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U n t er r i ch t spl a n
Eq uival e nt F rac t io ns
Altersgruppe: 3 r d Gr ade , 4 t h Gr ade
Virginia - Mathematics Standards of Learning (2009): 4 .2a, 4 .2b,
4 .3 d
Virginia - Mathematics Standards of Learning (2016): 4 .2.b, 4 .3 .d
Fairfax County Public Schools Program of Studies: 4 .2.a.5 , 4 .2.b.1,
4 .2.b.2, 4 .3 .d.1, 4 .3 .d.3
Online-Ressourcen: S ame S ame
Opening
T eacher
present s
St udent s
pract ice
Class
discussion
5
12
14
12
4
min
min
min
min
min
Closing
M at h Obj e c t i v e s
E x pe r i e nc e a visual model for fractions
P r ac t i c e representing fractions
L e ar n to write equivalent fractions
De v e l o p visual and algebraic ways to identify equivalent
fractions
Ope ni ng | 5 min
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Display the following quote:
“You better cut the pizza in four pieces because I’m not hungry enough
to eat six.” - Yogi Berra
A sk : What do you think of this quote?
It’s a funny statement because the pizza remains the same size
whether it is cut into 4 slices or 6 slices. If the pizza was cut into
4 slices and Yogi Berra ate 4, then he ate the whole pie. The fact
that there were fewer slices does not change the size of the
pizza. If it was cut into 6 slices and he ate all 6, he ate the same
amount of pizza.
S ay : Let’s think about both of these pizzas – the one with 4 slices
and the one with 6.
Display the following diagrams:
A sk : How many slices would we eat of each to eat half the pizza?
We would eat 2 slices of the 4-slice pizza and 3 slices of the 6slice pizza.
A sk : If we had a pizza that was cut into 2 slices, how many slices
would we eat to eat half the pizza?
We would eat 1 slice.
Display the following:
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S ay : In each case, we ate half the pizza. So 1 piece out of 2 is .
And 2 pieces out of 4, or , is . And 3 pieces out of 6, or , is .
Today we’re going to talk about e q ui v al e nt f r ac t i o ns .
Equivalent fractions are fractions that have the same value, even
though they may look different.
Display the following:
S ay : One half, , and are examples of equivalent fractions.
T e ac he r pr e se nt s M at h game : S ame S ame - E q ui v al e nt
F r ac t i o ns: L e v e l I I | 12 min
Present Matific ’s episode S ame S ame - E q ui v al e nt
F r ac t i o ns: L e v e l I I to the class, using the projector.
The goal of the episode is to determine whether or not a specified
fraction of bread can be covered with two differently-sized strips of
cheese.
E x a m p le :
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S ay : Please read the instructions.
Students can read the instructions.
S ay : There are two slices of bread pictured and two sets of cheese
strips. Let’s start with the top slice. We can definitely cover the
correct fraction of the bread with these cheese strips. How many
cheese strips do we need?
Move the number of cheese strips that the students suggest onto
the top slice of bread.
S ay : Now let’s see if we can cover the same fraction of bread on
the bottom slice.
Ask a student to come to the front of the room and move cheese
strips from the bottom pile onto the bottom slice of bread.
A sk : Is it possible to cover the same portion of bread with the
bottom pile of cheese strips?
If it is possible, make sure both slices of bread are correctly
covered and then click
. If it is not possible, click
.
If the answer is correct, the episode will present a proportion showing
the equal fractions. Click on the to proceed.
If the answer is incorrect, the bread and the problem will wiggle.
The episode will present a total of 6 problems.
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S t ude nt s pr ac t i c e M at h game : S ame S ame - E q ui v al e nt
F r ac t i o ns: L e v e l I | 14 min
Have the students play S ame S ame - E q ui v al e nt F r ac t i o ns:
L e v e l I and S ame S ame - E q ui v al e nt F r ac t i o ns: L e v e l I I on
their personal devices. Circulate, answering questions as necessary.
C l ass di sc ussi o n | 12 min
S ay : Let’s return to the half pizza we were talking about at the
beginning of class.
Display the following:
A sk : In what other ways could we cut and eat the pizza in order to
eat half of it?
Answers will vary. Possible responses: We could cut the pizza
into 8 slices and eat 4, we could cut the pizza into 12 slices and
eat 6, etc.
A sk : Without looking at the diagrams, how can we tell that these
fractions are equivalent to ?
Answers will vary. Some students may note that the denominator
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is twice the numerator in each fraction. Others may note that if
you list the fractions in order by numerator (
…), then the
numerators increase by 1 and the denominators increase by 2.
Still others may observe that if you multiply the numerator and
denominator of by the same number, the resulting fraction is
equal to .
A sk : How do quarters compare to halves?
Quarters are half the size of halves.
A sk : Why does it make senses that is equal to ?
Since quarters are half the size of halves, we need twice as many
of them to take up the same amount of space.
S ay : Let’s consider another fraction: . What size piece is half the
size of thirds?
Sixths are half the size of thirds.
A sk : So how many sixths are equivalent to ? How do you know?
Four sixths are equivalent to . Since sixths are half as big as
thirds, we need twice as many of them to take up the same
amount of space. We had 2 thirds. Twice as many pieces is 4. We
need 4 sixths.
Display the following equation:
A sk a student to come to the board to draw a diagram
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demonstrating that is equal to .
S ay : Now let’s consider . Name a fraction that is equivalent to .
Possible responses:
etc.
A sk : How do you know that
is equivalent to ?
Answers may vary. Some possible responses:
1. Fifteenths are one third the size of fifths. To cover the same
amount of space, we need 3 times as many pieces. So instead of
3 pieces, we need 9. Nine fifteenths is equivalent to .
2. If we multiply by , we get
. Multiplying by is the same as
multiplying by 1, since is equal to 1. When we multiply by 1, we
do not change the original number. So when we multiplied by ,
we did not change the number. So our result,
equivalent to .
C l o si ng | 4 min
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, must be
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A sk : What are equivalent fractions?
Equivalent fractions are fractions that are equal.
S ay : State 3 fractions that are equivalent to .
Possible responses:
S ay : State 3 fractions that are equivalent to .
Possible responses:
S ay : In this episode, sometimes it was impossible to make
equivalent fractions. State an example of when that might happen
and why.
A possible response: It would be impossible if the episode gave
us thirds and fifths and asked us to cover of the bread. We can
cover of the bread with the thirds – just use 1 strip. However,
we cannot cover of the bread with fifths. One fifth strip is too
small and 2 fifth strips are too large.
A sk : If the episode asked us to cover of the bread with cheese,
for what size strips is it possible? How do you know?
It is possible with fifths, tenths, fifteenths, twentieths, etc. If the
denominator is any multiple of 5, we can use it to cover of the
bread. This is because if the denominator is a multiple of 5, then
a multiple of the strip fits exactly within a single strip of size .
For example, 2 tenths fit inside , because each tenth strip is half
the size of each fifth strip. Each fifteenth strip is one third the
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size of each fifth strip, so we can use fifteenths to cover of the
bread.
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