Transcript Welcome to 6th Grade Ma+h

Chapter 3
Ratios and Rates
(Part 2)
Day…..
1. Introducing Rates
2. Graphing Rate of Change
3. Unit Rates
4. 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….
Identify and
determine
equivalent rates.
Introducing Rates
Essential Understanding:
• A rate is a ratio that compares two quantities with different kinds of units.
Examples:
1)
Driving 120 miles in two hours.
2)
Paying $2.49 per gallon.
3)
Reading 15 pages in 20 minutes.
4)
Making $15 an hour.
• Because rates compare quantities with different units, the units must be
included when writing or solving rates.
Example:
• Just like before we must be careful to write the units (labels) in the order they
are given or answer the question in the order the units are asked.
Example:
Introducing Rates
Essential Understanding:
• Because rates are ratios (just like fractions are ratios) all the
rules and procedures for ratios apply. Such as…..
 Rates can be written in three forms
Example:
 Rates can be scaled up and down to generate equivalent
rates or determine an unknown variable.
Example:
 You can also determined if rates are equivalent by finding
their cross products, unit rates, or simplest form.
Example:
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)
Practice
Clear your desk of everything except
for a pencil and a calculator.
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?
How many vents can he make it two days? A week?
Homework Check
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 plot the rate of
change on a graph to
determine an unknown
variable.
Unit Rates
Essential Understanding:
• A unit rate is a rate that has been simplified to a
denominator of 1.
Example:
• Remember a rate is a ratio and it must be scaled down by
division (not subtraction) to find its simplest form.
Example:
• However, the quickest way to determine a unit rate is to
divide the numerator by the denominator and place the
quotient over a 1.
Example:
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)
Rate of Change
Essential Understanding:
• A line graph can be used to organize and
illustrate equivalent rates. This is preferable to
a ratio table, when illustrating rate of change.
Such as changes over time, speed, distance,
and profit/loss ($).
Please open your book to page 162
Watch This
• http://learnzillion.com/lessons/615-graphingrate-problems-using-a-table
(7 minutes)
Practice
Take out your white boards.
Wrap it Up
• Review
• Questions
• Exit Tickets
Day 3
Bell Work
A store sold 255 DVDs in 5 days. If sales continue
at this rate, how many DVDs can the expect to
sell by the 10th day? 15th day? 30th day?
Graph the rate of change for each day given on
the provided graph card.
Homework Check
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….
Solve unit rate problems
including those involving
unit pricing and constant
speed.
Station Rotations
1. Write your exit ticket.
2. Pack up everything but a pencil and a
calculator.
3. You will have 15 minutes per station
1st Rotation
2nd Rotation
3rd Rotation
4th Rotation
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)
Wrap it Up
• Review
• Questions
• Exit Tickets
Day 4
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
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.
pOp Quiz
• Take out a pencil and a calculator.
• Clear your desk of everything else.
Let’s Review
Complete Chapter
Study Guide
Wrap it Up
• Review
• Questions
• Exit Tickets
Day 5
No School

I Can….
Use ratio and rate
reasoning to solve realworld and mathematical
problems
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?
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