Simplify
1.
1
4
2.
2
3
2
3
3.
3
5
5
4. 4
1
4
5 Minute Check
Simplify
1.
1
4
2
5 Minute Check
5 Minute Check
Simplify
1.
1
4
2
1
÷
4
2
1
1
4
1
2
·
=
1
8
Simplify
2. 3
2
3
5 Minute Check
5 Minute Check
Simplify
2. 3
2
3
3
1
3
1
÷
2
3
·
3
2
=
9
2
1
2
=4
Simplify
3.
3
5
5
5 Minute Check
5 Minute Check
Simplify
3
5
3.
5
3
5
3
5
÷
5
1
·
1
5
=
3
25
Simplify
4. 4
1
4
5 Minute Check
5 Minute Check
Simplify
4. 4
1
4
4
1
1
4
÷
4
1
·
4
1
= 16
Friday, Jan 9
Lesson 7.1.3/7.1.4
Convert Unit Rates/
Proportional and Nonproportional
Relationships
Convert Unit Rates
Objective: To convert units of measure
between derived units to solve problems.
Convert Unit Rates
The relationships among some commonly used
customary and metric units are shown in the
tables below.
Convert Unit Rates
Each of the relationships in the tables can be
written as a unit ratio. A unit ratio, like a unit
rate, has a denominator of one unit.
Convert Unit Rates
A remote control car travels at a rate of 10
feet per second. How many inches per
second is this?
How to Convert Unit Rates
Step 1 – Write the complete rate as a fraction
with units .
Convert Unit Rates
A remote control car travels at a rate of 10
feet per second. How many inches per
second is this?
10 ft
1s
How to Convert Unit Rates
Step 1 – Write the complete rate as a fraction
with units .
Convert Unit Rates
A remote control car travels at a rate of 10
feet per second. How many inches per
second is this?
10 ft
1s
How to Convert Unit Rates
Step 2 – Determine the units of the answer
and write as a fraction.
Convert Unit Rates
A remote control car travels at a rate of 10
feet per second. How many inches per
second is this?
10 ft
in
Leave space for the
1s
1s
=
conversion rate.
How to Convert Unit Rates
Step 2 – Determine the units of the answer
and write as a fraction.
Convert Unit Rates
A remote control car travels at a rate of 10
feet per second. How many inches per
second is this?
10 ft
in
Leave space for the
1s
1s
=
conversion rate.
How to Convert Unit Rates
Step 3 – Determine the units of the
conversion rate(s).
Convert Unit Rates
A remote control car travels at a rate of 10
feet per second. How many inches per
second is this?
conversion rate .
10 ft
in
in
1s
ft
1s
=
How to Convert Unit Rates
Step 3 – Determine the units of the
conversion rate(s).
Convert Unit Rates
A remote control car travels at a rate of 10
feet per second. How many inches per
second is this?
conversion rate .
10 ft
in
in
1s
ft
1s
=
The conversion rate units are determined by the
original rate units and the answer units.
In the above case, we need to cancel the “ft” units
and replace with “in” units. Notice the conversion
rate has “ft” in the denominator, so it will cancel the
“ft” of the original rate.
Convert Unit Rates
A remote control car travels at a rate of 10
feet per second. How many inches per
second is this?
10 ft
in
in
1s
ft
1s
=
conversion rate.
How to Convert Unit Rates
Step 4 – Complete the conversion rate(s).
Eg. How many inches in how many feet?
Convert Unit Rates
A remote control car travels at a rate of 10
feet per second. How many inches per
second is this?
10 ft 12 in
in
1s
1 ft
1s
=
conversion rate.
How to Convert Unit Rates
Step 4 – Complete the conversion rate(s).
Convert Unit Rates
A remote control car travels at a rate of 10
feet per second. How many inches per
second is this?
10 ft 12 in
in
1s
1 ft
1s
=
How to Convert Unit Rates
Step 5 – Multiply and cancel units.
Convert Unit Rates
A remote control car travels at a rate of 10
feet per second. How many inches per
second is this?
10 ft 12 in
120 in
1s
1 ft
1s
=
How to Convert Unit Rates
Step 5 – Multiply and cancel units.
Convert Unit Rates
A swordfish can swim at a rate of 60 miles per
hour. How many feet per hour is this?
Step 1 - ?
