Transcript Equivalent Rational Numbers and Percents Unit: 01 Lesson: 01

Equivalent Rational
Numbers and
Percents
Unit: 01 Lesson: 01
Equivalent Rational Numbers and Percents
Unit: 01 Lesson: 01 Table of Contents
1. Lesson Synopsis
2. TEKS
3. Content and Language Objective
4. Vocabulary
5. TAKS Warm-up (one for every day)
6. Engage
7. Explore/Explain (1-9)
8. Elaborate
9. Evaluate
The students will match equivalent forms of
non-negative rational numbers (whole numbers,
fractions and decimals). Different forms of nonnegative rational numbers are generated and
the strategies used to generate equivalent nonnegative rational numbers are discussed.
Percents are represented using manipulatives,
fractions and decimals. Various strategies to
compare and order non-negative rational
numbers are investigated.
(6.1) Number, operation, and quantitative
reasoning. The student represents and uses rational
numbers in a variety of equivalent forms.
(6.1A) compare and order non-negative rational
numbers;(6.1B) generate equivalent forms of
rational numbers including whole numbers,
fractions, and decimals; (6.3) Patterns,
relationships, and algebraic thinking. The student
solves problems involving direct proportional
relationships. (6.3B) represent ratios and percents
with concrete models, fractions, and decimals.
SWBAT generate equivalent forms of nonnegative rational numbers (whole numbers,
fractions, decimals) and percents using a
variety of models. Represent percents with
concrete models, fractions, and decimals
and justify the equivalence of the variety of
forms.
Students will write a paragraph to describe
how the number line is a tool that may be
used to compare and order a set of nonnegative rational numbers.
-ascending
-decimals
-rational
numbers
-percents
-improper
-fractions
fractions
-equivalence
-mixed numbers -whole numbers
-descending
-non-negative
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Day 1
Day 1
What information from the problem do you need
to solve the problem? Explain.
Day 1
What two pizza models can you shade to represent
2/3? Explain
Day 1
A
B
How can you verify that your shaded model
represents 2/3?
Day 1
A
B
How does the four-sixths you shaded relate to the
two thirds you shaded?
Day 1
A
B
Are there two different pizza models that could be
shaded to represent 2/3? Explain.
Day 1
E
D
G
I
What two pizza models can you shade to
represent 3/4? Explain.
Day 1
E
D
G
I
How can you verify that your shaded models
represents ¾?
Day 1
E
D
G
I
How does the six-eighths you shaded relate to the
three-fourths you shaded?
Day 1
I
G
D
E
What two pizza models can you shade to represent
¼? Explain
Day 1
I
G
D
E
How can you verify your shaded models represent
¼?
Day 1
I
G
D
E
How does the two-eighths you shaded relate to the
one-fourth you shaded?
Day 1
A and B
E,D,G,I
E, G, D, I
Would you reconsider some of your choices?
Explain.
Day 1
What information from the problem did you use
to work this problem? Explain.
Day 1
What were your choices for 2/3? ¾? ¼?
Day 1
A and B
E,D,G,I
E, G, D, I
Do you agree or disagree with these choices?
Explain.
Day 1
Does anyone have a different combination of
choices for 2/3? ¾? ¼? Explain your
combination of choices.
Day 1
Have we listed ALL different possible
combinations? Explain.
Day 1
Why was the pizza model for C, F, or H not
selected? Explain.
Day 2 & 3
What labels are on your ruler?
What numbers are on your ruler?
What do you notice about the numbers on your ruler?
If “0” is not shown on your ruler, where is it located?
What do you notice about the distance between each
whole number on the side labeled in inches?
Day 2 & 3
Find the 0 inch and 1 inch mark on your
ruler.
How many equal size spaces are between 0
and 1 on the inch edge of your ruler? 16
How many marks are between 0 and 1 on your
ruler? 15
What do you think these marks represent?
Explain.
Day 2 & 3
If this strip
represents a
“magnified”
inch, where do
we place 0
and 1?
Day 2 & 3
If this strip
represents a
“magnified”
inch, where do
we place 0
and 1?
