6)
-5 -4 -3 -2 -1
-50 × 7 = -350; -$350
1
20. In 5 minutes, a seal descended 24 feet. What was the average rate of
change in the seal’s elevation per minute?
Start at - _25 . Move | - _45 | = _45 unit to the right because you are
subtracting a negative number. - _25 - (- _45 ) = _25
24 = -4.8; -4.8 feet per minute
- __
5
Unit 1
49
50
Unit 1
Number and Operations
50
UNIT 2
Ratios and
Proportional
Relationships
Additional Resources
Personal
Math Trainer
my.hrw.com
Online
Assessment and
Intervention
Assessment Resources
• Leveled Unit Tests: A, B, C, D
• Performance Assessment
Study Guide Review
Vocabulary Development
Integrating the ELPS
Encourage English learners to refer to their notes and the illustrated, bilingual glossary as
they review the unit content.
c.4.F Use visual and contextual support … to read grade-appropriate content area text … and develop
vocabulary … to comprehend increasingly challenging language.
MODULE 2 Rates and Proportionality
7.4.A, 7.4.B, 7.4.C, 7.4.D
Key Concepts
• A rate is a comparison of two quantities with different units. A unit rate is a rate with a
denominator of 1 unit. (Lesson 2.1)
• Two quantities, x and y, have a proportional relationship in which the constant ratio is k if
y
you can describe the relationship using the equation _x = k. (Lesson 2.2)
• A graph represents a proportional relationship if it is a line that goes through the origin.
(Lesson 2.3)
MODULE 3 Proportions and Percent
7.4.D, 7.4.E
Key Concepts
• A conversion factor, or a ratio of two equivalent measurements, can be used to convert
measurements from one system of measurement to another. (Lesson 3.1)
• To find a percent of change, subtract the greater value from the lesser value and divide the
answer by the original value. (Lesson 3.2)
• A percent increase is also known as a markup, and a percent decrease is also known as a
markdown. (Lesson 3.3)
141
Unit 2
UNIT 2
Ratios and
Proportional
Relationships
Additional Resources
Personal
Math Trainer
my.hrw.com
Online
Assessment and
Intervention
Assessment Resources
• Leveled Unit Tests: A, B, C, D
• Performance Assessment
143
Unit 2
Study Guide Review
MODULE 4 Proportionality in Geometry
7.5.A, 7.5.B, 7.5.C
Key Concepts
• Similar polygons are identified by verifying that all corresponding angles are congruent
and all corresponding side lengths are proportional. (Lesson 4.1)
• Indirect measurement is a method of using proportions to find an unknown length or
distance in similar figures. (Lesson 4.2)
• In a scale drawing, the dimensions of an object are related to the dimensions of the actual
object by a ratio called the scale factor. (Lesson 4.3)
Review
MODULE
?
2
Rates and Proportionality
Key Vocabulary
complex fraction (fracción
compleja)
constant of proportionality
(constante de
proporcionalidad)
proportion (proporción)
proportional relationship
(relación proporcional)
ESSENTIAL QUESTION
How can you use rates and proportionality to solve real-world
problems?
EXAMPLE 1
A store sells onions by the pound. Is the relationship between
the cost of an amount of onions and the number of pounds
proportional? If so, write an equation for the relationship, and
represent the relationship on a graph.
Number of pounds
Cost ($)
2
5
6
3.00
7.50
9.00
?
rate of change (tasa de
cambio)
Pay ($)
40
80
3
1
5
80
40
6
O
100 120
(6, 120)
(4, 80) (5, 100)
(2, 40)
2
4
6
8 10
Hours worked
Key Vocabulary
Proportions and Percent
How can you use proportions and percent to solve real-world
problems?
conversion factor (factor
de conversión)
percent decrease
(porcentaje de
disminución)
percent increase (porcentaje
de aumento)
principal (capital)
simple interest (interés
simple)
Convert each measurement to meters. Use 1 yard ≈ 0.914 meter.
$7.50
$1.50
_______
= _______
5 pounds
1 pound
$9.00
$1.50
_______ = _______
6 pounds
1 pound
1 yard
40 yards
1 yard
Length: _________
= __________
0.914 meter
36.56 meters
The rates are constant, so the relationship is proportional.
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4
120
EXAMPLE 1
June’s garden is in the shape of a rectangle with a width of
20 yards and a length of 40 yards. She plans to fence it in,
using fencing that costs $30 per meter. What will be the total
cost of the fencing?
Write the rates.
Plot the ordered pairs (pounds, cost): (2, 3), (5, 7.5), and (6, 9).
Connect the points with a line.
The total cost of the fencing is $30(109.68) = $3,290.40.
(6, 9)
(5, 7.5)
8
6
4
O
EXAMPLE 2
Donata had a 25-minute commute from home to work. Her
company moved, and now her commute to work is 33 minutes
long. Does this situation represent an increase or a decrease?
Find the percent increase or decrease in her commute to work.
(2, 3)
2
2
4
6
20 yards
Width: _________
= __________
0.914 meter
18.28 meters
Find the perimeter P: P = 2 + 2w = 2(36.56) + 2(18.28) = 109.68 meters
Cost of Onions
10
Cost ($)
The equation for the relationship is y = 1.5x.
2
160
ESSENTIAL QUESTION
unit rate (tasa unitaria)
$3.00
$1.50
cost
______________
: _______ = _______
1 pound
number of pounds 2 pounds
The constant rate of change is $1.50 per pound, so the
constant of proportionality is 1.5. Let x represent the
number of pounds and y represent the cost.
MODULE
Hours worked
Juan's Pay
200
8 10
Pounds
This situation represents an increase. Find the percent increase.
EXERCISES
amount of change = greater value – lesser value
1. Steve uses _89 gallon of paint to paint 4 identical birdhouses.
How many gallons of paint does he use for each birdhouse?
33 – 25 = 8
(Lesson 2.1) 9
percent increase = ______________
original amount
2
_
gal
amount of change
8
__
= 0.32 = 32%
25
2. Ron walks 0.5 mile on the track in 10 minutes. Stevie walks
0.25 mile on the track in 6 minutes. Find the unit rate for
each walker in miles per hour. Who is the faster walker?
Ron: 3 miles per hour, Stevie:
2.5 miles per hour. Ron is the faster walker.
© Houghton Mifflin Harcourt Publishing Company
Study Guide
3. (Lessons 2.2, 2.3) The table below shows the proportional
relationship between Juan’s pay and the hours he works.
Complete the table. Plot the data and connect the points
with a line. (Lessons 2.2, 2.3)
Pay ($)
UNIT 2
Donata’s commute increased by 32%.
(Lesson 2.1)
Unit 2
141
142
Unit 2
Ratios and Proportional Relationships
142
EXERCISES
Convert each measurement. (Lesson 3.1)
B. Find the unknown angle measure y.
1. 7 centimeters ≈
2.76
inches
2. 10 pounds ≈
3. 24 kilometers ≈
14.91
miles
4. 12 quarts ≈
y = 35°
4.54
11.35
EXAMPLE 2
Use the scale drawing to find the perimeter of Tim’s yard.
liters
5. Michelle purchased 25 audio files in January. In February
she purchased 40 audio files. Find the percent increase.