Convert Unit Rates
A swordfish can swim at a rate of 60 miles per
hour. How many feet per hour is this?
60 mile
1h
Step 2 - ?
Convert Unit Rates
A swordfish can swim at a rate of 60 miles per
hour. How many feet per hour is this?
60 mile
1h
Step 3 – ?
=
ft
1h
Convert Unit Rates
A swordfish can swim at a rate of 60 miles per
hour. How many feet per hour is this?
60 mile
1h
ft
mile
=
ft
1h
Remember – we want to cancel the “mile” unit in the
numerator of the original rate. In order to do so,
the conversion rate must have a “mile” unit in the
denominator.
Step 4 – ?
Convert Unit Rates
A swordfish can swim at a rate of 60 miles per
hour. How many feet per hour is this?
60 mile
1h
5280 ft
1 mile
=
ft
1h
How many feet in how many miles?
Step 5 – ?
Convert Unit Rates
A swordfish can swim at a rate of 60 miles per
hour. How many feet per hour is this?
60 mile
1h
5280 ft
1 mile
=
316, 800 ft
1h
Convert Unit Rates
A gull can fly at a speed of 22 miles per hour.
How many feet per hour can the gull fly?
Do this on your own.
Convert Unit Rates
A gull can fly at a speed of 22 miles per hour.
How many feet per hour can the gull fly?
22 miles
1h
5280 ft
1 mile
=
116,160 ft
1h
Convert Unit Rates
Marvin is walking at a speed of 7 feet per
second. How many feet per hour is this?
Do this on your own.
Convert Unit Rates
Marvin is walking at a speed of 7 feet per
second. How many feet per hour is this?
7 ft
1s
420 ft
1 min
60 s
1 min
=
60 min
1h
420 ft
1 min
=
25,200 ft
1h
Or you can create one large conversion rate…
Convert Unit Rates
Marvin is walking at a speed of 7 feet per
second. How many feet per hour is this?
7 ft
1s
60 s · 60 min
1 min · 1 h
=
25,200 ft
1h
Proportional and Nonproportional
Relationships
Objective: To identify and understand
proportional and nonproportional
relationships.
Proportional and Nonproportional
Relationships
Two quantities are proportional if they have a
constant ratio or rate.
All of the ratios above are equivalent ratios
because they all have the same value.
Proportional and Nonproportional
Relationships
For relationships in which the ratio is not
constant, the two quantities are
nonproportional.
Proportional and Nonproportional
Relationships
Andrew earns $18 per hour for mowing lawns.
Is the amount of money he earns
proportional to the number of hours he
spends mowing? Explain.
How to Determine if a Rate or Ratio is
Proportional.
Step 1 – Make a table.
Proportional and Nonproportional
Relationships
Andrew earns $18 per hour for mowing lawns.
Is the amount of money he earns
proportional to the number of hours he
spends mowing? Explain.
How to Determine if a Rate or Ratio is
Proportional.
Step 1 – Make a table.
Proportional and Nonproportional
Relationships
Andrew earns $18 per hour for mowing lawns.
Is the amount of money he earns
proportional to the number of hours he
spends mowing? Explain.
How to Determine if a Rate or Ratio is
Proportional.
Step 2 – Simplify the rates or ratios.
Proportional and Nonproportional
Relationships
Andrew earns $18 per hour for mowing lawns.
Is the amount of money he earns
proportional to the number of hours he
spends mowing? Explain.
How to Determine if a Rate or Ratio is
Proportional.
Step 2 – Simplify the rates or ratios.
Proportional and Nonproportional
Relationships
Andrew earns $18 per hour for mowing lawns.
Is the amount of money he earns
proportional to the number of hours he
spends mowing? Explain.
How to Determine if a Rate or Ratio is
Proportional.
Step 2 – Simplify the rates or ratios.
Since all rates can be simplified to 18, they
are proportional.
Proportional and Nonproportional
Relationships
Uptown Tickets charges $7 per baseball
ticket plus a $3 processing fee per order. Is
the cost of an order proportional to the
number of tickets ordered? Explain.
Step 1 - ?
Proportional and Nonproportional
Relationships
Uptown Tickets charges $7 per baseball
ticket plus a $3 processing fee per order. Is
the cost of an order proportional to the
number of tickets ordered? Explain.
Step 2 - ?
