Lesson Planning

1. 6th
Grade
Math:
Equivalent
Ratios
Standards:
• 6.4(E)
Represent
ratios
and
percents
with
concrete
models,
fractions,
and
decimals.
• 6.4(C)
Give
examples
of
ratios
as
multiplicative
comparisons
of
two
quantities
describing
the
same
attribute.
• 6.4(B)
Apply
qualitative
and
quantitative
reasoning
to
solve
prediction
and
comparison
of
real-­‐world
problems
involving
ratios
and
rates
Unit
Focus:
The
focus
of
this
unit
is
to
develop
an
understanding
of
ratios
and
rates.
Students
learn
that
ratios
compare
the
same
types
of
measures
and
represent
part:whole
and
part:part
relationships.
They
also
learn
that
ratios
that
compare
different
types
of
measures
are
called
rates.
Students
apply
these
concepts
to
a
variety
of
real
world
and
mathematical
situations,
including
problems
involving
measurement
conversions
and
percents.
In
the
culminating
performance
task,
students
plan
a
recipe,
using
ratios
to
find
the
quantities,
unit
rates,
and
costs
of
ingredients
for
different
numbers
of
servings.
Objectives/Outcomes:
Students
will
be
able
to…
• Identify
and
write
ratios.
• Represent
ratios
with
concrete
models.
• Represent
ratios
with
fractions
and
decimals.
• Represent
percents
with
concrete
models.
• Represent
percents
with
fractions
and
decimals.
• Generate
equivalent
ratios.
• Use
ratio
and
rate
reasoning
to
solve
real-­‐world
and
mathematical
problems.
• Solve
unit
rate
problems
(including
unit
pricing
and
constant
speed).
• Solve
percent
problems,
including
finding
a
percent
of
a
quantity
as
a
rate
per
100
and
finding
the
whole,
given
the
part
and
the
percent.
• Use
multiple
representations
such
as
tape
diagrams,
double
number
line
diagrams,
or
equations
to
solve
rate
and
ratio
problems.

2. Prior
Knowledge
Required:
• Students
will
be
able
to
multiply
fractions.
• Students
are
able
to
find
equivalent
fractions
without
manipulatives.
Big
Ideas:
• Connecting
ratio
and
rate
to
whole
number
multiplication
and
division
• Using
concepts
of
ratio
and
rate
to
solve
problems
Essential
Questions:
• When
is
it
useful
to
be
able
to
relate
one
quantity
to
another?
• How
are
ratios
and
rates
used
in
everyday
life?
How
would
life
be
different
without
ratios
and
rates?
Academic
Vocabulary:
• Ratio
• Rate
• Compare
• Equivalent
• Quantity
Content
and
Pedagogy:
Ratio:
A
ratio
expresses
the
relationship
between
two
quantities.
Ratios
compare
two
measures
of
the
same
types
of
things.
Examples:
the
number
of
one
color
of
marble
to
another
color
of
marbles,
or
the
number
of
cats
to
dogs.
Ratios
can
compare
parts
to
a
whole
(part:whole).
Example:
12
of
the
15
students
are
playing
soccer
(12/15).
Ratios
can
also
compare
a
part
of
one
whole
to
another
part
of
the
same
whole
(part:part).
Example:
The
ratio
of
green
marbles
in
the
jar
to
red
marbles
in
the
jar
is
4:2.
Ratios
can
be
expressed
in
following
notation:
x:y,
x/y,
or
x
to
y.
Rate:
When
a
ratio
compares
two
different
types
of
measures,
it
is
called
a
rate.
Examples:
5
gallons
of
paint
are
needed
to
paint
8
walls
(5:8).
3
shirts
for
$20
(3/$20)

