Chapter 3
Ratios and Rates
Day…..
1. Introducing Rates
2. Unit Rates
3. Graphing Rates of Change
4. Rates and Ratios in Review
5. Pop Quiz
Day 1
Bell Work
Walt can mow 500ft2 in10 minutes. If he
does not slow down, how long will it take
him to mow his parents lawn that measures
3,500ft2?
Justify your Response
Vocabulary
• Rate – A ratio comparing two quantities with different kinds of units.
(Example: 4 tires: 1 car)
• Unit Rate – a rate that is simplified so that it has a denominator of one.
(Example:
5 𝑠𝑡𝑢𝑑𝑒𝑛𝑡𝑠
1 𝑡𝑒𝑎𝑐ℎ𝑒𝑟
)
• Ratio – A comparison of two quantities by division.
𝑎
(Example: a:b, a to b, )
𝑏
• Equivalent Ratio – ratios the express the same relationship between two
quantities.
(Example: 10:15 is equivalent to 2:3 and 20:30)
• Scaling – to multiply or divide two related quantities by the same number.
(Example:
4 20
x
2 20
=
80
40
)
• Ratio Table – a table with columns filled with pairs of numbers that have
the same ratio.
Nails Used
5
10
15
Example:
Shelves Hung
1
2
3
I Can….
Explore rates using
models.
Introducing Rates
Essential Understanding:
• A rate is a ratio that compares two quantities with
different kinds of units. For example: 120 miles in two
hours.
• Because rates compare quantities with different units, the
units must be included when writing or solving rates.
• Just like before we must be careful to write the units in
the order they are given.
• Because rates are ratios, they can be written in all three
forms; colon 120 miles: 2 hours, 120 miles in two hours,
120 𝑚𝑖𝑙𝑒𝑠
and
.
2 ℎ𝑜𝑢𝑟𝑠
Watch This
• http://learnzillion.com/lessons/839understand-rates-as-a-type-of-ratio
(6 minutes)
• http://learnzillion.com/lessons/614-solve-rateproblems-using-multiplicative-reasoning
(7 minutes)
Wrap it Up
• Review
• Questions
• Exit Tickets
Day 2
Bell Work
Mark works in a factory where he is paid
buy the piece to put together roof vents. He
clocked himself one day and found he could
make one roof vent in 20 minutes. If he
works an 8 hour shift, how many roofs vents
can he make in one day?
Homework Check
No New
Vocabulary
Vocabulary
• Rate – A ratio comparing two quantities with different kinds of units.
(Example: 4 tires: 1 car)
• Unit Rate – a rate that is simplified so that it has a denominator of one.
(Example:
5 𝑠𝑡𝑢𝑑𝑒𝑛𝑡𝑠
1 𝑡𝑒𝑎𝑐ℎ𝑒𝑟
)
• Ratio – A comparison of two quantities by division.
𝑎
(Example: a:b, a to b, )
𝑏
• Equivalent Ratio – ratios the express the same relationship between two
quantities.
(Example: 10:15 is equivalent to 2:3 and 20:30)
• Scaling – to multiply or divide two related quantities by the same number.
(Example:
4 20
x
2 20
=
80
40
)
• Ratio Table – a table with columns filled with pairs of numbers that have
the same ratio.
Nails Used
5
10
15
Example:
Shelves Hung
1
2
3
I Can….
Determine unit rates
And
Solve unit rate problems
including those involving
unit pricing and constant
speed.
Unit Rates
Essential Understanding:
• A unit rate is a rate that has been simplified to a
denominator of 1.
• Remember a rate is a ratio and it must be scaled
down by division.
• To determine a unit rate, you simply divide the
numerator by the denominator and place the
quotient over a denominator of 1.
Watch This
• http://learnzillion.com/lessons/840-createunit-rate-using-diagram
(5 Minutes)
• http://learnzillion.com/lessons/841-create-unitrate-using-tape-diagram
(5 minutes)
Practice
Please take out your maker boards
Wrap it Up
• Review
• Questions
• Exit Tickets
Day 3
Bell Work
1. Mr. Vanderson drove 110 miles in 2 hours.
How fast did Mr. Vanderson drive?
2. Nikki can bounce a basket ball 900 times in 20
minutes. How may times can Nikki bounce a
basketball in one minute.
3. Dakota walked 12 blocks to his uncle’s house in
30 minutes. How many minutes did it take
Dakota to walk 1 block?
Homework Check
No New
Vocabulary
Vocabulary
• Rate – A ratio comparing two quantities with different kinds of units.
(Example: 4 tires: 1 car)
• Unit Rate – a rate that is simplified so that it has a denominator of one.