60% increase
for the dog? (Lesson 3.2)
63 pounds
MODULE
© Houghton Mifflin Harcourt Publishing Company
?
4
Q
3.5s; $17.50
Proportionality in Geometry
How can you use proportionality in geometry to solve real-world
problems?
Write a proportion using corresponding sides NO and QR, NP and QS.
Write a proportion using corresponding
sides NO and QR, NP and QS.
Substitute the known lengths of the sides.
x = 7 cm
Key Vocabulary
6m
circumference
(circunferencia)
corresponding angles
(ángulos
correspondientes)
59°
65°
4m
80°
90°
125°
8m
T
15 m
P
10 m
N
80°
60°
6.5 m
9m
O
85°
12 m
R
125°
S
1. Are the four-sided shapes similar? Explain.
No; Corresponding angles do not have the same measures.
corresponding sides (lados
correspondientes)
Also, corresponding sides are not proportional. For example,
diameter (diámetro)
indirect measurement
(medición indirecta)
angles N and R do not have the same measure, and
PO ___
MN _
4
___
= 23 or _46 , but ___
= 6.5
.
TS
QR
pi (pi)
radius (radio)
2. △JNZ ~ △KOA. Find the unknown
measures. (Lesson 4.2)
J
similar shapes (formas
semejantes)
A. Find the unknown side x.
2 is a factor of 14.
Since 2 × 7 = 14, multiply 1 by 7 to
find the value of x.
M
scale (escala)
scale drawing (dibujo a
escala)
EXAMPLE 1
△NOP ~ △QRS. Find the unknown measures.
4 to find a factor of 14.
Simplify __
8
4 cm
2 cm : 14 ft
Determine if the shapes are similar. (Lesson 4.1)
$67.58
ESSENTIAL QUESTION
NO ___
___
= NP
QR
QS
4 __
x
_
= 14
8
1 __
x
_
= 14
2
1 ×7 __
_
= x
2 ×7 14
15 cm in the drawing equals 105 feet in
the actual yard. Tim’s yard is 105 feet long.
4 cm in the drawing equals 28 feet in the
actual yard. Tim’s yard is 28 feet wide.
EXERCISES
8. A sporting goods store marks up the cost s of soccer
balls by 250%. Write an expression that represents the
retail cost of the soccer balls. The store buys soccer balls
for $5.00 each. What is the retail price of the soccer balls?
(Lesson 3.3)
1________
cm × 15
15 cm
= _____
7 ft × 15
105 ft
Perimeter is twice the sum of the length and the width. So the
perimeter of Tim’s yard is 2(105 + 28) = 2(133), or 266 feet.
7. The original price of a barbecue grill is $79.50. The grill
is marked down 15%. What is the sale price of the grill?
(Lesson 3.3)
1 cm in the drawing equals 7 feet in
the actual yard.
1_______
cm × 4
4 cm
= ____
7 ft × 4
28 ft
6. Sam’s dog weighs 72 pounds. The vet suggests that for
the dog’s health, its weight should decrease by 12.5
percent. According to the vet, what is a healthy weight
15 cm
2 cm
1 cm
____
= ____
14 ft
7 ft
Q
59°
14 cm
N
8 cm
4 cm
86°
y
P 6 cm O
R
12 cm S
86°
35°
x
Unit 2
143
144
x=
8.5
y=
17
r=
28°
s=
62°
8 in. 62°
N
A
y in.
r
15 in.
28°
x in.
Z
K
s
O
4 in.
© Houghton Mifflin Harcourt Publishing Company
(Lesson 3.2)
∠S and ∠P are corresponding angles.
kilograms
Unit 2
Ratios and Proportional Relationships
144
(Lesson 4.3)
Unit 2 Performance Tasks (cont'd)
3 cm
3. In the scale drawing of a park, the scale is
1 cm: 10 m. Find the area of the actual park.
1.5 cm
450 m2
2. The table below shows how far several animals can travel at their
maximum speeds in a given time.
1 cm : 10 m
4. The circumference of the larger circle is 15.7 yards.
Find the circumference of the smaller circle.
(Lesson 4.4)
Animal Distances
4 yd
12.56 yd
5 yd
Unit 2 Performance Tasks
Animal
Distance traveled (ft)
Time (s)
elk
33
giraffe
115
1
_
2
2_12
zebra
117
2
a. Write each animal’s speed as a unit rate in feet per second.
Elk: 66 ft/s
1.
Landscape Architect A landscape architect
creates a scale drawing of her plans for a garden. She draws the plans
on a sheet of paper that measures 8_12 inches by 11 inches. On the righthand side of the paper, there is a column 2_12 inches wide that includes
the company name and logo. The drawing itself is 5_12 inches by 7_21
inches. The scale of the drawing is 1 inch = 10 feet.
CAREERS IN MATH
Giraffe: 46 ft/s
Zebra: 58.5 ft/s
b. Which animal has the fastest speed?
elk
2 12 in.
c. How many miles could the fastest animal travel in 2 hours if it
maintained the speed you calculated in part a? Use the formula
d = rt and round your answer to the nearest tenth of a mile.
Show your work.
5 12 in.
8 12 in.
66 ft/s ∙ 60 s = 3,960 ft; 3,960 ft ∙ 1 mi/5,280 = 0.75
7 12 in.
mi/min; 0.75 mi/min ∙ 120 min = 90 miles; 90 miles
a. The landscape architect wants to make a larger drawing on a sheet
of paper that measures 11 inches by 17 inches. The larger drawing
should include the same 2_12 inch column on the side. There should
be at least _21 inch of space on all sides of the drawing. What are the
dimensions of the area she can use to make the new drawing?
d. The data in the table represents how fast each animal can travel
at its maximum speed. Is it reasonable to expect the animal from
part b to travel that distance in 2 hours? Explain why or why not.
It is not reasonable. Sample answer: An animal probably
10 in. by 13.5 in.
cannot travel at its maximum speed for 2 full hours.
b. How large can she make the scale drawing without changing any of
the proportions? Justify your reasoning.
9.9 in. by 13.5 in. The available area for the new drawing is 10
inches by 13.5 inches. If you increase the width of the drawing
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© Houghton Mifflin Harcourt Publishing Company
11 in.
from 5.5 inches to 10 inches, you must increase the length to about
13.63 in., which is longer than the 13.5 inches allowed. You can
only increase the 7.5 inch length to 13.5 inches.
Unit 2
145
146
Unit 2
Ratios and Proportional Relationships
146
UNIT 3
Probability and
Statistics
Additional Resources
Personal
Math Trainer
my.hrw.com
Online
Assessment and
Intervention
Assessment Resources
• Leveled Unit Tests: A, B, C, D
• Performance Assessment
Study Guide Review
Vocabulary Development
Integrating the ELPS
Encourage English learners to refer to their notes and the illustrated, bilingual glossary as
they review the unit content.
c.4.E Read linguistically accommodated content area material with a decreasing need for linguistic
accommodations as more English is learned.