Day 2 & 3
Day 2 & 3
How can we
mark the
rectangle in
two equal
parts?
Day 2 & 3
What does each part
represent?
How would
we count if
we begin at 0
and count
each equal
size part?
Day 2 & 3
Repeat the
process for the
fourth, eighth
and sixteenth
strip.
Day 2 & 3
What do you notice
about the positions
for 1/2 , 2/4, 4/8
and 8/16 on the
fraction strip rulers?
Day 2 & 3
What other
equivalent fractions
do you notice on
the fraction strip
ruler?
Day 2 & 3
What is another
method we can use
to verify when
fractions are
equivalent?
Day 2 & 3
How is the fraction
strip for sixteenths
similar to the
markings between
0 inch and 1 inch
on your ruler?
Day 2 & 3
How is the fraction
strip for sixteenths
similar to the
markings between
1 inch and 2 inch
on your ruler?
Day 2 & 3
What fraction of an inch is the first consecutive
mark after 0 on your ruler? Second consecutive
mark?
Day 2 & 3
Locate the mark on your ruler between 0 inch and
1 inch to represent ½ of an inch. ¾ of an inch. 3/8
of an inch. 1 inch.
Day 2 & 3
What fraction of an inch would 10 consecutive
marks after 0 inch on your ruler represent? 2
consecutive marks?
Day 2 & 3
Locate the mark on your ruler between 0 inch and
2 inches to represent 1 ½ inch. What are some
other names for this location?
Day 2 & 3
What fraction would be 20 consecutive marks
after 0 on your ruler?
Day 2 & 3
In your journal:
Use your ruler to draw a line segment 3/8 of an
inch. Justify your response.
Use your ruler to draw a line segment 2 ¾ inches.
Justify your response.
Use your ruler to draw a line segment 26/16
inches? Justify your response.
Day 4
0
1
How is a ruler like a number line? Different
from a number line?
Day 4
0
1
What would be a good fraction to place first
on this number line?
Day 4
0
1
Does anyone have another card equivalent
to ½? Justify your response.
Day 4
0
1
Does anyone have a card equivalent to 0?
Justify your response.
Day 4
0
1
Does anyone have another card equivalent
to 1? Justify your response.
Day 4
0
1
Does anyone have another card equivalent
to ¼ and where would it be placed on the
number line? 3/4? Justify your response.
Day 4
0
1
Give me an example of two fractions with
the same numerator, but different
denominators?
Day 4
0
1
What do you notice about fractions with the
same numerator, but different
denominators?
Day 4
In your journal:
Draw the number line and…
0
1
Day 5 & 6
How can you verify
½ of the paper has
been shaded?
Day 5 & 6
How can you verify
½ and 2/4 are
equivalent
fractions?
Day 5 & 6
How can you verify
which fraction has
the greater value?
Day 5 & 6
Day 5 & 6
How do we
determine what part
of the twelfths
square pizza model
to shade and
represent 2/3?
Explain
For every 3
fractional parts,
shade 2 parts: 8twelfths of the
model are shaded.
Day 5 & 6
How do we verify
that 2/3 of the
square pizza model
has been shaded?
Explain
Divide the square
pizza model into 3
fractional parts by
outlining groups of
twelfths. There will be
4 twelfths outlined in
each 1-third fractional
part.
Day 5 & 6
How do we determine which part
of the twentieths square pizza
model to shade to represent 2/3?
Explain
For every 3 fractional parts,
shade 2 parts. Because 3 is not a
factor of 20, we would have to
shade a portion of a twentieth
fractional part instead of the
whole fractional part. Therefore it
is not possible.
Day 5 & 6
How do we verify that we are not
able to shade complete twentieths
fractional parts to represent 2/3 of
the twentieths square pizza
model? Explain
Divide the square pizza model
into 3 fractional parts by outlining
groups of twentieths putting 7
twentieths in each group. There
will not be enough fractional
parts to make three complete
groups of “thirds” since 3 is not a
factor of 20.