3. Unit
Rate:
A
unit
rate
is
a
rate
which
compares
a
quantity
to
one
of
the
other
quantity.
Examples:
Miles
per
hour,
cost
per
foot,
eggs
per
carton.
Proportion:
A
proportion
is
an
equation
written
in
a
form
that
states
that
two
ratios
are
equal.
A/B
=
C/D
Anticipated
Student
Preconceptions/Misconceptions:
•
Students
may
be
confused
about
the
order
of
the
quantities.
For
example,
a
comparison
of
2
wins
to
3
losses
is
written
as
2:3,
and
not
3:2.
It
is
helpful
if
students
begin
labeling
the
quantities
of
the
things
they
are
comparing
both
in
writing
and
orally.
•
Students
may
have
difficulty
distinguishing
a
part:part
ratio
from
a
part:whole
ratio.
For
example,
“There
are
12
girls
compared
to
11
boys
in
the
class
(12:11),
but
12
of
the
23
students
in
the
class
are
girls
(12:23).”
Lesson
One
Sequence:
Briefly
introduce
the
concept
of
ratio
and
the
key
vocabulary
and
notation
associated
with
it.
Nearpod
Presentation:
• The
presentation
begins
by
having
students
explain
in
picture,
numbers,
or
words
what
ratio
means.
• The
definition
of
ratio
is
given,
along
with
a
pictorial
and
numerical
representation.
• Simplifying
ratios
is
discussed.
If
two
ratios
simplify
to
the
same
things,
then
they
are
equivalent.
• To
find
an
equivalent
ratio,
multiply
or
divide
the
given
ratio
by
a
form
of
“1”.
• Student
practice:
You
mix
green
paint
in
the
ratio
of
2
parts
blue
to
5
parts
yellow.
What
is
the
ratio
of
blue
to
yellow
paint?
Students
respond
by
writing
their
answer
on
the
iPad
screen,
and
press
“submit”.
• The
next
slide
shows
the
correct
answer.
• Equivalent
ratios
can
be
organized
using
a
table.
• Student
practice:
Complete
the
ratio
table
for
orange
paint
mixed
from
3
parts
red
to
8
parts
yellow.
Students
will
fill
in
the
table
to
create
equal
ratios.
• The
next
slide
shows
the
correct
answers,
along
with
teacher
explanation.
View
a
teaching
video
on
ratios:

4. • At
the
learnalberta.ca
website
there
are
a
variety
of
teaching
videos.
This
is
a
Mathematics-­‐Grade
6
Spy
Guys
Ratio
video.
http://www.learnalberta.ca/content/mesg/html/math6web/index.html?pag
e=lessons&lesson=m6lessonsshell03.swf
• http://www.youtube.com/watch?v=eT1yYqmjHPY
• http://www.youtube.com/watch?v=yztq_ELjfSw&feature=related
(Teaching
videos
focusing
on
the
definition
of
ratio
and
the
ways
that
a
ratio
can
be
expressed.)
Revisit
student
ideas:
• Are
there
any
ideas
that
need
to
be
refined
based
on
the
activities
and
the
videos?
• Do
students
want
to
contribute
additional
thoughts
to
the
chart
about
ratios?
• Do
they
want
to
delete
flawed
ideas
from
the
chart?
Extended
Learning/Practice
(homework):
• Students
find
three
examples
of
ratios
in
the
real
world.
They
can
find
examples
on
the
internet,
in
newspapers,
or
in
their
own
homes.
For
each,
they
write
down
the
ratio
and
discuss
its
meaning.
Example:
The
ratio
of
citizens
who
voted
in
the
last
election
compared
to
those
who
didn’t
vote
was
1:6.
Analysis:
Not
very
many
people
voted.
A
few
people
are
making
decisions
for
the
whole
city.
Example:
Two
of
my
sisters
have
jobs
after
school.
The
ratio
of
their
hourly
pay
is
$7:$10.
Analysis:
The
sister
who
makes
$7
an
hour
could
ask
for
a
raise
in
her
hourly
rate,
but
she
is
younger
and
has
less
experience,
so
it
is
probably
fair.
Lesson
Two
Sequence:
• In
this
lesson,
the
focus
is
on
writing
ratios
that
accurately
represent
mathematical,
tabular,
or
pictorial
situations.
In
the
next
lesson,
students
will
be
asked
to
express
ratios
in
simplest
form.
• Students
work
in
groups
of
3
to
briefly
share
their
“ratios
in
the
real
world
homework”.
Each
group
shares
one
good
example
with
the
rest
of
the
class.
Student
1
reads
the
example
so
that
the
teacher
can
record
it
on
the
board.
Student
2
tells
which
notation
to
use
in
the
written
ratio.
Student
3
explains
the
meaning
of
the
ratio
and
any
inferences
that
can
be
made.
This
activity
reviews
the
previous
lesson,
and
pre-­‐assesses
student
readiness
for
writing
ratios.
• Students
practice
writing
ratios
based
on
the
following
types
of
problems:
o Pictures
of
objects
in
scattered
arrangements