MODULE 5 Experimental Probability
7.6.A, 7.6.B, 7.6.C, 7.6.H, 7.6.I
Key Concepts
number of favorable outcomes
• The probability of an event, or ______________________
, measures the likelihood that
total number of possible outcomes
the event will occur. (Lesson 5.1)
• The probability of an event can be from 0 to 1, inclusive. (Lesson 5.1)
• The experimental probability of an event can be found by comparing the number of times
an event occurs to the total number of trials. (Lesson 5.2)
• A compound event is an event that includes two or more simple events. (Lesson 5.3)
MODULE 6 Experimental Probability
7.6.A, 7.6.D, 7.6.E, 7.6.H, 7.6.I
Key Concepts
• Theoretical probability is the probability that an event occurs when all the outcomes of
the experiment are equally likely. (Lesson 6.1)
• To find the theoretical probability, compare the number of ways the event can occur by
the total number of equally likely outcomes. (Lesson 6.1)
• The event with the higher probability, experimental or theoretical, is more likely to occur.
(Lesson 6.3)
213
Unit 3
Review
Study Guide
MODULE
?
5
5. Christopher picked coins randomly from his piggy
bank and got the numbers of coins shown in the table.
Find each experimental probability. (Lessons 5.2, 5.3)
Experimental Probability
How can you use experimental probability to solve real-world
problems?
Senior
Adult
Young
adult
Child
Female
5
8
2
14
Male
3
10
1
17
What is the experimental probability that
his next new patient is a female adult?
(
)
new patient is a
of female adults
__________________
P
= number
total number of patients
female adult
c. The next coin that Christopher picks is a penny or a nickel.
© Houghton Mifflin Harcourt Publishing Company
8
2
= __
P = __
15
60
P = _16
3. Picking a blue marble from a bag of
4 red marbles, 6 blue marbles, and
1 white marble.
6
P = __
11
MODULE
MODULE
?
6
Theoretical Probability
theoretical probability
(probabilidad teórica)
How can you use theoretical probability to solve real-world
problems?
EXAMPLE 1
A. Lola rolls two fair number cubes. What is the probability that the
two numbers Lola rolls include at least one 4 and have
a product of at least 16?
There are 5 pairs of numbers that include a
4 and have a product of at least 16:
)
(4, 4), (4, 5), (4, 6), (5, 4), (6, 4)
31
P = __
60
1
2
3
4
5
1
1
2
3
4
5
6
6
2
2
4
6
8
10
12
Find the probability.
3
3
6
9
12
15
18
number of possible ways
5
P = ______________________________ = ___
4
4
8
12
16
20
24
36
5
5
10
15
20
25
30
B. Suppose Lola rolls the two number cubes
180 times. Predict how many times she
will roll two numbers that include a pair of
numbers like the ones described above.
6
6
12
18
24
30
36
total number of possible outcomes
2. Picking a 7 from a standard deck of
52 cards. A standard deck includes 4 cards
of each number from 2 to 10.
Key Vocabulary
ESSENTIAL QUESTION
new patient is
number of children
P
= __________________
total number of patients
a child
EXERCISES
Find the probability of each event. (Lesson 5.1)
1. Rolling a 5 on a fair number cube.
54
82
___
< ___
; more customers than usual brought their own bags.
100
124
sample space (expacio
muestral)
simulation (simulación)
trial (prueba)
9
__
23
6. A grocery store manager found that 54% of customers usually bring
their own bags. In one afternoon, 82 out of 124 customers brought
their own grocery bags. Did a greater or lesser number of people
than usual bring their own bags? (Lesson 5.4)
outcome (resultado
(probabilidad))
probability (probabilidad)
What is the experimental probability that
his next new patient is a child?
(
6
6
__
23
17
__
23
b. The next coin that Christopher picks is not a quarter.
simple event (suceso simple)
EXAMPLE 2
For one month, a doctor
recorded information
about new patients as
shown in the table.
Quarter
8
compound event (suceso
compuesto)
experiment (experimento
(probabilidad))
experimental probability
(probabilidad
experimental)
number of red marbles
P(picking a red marble) = _____________________
number of total marbles
There are 2 red marbles.
2
__
=
7 The total number of marbles is 2 + 5 = 7.
Dime
2
complement (complemento)
event (suceso)
EXAMPLE 1
What is the probability of picking a red marble from a jar with
5 green marbles and 2 red marbles?
Nickel
7
a. The next coin that Christopher picks is a quarter.
Key Vocabulary
ESSENTIAL QUESTION
Penny
4
1
= __
P = __
52
13
One way to answer is to write and solve an equation.
5 × 180 = x
___
4. Rolling a number greater than 7 on a
12-sided number cube.
36
25 = x
5
P = __
12
© Houghton Mifflin Harcourt Publishing Company
UNIT 3
Multiply the probability by the total number of rolls.
Solve for x.
Lola can expect to roll two numbers that include at least one 4 and have a
product of 16 or more about 25 times.
Unit 3
213
214
Unit 3
Probability and Statistics
214
EXAMPLE 2
A store has a sale bin of soup cans. There are 6 cans of chicken
noodle soup, 8 cans of split pea soup, 8 cans of minestrone, and 13
cans of vegetable soup. Find the probability of picking each type of
soup at random. Then predict what kind of soup a customer is most
likely to pick.
7. Suppose you know that over the last 10 years, the probability that
your town would have at least one major storm was 40%. Describe
a simulation that you could use to find the experimental probability
that your town will have at least one major storm in at least 3 of the
next 5 years. (Lesson 6.4)
Sample answer: Use whole numbers from 1 to 5. Let 1 and 2 represent
6
8
P(chicken noodle) = ___
P(split pea) = ___
35
35
13
8
___
P(vegetable) = ___
P(minestrone) =
35
35
The customer is most likely to pick vegetable soup. That is the event that has the greatest
probability.
a year with a major storm and 3, 4, and 5 represent a year without a
major storm. Perform 10 trials by randomly generating 10 sets of 5
numbers. Count the sets that model 3 or more storms and divide by 10.
EXERCISES
Find the probability of each event. (Lessons 6.1, 6.2)
8
P = __
= _2
12 3
3. Tania flips a coin three times. The coin
lands on heads twice and on tails once,
not necessarily in that order.
P = _3
8
2. Theo spins a spinner that has 12 equal
sections marked 1 through 12. It does not
land on 1.
1.
11
P = __
12
CAREERS IN MATH Meteorologist A meteorologist predicts a
20% chance of rain for the next two nights, and a 75% chance of rain on
the third night.
a. On which night is it most likely to rain? On that night, is it likely to
rain or unlikely to rain?
4. Students are randomly assigned
two-digit codes. Each digit is either
1, 2, 3, or 4. Guy is given the number 11.
1
P = __
16
the third night; likely
b. Tara would like to go camping for the next 3 nights, but will not go
if it is likely to rain on all 3 nights. Should she go? Use probability to
justify your answer.