(It doesn’t matter which unit is top or bottom)
Proportional and Nonproportional
Relationships
Uptown Tickets charges $7 per baseball
ticket plus a $3 processing fee per order. Is
the cost of an order proportional to the
number of tickets ordered? Explain.
Since all rates do not simplify to the same,
they are nonproportional.
Proportional and Nonproportional
Relationships
You can use recipe shown to make fruit
punch. Is the amount of sugar used
proportional to the amount of mix used?
Explain.
Do this on your own.
Proportional and Nonproportional
Relationships
You can use recipe shown to make fruit
punch. Is the amount of sugar used
proportional to the amount of mix used?
Explain.
Since all rates can be simplified to 0.5, they
are proportional.
Proportional and Nonproportional
Relationships
The tables shown represent the number of
pages Martin and Gabriel read over time.
Which situation represents a proportional
relationship between the time spent reading
and the number of pages read? Explain.
Do this on your own.
Proportional and Nonproportional
Relationships
The tables shown represent the number of pages
Martin and Gabriel read over time. Which
situation represents a proportional relationship
between the time spent reading and the number of
pages read? Explain.
Only Martin’s ratios can be simplified to the
3
5
same ( ).
Proportional and Nonproportional
Relationships
The Vista Marina rents boats for $25 per
hour. In addition to the rental fee, there is a
$12 charge for fuel. Is the number of hours
you rent the boat proportional to the total
cost? Explain.
Do this on your own.
Proportional and Nonproportional
Relationships
The Vista Marina rents boats for $25 per
hour. In addition to the rental fee, there is a
$12 charge for fuel. Is the number of hours
you rent the boat proportional to the total
cost? Explain.
No, The cost to times ratios are not the
same.
Proportional and Nonproportional
Relationships
Which situation represents a proportional
relationship between the number of laps run
by each student and their time?
Proportional and Nonproportional
Relationships
Which situation represents a proportional
relationship between the number of laps run
by each student and their time?
Desmond’s time is proportional. It takes him
73s for every lap.
Proportional and Nonproportional
Relationships
Plant A is 18 inches tall after 1 week, 36
inches after 2 weeks, 56 inches after 3
weeks. Plant B is 18 inches tall after 1 week,
36 inches after 2 weeks, 54 inches after 3
weeks. Which represents a proportional
relationship between the height and number
of weeks?
Proportional and Nonproportional
Relationships
Plant A is 18 inches tall after 1 week, 36 inches
after 2 weeks, 56 inches after 3 weeks. Plant B is
18 inches tall after 1 week, 36 inches after 2
weeks, 54 inches after 3 weeks. Which represents
a proportional relationship between the height
and number of weeks?
Plant A
Plant B
Height
18
36
56
Height
18
36
54
Weeks
1
2
3
Weeks
1
2
3
Plant B grows at 18 inches per week.
Proportional and Nonproportional
Relationships
Johanna’s parents give her $10 per week for lunch money.
Blake ran laps around the gym. His times are shown
in the table. Blake is trying to decide whether
the number of laps is proportional to the
time. Find his mistake and correct it.
Proportional and Nonproportional
Relationships
Johanna’s parents give her $10 per week for lunch money.
Blake ran laps around the gym. His times are shown
in the table. Blake is trying to decide whether
the number of laps is proportional to the
time. Find his mistake and correct it.
They are not
proportional.
The 1st min was
25 sec per lap, the
2nd min was 33 sec
per lap.
Proportional and Nonproportional
Relationships
Johanna’s parents give her $10 per week for lunch money.
True or false? If a function rule has only
multiplication and/or division it is a proportional
relationship. Give examples to support your answer.
Proportional and Nonproportional
Relationships
Johanna’s parents give her $10 per week for lunch money.
True or false? If a function rule has only
multiplication and/or division it is a proportional
relationship. Give examples to support your answer.
If a simplified function rule has only multiplication
and/or division it is a proportional relationship.
Proportional
Nonproportional
x
1
2
3
3x
3
6
9
x
3x +2
1
5
2
8
3
11
Proportional and Nonproportional
Relationships
Agenda Notes
Complete the Mid-Chapter Check on page
44 and bring to my desk.
Homework –
Homework Practice 7.1.3 and 7.1.4
Due Mon, Jan 12
Mid-Chapter 7.1 Quiz - Monday, Jan 12