21st Century Lessons
Unit Conversions Using
Equivalent Ratios
Primary Lesson Designer:
Lisa Schad
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This project is funded by the
American Federation of Teachers.
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21st Century Lessons – Teacher Preparation
Please do the following as you prepare to deliver this lesson:
•
Spend AT LEAST 30 minutes studying the
Lesson Overview, Teacher Notes on each
slide, and accompanying worksheets.
•
Set up your projector and test this PowerPoint file to make
sure all animations, media, etc. work properly.
•
Feel free to customize this file to match the language and
routines in your classroom.
*1st Time Users of 21st Century Lesson:
Click HERE for a detailed description of our project.
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Lesson Overview (1 of 4)
Lesson Objective
Students will be able to convert a measurement from one unit to
another using equivalent ratios. LANGUAGE OBJECTIVE: SWBAT
learn & use unit conversion vocabulary.
Lesson Description Students will build on their understanding of equivalent ratios from
the ratios unit to convert units in a method that precedes and will
eventually be replaced by formal proportions work in 7th grade.
Instead of a cross-multiplication solution, students are taught to set
up equivalent ratios in fraction form (much as they would do for
equivalent fractions) and use a common conversion factor to make
the ratios equivalent. This lesson is almost exclusively guided
practice so that students can develop a confidence and competence
with the method. There is a later lesson that applies these skills –
both are in service of CCSS 6RP3d. The language work in this lesson
is to reinforce the understanding of what this skill is. Students learn
vocabulary, connect to their understanding of measurement units and
make connections to equivalent fractions and the earlier equivalent
ratios work in this unit by speaking with other students.
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Lesson Overview (2 of 4)
Equivalent ratios – ratios in fraction form that have the same relationship of 2
Lesson
Vocabulary quantities.
Conversion - The act of changing from one thing to another
Unit - A standard quantity used to measure. Example: inches, cm
Conversion Factor - A number that is multiplied or divided to change from one
system of measurement to another.
Units of measure – a standard quantity used to measure (ex in or cm)
Rate - a ratio showing the relationship of 2 different measurement units
Unit rate – a rate where one measurement has a value of 1.
Materials
Powerpoint, In-Class worksheet, Unit Conversion Tables, Homework, calling
sticks, timer (Additional Materials: Advanced Worksheet and for students who
require accommodations/modifications – a How To Guide and a Class
worksheet with larger spaces.)
Common
Core
State
Standard
6RP3d Use ratio and rate reasoning to solve real-world and mathematical
problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams,
double number line diagrams, or equations. Use ratio reasoning to convert
measurement units; manipulate and transform units appropriately when
multiplying or dividing quantities. http://www.corestandards.org/
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Lesson Overview (3 of 4)
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Scaffolding
This lesson is designed using the SIOP model of instruction which is
specifically attuned to the needs of English-language learners.
These methods utilize multiple modalities making the lesson also
particularly attuned to special learning needs. The new skill in this
lesson is broken down into clearly described steps, students follow
along on a clearly marked worksheet, and there are opportunities
to work with other students, receive immediate clarification for
how to use the method correctly, and to speak and listen about the
method.
Enrichment
Students who master the skill quickly should be encouraged to do
many more conversions as the more practice one gets the more the
skill becomes reliable and easily retrievable in the future. An
advanced additional practice worksheet is available.
Online Resources for
Absent Students
At this LearnZillion link http://learnzillion.com/lessonsets/87using-ratios-to-convert-unit-measures students can see multiple
videos on unit conversion even if the method is slightly different
from the one presented in this lesson.
Lesson Overview (4 of 4)
Before and After
Students have learned multiple methods for considering ratio
relationships and should, at this point, be ready for a shorter
method for moving from one equivalent ratio to another. This
lesson builds on the strengths students should now have in
thinking about equivalent ratios (for example in a table) to a
method that is all but in name a proportion. This is intentional as
building and solving proportions is a big focus of the work in this
strand in grade 7. This lesson should help students to be ready for
making the transition to more traditional ratio/proportion work.
Topic Background The skill of unit conversion has immediate real-world benefits that
later word problems can illustrate and is also extremely useful for
many of the sciences. The Common Core Progressions document
encourages thinking about unit conversion factors as unit rates to
better build off the ratios work that the standards outline. This
lesson attempts to bridge that work with a method that will make
use of student strengths (ratio thinking, equivalent fractions) as
well as preparing them for proportional reasoning.