Day 5 & 6
How do we determine what part of
the hundredths square pizza
model to shade and represent
2/3? Explain
For every 3 fractional parts,
shade 2 parts. Since 3 is not a
factor of 100 the model will not
work.
Day 5 & 6
How do we verify that we are not
able to shade complete
hundredths fractional parts to
represent 2/3 of the hundredths
square pizza model? Explain
If we divide the square pizza
model into 3 fractional parts by
outlining groups of hundredths,
there will not be enough
hundredths since 3 is not a factor
of hundredths.
Day 5 & 6
For problem 1
where is the
numerator
represented in the
diagram?
The shading that
covers eight of
the 12 fractional
parts.
Day 5 & 6
How can we
define numerator?
Indicates how
many of the
fractional parts
we need. In this
case by shading.
Day 5 & 6
For problem 1
where is the
denominator
represented in the
diagram?
The number of
fractional parts in
the model. There
are 12 equal size
parts: twelfths.
Day 5 & 6
How can we
define
denominator?
The type of
fractional part of
the whole. The
number of equal
size parts the
whole has been
divided into.
Day 5 & 6
How can we
define fraction?
Tells the
relationship
between the part
(numerator) and
the whole
(denominator).
Day 5 & 6
Is the fraction
more or less than
½? Explain
Day 5 & 6
What is the
relationship
between the
numerator and the
denominator in
problem 1?
Day 5 & 6
What is the
relationship
between the
numerator and the
denominator in
problem 2?
Day 5 & 6
What is the
relationship
between the
numerator and the
denominator in
problem 3?
Day 5 & 6
What is the
relationship
between the
numerator and the
denominator in
problem 4?
Day 5 & 6
How can we define equivalent fractions?
Two fractions that have equal value if
the whole for each fraction is the same
whole unit.
Day 5 & 6
What are the
equivalent
fractions in
Problem 1?
Day 5 & 6
What are the
equivalent
fractions in
problem 2?
Day 5 & 6
What are the
equivalent
fractions in
problem 3?
Day 5 & 6
What are the
equivalent
fractions in
problem 4?
Day 5 & 6
Homework
Complete Subdividing Fractional Parts
Due TOMORROW
Day 7
How does the number
of strawberry filling
parts in the second
model compare to the
number of strawberry
filling parts in the first
model? Explain
Both models
have the same
area of
strawberry filling.
Day 7
How does the number
of fractional parts in the
second model
compare to the number
of fractional parts in the
first model? Explain
The size of the
cake in both
models is equal.
Day 7
How can you verify
eight twelfths is an
equivalent fraction for
two thirds in model 1
and model 2?
We shaded 2
parts for every 3
in the twelfths
model.
Day 7
How could we record
the representation
between model 1 and
model 2 using number
sentences? Explain.
x4
2
8
=
3
12
x4
Day 7
How many rows do
you have after cutting
the second model into
the given number of
pieces?
2 rows
Day 7
How will you determine
how many pieces of
cake to shade in the
second model to
represent one half from
the first model?
One half means
to shade 1 part
for every 2
fractional parts.
Day 7
Explain why the two
fraction models are
equivalent.
They are both
equal in size.
Day 7
What number sentence
would represent the
relationship between the
shaded parts
(numerators) in the first
and second model?
x2
1
2
=
2
4
x2
Day 7
How are the digits in a
decimal related to the
fractional
representation of the
decimal?
Day 7
How is the place value
position in a decimal
related to the fraction
representation of the
decimal?
The right-most place
value position is the
denominator of the
fraction
Day 7
Homework
Complete “Express” Fractions and
Decimals
Due TOMORROW
Day 8
0.0
Please write the decimal representation of your
fraction card on a sticky note. When finished
place the sticky note on the fraction card so you
can see both the fraction and the decimal.
1.0
Day 8
0.0
1.0
Is your fraction written in simplest form?
If not, how can you write it in simplest form?
Divide the numerator and denominator by the same
number until the only common factor between the
numerator and the denominator is 1.
Day 8
0.0
1.0
What do we know about the relationship between
fractions and decimals?