5. o Working
backward:
In
the
diagram,
what
does
the
ratio
___:___
represent
o Shapes
divided
into
equal
parts
with
some
parts
shaded.
Write
the
ratios
for
shaded
to
non-­‐shaded
or
shaded
to
total.
Technology
resources:.
These
resources
facilitate
students
model
with
mathematics
(SMP.4)
The
first
one
may
be
very
useful
for
students
with
disabilities
or
ELLs.
• http://www.thinkingblocks.com/ThinkingBlocks_Ratios/
TB_Ratio_Main.htmlInteractive
site
where
students
are
taught
how
to
use
blocks
to
model
ratio
problems.
Problems
may
ask
students
to
find
one
of
the
two
quantities
in
the
ratio,
the
difference
between
the
two
quantities,
or
the
total.
Provides
a
video
with
step-­‐by-­‐step
clear,
visual,
auditory
demonstration
of
using
blocks
to
solve
ratio
problems.
Teachers
can
use
to
guide
instruction
with
block
manipulatives
,
or
students
can
virtually
manipulate
blocks.
http://illuminations.nctm.org/LessonDetail.aspx?
id=L722
Pairs
(or
groups)
of
students
use
a
cup
of
beans
to
find
ratios
to
express
the
number
of
marked
beans
in
the
cup
compared
to
the
total
number
of
beans
in
the
cup.
Theoretically,
each
sample
should
be
essentially
the
same.
The
decimal
representation
of
each
ratio
confirms
that
ratios
are,
indeed,
approximately
equivalent.
• http://www.math-­‐aids.com.Ratios/
Practice
sheets
that
use
shapes
to
help
students
explore
ratio
relationships.
**Note:
Some
students
may
benefit
from
using
actual
manipulatives
that
they
can
move
around.
Assessment:
Exit
ticket:
We
know
that
all
ratios
can
be
written
in
fraction
form.
Are
all
fractions
ratios?
Why
or
why
not?
(Students
write
a
response,
explaining
their
thinking
on
a
card
or
paper
scrap.
After
putting
their
names
on
them,
they
turn
them
in
on
their
way
out.)
Extended
Learning/Practice
(homework):
• Students
write
ratios
in
the
form
requested
for
6
different
situations.
• Students
create
a
ratio
problem
for
someone
else
to
solve.
Include
pictures
of
objects,
the
question
(what
ratio
the
student
wants
the
solver
to
find),
and
the
form
in
which
the
student
wants
the
ratio
written.

6. CEP
800:
Lesson
Planning
Project
1. Content:
The
focus
of
this
unit
is
to
develop
an
understanding
of
ratios
and
rates.
Students
learn
that
ratios
compare
the
same
types
of
measures
and
represent
part
to
whole
and
part
to
part
relationships.
They
also
learn
that
ratios
that
compare
different
types
of
measures
are
called
rates.
Students
apply
these
concepts
to
a
variety
of
real
world
and
mathematical
situations,
including
problems
involving
measurement
conversions
and
percents.
In
the
culminating
performance
task,
students
plan
a
recipe,
using
ratios
to
find
the
quantities,
unit
rates,
and
costs
of
ingredients
for
different
numbers
of
servings.
The
students
learned
about
fractions
in
the
previous
unit,
and
struggled
greatly
with
the
concept.
Therefore,
they
are
likely
to
have
some
difficulty
with
ratios
and
rates
as
well.
To
help
them
be
more
successful,
manipulatives
and
models
will
be
essential
to
helping
them
understand
the
concept,
and
will
be
used
wherever
possible
throughout
the
unit.
Texas
State
Standards:
• 6.4(E)
Represent
ratios
and
percents
with
concrete
models,
fractions,
and
decimals.
• 6.4(C)
Give
examples
of
ratios
as
multiplicative
comparisons
of
two
quantities
describing
the
same
attribute.
• 6.4(B)
Apply
qualitative
and
quantitative
reasoning
to
solve
prediction
and
comparison
of
real-­‐world
problems
involving
ratios
and
rates
2.
Technology:
I
believe
that
technology
is
a
very
effective
way
of
teaching
new
things
in
the
classroom.
The
teacher
is
able
to
take
a
different
approach,
and
the
students
are
exposed
to
so
many
different
ways
of
finding
information
and
presenting
it.
Technology
should
promote
a
change
in
the
way
that
information
is
learned.
If
it
is
easier
for
a
teacher
to
just
print
out
information
and
have
the
students
read
it
and
complete
a
worksheet,
it
really
is
not
effective.
The
use
of
technology
in
the
classroom
should
give
a
student
a
different
opportunity
to
learn
by
being
actively
engaged
in
what
they
are
doing.
It
is
important
that
the
use
of
technology
is
fun,
but
entertainment
should
not
be
the
primary
focus.
Teachers
can
use
Power
Point
in
the
classroom
in
various
different
ways.
First
and
foremost,
this
program
can
be
used
to
present
information
to
the
students
in
a
slide
show
format.
The
teacher
can
include
pictures,
internet
links,
video
clips,
and
sound
to
the
presentation
to
make
it
more
interesting
to
the
audience.
Not
only
is
a
Power
Point
slideshow
a
better