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Warm Up
OBJECTIVE SWBAT convert a measurement from one unit to another
using equivalent ratios.
LANGUAGE OBJECTIVE: SWBAT learn & use unit conversion vocabulary.
Directions: Make equivalent ratios.
x 2¼
x 3.5
1.)
1 3.5
=
2 7
x 3.5
2.)
2
1
1
4
=
9
4
x 2.5
3.)
x 2¼
5 12.5
=
6 15
x 2.5
1 4 9 9
4´2 = ´ = =9
4 1 4 1
Agenda
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Agenda:
OBJECTIVE: Students will be able to convert a measurement from one
unit to another using equivalent ratios.
LANGUAGE OBJECTIVE: SWBAT learn & use unit conversion vocabulary.
1) Warm Up - you
2) Launch – Vocabulary Definitions - you
3) Launch – What are units? – partners
4) Explore – Roller Coaster Problem - you
5) Mini-Lesson – New Skill: Unit Conversions - me
6) Guided Practice – Convert units practice problems - us
7) Summary - us
8) Exit Ticket - you
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Launch - Vocabulary
How many inches is 2 feet?
There
inches in 1 foot.
2Hint:
feet
isare
2412inches.
1 foot = 12 inches
2 feet = 24 inches
Agenda
10
Launch - Vocabulary
How many inches is 2 feet?
2 feet is 24 inches.
You have just made a unit conversion.
1 foot = 12 inches
Feet and inches are the
units of measure.
this is your conversion factor
Today we will learn how to convert units with ratios.
Agenda
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Launch - Vocabulary
One minute: Write the definitions of
these terms on your worksheet.
• Conversion
• The act of changing from one thing
to another
• Units (of measure) • A standard quantity used to
measure. Example: inches, cm
• Conversion Factor • The ratio of a measurement in one
unit to the equivalent numerical
value in another unit. (ex. 12
inches/1 foot = 12/1 or 12)
Agenda
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Launch – Think, Write, Pair, Share
Pair: Talk
to your
elbow
partner.
Share
units.
Share:
Students
will
be
selected
at units
random
Think:
What
are
some
units
for measuring
Write:
Write
at least
two
different
forinto Write
1
Writecategory
units
that
you
have before. min
share
3down
units
from
each
category.
each
below?
measuring
inany
each
category
ondidn’t
your worksheet.
Length
Volume
Weight
Agenda
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Launch – Think, Write, Pair, Share
Share: Students will be selected at random to
share 3 units from each category.
Length
Volume
Weight
Inch
Foot
Yard
Mile
Cup
Fluid ounce
Quart
Pint
Gallon
Pound
Ounce
Ton
Centimeter
Millimeter
Meter
Kilometer
Liter
Milliliter
1
min
Gram
Kilogram
Metric ton
Agenda
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Explore
Emily, Lilo, and Henry are
going to go to Six Flags on
a field trip. They all want
to go on the Batman
roller coaster ride, but
they have to make sure
they are each tall enough
to go on the ride.
Agenda
15
Explore
Their teacher looks up the
height requirement and it
is 54 inches. The students
know their heights in feet
but not in inches. Help
them to figure out if they
are each tall enough to
ride the Batman roller
coaster.
Agenda
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Explore
Emily
4 feet, 4 inches
Lilo
4 ½ feet
Henry
4 ¾ feet
You must be 54 inches tall to ride the Batman roller
coaster. Who can and who cannot go on this ride?
Take 5 minutes to work on this problem on
your own.
Agenda
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Explore
Emily
4 feet, 4 inches
Lilo
4 ½ feet
Henry
4 ¾ feet
You must be 54 inches tall to ride the Batman roller
coaster. Who can and who cannot go on this ride?
Think, Write, Pair, Share: What makes this
problemHow
Share:
difficult?
could we make this problem
Write your
easier
to do?
thoughts on your worksheet.
Then share with your partner.
Agenda
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New Skill – Unit Conversion Using Ratios
We need to
convert units!
Let’s change the 54 inches to feet.
First we need the unit conversion rate. Let’s
look on a unit conversion table to find the
information.
Agenda
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Mini-Lesson: Unit Conversion Using Ratios
Let’s change the 54 inches to feet.
