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U n t er r i ch t spl a n
Divis io n wit h Unit F rac t io n
Altersgruppe: Y e ar 5 , Y e ar 6
Maths Standards: 5 .N A .1b, 6.N A .1b
Online-Ressourcen: P o ur a S har e
Opening
T eacher
present s
St udent s
play
Class
discussion
6
15
15
6
5
min
min
min
min
min
Closing
ZIE L E :
E x pe r i e nc e division as repeated subtraction
P r ac t i c e division of one by a whole number
L e ar n division facts
De v e l o p algebra skills
Ope ni ng | 6 min
Present the students with the following assignment:
Compare each pair of fractions by writing a or symbol in the space
between them. Then answer the question that follows.
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1.
2.
3.
When fractions have the same numerator, how do you know which is
bigger? Why?
Students should write their answers in their notebooks.
When the students have finished writing, share.
Ask: Which fraction is bigger, or ? Should I use a less than
symbol or
a greater than symbol?
is bigger. Use a greater than symbol:
.
A sk: Which fraction is bigger, or ? Should I use a less than symbol
or a greater than symbol?
is bigger. Use a less than symbol:
.
A sk: Which fraction is bigger, or ? Should I use a less than
symbol or a greater than symbol?
is bigger. Use a greater than symbol:
.
A sk: How do we compare fractions that have the same numerator?
How do you know?
When fractions have the same numerator, we look at their
denominators. The fraction with the smaller denominator is
larger. Denominators determine the size of the piece. Smaller
denominators mean larger pieces. For example, let’s look at
fourths and sixths. Fourths divide a unit into four equal parts.
Sixths divide a unit into six equal parts. The fourths must be
bigger than the sixths because we need fewer of them to make
the unit. Let’s say we have three fourths and three sixths. In both
cases, we have three pieces. Since each piece is larger in fourths,
three fourths is greater than three sixths.
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T e ac he r pr e se nt s P o ur a S har e - Di v i di ng Uni t F r ac t i o ns |
15 min
Present Matific ’s episode P o ur a S har e - Di v i di ng Uni t
F r ac t i o ns to the class, using the projector.
The goal of the episode is to equally distribute one liter of juice among
different numbers of glasses.
E x a m p le :
A sk a student to read the instruction at the bottom of the screen.
Distribute the juice evenly between the monsters’ glasses.
S ay: One glass is full. We want to distribute the juice fairly among
all the glasses. What information is relevant?
We need to know how many glasses there are.
S ay: After we establish the number of glasses, how do we
determine which measuring cup to use?
A possible response: The measuring cups are all unit fractions.
The number of glasses will determine the denominator of the
fraction on the measuring cup.
Move the measuring cup that the students have chosen down onto
the counter.
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Pour the juice from the full glass into the measuring cup by moving
the glass to the right of the measuring cup so that the cup becomes
highlighted in yellow.
Pour the juice from the measuring cup into an empty glass. Repeat
until you have poured juice into all of the glasses.
When you are satisfied that the glasses are equally full, click on
.
If the juice is properly distributed, the episode will proceed to a new situation.
If the juice is not properly distributed, the instructions will wiggle.
The episode will present three more situations.
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S t ude nt s pl ay P o ur a S har e - Di v i di ng Uni t F r ac t i o ns | 15
min
Have the students play P o ur a S har e - Di v i di ng Uni t
F r ac t i o ns on their personal devices. Depending on time and skill
level, students may also proceed to P o ur a S har e - Di v i di ng
F r ac t i o ns and P o ur a S har e - Di v i si o n and E q ual S har e s .
Circulate, answering questions as necessary.
C l ass di sc ussi o n | 6 min
S ay: Describe what happened in the episode.
We divided juice equally among glasses.
S ay: In each case, we started with one liter of juice. Let’s say we
wanted to divide it among five glasses. Which measuring cup should
we use?
We should use the cup labeled .
Ask: How much juice does each monster get?
Each monster gets of a liter.
S ay: Instead, let’s consider starting with a 2-liter pitcher full of
juice. Now which measuring cup do we use? Why?
We can still use the measuring cup labeled because we are still
dividing into five parts.
Ask: How much juice does each monster get? How do you know?
Each monster gets of a liter of juice. We can think of this in two
ways:
. Now we are distributing two liters, twice the original. So each
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monster should get twice her original portion, or of a liter.
. Fill it with juice. Pour the juice into an empty glass. Repeat four
times. Now all five glasses have of a liter of juice. There is still
more juice in the pitcher. Repeat the process. Fill the measuring
cup, and empty it into each glass once again. Now we have poured
into each glass twice, and the pitcher is empty. Each glass contains
of a liter.
S ay: When we had one liter of juice and split it among five glasses,
each monster got of a liter. When we had two liters of juice and
split it among five glasses, each monster got of a liter. If we have
a pitcher with four liters of juice and we want to split it among five
glasses, how much juice will each monster get? How do you know?
Again, one liter of juice gave each monster of a liter. So if we
multiply the amount of juice by four, then we need to multiply
each monster’s portion by four. So each monster gets of a liter.
S ay: Let’s suppose instead that we have two liters of juice and
seven glasses. How much would each monster get? How do you
know?
One liter of juice split among seven monsters would give each
monster of a liter. So twice the amount of juice (two liters)
would give each monster a portion serving twice as big. So each
monster gets of a liter.
S ay: Let’s generalize. Describe the number that belongs in the
blank.
If we equally split one liter of juice among a bunch of glasses, then each
glass gets _ _ _ _ _ liter.
The missing number is a unit fraction where the denominator is
equal to the number of glasses.
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S ay: Describe the number that belongs in the blank.
If we equally split four liters of juice among a bunch of glasses, then each
glass gets _ _ _ _ _ liter.
The missing number is a fraction with a numerator of four and a
denominator equal to the number of glasses.
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C l o si ng | 5 min
Say: We’ve been dividing in this episode. For example, one liter of
juice divided among three glasses means we pour of a liter of juice
into each glass. How can we write this as a division problem?
Ask: What is the division problem when we divide one liter of juice
among six glasses?
Ask: What is the division problem when we divide one liter of juice
among eight glasses?
Say: If we know that
, then we also know two other facts. We
know that
and
. Now we know that
other facts do we know based on this one?
and
Ask: What other facts do we know from
?
and
Ask: What other facts do we know from
?
and
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