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U n t er r i ch t spl a n
Ad d F rac t io ns
Altersgruppe: 5 t h Gr ade
Virginia - Mathematics Standards of Learning (2009): 3 .7 , 4 .5 b, 5 .6
Virginia - Mathematics Standards of Learning (2016): 4 .5 .b, 4 .5 .c ,
5 .6.a
Fairfax County Public Schools Program of Studies: 3 .7 .a.5 , 4 .5 .b.2,
4 .5 .b.3 , 5 .6.a.1, 5 .6.a.2, 5 .6.a.4
Online-Ressourcen: B al l o o n Go e s Up
Opening
T eacher
present s
St udent s
pract ice
Class
discussion
10
15
12
8
min
min
min
min
M at h Obj e c t i v e s
E x pe r i e nc e the meaning of fraction addition.
P r ac t i c e fraction addition.
L e ar n about the “common denominator”.
De v e l o p technique for adding fractions.
Ope ni ng | 10 min
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Present the following scenario to your class: A pizza tray is made up of 8
separate pieces (shown below).
A s k : What fraction of the pizza am I eating if I eat 1 slice?
The answer is
.
Explain that if I am eating 1 slice out of a possible 8 slices in the whole, it
means that 1 is the numerator and 8 is the denominator.
A s k : What fraction of the pizza am I eating if I eat 5 slices?
The answer is
.
Again explain that if I am eating 5 slices out of a possible 8 slices in the
whole, it means that 5 is the numerator and 8 is the denominator.
A s k : How many slices of pizza am I eating if I eat
of the pizza tray?
The answer is 4 slices of pizza.
Explain that one way to solve it is to take a group of slices as the number of
the denominator and eat slices from that group as the number of the
numerator. In this case we should eat 1 slice out of every group of 2 slices of
pizza, which adds up to 4 slices of pizza.
A s k : How many slices of pizza am I eating if I eat
of the pizza tray?
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The answer is 2 slices of pizza.
Explain that we eat 1 slice out of every group of 4 slices of pizza, which adds
up to 2 slices of pizza.
Move to a scenario where there are two different people who are eating the
pizza.
For example, s a y : You shared this pizza with a friend. And let’s say you ate
of the pizza and your friend ate
been eaten?
of the pizza. How many pizza slices have
The answer is 6 slices of pizza, because
tray is 2 slices.
of the tray is 4 slices and
of the
Continue to a s k : And what fraction of the pizza has been eaten?
Explain that because 6 slices of pizza have been eaten it means that the
answer is
.
Mention that later in the lesson we will learn another method for solving
these types of problems.
T e ac he r pr e se nt s M at h game : B al l o o n Go e s Up - A dd
F r ac t i o ns | 15 min
Present Matific ’s episode B a llo o n G o e s Up - A d d F r a c t io n s to the
class, using the presentation mode, on the projector.
This episode practices addition of fractions. A group of birds is displayed.
You have to give balloons of one color to a designated fraction of the birds,
and balloons of another color to another designated fraction of the birds.
Finally, you have to determine what fraction of the birds has a balloon.
E x a m p le :
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S a y : Please read the instruction at the bottom of the screen.
Students can read the instruction.
A s k : So we are looking for how many birds are three-fifth of 15 birds?
The answer is 9 birds.
Remind the students that in order to find a part of a whole one should take a
group of birds as the number of the denominator and give balloons to birds
from that group which will be the number of the numerator. In this case, we
should give 3 balloons to every group of 5 birds, which adds up to 9 birds.
E x a m p le :
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A s k : Now we are asking how many birds are equal to one-third of 15 birds?
The answer is 5 birds.
E x a m p le :
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A s k : Now we are being asked what fraction of the birds has balloons?
The answer is
.
A sk : How did we do it?
The answers may vary. Explain the two different options of solving the
problem: either we count the number of birds that has balloons and divide it
by the total number of birds, or we add the first fraction to the second one,
by using common denominator, i.e.
.
Emphasize that the two options are, eventually, the same. But it is important
to understand that later we will not have the birds and we will need to know
how to add fractions without them.
So how would we solve addition of fractions?
First of all we should distinguish between cases in which the denominators
are equal and cases in which the denominators are different.
In the first case, when the denominators are equal, we add the numerator of
the first fraction to the numerator of the second and leave the denominator
without a change, e.g.
. It is because the numerator is
counting the number of seventh. The first fraction states that there is 1
seventh and the second fraction states that there are 3 seventh. Now, 1
seventh plus 3 sevenths are 4 sevenths, just like 1 car plus 3 cars are 4 cars.
In the second case, when the denominators are different, we cannot add the
numerators because they count different things.
Let’s have a look at the next exercise:
We cannot add 3 fifths to 1 third just as we cannot add 3 cars to a 1 house.
The numerators are counting different things! That’s why we should first find
the “common denominator”, which allow us to count the same things.
First of all, we look for a number which is a product of the two different
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denominators – 5 and 3. This number would be 15. Then, we multiply each
numerator and the denominator by the same number, i.e.
and
,
.
Finally, after we have a common denominator, we can add them up because
now the numerators are counting the same thing:
fifteenths, and together it’s 14 fifteenths, i.e.
is 9 fifteenths and
is 5
S t ude nt s pr ac t i c e M at h game : B al l o o n Go e s Up - A dd
F r ac t i o ns | 12 min
Have students play B a llo o n G o e s Up - A d d F r a c t io n s on their personal
devices.
Circulate, answering questions as necessary.
Make sure that the students try to answer the questions not only by
counting the number of balloons but also by adding fractions.
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C l ass di sc ussi o n | 8 min
Discuss any challenges the students face while working individually.
Ask the class for responses as to how they dealt with any common issues
their classmates brought up.
Ask the students to find the common denominator in the following cases
(write on the board):
and
and
and (encourage students to simplify before finding the common
denominator)
and (this is a special case as the first fraction can be simplified to ½,
making the common denominator 2).
Solve those final exercises with the class:
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