Transcript Tuesday, Oct 30 - Xenia Community Schools

5 Minute Check
Complete in your notes.
1. 20 mi/h = ? ft/min
2. 16cm/min = ? m/h
3. 45 mi/h = ? ft/s
4. 26cm/s = ? m/min
You can use your calculator for this lesson.
5 Minute Check
Complete in your notes.
1. 20 mi/h = ? ft/min
5 Minute Check
Complete in your notes.
1. 20 mi/h = ? ft/min
20 𝑚𝑖
1ℎ
·
5280 𝑓𝑡 ·1 ℎ
1 𝑚𝑖 · 60 𝑚𝑖𝑛
=
105600 𝑓𝑡
60 𝑚𝑖𝑛
=
1760 𝑓𝑡
1 𝑚𝑖𝑛
5 Minute Check
Complete in your notes.
2. 16cm/min = ? m/h
5 Minute Check
Complete in your notes.
2. 16cm/min = ? m/h
16 𝑐𝑚
1 𝑚𝑖𝑛
·
1 𝑚 · 60 𝑚𝑖𝑛
100 𝑐𝑚 · 1 ℎ
=
960 𝑚
100 ℎ
3
5
= 9 m/h
5 Minute Check
Complete in your notes.
3. 45 mi/h = ? ft/s
5 Minute Check
Complete in your notes.
3. 45 mi/h = ? ft/s
45 𝑚𝑖
1ℎ
·
5280 𝑓𝑡 ·1 ℎ·1 𝑚𝑖𝑛
1 𝑚𝑖 · 60 𝑚𝑖𝑛· 60 𝑠
=
237600 𝑓𝑡
3600 𝑠
=
66 𝑓𝑡
1𝑠
5 Minute Check
Complete in your notes.
4. 26cm/s = ? m/min
5 Minute Check
Complete in your notes.
4. 26cm/s = ? m/min
26 𝑐𝑚
1𝑠
·
1 𝑚 · 60 𝑠
100 𝑐𝑚 ·1 𝑚𝑖𝑛
=
1560 𝑚
100 𝑚𝑖𝑛
3
5
= 15 m/min
Wednesday, Jan 7
Lesson 7.1.4
Proportional and Nonproportional
Relationships
Solve One-Step Inequalities
Solve One-Step Inequalities
Solve One-Step Inequalities
Solve One-Step Inequalities
Solve One-Step Inequalities
Solve One-Step Inequalities
Solve One-Step Inequalities
Solve One-Step Inequalities
Solve One-Step Inequalities
Solve One-Step Inequalities
Solve One-Step Inequalities
Solve One-Step Inequalities
Solve One-Step Inequalities
Solve One-Step Inequalities
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
Homework –
Homework Practice 7.1.4
Due Thursday, Jan 8
Mid-Chapter 7.1 Quiz –
Changed to Friday, Jan 9