Yes; the probability of its raining on all 3 nights is 0.2 ∙ 0.2 ∙ 0.75 =
5. Patty tosses a coin and rolls a number cube. (Lesson 6.3)
0.03, or only a 3% chance. It is very unlikely to rain on all 3 nights.
a. Find the probability that the coin lands on heads and the cube
lands on an even number.
P = _1
2. Sinead tossed 4 coins at the same time. She did this 50 times, and 6 of
those times, all 4 coins showed the same result (heads or tails).
© Houghton Mifflin Harcourt Publishing Company
4
b. Patty tosses the coin and rolls the number cube 60 times. Predict
how many times the coin will land on heads and the cube will
land on an even number.
a. Find the experimental probability that all 4 coins show the same
result when tossed.
0.12
15 times
b. Can you determine the experimental probability that no coin shows
heads? Explain.
6. Rajan’s school is having a raffle. The school sold raffle tickets with
3-digit numbers. Each digit is either 1, 2, or 3. The school also sold
2 tickets with the number 000. Which number is more likely to be
picked, 123 or 000? (Lesson 6.3)
No; we aren't told how many times all tails came up.
c. Suppose Sinead tosses the coins 125 more times. Use experimental
probability to predict the number of times that all 4 coins will show
heads or tails. Show your work.
000
© Houghton Mifflin Harcourt Publishing Company
1. Graciela picks a white mouse at random
from a bin of 8 white mice, 2 gray mice,
and 2 brown mice.
Unit 3 Performance Tasks
125 ∙ 0.12 = 15 times
Unit 3
215
216
Unit 3
Probability and Statistics
216
UNIT 4
Multiple
Representations of
Linear Relationships
Additional Resources
Personal
Math Trainer
my.hrw.com
Online
Assessment and
Intervention
Assessment Resources
• Leveled Unit Tests: A, B, C, D
• Performance Assessment
Study Guide Review
Vocabulary Development
Integrating the ELPS
Encourage English learners to refer to their notes and the illustrated, bilingual glossary as
they review the unit content.
c.4.E Read linguistically accommodated content area material with a decreasing need for linguistic
accommodations as more English is learned.
MODULE 7 Linear Relationships
7.7
Key Concepts
• In a linear relationship, as one quantity changes by a constant amount, the other quantity
also changes by a constant amount. (Lesson 7.1)
• One way to describe a linear relationship is to write an equation in the form of
y = mx + b, where m is the rate of change and b is the value of y when x is 0.
(Lesson 7.2)
MODULE 8 Equations and Inequalities
7.10.A, 7.10.B, 7.10.C, 7.11.A, 7.11.B
Key Concepts
• To solve a two-step equation or inequality, use inverse operations. (Lessons 8.1, 8.3)
• Use substitution to check if a given value is a solution of an equation or inequality.
(Lessons 8.2, 8.4)
271
Unit 4
Study Guide
?
7
3. Steve is saving for his daughter’s college education. He opens an
account with $2,400 and deposits $40 per month. Represent the
relationship using a table and an equation. (Lesson 7.2)
Linear Relationships
Months
Savings ($)
Key Vocabulary
linear relationship (relación
lineal)
ESSENTIAL QUESTION
y = 40x + 2,400
How can you use linear relationships to solve real-world problems?
4. Tonya has a 2-page story she wants to expand.
She plans to write 3 pages per day until it is
done. Represent the relationship using a table,
an equation, and a graph. (Lesson 7.2)
EXAMPLE
Ross earns a set rate of $10 for babysitting, plus $6 per hour.
Represent the relationship using a table, an equation, and a graph
of the linear relationship.
Amount ($)
0
$10
1
$16
2
$22
3
$28
4
$34
Days
Total pages
Babysitting Fees
40
Amount ($)
Hours
(2, 22)
16
8
Amount = $10 + $6 per hour
O
MODULE
(1, 16)
(0, 10)
?
2
4
6
Hours
8
3
11
12
8
4
(3, 11)
(2, 8)
(1, 5)
(0, 2)
O
2
4
8
6
Hours
8
10
Equations and Inequalities
How can you use equations and inequalities to solve real-world problems?
EXAMPLE 1
A clothing store sells clothing for 2 times the wholesale cost plus $10.
The store sells a pair of pants for $48. How much did the store pay
for the pants? Represent the solution on a number line.
EXERCISES
1. The cost of a box of cupcakes is $1.50 per cupcake plus $3. Complete
the table to represent the linear relationship. (Lesson 7.1)
© Houghton Mifflin Harcourt Publishing Company
2
8
ESSENTIAL QUESTION
10
y = 10 + 6x
Number of cupcakes
1
2
3
Let w represent the wholesale cost of the pants, or the price paid by the store.
2w + 10 = 48
4
2w = 38
$4.50 $6.00 $7.50 $9.00
Cost of cupcakes ($)
w = 19
10 11 12 13 14 15 16 17 18 19 20
Subtract 10 from both sides.
Divide both sides by 2.
The store paid $19 for the pants.
2. The score a student receives on a standardized test based on the
number of correct answer is shown in the table. Use the table to give
a verbal description of the relationship between correct answers and
score. (Lesson 7.1)
Score
1
5
16
(3, 28)
24
Write an equation for the amount y in dollars
earned for x hours.
Correct answers
0
2
20
y = 3x + 2
(4, 34)
32
0
2
4
6
2,400 2,480 2,560 2,640
5
10
15
20
25
EXAMPLE 2
Determine which, if any, of these values makes the inequality
-7x + 42 ≤ 28 true: x = -1, x = 2, x = 5.
210
220
230
240
250
−7(−1) + 42 ≤ 28
A student’s score is 200 plus 2 points per correct answer.
x = 2 and x = 5
Unit 4
271
272
−7(2) + 42 ≤ 28
−7(5) + 42 ≤ 28
© Houghton Mifflin Harcourt Publishing Company
MODULE
Review
Pages
UNIT 4
Substitute each value for x
in the inequality and evaluate
the expression to see if a true
inequality results.
Unit 4
Multiple Representations of Linear Relationships
272
Unit 4 Performance Tasks
1. The cost of a ticket to an amusement park is $42 per person.
For groups of up to 8 people, the cost per ticket decreases by $3
for each person in the group. Marcos’s ticket cost $30. Write and
solve an equation to find the number of people in Marcos’s group.
(Lessons 8.1, 8.2)
1.
42 - 3n = 30; n = 4
- 12
x=9
-8
-4
0
Spring Stretch
64
48
32
16
a. Write an equation for the line. Explain, using the graph and
then using the equation, why the relationship is proportional.
Solve each equation. Graph the solution on a number line.
(Lesson 8.2)
2. 8x - 28 = 44
CAREERS IN MATH Mechanical Engineer A mechanical
engineer is testing the amount of force needed to make a spring
stretch by a given amount. The force y is measured in units called
Newtons, abbreviated N. The stretch x is measured in centimeters.