(Example:
5 𝑠𝑡𝑢𝑑𝑒𝑛𝑡𝑠
1 𝑡𝑒𝑎𝑐ℎ𝑒𝑟
)
• Ratio – A comparison of two quantities by division.
𝑎
(Example: a:b, a to b, )
𝑏
• Equivalent Ratio – ratios the express the same relationship between two
quantities.
(Example: 10:15 is equivalent to 2:3 and 20:30)
• Scaling – to multiply or divide two related quantities by the same number.
(Example:
4 20
x
2 20
=
80
40
)
• Ratio Table – a table with columns filled with pairs of numbers that have
the same ratio.
Nails Used
5
10
15
Example:
Shelves Hung
1
2
3
I Can….
Plot a rate of change
on a graph.
Rate of Change
Essential Understanding:
• A graph can be used to illustrate a rate of
change, such as changes over time and
distance.
Please open your book to page 162
Watch This
• http://learnzillion.com/lessons/615-graphingrate-problems-using-a-table
(7 minutes)
Your Turn….
• Clear your desk of everything but a pencil and
a calculator.
Wrap it Up
• Review
• Questions
• Exit Tickets
Day 4
Bell Work
A store sold 255 DVDs in 5 days. If sales continue
at this rate, how many DVDs can the expect to
sell in 30 days?
Graph the rate of change for each day on the
given graph card.
Homework Check
No New
Vocabulary
Vocabulary
• Rate – A ratio comparing two quantities with different kinds of units.
(Example: 4 tires: 1 car)
• Unit Rate – a rate that is simplified so that it has a denominator of one.
(Example:
5 𝑠𝑡𝑢𝑑𝑒𝑛𝑡𝑠
1 𝑡𝑒𝑎𝑐ℎ𝑒𝑟
)
• Ratio – A comparison of two quantities by division.
𝑎
(Example: a:b, a to b, )
𝑏
• Equivalent Ratio – ratios the express the same relationship between two
quantities.
(Example: 10:15 is equivalent to 2:3 and 20:30)
• Scaling – to multiply or divide two related quantities by the same number.
(Example:
4 20
x
2 20
=
80
40
)
• Ratio Table – a table with columns filled with pairs of numbers that have
the same ratio.
Nails Used
5
10
15
Example:
Shelves Hung
1
2
3
I Can….
Use ratio and rate
reasoning to solve realworld and mathematical
problems
Station Rotations
1. Write your exit ticket.
2. Pack up everything but a pencil.
3. You will have 15 minutes to complete each
rotation
1st Rotation
2nd Rotation
3rd Rotation
4th Rotation
Wrap it Up
• Review
• Questions
• Exit Tickets
Day 5
Bell Work
1. A 5lb sack of potatoes cost $4.32. An 8lb sack of
potatoes cost $6.78. Which is the better deal?
1. Jessie says she will charge Jim $45.00 for 3 hours of
tutoring. Mark says he will charge Jim $90.00 for 5
hours of tutoring. Who offers Jim the better hourly
rate of pay?
Homework Check
No New
Vocabulary
Vocabulary
• Rate – A ratio comparing two quantities with different kinds of units.
(Example: 4 tires: 1 car)
• Unit Rate – a rate that is simplified so that it has a denominator of one.
(Example:
5 𝑠𝑡𝑢𝑑𝑒𝑛𝑡𝑠
1 𝑡𝑒𝑎𝑐ℎ𝑒𝑟
)
• Ratio – A comparison of two quantities by division.
𝑎
(Example: a:b, a to b, )
𝑏
• Equivalent Ratio – ratios the express the same relationship between two
quantities.
(Example: 10:15 is equivalent to 2:3 and 20:30)
• Scaling – to multiply or divide two related quantities by the same number.
(Example:
4 20
x
2 20
=
80
40
)
• Ratio Table – a table with columns filled with pairs of numbers that have
the same ratio.
Nails Used
5
10
15
Example:
Shelves Hung
1
2
3
I Can….
• Relate ratios and rates to the
multiplication and division of
fractions.
• Look at my answer to check that
I answered what was asked and see
if my answer makes sense.
Let’s Review
Please
Take out your
Study Guide
pOp Quiz
• Take out a pencil and a calculator
• Clear everything else from your desk
Wrap it Up
• Classroom Store
• Exit Tickets
Computer Station
• http://learnzillion.com/lessons/842-define-unitrate-using-double-number-line
• http://learnzillion.com/lessons/613-solve-rateproblems-using-double-number-lines
• http://learnzillion.com/lessons/612-solve-formissing-values-in-rate-problems-using-a-table
(6 minutes per video)