A rate is a ratio
showing the
relationship of 2 different
measurement units.
First we need the unit conversion rate.
Put your finger on the unit conversion rate.
Agenda
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Mini-Lesson: Unit Conversion Using Ratios
Next we will write the conversion rate as a
ratio in fraction form:
Does it matter if I
write the ratio with
1 foot on the top or
the bottom?
1 foot or 12 inches
12 inches
1 foot
What do you think?
This is a unit rate because it is 12 inches per 1 foot.
A unit rate is a
rate where one
measurement has a value of 1.
Agenda
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Launch
convert
means change
To convert
54 inches into feet
we will make an
equivalent ratio. We
write the unit
conversion ratio as a
rate in fraction form
and set it equal to
another ratio.
1 foot
=
12 inches
feet
inches
Agenda
22
Launch
We write the unit conversion ratio as a rate
in fraction form and set it equal to another
ratio.
1 foot
feet
12 inches
You could also write:
=
inches
12 inches =
1 foot
inches
feet
The important thing to remember is that the units on top
must match. And the units on the bottom must match.
Agenda
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Launch
Next we put in the number we are
converting into the second ratio. We are
converting 54 inches into feet. Should we put
54 on the top or the bottom of the ratio?
1 foot
=
12 inches
feet
54 inches
inches
Agenda
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Launch
Now, to find the feet, we need to find the
factor we multiply by to make these two
ratios equivalent.
That is,
What do I multiply
12 by to get 54?
1 foot
feet
=
12 inches
54 inches
Put your
hand
Where
have
weup
x?
Equivalent means
equal value.
whenthis
youbefore
think in
done
you lesson?
know.
this
Agenda
25
Launch
Next, to find the feet, we need to find the
factor we multiply by to make these 2 ratios
equivalent.
12 x ___ = 54
1 foot
feet
=
12 inches
54 inches
x?
so…
54 ÷ 12 =4.5
___
Agenda
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Launch
I use the same factor top and bottom to
make an equivalent ratio.
x
4.5
So,
54 inches = 4.5 feet
1 foot
4.5 feet
=
Now we can solve
12 inches
54 inches
x
4.5
the problem!
4.5 is your
conversion factor.
Agenda
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Launch
Emily is 4 feet 4 inches
Lilo is 4½ feet tall
Henry is 4¾ feet tall
Remember that
1 foot is 12 inches
so 0.5 feet is 6 inches.
You must be 54 inches or 4.5 feet to ride the coaster.
So who can and who cannot ride Batman?
Take a few minutes to find the answer to this question. Write
it on your worksheet.
Agenda
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Launch
Time to Discuss It!
Emily is 4 feet 4 inches Cannot go
Lilo is 4½ feet tall Can go
Henry is 4¾ feet tall Can go
You must be 54 inches or 4.5 feet to ride the coaster.
Lefty
tellcan
Righty:
Explain
howride
to use
equivalent ratios
So who
and who
cannot
Batman?
to convert 54 inches to 4.5 feet.
Righty tell Lefty: Explain how to use the 4.5 feet to
solve the problem.
Agenda
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Practice
Let’s practice setting up equivalent ratios to solve
unit conversion problems.
Practice Problem #1
2.5 yards = ____ feet
Check your worksheet if
you forget your vocabulary.
First, find the
conversion rate.
Then, set up the
conversion rate as a
ratio in fraction form.
Agenda
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Practice
Let’s practice setting up equivalent ratios to solve
unit conversion problems.
Practice Problem #1
2.5 yards = ____ feet
3 feet
1 yard
First, find the
conversion factor.
Then, set up the
conversion factor as a
rate in fraction form.
Agenda
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Practice
Let’s practice setting up equivalent ratios to solve
unit conversion problems.
Practice Problem #1
2.5 yards = ____ feet
3 feet
1 yard
=
feet
yards
Now make another
equivalent ratio.
Units must be the
same across the top
and the bottom.
Agenda
32
Practice
Let’s practice setting up equivalent ratios to solve
unit conversion problems.
Practice Problem #1
2.5 yards = ____ feet
3 feet =
feet
1 yard 2.5 yards
Then put the
information from the
problem into the
second ratio.
Agenda
33
Practice
Let’s practice setting up equivalent ratios to solve
unit conversion problems.