Decimals may be written as fractions with
denominators of 10,100, 1000 etc…
Day 8
0.0
1.0
What is one method we may use to write
equivalent fractions?
Multiply or divide the numerator and
denominator of a fraction by the same
number to get an equivalent fraction.
Day 8
0.0
1.0
If I give you the problem:
3 X 25 ? = 75
=
4 X 25100
How could you solve it?
Day 8
0.0
1.0
How could you determine if the denominator of
your fraction is a factor of 10, 100, 1000, etc.?
You could divide 10, 100, 1000, etc by the
denominator. If the quotient is a whole
number the answer is yes.
Day 8
0.0
1.0
What is another method we could use to write a
fraction as a decimal?
The fraction bar in a fraction means ÷, so we
could divide the numerator by the
denominator.
Day 8
0.0
1.0
Previously we placed these fraction cards on a
number line. Today we are going to use the
decimal representation of the fraction and place it
on the number line.
Day 8
0.0
1.0
What would be a good decimal to place first?
Explain.
0.5: halfway between 0.0 and 1.0
Day 8
0.0
1.0
What would be the next decimal to place
second? Explain
0.25: halfway between 0.0 and 0.5
Day 8
0.0
1.0
What would be a good decimal to place third?
Explain.
0.75: halfway between 0.5 and 1.0
Day 8
0.0
How can we use the existing decimals on the
number line to place other decimals on the
number line?
Look at the place value positions of the
decimals and compare the digits in the
corresponding place value positions.
1.0
Day 8
0.0
1.0
Which representation, fraction or decimal, do you
prefer to use when placing numbers on a number
line?
Day 8
0.0
1.0
What strategy did you use to place the numbers
on the number line?
Compared my decimal to the reference point
of 0.0, 0.5 and 1.0.
Day 8
0.0
1.0
What do you know about numbers to the left of a
given number?
The numbers to the left are smaller in value
than the numbers to the right.
Day 8
0.0
Using the number line you drew on day 4, write
the decimal representation of each fraction in
your journals/notebooks.
1.0
Day 8
Day 8
How can we convert these fractions to decimals?
Divide the numerator by the denominator
When you convert a fraction to a decimal by dividing the
numerator by the denominator, when do you stop
dividing?
When the remainder equals zero or the digits in
the quotient start repeating
What would be the decimal representation for 8/15? 0.53
What would be the decimal representation for 5/32?
0.15625
How can we verify the twelfths are in the appropriate
place on the number line?
Look at the place value positions of the decimals and
compare the digits in the corresponding place value position.
Day 8
What do you notice about the decimal values close to 0?
Digit in the tenths place value position is 0.
What do you notice about the decimal values close to 1?
Digit in the tenths place value position is 9.
What do you notice about the decimal values close to ½?
Digit in the tenths place value position is 4 or
5.
Day 7
Write the
decimal
representation
below the
equivalent
fraction
representation.
Day 8
Homework
Complete Creating Equivalent Fractions
Due TOMORROW
Day 9
How can you
change this
mixed number
to a decimal?
Day 9
How can you
change this
mixed number
to an improper
fraction?
Day 9
How can you
change this
improper
fraction to a
mixed number?
Day 9
How can you
change this
decimal greater
than 1 to a
mixed number?
Day 9
Day 9
Day 10 &11
If this large square
equals one whole,
what is the fraction
value of one small
square? Explain
One hundredth = 1/100
Day 10 &11
If this large square
equals one whole,
what is the decimal
value of one small
square? Explain
One hundredth = 0.01
Day 10 &11
If this large square
equals one whole,
what is the fraction
value of one column?
Explain
One tenth = 1/10
Day 10 &11
If this large square
equals one whole,
what is the decimal
value of one column?
Explain
One tenth = 0.1
Day 10 &11
If we fold one grid into
two equal parts and
shade 1 of the 2 parts,
how many squares
would we shade?
50 small squares
Day 10 &11
What are the different
fractions we can
show with this
model?