Her results are shown in the graph.
Force (N)
EXERCISES
y = 8x; The graph is a straight line through the
4
8
O
2
4
6
8 10
Stretch (cm)
origin, and therefore is a proportional relationship; the equation
12
is of the form y = kx, where k ≠ 0, and therefore is a proportional
3. -5z + 4 = 34
- 12
x = -6
-8
-4
relationship.
0
4
8
12
b. Identify the rate of change and the constant of proportionality.
8 N/cm; 8
4. Prudie needs $90 or more to be able to take her family out to dinner.
She has already saved $30 and wants to take her family out to eat in
4 days. (Lesson 8.3)
c. What is the meaning of the constant of proportionality in the context
of the problem?
Every centimeter of stretch of the spring requires 8 Newtons of force.
a. Suppose that Prudie earns the same each day. Write an inequality
to find how much she needs to earn each day.
2. A math tutor charges $30 for a consultation, and then $25 per hour. An
online tutoring service charges $30 per hour.
30 + 4x ≥ 90
a. Does either service represent a proportional relationship? Explain.
b. Suppose that Prudie earns $18 each day. Will she have enough
money to take her family to dinner in 4 days? Explain.
The online service represents a proportional relationship; the math
Yes, x = 18 is a solution of the inequality.
tutor’s charge does not. Sample answer: The equation representing
Solve each inequality. Graph and check the solution. (Lesson 8.4)
the cost of the online service is of the form y = kx, while the
equation for the tutor is not.
y>6
- 12
-8
-4
0
4
8
b. Write an equation for the cost c of h hours of tutoring for either
service. Which service charges less for 4 hours of tutoring? Show
your work.
12
math tutor: c = 30 + 25h; online service: c = 30h
6. 7x - 2 ≤ 61
For 4 hours, the math tutor charges = 30 + 25(4) = $130. The online
x≤9
- 12
service charges c = 30(4) = $120. The online service charges less.
-8
-4
0
4
8
© Houghton Mifflin Harcourt Publishing Company
© Houghton Mifflin Harcourt Publishing Company
5. 15 + 5y > 45
12
Unit 4
273
274
Unit 4
Multiple Representations of Linear Relationships
274
UNIT 5
Geometric
Relationships
Additional Resources
Personal
Math Trainer
my.hrw.com
Online
Assessment and
Intervention
Assessment Resources
• Leveled Unit Tests: A, B, C, D
• Performance Assessment
Study Guide Review
Vocabulary Development
Integrating the ELPS
Encourage English learners to refer to their notes and the illustrated, bilingual glossary as
they review the unit content.
c.4.E Read linguistically accommodated content area material with a decreasing need for linguistic
accommodations as more English is learned.
MODULE 9 Applications of Geometry Concepts
7.8.C, 7.9.B, 7.9.C, 7.11.C
Key Concepts
• The sum of the measures of a pair of complementary angles is 90°, and the sum of the
measures of a pair of supplementary angles is 180°. (Lesson 9.1)
• Vertical angles are the opposite angles formed by two intersecting lines which are
congruent. (Lesson 9.1)
• To find the circumference of a circle, or the distance around the circle, use the formula
C = πd or C = 2πr. (Lesson 9.2)
• To find the area of a circle, use the formula A = πr 2. (Lesson 9.3)
MODULE 10 Volume and Surface Area
7.8.A, 7.9.A, 7.9.D
Key Concepts
• To find the volume of a prism, use the formula V = Bh, where B is the area of the base.
(Lessons 10.1, 10.2)
• To find the volume of a pyramid, use the formula V = __13 Bh, where B is the area of the base.
(Lessons 10.1, 10.2)
• The lateral surface area of a figure is the area of all the lateral, or side, faces of the figure.
(Lesson 10.3)
• The total surface area of a figure is the area of all the faces of the figure. (Lesson 10.3)
337
Unit 5
UNIT 5
Study Guide
?
9
Review
Applications of Geometry
Concepts
ESSENTIAL QUESTION
How can you apply geometry concepts to solve real-world
problems?
EXAMPLE 1
Find (a) the value of x and (b) the measure of ∠APY.
a. ∠XPB and ∠YPB are supplementary.
A
3.
Key Vocabulary
C ≈ 69.08 in., A ≈ 379.94 in2
adjacent angles (ángulos
adyacentes)
complementary
angles (ángulos
complementarios)
congruent angles (ángulos
congruentes)
supplementary
angles (ángulos
suplementarios)
C ≈ 28.26 m, A ≈ 63.59 m2
Find the area of each composite figure. Round to the nearest
hundredth if necessary. (Lesson 9.4)
4.
5.
9 in.
9 in.
20 cm
13 in.
vertical angles (ángulos
opuestos por el vértice)
99 in2
Area
3x = 102°
B
MODULE
MODULE
x = 34°
?
b. ∠APY and ∠XPB are vertical angles.
m∠APY = m∠XPB = 3x = 102°
16 cm
Area
420.48 cm2
Key Vocabulary
lateral area (área lateral)
lateral faces (cara lateral)
ESSENTIAL QUESTION
How can you use volume and surface area to solve real-world problems?
net (plantilla)
total surface area (área de
superficie total)
The figure is a rectangular pyramid.
Volume = _13Bh
≈ 0.5(3.14)25
= _13(144)(8)
≈ 39.25 cm2
Area of rectangle = ℓw
6 cm
Volume and Surface Area
EXAMPLE
The height of the figure whose net is shown is 8 feet. Identify the
figure. Then find its volume, lateral area, and total surface area.
Area of semicircle = 0.5(πr2)
10 cm
10
10
pyramid (pirámide)
EXAMPLE 2
Find the area of the composite figure. It consists of a semicircle
and a rectangle.
© Houghton Mifflin Harcourt Publishing Company
4.5 m
22 in.
3x + 78° = 180°
Y
P
3x 78°
X
2.
Lateral Area
()
4 _12 (12)(8) = 192
Total Surface Area
= 384
The volume of the rectangular pyramid is 384 cubic feet,
the lateral surface area is 192 square feet, and the total
surface area is 336 square feet.
= 10(6)
= 60 cm2
8 ft
12 ft
192 + 122 = 192 + 144
= 336
© Houghton Mifflin Harcourt Publishing Company
MODULE
Find the circumference and area of each circle. Round to the nearest
hundredth. (Lessons 9.2, 9.3)
The area of the composite figure is approximately 99.25 square centimeters.
EXERCISES
EXERCISES
1. Identify the figure represented by the net. Then find its lateral area
and total surface area. (Lesson 10.3)
1. Find the value of y and the measure of ∠YPS (Lesson 9.1)
R
140° 5y
P
Y
y=
Z
m ∠YPS =
triangular prism
8°
lateral area = 468 ft2
40°
total surface area = 618 ft2
10 ft
15 ft
13 ft
13 ft
13 ft
13 ft
S
Unit 5
337
338 2.
Unit 5
Geometric Relationships
338
Unit 5 Performance Tasks (cont'd)
Find the volume of each figure. (Lessons 10.1, 10.2)
2.