Practice Problem #1
2.5 yards = ____ feet
3 feet =
feet
1 yard 2.5 yards
?
x x2.5
Find the conversion
factor that we multiply
or divide by to move
from left to right.
1 x ___ = 2.5
Agenda
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Practice
Let’s practice setting up equivalent ratios to solve
unit conversion problems.
Practice Problem #1
7.5 feet
2.5 yards = ____
x 2.5
3 feet = 7.5 feet
1 yard 2.5 yards
Multiply by the same
factor top and
bottom to make an
equivalent ratio.
x 2.5
Agenda
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Practice
Practice Problem #2
3.5 cups
28 fluid ounces = ____
Practice Problem #3
36 ounces
2¼ pounds = ____
x 3.5
xx2¼
?
1 cup = 3.5 cups 1 pound 2¼ pounds
=
8 fl.oz. 28 fl.oz. 16 oz
36 oz
xx3.5
?
x 2¼
Agenda
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Practice
Practice Problem #4
4 meters
13.2 feet = ____
x4
Practice Problem #5
2.25 kg
5 pounds = ____
x ?5
1 meter = 4 meters 1 pound 5 pounds
=
3.3 feet 13.2 feet 0.45 kg 2.25 kg
x 4?
x5
Agenda
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Practice
Practice Problem #6
5 liters
10 quarts = ____
x 2.5
2.5 gallons
1 gallon
=
10 quarts
4 quarts
x x2.5
?
xx2.5
?
2.5 gallons
1 gallon
=
5 liters
3.8 liters
x 2.5
Agenda
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Summary
Today we learned how to convert units using equivalent fractions. Fill
in the vocabulary words to complete the explanation of how to do it.
1.) Write the ____________
_________ as a ratio in fraction
form.
2.) Make an ___________ _______
by setting it equal to another ratio.
3.) We put the number we know into
the 2nd ratio & find the ___________
___________.
4.) Then _________ the units by
multiplying by the conversion factor.
x ?2
2 feet
1 foot
=
12 inches 24 inches
x2
Word Bank:
convert ratio
conversion rate
equivalent ratio
conversion factor
Agenda
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Summary
Today we learned how to convert units using equivalent fractions. Fill
in the vocabulary words to complete the explanation of how to do it.
conversion
1.) Write the ____________
rate
_________
as a ratio in fraction
form.
2.) Make an ___________
equivalent _______
ratio
by setting it equal to another ratio.
3.) We put the number we know into
conversion
the 2nd ratio & find the ___________
factor
___________.
convert the units by
4.) Then _________
multiplying by the conversion factor.
x ?2
2 feet
1 foot
=
12 inches 24 inches
x2
Word Bank:
convert ratio
conversion rate
equivalent ratio
conversion factor
Agenda
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Exit Ticket
Solve the problem. Put your thumb up when you are done.
90 inches = _____ yards
Choose the best answer from the four given below.
When you hear the answer you chose, put your hand up.
Write it down next to your work.
A.
B.
C.
D.
1½ yards
2½ yards
30 yards
270 yards
Agenda
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21st Century Lessons
The goal…
The goal of 21st Century Lessons is simple: We want to assist teachers, particularly in
urban and turnaround schools, by bringing together teams of exemplary educators
to develop units of high-quality, model lessons. These lessons are intended to:
•Support an increase in student achievement;
•Engage teachers and students;
•Align to the National Common Core Standards and the Massachusetts curriculum
frameworks;
•Embed best teaching practices, such as differentiated instruction;
•Incorporate high-quality multi-media and design (e.g., PowerPoint);
•Be delivered by exemplary teachers for videotaping to be used for professional
development and other teacher training activities;
•Be available, along with videos and supporting materials, to teachers free of charge via the
Internet.
•Serve as the basis of high-quality, teacher-led professional development, including mentoring
between experienced and novice teachers.
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21st Century Lessons
The people…
Directors:
Kathy Aldred - Co-Chair of the Boston Teachers Union Professional Issues Committee
Ted Chambers - Co-director of 21st Century Lessons
Tracy Young - Staffing Director of 21st Century Lessons
Leslie Ryan Miller - Director of the Boston Public Schools Office of
Teacher Development and Advancement
Emily Berman- Curriculum Director (Social Studies) of 21st Century Lessons
Carla Zils – Curriculum Director (Math) of 21st Century Lessons
Brian Connor – Technology Coordinator
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