½ = 1 of 2 parts :
5/10 = 5 of 10 columns :
50/100 = 50 of 100 squares
Day 10 &11
What are the different
decimals we can write
for this model?
0.5 = five tenths
or
0.50 = fifty hundreths
Day 10 &11
If we fold one grid into
four equal parts and
shade 1 of the 4 parts,
how many small
squares would we
shade?
25 small squares
Day 10 &11
What are the different
fractions we can
show with this
model? Explain
1/4 = 1 of 4 parts :
25/100 = 25 of 100 squares
Day 10 &11
What is the decimal
we can write for this
model? Explain
0.25 = two tenths, five
hundredths or twenty
five hundredths
Day 10 &11
Glue the two models into your journal/notebook.
Record the different equivalent fraction forms.
Day 10 &11
When we see the fraction, 50/100,
or the decimal, 0.50, we say “fifty
hundredths.” In math, another
name we may use for hundredths
is “percent.” The symbol we use
for percent is “%”, so fifty percent
written with math symbols is 50%.
Day 10 &11
What is another name we can say
for “twenty five hundredths”?
Twenty five percent
Day 10 &11
How would we say twenty five
hundredths using math symbols?
25%
Day 10 &11
What percent
would we
state for the
large square?
Explain
100%
Day 10 &11
How many
small
squares
are
shaded?
Day 10 &11
How would
we write this
as a fraction
with a
denominator
of 100?
Day 10 &11
How
would we
write this
as a
percent?
Day 10 &11
Day 10 &11
If this strip represents one whole
and we fold it into 2 equal parts
and shade 1 of the 2 parts, what
fraction does this model
represent?
½
Day 10 &11
How can we express ½ as a
fraction with a denominator of
100?
50/100
Day 10 &11
How can we express this as a
percent?
50/100 = 50%
Day 10 &11
How is the percent
bar like a fraction
strip?
Both represent a
part of a whole.
The fraction strip
shows the parts
as fractions or
decimals. The
percent bar
shows the parts
as percents.
Day 10 &11
Write an
equivalent
fraction that
has a
denominator
of 100.
Day 10 &11
How would
you write this
as a
percent?
Day 10 &11
What
percent
would you
write for this
decimal?
Day 10 &11
Write the
percent
representation
with the
equivalent
fraction
representation
on your
handout.
Day 10 &11
Homework
Complete Cracking the Code
Due TOMORROW
Day 12
&13
Use the base-ten
blocks to model
each situation and
complete Decimal
Models worksheet.
Day 12
&13
Facilitation Questions-Engage Phase
Which of the base-ten pieces represents tenths?
Hundredths? A whole?
The bar represents tenths. The unit piece represents
hundredths. The flat represents one whole.
What digit is in the tenths place?
Responses may vary. Possible responses: 3, 4, 0
How would you model 0.3 using the base-ten blocks?
Three bars
What digit is in the hundredths place?
Responses may vary. Possible responses: 5, 8, 0
Day 12
&13
Facilitation Questions-Engage Phase
How would you model 0.05 using the base-ten blocks?
Five unit pieces
How could you use the models to order the decimals
from the least to greatest?
Responses may vary. Possible response: by looking for
the model that used the greatest number of unit pieces.
When comparing decimals, what does the symbol <
mean? The symbol >?
Less than, greater than
Day 12
&13
Cut out each piece of
fudge
Use the fudge pieces
and base-ten blocks to
complete the table on
Peanut Butter Fudge
DO NOT complete the
shaded row of the table.
Day 12
&13
What do you observe when using the fudge
piece to cover the base-ten flat?
Responses may vary. Possible response: Each piece of
the fudge covers different amounts of the base-ten flat.
What type of manipulation could you do to the
fudge piece to cover the base-ten flat?
Responses may vary. Possible response: The fudge
piece can be turned around or cut into smaller parts..
How may of that fudge piece covered the baseten flat?
Responses may vary (see answer key)
Day 12
&13
How can you use the number of times the fudge piece
fit on the base-ten flat to determine the fractional part
of the flat covered by the piece of fudge?