3.
b. How many square feet of material does Miranda need to make the
tent (including the floor)? Show your work.
9m
()
6m
5 in.
7 in.
2
c. What is the volume of the tent? Show your work.
4m
( _12 )(8)(6)( 9 _12 ) = 228 ft
36 m3
420 in3
( ) ( 7 _14 )+ ( 9 _21 )(8) = 48 + 137.75 + 76 = 261.75 ft
2 _12 (8)(6) + 2 9 _12
12 in.
d. Suppose Miranda wants to increase the volume of the tent by 10%.
The specifications for the height (6 feet) and the width (8 feet) must
stay the same. How can Miranda meet this new requirement? Explain.
4. The volume of a rectangular pyramid is 1.32 cubic inches. The height
of the pyramid is 1.1 inches and the length of the base is 1.2 inches.
Find the width of the base of the pyramid. (Lesson 10.1)
3
She will need to change the length, 9 _12 ft, so that the new volume is
3 in.
( 1__101 ) (228) = 250 _45 ft . That is ( _12 )(8)(6)ℓ = 250 _45, so ℓ = 10 __209 ft .
3
5. The volume of a triangular prism is 264 cubic feet. The area of a base
of the prism is 48 square feet. Find the height of the prism.
2. Li is making a stand to display a sculpture made in art class. The stand
will be 45 centimeters wide, 25 centimeters long, and 1.2 meters high.
5.5 ft
(Lesson 10.2)
a. What is the volume of the stand? Write your answer in cubic
centimeters.
100 cm
V = (45 cm)(25 cm)(1.2 m) _____
= 135,000
m
(
Unit 5 Performance Tasks
1.
Product Design Engineer Miranda
is a product design engineer working for a sporting goods
company. She designs a tent in the shape of a triangular prism.
The dimensions of the tent are shown in the diagram.
CAREERS IN MATH
a. Draw a net of the triangular prism and label the dimensions.
b. Li needs to fill the stand with sand so that it is
heavy and stable. Each piece of wood is
1 centimeter thick. The boards are put together
as shown in the figure, which is not drawn to
scale. How many cubic centimeters
1.2 m
of sand does she need to fill the stand?
Explain how you found your answer.
1
7—
4 ft
6 ft
)
1
9—
2 ft
8 ft
cm3
1 cm
1.2 m
The dimensions of the interior of the
© Houghton Mifflin Harcourt Publishing Company
1 ft
7—
and (25 - 2) cm, because each
8 ft
4
25 cm
Side View
piece of wood is 1 cm thick. The
1 ft
7—
4
45 cm
Front View
© Houghton Mifflin Harcourt Publishing Company
stand are (45 - 2) cm, (120 - 2) cm,
6 ft
interior volume is V = (43 cm)
1 ft
9—
2
(118 cm)(23 cm) = 116,702 cm3.
6 ft
Unit 5
339
340
Unit 5
Geometric Relationships
340
UNIT 6
Measurement
and Data
Additional Resources
Personal
Math Trainer
my.hrw.com
Online
Assessment and
Intervention
Assessment Resources
• Leveled Unit Tests: A, B, C, D
• Performance Assessment
Study Guide Review
Vocabulary Development
Integrating the ELPS
Encourage English learners to refer to their notes and the illustrated, bilingual glossary as
they review the unit content.
c.4.E Read linguistically accommodated content area material with a decreasing need for linguistic
accommodations as more English is learned.
MODULE 11 Analyzing and Comparing Data
7.6.G, 7.12.A
Key Concepts
• Circle graphs and bar graphs represent data by showing portions of a set of data grouped
by categories. (Lesson 11.1)
• To compare dot plots, look at the shape, center, and spread of the dot plots. (Lesson 11.2)
• To compare box plots, look at the median, interquartile range, and shape of the box plots.
(Lesson 11.3)
393
Unit 6
MODULE 12 Random Samples and Populations
7.6.F, 7.12.B, 7.12.C
Key Concepts
• A random sample is a sample in which every member of your population has an equal
chance at being selected. If a sample is not random, it is called a biased sample.
(Lesson 12.1)
• Dot plots and box plots can be used to represent data from a random sample and to make
inferences about data from a random sample. (Lesson 12.2)
• Random samples from two or more populations can be compared by comparing the dot
and box plots representing the data. (Lesson 12.3)
Unit 6 Performance Tasks
The Performance Tasks provide students with the opportunity to apply concepts from this
unit in real-world problem situations.
CAREERS IN MATH
For more information about careers in
mathematics as well as various
mathematics appreciation topics, visit
the American Mathematical Society at
www.ams.org
CAREERS IN MATH
Entomologist In Performance Task item 1, students can see how an entomologist uses
mathematics on the job.
SCORING GUIDES FOR PERFORMANCE TASKS
1. MATHEMATICAL PROCESSES
Task
395
Unit 6
7.1.A, 7.1.E, 7.1.F, 7.1.G
Possible Points (Total: 6)
a
1 point for the correct medians of 11 for Type A and 11 for Type B, 1 point for
the correct ranges of 4 for Type A and 10 for Type B, and 1 point for the correct
interquartile ranges of 3 for Type A and 2 for Type B.
b
1 point for the answer that range makes Type A appear more consistent, 1 point for
the answer that interquartile range makes Type B appear more consistent, and 1 point
for any reasonable choice and explanation, for example: Type A is actually more
consistent because it has a much smaller range, while its IQR is only slightly larger.
MODULE
MODULE
?
11
11
Review
Analyzing and Comparing
Data
EXERCISES
1. Five candidates are running for the position of School
Superintendent. Find the percent of votes that each
candidate received. (Lesson 11.1)
Key Vocabulary
Candidate A: 16.5%, Candidate B: 21%,
circle graph (gráfica
circular)
Candidate C: 20%, Candidate D: 20.5%,
ESSENTIAL QUESTION
Candidate E: 22%
How can you solve real-world problems by analyzing
and comparing data?
EXAMPLE 1
There are 500 students at Trenton Middle School. The
percent of students in each grade level is shown in
the circle graph. Calculate the number of students in
each grade.
43% = 0.43
31% = 0.31
70
60
0
A
B
C
D
E
Candidates
Middle School Students by Grade
8th grade
26%
6th grade
43%
0 1 2 3 4 5 6 7
Time Online (h)
0.43 × 500 = 215 0.31 × 500 = 155 0.26 × 500 = 130
0 1 2 3 4 5 6 7
Time Reading (h)
2. Compare the shapes, centers, and spreads of the dot plots.
7th grade
31%
Shape: Online: The
data are clustered to the right. Reading: The data
have two clusters, one at the left and one at the right.
EXAMPLE 2
The box plots show the amount that each employee from the same
office donated to two charities. Compare the shapes, centers and
spreads of the box plots.
Center: Online: The
data have a single peak at 6. Reading: The data
have two peaks, at 0 and 6.
Spread: Online: The
Charity A
data are spread from 4 to 7 with an outlier at 0.