7. visual
for
students,
but
it
is
also
very
easy
to
create
and
edit.
Recently,
I
discovered
a
new
spin
on
Power
Point
that
will
forever
change
the
way
that
I
use
Power
Point
in
my
classroom.
I
was
introduced
to
Nearpod
during
at
a
faculty
meeting
by
another
staff
member
who
had
discovered
it
and
wanted
to
share
it
with
all
of
us.
Nearpod
allows
you
to
take
your
Power
Point
Presentations
and
upload
them
to
their
app,
and
use
them
in
a
more
interactive
way.
You
can
create
multiple
choice
and
open-­‐ended
questions
to
include
in
the
presentation
to
use
to
check
for
understanding.
Each
student
will
have
their
own
device
(ie.
iPad,
iPod,
smart
phone),
and
they
will
need
to
download
the
app.
They
will
login
using
a
class
code
to
be
able
to
view
the
presentation.
Once
logged
in,
I
will
begin
my
presentation.
The
students
are
able
to
view
it
directly
in
front
of
them
on
their
device.
Along
the
way
there
are
questions
that
students
can
answer,
and
I
can
see
their
responses
on
my
screen.
The
teacher
can
see
instantly
whether
the
students
understand,
or
if
the
content
needs
further
explanation.
In
addition,
there
are
several
math
websites
available
that
have
interactive
lessons
that
are
similar
to
using
math
manipuatives.
Websites
such
as
Thinking
Blocks
and
Illuminations
are
excellent
math
resources
to
be
used,
and
I
did
have
my
students
use
these
sites
when
I
taught
this
lesson.
3. Pedagogy:
In
creating
this
lesson
for
students
with
special
needs,
I
focused
on
the
cognitivism
learning
theory,
which
focuses
on
how
the
mind
processes
and
uses
information.
Within
cognitivism,
tasks
are
analyzed
and
then
broken
down
into
smaller
steps
or
chunks.
Information
is
then
taught
from
the
most
simple
to
the
most
complex
based
on
the
learner's
prior
knowledge.
Cognitive
learners
use
schema
or
mental
maps
to
help
organize
information
and
tie
the
material
to
existing
knowledge
to
aid
memorization.
This
method
pays
attention
to
the
learner's
specific
differences
by
accommodating
and
approaching
information
in
various
ways.
This
lesson
would
be
considered
to
be
active
learning
because
they
are
engaged
in
listening,
reading,
writing,
and
solving
problems
throughout
the
lesson.
I
begin
the
lesson
by
having
students
explain
what
a
ratio
is
by
using
numbers,
pictures,
or
words.
This
assesses
their
prior
knowledge
to
the
subject.
I
begin
the
lesson
by
giving
students
the
definition,
along
with
pictorial
and
numerical
representations.
I
take
this
information
and
build
onto
it,
having
students
practice
reading
a
word
description,
and
translating
it
into
a
number
ratio.
We
then
go
on
to
build
ratio
tables,
and
determine
the
relationships
between
the
numbers,
and
how
they
are
equivalent.
This
type
of
presentation
will
appeal
to
both
visual
learners
and
auditory
learners,
because
students
will
be
able
to
see
the
information,
and
hear
the
teacher
explain
the
information.
They
also
have
the
opportunity
for

