Learning Coach — Comparing and Ordering with Denominators
Objectives
Students will:
Compare the denominators of fractions.
Skills Needed
Students must be able to:
Use <, >, and = to compare fractions with the same numerator.
Put fractions with the same numerator in order from greatest to least or least to greatest.
Create fraction models with a number line to compare and order fractions.
Materials Needed
Students will need:
crayons or colored pencils
pen or pencil
Keywords
fraction
fraction model
denominator
Let’s Learn!
How do you compare fractions that have the same numerator?
Goal:
Goal:
Think About It!
Goal: Recognize how to find out what
makes a fraction greater or lesser when fractions have
the same numerator.
Daniel is excited to read about the super celebration.
Superheroes Donte and Ian cut the cookie cakes into different
numbers of pieces. Each cake is the same size and shape. Donte
and Ian want to know which cake has the biggest pieces and which
cake has the smallest pieces.
Each part of each cookie cake is a fraction with a numerator and
a denominator. Donte will use his fraction powers to show the
parts of the first two cakes!
Click on the box to see the fractions of the first two
cookie cakes!
Two cookies. The oatmeal raisin cookie is partitioned
into 2 equal parts. The double chocolate cookie is
partitioned into 3 equal parts.
The oatmeal cookie's parts are labeled 12.
The double chocolate cookie's parts are labeled 13.
The oatmeal raisin cookie cake has two equal parts. Each
of these parts is 12. The double
chocolate cookie cake has three equal parts. Each of these
parts is 13.
Each part of the cookie cakes has the same numerator, 1. That is
because each part is 1 part out of the whole of each cookie. Ian
used his fraction superpower to show one piece of each cookie cake
and its fraction.
Which piece is bigger, the oatmeal raisin half or the double
chocolate third? Donte says that the half looks bigger than the
third, but he wants to make sure. Ian flew in two number lines
to compare the two fractions: 12 and 13 . Because the fractions have different
denominators, the number lines have different numbers of parts
too!
First, Ian shows 12 on the first number line by
drawing a purple line to 12. Click on the empty
number line to show 12.
Number line from 0 to 1 with 2 spaces between. The
number line is labeled from 02 to 22
Number line from 0 to 1 with 2 spaces between. The
number line is labeled from 02 to 22. One part is filled in to 12.
Then Ian shows 13 on the second number line by
drawing a brown line to 13. Click on the empty
number line to see how he shows 13.
Number line from 0 to 1 with 3 spaces between. The
number line is labeled from 03 to 33
Number line from 0 to 1 with 3 spaces between. The
number line is labeled from 03 to 33. One part is filled in to 13.
Ian flew in red lines to show where the fractions end on the
number lines. Even though the number lines are divided into
different fractions, the lines themselves are the same size.
Donte used his fraction powers to see that 12
is greater than 13. 12 is
greater than 13 because it is closer to 1 on
the number line!
Two number lines. Top number line from 0 to 1 with 2 spaces
between. The number line is labeled from 02
to 22. One part is filled in to 12. Bottom number line from 0 to 1 with 3
spaces between. The number line is labeled from 03 to 33. One part is filled
in to 13.
Each number line has a dotted line extending from their
filled in part. The top number line is longer.
The 2 in the denominator of 12 is less than the
3 in the denominator of 13. This is because the
smaller the denominator, the bigger the parts! When you cut the
same size space into more parts, the parts get smaller.
12>13. The denominators are
circled.
2 is less than 3
Ian says that you can also use lines with dots or just dots to
show each fraction.
Two number lines. Top number line from 0 to 1 with 2
spaces between. The number line is labeled from 02 to 22. One part is filled
in to 12. Bottom number line from 0 to 1
with 3 spaces between. The number line is labeled from 03 to 33. One part is filled
in to 13.
Ian’s number lines with lines and dots
Two number lines. Top number line from 0 to 1 with 2
spaces between. The number line is labeled from 02 to 22. Dot on 12. Bottom number line from 0 to 1 with 3
spaces between. The number line is labeled from 03 to 33. Dot on 13.
Ian’s number lines with dots
Ian also says that you can use < (less than), > (greater than), or = (equal to) to compare
fractions. He came up with a super rule for comparing fractions:
If the numerator is the same, the fraction with the smaller
denominator is the greater fraction!
Click each slide to compare the fractions with the superheroes!
Alani wants a piece of the double chocolate cookie cake.
It is cut into thirds. Joe wants a piece of the
strawberry frosted cookie cake. It is cut into fourths.
Which superhero will get more cookie cake?
Left: 13 piece of a double
chocolate cookie cake.
Right: 14 piece of a frosted cookie
cake.