Reading: The data are spread from 0 to 6 with a gap from 3 to 4.
Charity B
3. Calculate the medians of the dot plots. Online:
8 12 16 20 24 28 32 36 40 44 48 52
© Houghton Mifflin Harcourt Publishing Company
80
The dot plots show the number of hours a group of students
spend online each week, and how many hours they spend reading.
Compare the dot plots visually. (Lesson 11.2)
26% = 0.26
There are 215 6th graders, 155 7th graders, and 130
8th graders.
Votes
90
4. Calculate the ranges of the dot plots. Online:
Shapes: The lengths of the boxes are similar, as are the overall lengths
of the graphs. The whiskers for the two graphs are very different. The
whiskers for Charity A are similar in length. The left whisker for Charity B
is much shorter than the right one.
The box plots show the math and
reading scores on a standardized test
for a group of students. Use the box
plots shown to answer the following
questions. (Lesson 11.3)
Centers: The median for Charity A is $40, and for Charity B is $20. That
means the median donor gave $20 more for Charity A.
6; Reading: 5
7; Reading: 6
© Houghton Mifflin Harcourt Publishing Company
Study Guide
Number of votes
UNIT 6
Math Scores
Reading Scores
2
4
6
8 10 12 14 16 18 20 22
5. Compare the maximum and minimum values of the box plots.
Spreads: The interquartile range for Charity A is 44 - 32 = 12. The
interquartile range for Charity B is slightly less, 24 - 14 = 10.
The minimum value of both plots is 4, and the maximum of both plots is 20.
6. Compare the interquartile spread of the box plots.
The donations varied more for Charity B and were lower overall.
The interquartile range of the math scores is 14 - 6 = 8. The
interquartile range of the reading scores is 18 - 10 = 8.
Unit 6
393
394
Unit 6
Measurement and Data
394
MODULE
MODULE
?
12
12
Random Samples and
Populations
ESSENTIAL QUESTION
How can you use random samples and populations to solve
real-world problems?
3. Mr. Puccia teaches Algebra 1 and Geometry. He randomly selected
10 students from each class. He asked the students how many hours
they spend on math homework in a week. He recorded each set of
data in a list. (Lesson 12.3)
Algebra 1: 4, 0, 5, 3, 6, 3, 2, 1, 1, 4
Geometry: 7, 3, 5, 6, 5, 3, 5, 3, 6, 5
Key Vocabulary
biased sample (muestra
sesgada)
population (población)
random sample (muestra
aleatoria)
a. Make a dot plot for Algebra 1. Then find the mean and
the range for Algebra 1.
sample (muestra)
0 1 2 3 4 5 6 7
Algebra 1
mean = 2.9, range = 6 - 0 = 6
EXAMPLE
An engineer at a lightbulb factory chooses a random sample of 100
lightbulbs from a shipment of 2,500 and finds that 2 of them are
defective. How many lightbulbs in the shipment are likely to be defective?
b. Make a dot plot for Geometry. Then find the mean and
the range for Geometry.
mean = 4.8, range = 7 - 3 = 4
defective lightbulbs
defective lightbulbs in population
_______________
= _________________________
size of sample
size of population
2
x
___ = ____
100
2,500
2 · 25
x
______
= ____
100 · 25
2,500
c. What can you infer about the students in the Algebra 1
class compared to the students in the Geometry class?
0 1 2 3 4 5 6 7
Geometry
Sample answer: The students in the Geometry class spend more
time on math homework than the students in the Algebra class.
x = 50
In a shipment of 2,500 lightbulbs, 50 are likely to be defective.
Unit 6 Performance Tasks
EXERCISES
1.
1. Molly uses the school directory to select at random 25 students
from her school for a survey on which sports people like to watch
on television. She calls the students and asks them, “Do you think
basketball is the best sport to watch on television?” (Lesson 12.1)
a. Did Molly survey a random sample or a biased sample of the
students at her school?
random
Type A
Type B
7
9
11
13
15
Number of Butterflies
17
a. Find the median, range, and interquartile range for each data set.
b. Was the question she asked an unbiased question? Explain your
answer.
Type A: median = 11; range = 4; IQR = 3
Type B: median = 11; range = 10; IQR = 2
No. Sample answer: It assumes the person watches basketball
on television.
b. Which measure makes it appear that flower type A had a more
consistent number of butterfly visits? Which measure makes it
appear that flower type B did? If you had to choose one flower as
having the more consistent visits, which would you choose? Explain
your reasoning.
2. There are 2,300 licensed dogs in Clarkson. A random sample of
50 of the dogs in Clarkson shows that 8 have ID microchips
implanted. How many dogs in Clarkson are likely to have ID
microchips implanted? (Lesson 12.2)
The range makes Type A appear more consistent. The interquartile
368 dogs
© Houghton Mifflin Harcourt Publishing Company
© Houghton Mifflin Harcourt Publishing Company
CAREERS IN MATH Entomologist An
entomologist is studying how two different
types of flowers appeal to butterflies. The
box-and-whisker plots show the number of
butterflies who visited one of two different
types of flowers in a field. The data were
collected over a two-week period, for one
hour each day.
range makes Type B appear more consistent. Possible explanation:
Type A is actually more consistent because it has a much smaller
range, while its IQR is only slightly larger.
Unit 6
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396
Unit 6
Measurement and Data
396
UNIT 7
Personal Financial
Literacy
Additional Resources
Personal
Math Trainer
my.hrw.com
Online
Assessment and
Intervention
Assessment Resources
• Leveled Unit Tests: A, B, C, D
• Performance Assessment
Study Guide Review
Vocabulary Development
Integrating the ELPS
Encourage English learners to refer to their notes and the illustrated, bilingual glossary as
they review the unit content.
c.4.E Read linguistically accommodated content area material with a decreasing need for linguistic
accommodations as more English is learned.
MODULE 13 Taxes, Interest, and Incentives
7.13.A, 7.13.E, 7.13.F
Key Concepts
• To find the tax on an item, multiply the amount of tax, written as a decimal, by the price of
the item. (Lesson 13.1)
• To calculate compound interest, use the formula A = P(1 + r) t. (Lesson 13.2)
• Interest paid only on the principal is simple interest, while compound interest is interest
paid on the principal and interest the account has earned. (Lesson 13.2)
MODULE 14 Planning Your Future
COMMON
CORE
7.13.B, 7.13.C, 7.13.D
Key Concepts
• A budget is a plan to help you reach your financial goals and should consider fixed
expenses and variable expenses. (Lessons 14.1, 14.2)
• To calculate net worth, subtract liabilities, or debts you owe, from assets, or things you
own. (Lesson 14.3)
451
Unit 7
Study Guide
MODULE
MODULE
?