Responses may vary. Possible response: The
fractional part would be 1 out of how many times the
piece would need to be repeated to cover the whole
base-ten flat. For example: if it took 5 of the pieces
(each piece the same size) to cover the base-ten flat
then the fractional part of the base-ten flat would be 1
out of 5, or 1/5.
Day 12
&13
How can using the base-ten flat help you determine
how many hundredths your piece of fudge covers?
Responses may vary. Possible response: Since
the base-ten flat is made up of 100 unit pieces,
the number of units the fudge piece covers will
determine its value in hundredths. For example,
if the piece of fudge covers 20 hundredths, then
its value would be 0.20
Day 12
&13
Facilitation questionsExplain phase
What fractional part of
the whole is covered by
piece A? B? C? D?
Day 12
&13
How did you determine what fractional part of the
whole is covered by piece A? B? C? D?
Responses may vary. Possible response: I repeated the
piece until the base-ten flat. Since, the piece coved the
base-ten block 10 times. I knew that the piece of fudge
represented 1/10 of the base-ten flat.
How many hundredths are covered by piece A? B? C?
D?
10, 20, 25, 5
Day 12
&13
How did you determine the number of hundredths to
shade for piece A?
Responses may vary. Possible response: I placed the
piece of the 100 grid and counted the number of
hundredths the piece covered.
What decimal part of the base-ten flat is covered by piece
A? B? C? D?
0.10, 0.20, 0.25, 0.05
How does the number of hundredths covered relate to
your decimal?
Responses may vary. Possible response: Since there are
100 squares, I knew each square was equivalent to onehundredth. Therefore 10 squares are equivalent to 0.10
Day 12
&13
What is the fraction you wrote from the decimal for piece
A? B? C? D?
How did you write the fraction from your decimal?
Responses may vary. Possible response: I could write the
fraction by using place value. For example: The fraction
10/100 is read ten-hundredths: therefore, using place
value as a decimal it would be written 0.10 or 0.1
How is this fraction different from the fraction that
represents the fractional part of the base-ten flat? How
are they the same?
Responses may vary. Possible response: They have
different numerators and denominators. The fractions are
equivalent.
Day 12
&13
What does percent mean?
Responses may vary: Possible response: how many out
of 100
What would be 100% of the base-ten flat? How do you
know?
100 squares
What would be 50% of the base-ten flat? How do you
know?
50 squares
Day 12
&13
A 100-grid is often used to model percents, why do you
think this is?
Responses may vary. Possible response: The 100grid is made up of 100 equal parts.
Thinking of the base-ten flat as a 100-grid, what percent
represents fudge piece A? B? C? D? How do you know?
10%, 20%, 25%, 5%
Day 12
&13
What is the relationship between the fraction where the
denominator is 100 and the percent?
Responses may vary: Possible response: The percent is
the numerator.
What is the relationship between the decimal value and
the percent?
Responses may vary: Possible response: The percent is
the decimal times 100. (Demonstrate the relationship by
multiplying each decimal by 100)
What is the relationship between the fraction in simplest
form and the percent?
Responses may vary: Possible response: If the fraction
were rewritten with a denominator of 100, then that would
give you the percent.
Day 12
&13
How would you express 2% as a decimal?
0.02
How would you express 2% as a fraction in simplest
form?
1/50
What would the model of 2% look like? Why?
Responses may vary. Possible response: 100-grid with 2
squares shaded
What would the percents be for the shaded row of Peanut
Butter Fudge?
10%, 20%, 25%, 5%
Day 12
&13
Which fudge piece has the greatest value? How do you
know? C
Which fudge piece has the smallest value? How do you
know? D
What would be the order of the pieces if you order them
from greatest to least? C, B, A, D
How would you order 26%, 0.75, and 7/20 from least to
greatest?
26%, 7/20, 0.75
Day 12
&13
Work together to complete More Fudge-y-Ness.
Day 12
&13
How could you rewrite the fraction as a percent?
Write an equivalent fraction where the denominator is 100.
How could you use the model to write a fraction?