Alani and Joe put a fraction on each piece of cookie
cake. They noticed that the fractions have the same
numerator and different denominators. They think that
the 13 piece looks bigger than the 14 piece. They need to check their work by
comparing the fractions. Click the Show Me button to
compare the fractions by plotting them on number lines
and by looking at their denominators!
Alani’s fraction is the brown dot on the first
number line. Joe’s fraction is the pink dot on
the second number line.
Two number lines. Top number line from 0 to
1 with 3 spaces between. The number line is
labeled from 03 to 33. Dot on 13.
Bottom number line from 0 to 1 with 4 spaces
between. The number line is labeled from 04 to 44. Dot
on 14.
3 is less than 4!
13>14. The
denominators are circled.
So 13>14!
Alani’s piece is bigger. She will get more
cookie cake!
Donte wants two pieces of the chocolate chip cookie
cake. It is cut into sixths. Ian wants two pieces of the
banana cookie cake. It is cut into fifths. Which
superhero will get more cookie cake?
Left: 26 of a chocolate chip cookie
cake.
Right: 25 piece of a banana cookie
cake.
Donte and Ian circled their pieces but did not put
fractions on them. They noticed that the fractions have
the same numerator and different denominators. They
think that 26 of the chocolate chip
cookie cake looks smaller than 25 of
the banana cookie cake. They need to check their work by
comparing the fractions. Click the Show Me button to
compare the fractions by plotting them on number lines
and by looking at their denominators!
Donte’s fraction is the black dot on the first
number line. Ian’s fraction is the red dot on
the second number line.
Two number lines. Top number line from 0 to
1 with 6 spaces between. The number line is
labeled from 06 to 66. Dot on 26.
Bottom number line from 0 to 1 with 5 spaces
between. The number line is labeled from 05 to 55. Dot
on 25.
6 is greater than 5!
26<25. The
denominators are circled.
So 26<25!
Ian’s pieces are bigger. He will get more cookie
cake!
Joe and Donte want more cookie cake, but the cakes are
not done yet! They know that the first cake will be cut
into sevenths. The second cake will also be cut into
sevenths. Joe and Donte both want three pieces. Which
superhero will get more cookie cake?
Left: 37.
Right: 37.
Can the superheroes still compare without seeing the
cookie cakes? Yes! The fractions have the same numerator
and the same denominator. They can use number lines to
show their fractions! Click the Show Me button to
compare the fractions by plotting them on number lines
and by looking at their denominators!
Joe’s fraction is the blue dot on the first
number line. Donte’s fraction is the orange dot
on the second number line.
Two number lines. Top number line from 0 to
1 with 7 spaces between. The number line is
labeled from 07 to 77. Dot on 37.
Bottom number line from 0 to 1 with 7 spaces
between. The number line is labeled from 07 to 77. Dot
on 37.
7 is equal to 7!
So 37=37!
Both superheroes will get the same amount of
cake!
The superheroes want to share the cakes with their
teachers. There is a piece of the banana cookie cake
(15), a piece of the chocolate chip
cookie cake (16), and a piece of the
double chocolate cookie cake (13) left
over. Which cake has the most left over?
Left: 15.
Middle: 16.
Right: 13.
How can we compare these three fractions? By putting
them in order from greatest to least or least to
greatest! The superheroes want to show the fractions
from greatest to least. That means the greatest fraction
goes first and the least fraction goes last. Click the
Show Me button to compare the fractions by plotting them
on number lines and by looking at their denominators!
The banana cookie cake’s fraction is the red dot
on the second number line. The chocolate chip
cookie cake’s fraction is the black dot on the
last number line. The double chocolate cookie
cake’s fraction is the brown dot on the first
number line.
Three number lines. First number line from 0
to 1 with 3 spaces between. The number line
is labeled from 03 to 33. Dot on 13.
Second number line from 0 to 1 with 5 spaces
between. The number line is labeled from 05 to 55. Dot
on 15. Third number line
from 0 to 1 with 6 spaces between. The
number line is labeled from 06 to 66. Dot on 16.
The dot that is closest to 1 is the greatest
fraction. The dot that is closest to 0 is the
least fraction. That is because lesser numbers
are on the left and greater numbers are on the
right. To put the dots in order from greatest to
least, go from right to left!
13, 15, 16
13 is the greatest. That is
because it has the denominator with the least
value. 16 is the least. That is
because it has the denominator with the greatest
value. The double chocolate cookie cake has the
most left over!
Slide: 1/4
Question:
How can you compare or order fractions if you do not
have a number line or fraction picture?
When fractions have the same numerator, look at their
denominators to compare or order them!