13
13
Review
Taxes, Interest, and
Incentives
3. Bette has $10,000 to put into savings accounts. She puts half into an
account that earns simple interest at an annual rate of 3.1%. She puts
the other half into an account that earns interest at an annual rate of
2.6% compounded annually. After 10 years, which account will earn
more money? How much more? (Lesson 13.2)
Key Vocabulary
the simple interest account; $86.86
compound interest (interés
compuesto)
federal withholding
(retención fiscal federal)
ESSENTIAL QUESTION
4. Barack can buy a four pack of mangos for $2.76 or a six pack of
mangos for $4.32. Which is the better buy? Explain. (Lesson 13.3)
gross pay (paga bruta)
How can you solve real-world problems involving taxes, interest,
and incentives?
the four pack; the unit price of the four pack is $0.69, and the
interest (interés)
unit price of the six pack is $0.72.
net pay (paga neta)
sales tax (impuesto sobre
la venta)
EXAMPLE 1
Samuel puts $5,000 into a savings account that earns simple
interest at an annual rate of 1.2% for 5 years. Tinos puts the
same amount into a savings account that earns interest at an
annual rate of 1.2% compounded annually for 5 years. Which
account will earn more interest after 5 years?
simple interest (interés
simple)
MODULE
MODULE
taxable income (ingreso
sujeto a impuestos)
Samuel
Tinos
Use the formula for simple interest.
Use the formula for compound interest.
14
14
Planning Your Future
assets (activos)
?
ESSENTIAL QUESTION
How can you use mathematics to plan for a successful financial
future?
I=P×r×t
A = P(1 + r)
A = $5,000(1.012)5 = $5,307.29
Samuel earns $300 in interest.
Tinos earns $5,307.29 - $5,000 = $307.29.
EXAMPLE 1
The circle graph shows the Morales family’s monthly budget. Their
fixed expenses are housing, savings, and an emergency fund. Use
the graph to find the amount the family spends on fixed expenses.
t
Budget for Morales Family / Net Monthly Income = $5,200
Tinos’s account will earn more interest than Samuel’s account.
© Houghton Mifflin Harcourt Publishing Company
1. Find the sales tax for
each product, using a
sales tax rate of 8.5%.
Then find the product’s
total price and the total
for the entire purchase.
Round to the nearest
hundredth. (Lesson 13.1)
2. Claire earns a monthly
paycheck of $2,900.
Federal withholding is
12.8% of her gross pay.
Complete the table.
(Lesson 13.1)
Item
Unit
Price ($) Number
Subtotal
($)
Tax ($) Total ($)
Basketball
8.95
3
26.85
2.28 29.13
Tennis balls
(3 pack)
3.88
5
19.40
1.65 21.05
Total
Gross Pay
Transportation
(car expense,
bus passes)
8%
$2,900
Clothing
6%
Entertainment
4%
$371.20
Social Security
$179.80
Medicare
$42.05
Net Pay
income (ingreso)
Item
$2,306.95
Unit 7
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452
net worth (patrimonio neto)
planned savings (ahorros
previstos)
savings (ahorros)
variable expense (gasto
variable)
Emergency
fund
5%
Housing cost
(house payment
and insurance)
32%
Medical (insurance
and additional
expenses)
20%
50.18
Taxes
Federal Income Tax
budget (presupuesto)
fixed expenses (gastos fijos)
liabilities (pasivo)
I = $5,000 × 0.012 × 5 = $300
EXERCISES
Key Vocabulary
Savings
10%
Food
15%
Percent
Amount Available
Housing cost
32%
$1,664
Savings
10%
$520
Emergency fund
5%
$260
© Houghton Mifflin Harcourt Publishing Company
UNIT 7
Unit 7
Personal Financial Literacy
452
Unit 7 Performance Tasks
EXERCISES
For 1–3, use the graph from the Example. (Lessons 14.1)
1.
1. How much money does the Morales family spend on
clothing each month?
$312
2. How much more money does the Morales family spend
on food than on entertainment?
$572 per month
3. The air conditioning in the Morales’s house is broken.
The repair service estimated that the cost of repairing
it is $1,040. How many months of emergency funds will
the family use to fix the air conditioning?
CAREERS IN MATH Freelance Computer Programmer Andre
works as a freelance computer programmer, and his laptop has stopped
working. He is purchasing a new laptop, which he needs to have in 2 days
in order to meet a job deadline. He lives in Massachusetts, which has a
6.25% sales tax. He is considering these three options for the purchase:
Buy it online for $1,499, pay sales tax, and pay $24 priority
shipping.
Buy it in Massachusetts for $1,479.
Buy it in New Hampshire for $1,549 with no sales tax.
4 months
a. Calculate the total cost for each option. Which is the best deal?
4. Mr. and Mrs. Clark have two children. They live in Waco, Texas. They
may move to Austin to be closer to their parents. Their employers
pay for 100% of one parent’s health insurance premium and 50% of
the premium for other family members. Use an online family budget
estimator to estimate to the nearest dollar, the following for the
Clark family in Waco and in Austin. (Lesson 14.2)
online: $1,616.69; Massachusetts: $1,571.44; New Hampshire: $1,549;
Buying in New Hampshire is the best deal.
b. List other factors that relate to the purchase that could also affect
Andre’s decision.
Online is the most convenient option; he can place his order without
Answers may vary according to the online family estimator used.
leaving his home, but he cannot try it before purchasing. Buying in
Monthly Estimated
Budget for Waco ($)
Monthly Estimated
Budget for Austin ($)
Housing
$629
$836
transportation. If he buys in Massachusetts, he can likely have the
Food
$491
$491
laptop within the hour, which allows him to get back to work quickly.
Child Care
$635
$841
Medical Insurance
$301
$309
Medical Out-of-pocket
$118
$118
Transportation
$395
$482
Other Necessities
$309
$360
Total monthly expenses
$2,878
$3,437
Total Federal Tax Impact
$−19
$200
$2,859
$3,637
$17
$22
Necessary monthly income
Household Hourly Wage
5. Rashid paid off his car, which is worth $6,500. He has a
credit card balance of $325. He has $4,250 in his savings
account and $672 in his checking account. He owes $3,600
in student loans. He lives with his parents. What is Rashid’s
net worth? (Lesson 14.3)
New Hampshire means time spent driving or money to take public
2. Grant is going to purchase several large pizzas for a party. He has two
options for local pizza shops as described below.
Hank’s Pizza: For every two pizzas, get a third at half price.
Antonio’s: 20% off of all orders of $40 or more.
a. Write a paragraph that describes the other information Grant needs
in order to compare these options. Include both facts that relate to
the pizzas and facts that relate to the event.
Grant needs to know the cost of a large pizza at each shop. He also
needs to know how many pizzas he needs to purchase. He can
determine this by dividing the number of people at the event by
how many people one large pizza serves.
© Houghton Mifflin Harcourt Publishing Company
© Houghton Mifflin Harcourt Publishing Company
Item
b. Suppose large pizzas cost $13 at each shop. Compare the total cost
at each shop for 3 pizzas and for 6 pizzas.
3 pizzas: $32.50 at Hank’s Pizza, $39 at Antonio’s; 6 pizzas: $65 at
Hank’s Pizza, $62.40 at Antonio’s
$7,497
Unit 7
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Unit 7
Personal Financial Literacy
454