Responses may vary. Possible responses: I would count
the number of shaded squares, and then write a fraction
that represents the number shaded out of 100.
What type of model could be used to represent percents?
Responses may vary. Possible response: 100-grid
Day 12
&13
How could you use the model to determine the percent?
Responses may vary. Possible response: Since percents
are based out of 100, I would count the number of shaded
squares and write the percent. For example: 22 shaded
squares are 22%
How could you write a decimal as a fraction?
Use the place value as the denominator of the fraction.
Day 12
&13
Kim
Work together to complete Candy Bar Leftovers.
Day 12
&13
Complete the assessment
on your own.
Day 12
&13
Day 14
Numerator and Denominator
Relationships for One Half
What data will you put in the first column?
The numerators from equivalent fractions of one
half.
What data will you put in the last column?
The corresponding denominators from equivalent
fractions of one half.
Day 14
Numerator and Denominator
Relationships for One Half
What patterns do you see in the table?
The denominator is double the value of the
numerator.
What is the relationship between the numerator and
the denominator?
Two times the numerator is the denominator.
Day 14
Numerator and Denominator
Relationships for One Half
What number sentence would you write to represent
this relationship?
Numerator x 2 = Denominator
How could you use the number sentence to find
other equivalent fractions for one half?
Numerator x 2 = Denominator
Day 14
Numerator and Denominator
Relationships for One Half
How could you use the number sentence to find the
denominator if the numerator is 36?
Denominator = Numerator x 2
Denominator = 36 x 2 = 72
How could you use the number sentence to find the
numerator if the denominator is 36?
Denominator ÷ 2 = Numerator
36 ÷ 2 = 18
Day 14
Numerator and Denominator
Relationships for One Half
We want to write a number sentence that represents
the relationship between the numerators in the
equivalent fractions
8 ÷2 4
=
16 ÷ 2 8
Day 14
Numerator and Denominator
Relationships for One Half
Will this pattern work for the equivalent fractions
4 ÷4 1
8 = 2
÷4
Yes.
Day 14
Numerator and Denominator
Relationships for One Half
Why does this pattern work? Explain
Answers may vary. When we created equivalent
fractions for 1/2, such as 4/8, we did 1x4=4 to
show the relationship between the numerators,
and 2x4=8 to show the relationship between the
denominators. In both number sentences, the
pattern of “x 4” was maintained. Now to show
relationships between the numerators and the
denominators of the equivalent fractions
4/8=1/2, “undo” multiplication and use division.
Day 14
What is similar
about the
fractions 1/3
and 2/7?
Different?
Numerators are
the same.
Denominators
are different.
Day 14
Which fraction
is larger?
Explain
1/3 since thirds
are larger in
size than
sevenths if the
wholes are
equal size.
Day 14
Consider 3.5
and 4/5. What
is similar
about the two
fractions?
Different?
The
denominators
are the same.
The numerators
are different.
Day 14
Which fraction
is larger?
Explain
4/5: individual
fraction pieces
are the same
size, but there
are more
pieces for 4/5
Day 14
Consider 4/9
and 7/12.
What can we
do to compare
these two
fractions?
Use the
benchmark of ½
and the
relationship
between the
numerator and the
denominator.
Day 14
Consider ¾
and 4/5. What
can we do to
compare these
two fractions?
Consider both
fractions’
relationship to 1.
Day 14
Consider 4/7
and 9/14.
What can we
do to compare
these two
fractions?
Write equivalent
fractions so both
fractions have the
same denominator
and then compare
numerators.
Day 14
Homework
Complete Equivalent Fractions and
Beyond
Due TOMORROW
Day 15 &
16
Stations
You will complete 12 problems involving
equivalent rational numbers and comparing
rational numbers using models in six different
stations.
You MUST complete three stations each day.
Day 15 &
16
Stations
What model were you most comfortable using?
Why?
What model was most difficult for you to use?
Why?
Questions are to be answered on your own
Day 17
Complete the following
evaluation on your
own.
Turn it in when you are
finished.
End of Lesson 01