CorrectionKey=A Ratios and Proportionality MODULE 4
嚜燎atios and
Proportionality
?
MODULE
4
LESSON 4.1
ESSENTIAL QUESTION
Unit Rates
How can you use rates and
proportionality to solve
real-world problems?
7.RP.1
LESSON 4.2
Constant Rates
of Change
7.RP.2, 7.RP.2a,
7.RP.2b, 7.RP.2c
LESSON 4.3
Proportional
Relationships and
Graphs
7.RP.2a, 7.RP.2b,
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7.RP.2c, 7.RP.2d
Real-World Video
You can use rates to describe lots of real-world
situations. A cyclist can compute rates such as miles
per hour or rotations per minute.
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Math On the Spot
Animated Math
Personal Math Trainer
Go digital with your
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Scan with your smart
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video tutor, and more.
Interactively explore
key concepts to see
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Get immediate
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practice sets.
113
Are YOU Ready?
Personal
Math Trainer
Complete these exercises to review skills you will need
for this module.
Operations with Fractions
EXAMPLE
3
3
__
‾ _58 = __
℅ _85
10
10
Online Practice
and Help
my.
Multiply by the reciprocal of the divisor.
4
3
8
℅ __
= ___
5
10
Divide by the common factors.
12
= __
25
Simplify.
5
Divide.
10
2. _59 ‾ __
11
1. _34 ‾ _45
16 _
4. __
‾ 89
21
3. _38 ‾ _12
Ordered Pairs
y
5
x
-5
O
-5
To write the ordered pair for A,
start at the origin.
Move 2 units right.
Then move 4 units down.
The ordered pair for
point A is (2, -4).
5
A
Write the ordered pair for each point.
5. B
6. C
7. D
8. E
9. F
10. G
y
5
B
-5
E
F
O
G
-5
114
Unit 2
D
x
C
5
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EXAMPLE
Reading Start-Up
Visualize Vocabulary
Use the ? words to complete the graphic. You can put more
than one word in each bubble.
2 __
_
=3
4 6
36%
Vocabulary
Review Words
constant (constante)
? conversion factor
(factor de conversi車n)
? equivalent ratios (razones
equivalentes)
? percent (porcentaje)
rate (tasa)
? ratio (raz車n)
Preview Words
Uses of Ratios
12 inches
________
1 foot
6 to 1
Understand Vocabulary
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Match the term on the left to the definition on the right.
1. rate of change
A. Statement that two rates or ratios
are equivalent.
2. proportion
B. A rate that describes how one quantity
changes in relation to another quantity.
3. unit rate
C. Rate in which the second quantity is one unit.
complex fraction (fracci車n
compleja)
constant of proportionality
(constante de
proporcionalidad)
proportion (proporci車n)
proportional relationship
(relaci車n proporcional)
rate of change (tasa de
cambio)
unit rates (tasas unitarias)
Active Reading
Three-Panel Flip Chart Before beginning the
module, create a three-panel flip chart to help
you organize what you learn. Label each flap
with one of the lesson titles from this module.
As you study each lesson, write important ideas
like vocabulary, properties, and formulas under
the appropriate flap.
Module 4
115
GETTING READY FOR
Ratios and Proportionality
Understanding the standards and the vocabulary terms in the standards
will help you know exactly what you are expected to learn in this module.
Key Vocabulary
rate (tasa)
A ratio that compares two
quantities measured in
different units.
unit rate (tasa unitaria)
A rate in which the second
quantity in the comparison is
one unit.
7.RP.2b
Identify the constant of
proportionality (unit rate)
in tables, graphs, equations,
diagrams, and verbal
descriptions of proportional
relationships.
Key Vocabulary
constant (constante)
A value that does not change.
constant of
proportionality (constante de
proporcionalidad)
A constant ratio of two
variables related proportionally.
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Common Core
Standards
explained.
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116
Unit 2
What It Means to You
Given a rate, you can find the equivalent unit rate by dividing
the numerator by the denominator.
EXAMPLE 7.RP.1
Lisa hikes _13 mile every _61 hour.
How far does she hike in 1 hour?
1
_
3
1
1
_
_
_
1=3‾6
_
6
2
6
= _13 ﹞ __
1
1
= 2 miles
What It Means to You
You will determine the constant of proportionality for
proportional relationships.
EXAMPLE 7.RP.2b
The graph shows the distance a bicyclist
travels over time. How fast does the
bicyclist travel?
rise (distance)
slope (speed) = __________
run (time)
15
= __
1
The bicyclist travels at 15 miles per hour.
y
75
45
15
O
15
1
1
x
3
5
Time (h)
The bicyclist's speed is a unit rate. It is indicated on the graphed
line by the point (1, 15).
? Houghton Mifflin Harcourt Publishing Company ? Image Credits: ?David Epperson/PhotoDisc/Getty Images
Compute unit rates associated
with ratios of fractions, including
ratios of lengths, areas and other
quantities measured in like or
different units.
Distance (mi)
7.RP.1
LESSON
7.RP.1
4.1 Unit Rates
?
Compute unit rates associated
with ratios of fractions,
including ratios of lengths,
areas and other quantities
measured in like or different
units.
ESSENTIAL QUESTION
How do you find and use unit rates?
EXPLORE ACTIVITY
7.RP.1
Exploring Rates
Commonly used rates like miles per hour make it easy to understand
and compare rates.
Jeff hikes _12 mile every 15 minutes, or _14 hour. Lisa hikes _13 mile every
10 minutes, or _16 hour. How far do they each hike in 1 hour? 2 hours?
? miles
A Use the bar diagram to help you
determine how many miles Jeff
hikes. How many _14 -hours are in
1 hour? How far does Jeff hike in
1 hour?
1
4
hour
1
2
mile
1
4
1
4
hour
1
4
hour
hour
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B Complete the table for Jeff*s hike.
Distance (mi)
1
_
2
Time (h)
1
_
4
1
_
2
3
_
4
C Complete the bar diagram to
help you determine how far
Lisa hikes. How many miles
does she hike in 1 hour?
1
6
1
2
1
6
hour
hour
1
6
hour
1
6
hour
1
6
hour
1
6
hour
D Complete the table for Lisa*s
hike.
Distance (mi)
1
_
3
Time (h)
1
_
6
1
_
3
1
_
2
1
2
Lesson 4.1
117
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