Unit 5A RATIOS (Proportional Relationships)

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Unit 5ARATIOS(Proportional Relationships)

• Name
• Date
• Period

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RATIO
comparison
two quantities
A RATIO is a _________________ between
______________________. A ratio can be written
three different ways _______________
or _________________ or
_________________
to
colon
fraction

• one Pepsi costs 50 cents
•  
• 2. on a map one inch is equivalent to 50 miles
•  
• 3.one hand has five fingers
•  
• 4.the student/teacher ratio
•  
• 5.ratio of boys to girls

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ORDER MATTERS
Write each ratio in three different ways for the
following comparisons from the picture.
6. suns to stars   7. moons to stars   8. all
items to moons   9. stars to all items
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..two ratios equal to each other.
equivalent ratios..
Use a 1 in disguise to multiply or
divide.
Complete using lt, gt, or
Find the value of x to make equivalent fractions
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UNIT RATE
ratio
compares two
Rate is a __________ that ______________
___________ quantities measured in the same units
or different units. For example, cups to cups or
meters to seconds.
denominator is 1
Unit rate is a rate whose ____
___________________________.
divide
numerator
To convert a rate to a unit rate, _______________
both the __________________ and
_____________________ by the denominator.
denominator
Example 1 Mike travels 300 miles in 5 hours,
find Mikes rate.
Example 2 Stans heart beats 520 times every
four minutes, find Stans heartbeat per minute.
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Example 3 Find the rate of pay if you earn 52
for 8 hours of work.
Example 4 An area of 3 acres measure 14,520
square yards. How many square yards are there in
one acre?
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Example 5 Johanna sells pizza sauce and charges
3.00 for a 7-ounce jar or 16.00 for two jars
that hold a total of 37 ½ ounces. Is buying a
7-ounce jar a better deal than buying two jars
that hold 37 ½ ounces? How do you know?
Example 6 Mark hikes ½ mile every ¼ hour. Cheryl
hikes 1/3 mile every 1/6 hour. Who hikes faster?
How do you know?
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MODELS FOR RATIOS
Expectations for this grade level include complex
fractions. Students should be able to demonstrate
a variety of modeling techniques such as the
use of the tape diagrams and double number line
diagrams shown here, in addition to procedural
techniques.
Example Consider comparing the lengths of the
two worms below.
Write the ratio of the length of worm A to the
length of worm B
How many times longer is worm B than worm A?
The length of worm A is what part, or fraction,
of the length of worm B?
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Example 2 On a bicycle you can travel 20 miles
in 4 hours. What are the unit rates in this
situation (the distance you can travel in 1 hour
and the amount of time required to travel 1 mile)?


Example 3 If a person walks ½ mile in each ¼
hour, compute the unit rates (the distance
traveled in 1 hour and the amount of time
required to travel 1 mile).
___________
__________________________________________________
___
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PROPORTIONAL RELATIONSHIPS
Proportional relationships involve
____________________________of
________________________________________________
_______ in equivalent ratios.
(For example a
collection of ordered pairs in a function table.)
collections
pairs of measurements
(CCSS) Do the two quantities have a proportional
relationship? (CCSS) What is the constant of
proportionality (unit rate)?
Example 1
Is this a proportional relationship?
The constant of proportionality or unit rate is

Inches on map Distance in miles
1 5
2 10
3 15
4 20
5 25
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Example 2
proportionality
meters 3 6 9 12 15 18
seconds 2 4 6 8 10 12
The constant of _______________ or
___________________________ is
unit rate
Is this a proportional relationship?
Example 3
proportionality
The constant of _______________ or
_____________________________ is
x 4 5 6 7
y 5 6 7 8
unit rate
Is this a proportional relationship?
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CCSS 7.RP.2a-2 Decide whether two quantities are
in a proportional relationship, e.g., by graphing
on a coordinate plane and observing whether the
graph is a ________________________ through the
___________________ .
Straight line
point of origin
Example 1
Example 2  
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Example 4
Example 3
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Slope
Syllabus Objective (6.23) The student will use
the coordinate plane to represent slope, midpoint
and distance. Nevada State Standards (NSS)
limits finding distance with horizontal and
vertical lines only at this grade level.
the pitch of a roof grade of 6 up or down a
hill cold drink for 0.50 price for each
additional cold drink is 0.50 rate of change
is .50 We call the rate of change slope
Directions Determine if the slope is positive,
negative, zero or undefined.
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Example Find the slope of the line that connects
the points on the graph.
Rise Run
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Example Find the slope of the line.
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Example Use the given slope and point to graph
each line.
m 2 (3, 4)
m (3, 1)
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DISTANCE and MIDPOINT
Syllabus Objective (6.23) The student will use
the coordinate plane to represent slope, midpoint
and distance. Nevada State Standards (NSS)
limits finding distance with horizontal and
vertical lines only at this grade level.
Example Find the distance of the given segment
below.
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MIDPOINT
Example Find the midpoint of each segment.
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SITUATIONAL PROPORTIONAL RELATIONSHIPS.EXPLAIN
Example The graph shows the number of servings
in different amounts of ice cream. Explain what
the point (3,9) means on this graph. Identify the
unit rate and explain how to find the unit rate
using the graph
Example Using the graph to the left, write an
equation that gives the number of servings, y, in
x pints of ice cream.