8. independent
practice,
and
instant
feedback.
Following
the
presentation,
students
will
be
able
to
generate
equivalent
ratios.
4. Content
&
Pedagogy:
I
chose
this
particular
strategy
when
working
with
struggling
learners
to
help
them
stay
engaged
throughout
the
presentation,
but
it
also
allows
me
to
check
how
they
understand
the
content.
Had
it
been
a
regular
old
fashioned
Power
Point,
I
may
not
have
their
full
attention
throughout.
Furthermore,
to
check
for
understanding,
I
would
have
called
on
one
student.
Using
Nearpod,
I
am
able
to
see
the
responses
of
all
of
the
students.
One
of
the
benefits
of
the
Nearpod
app
is
that
students
are
not
able
to
scroll
ahead
in
the
presentation.
The
teacher
is
in
full
control
at
all
times.
Furthermore,
the
app
is
the
only
thing
that
is
open
on
the
iPad
when
the
presentation
is
running.
Unlike
on
the
computer,
where
student
often
minimize
the
screen,
and
try
to
work
on
other
things
or
websites
while
the
teacher
is
talking.
If
the
student
exits
the
presentation,
the
teacher
is
notified.
This
keeps
the
students
on
task,
and
they
can
be
held
accountable
if
they
are
not
doing
what
they
are
supposed
to
be
doing.
In
addition,
this
technology
is
useable
by
all
students
of
different
abilities.
It
is
very
easy
to
use,
and
students
don’t
have
to
be
able
to
type
fast
to
respond
to
questions,
and
there
isn’t
a
great
deal
of
reading.
They
can
use
their
finger
or
a
stylus
to
respond
to
questions
on
the
touch
screen.
5. Technology
&
Pedagogy:
The
technology
that
I
chose
compliments
the
teaching
strategies
well,
because
it
introduces
the
content
in
a
fun
and
engaging
manner,
and
then
students
have
the
opportunity
to
practice
problems
using
interactive
math
manipulatives.
The
content
is
also
taught
to
the
level
of
the
students
in
a
special
education
classroom.
The
introduction
breaks
down
the
different
aspects
of
ratios
and
rates,
defining
the
vocabulary
words,
presenting
pictures
and
models,
and
slowly
putting
the
topics
into
practice
by
writing
ratios,
and
then
later
solving
problems.
The
lesson
gradually
builds
onto
the
topic
at
an
appropriate
pace
for
students
with
learning
disabilities.
6. Technology
&
Content:
It
is
sometimes
difficult
to
incorporate
technology
into
a
math
class.
I
am
always
looking
for
new
math
websites
that
my
students
can
use
that
act
as
manipulatives.
I
also
use
Educreations
and
Powtoon
to
create
“how
to”
videos,
and
post
them
to
my
class
website.
Students
are
then
able
to
view
the
videos
at
home
when
they
are
completing
their
homework
or
studying
for
a
test.
The
great
thing
about
videos
is
that
they
can
be
paused
and
played
over
and
over
again.
For
this
lesson,
technology
was
used
to
introduce
the
topic
of
equivalent
fractions,
and
students
used
the
Thinking
Blocks
and
Illuminations
websites

9. to
work
out
practice
problems
involving
equivalent
ratios
and
solving
unit
rates.
It
is
very
important
for
students
with
learning
disabilities
to
be
able
to
use
manipulatives
when
learning
about
a
new
math
topic.
These
websites
allow
them
to
solve
problems
using
maniputlaives,
while
also
breaking
down
pieces
of
the
problem
in
a
more
logical
way.
7. Assessment:
As
discussed
before,
using
Nearpod,
I
was
able
to
assess
student
understanding
of
the
content
through
the
use
of
multiple
choice
and
open
ended
questions
at
different
points
throughout
the
presentation.
This
was
a
great
way
for
me
to
know
whether
I
needed
to
revisit
topics,
or
if
it
was
appropriate
to
move
on.
Furthermore,
after
students
have
the
opportunity
to
practice
using
the
ratios
and
rates
website
learning
tools,
they
will
complete
an
exit
ticket
about
relating
ratios
and
rates
to
real
life
situations.