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U n t er r i ch t spl a n
Pro b l e m So l ving : Ad d And
Sub t rac t F rac t io ns Wit h Like
De no minat o rs
Altersgruppe: 4 t h Gr ade , 5 t h Gr ade
Virginia - Mathematics Standards of Learning (2009): 3 .7 , 4 .5 b,
4 .5 d, 5 .6
Virginia - Mathematics Standards of Learning (2016): 4 .5 .b, 4 .5 .c
Fairfax County Public Schools Program of Studies: 3 .7 .a.5 , 4 .5 .b.2,
4 .5 .b.3 , 4 .5 .b.4 , 4 .5 .d.1, 5 .6.a.4
Online-Ressourcen: T ank Up
Opening
T eacher
present s
St udent s
pract ice
Mat h
Pract ice
Mat h
Worksheet
Pract ice
8
12
12
8
4
1
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min
min
min
min
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Closing
M at h Obj e c t i v e s
E x pe r i e nc e problem solving.
P r ac t i c e problem solving with addition and subtraction of
fractions with like denominators.
L e ar n that in order to solve a problem one must plan and think
ahead.
De v e l o p the ability to solve problems.
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Ope ni ng | 8 min
Draw on the board a pizza tray divided into 8 slices of pizza.
E x a m p le :
S ay : We used a pizza tray, which is divided into 8 equal parts. But,
we can divide a pizza tray into as many parts as we like. For
example, we can divide the pizza tray into 3 equal slices.
Draw on the board a pizza divided into 3 equal slices.
A sk : What value would we call each slice?
Third or .
A sk : What is the numerator and what is the denominator in this
fraction?
The numerator is 1 and the denominator is 3.
A sk : What is the meaning of the numerator and the denominator?
The denominator states the number of parts we divided the whole
into. In our case we divided the pizza tray into 3, so the
denominator is 3. The numerator states the number of parts we
refer to. In our case, if we want to refer to one slice of the
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fraction that represents it would be . One part out of three.
Draw on the board a pizza divided into 5 equal slices.
A sk : What would we call each slice?
A fifth or .
A sk : What is the numerator and what is the denominator in this
fraction?
The numerator is 1 and the denominator is 5.
A sk : What would we call two parts ?
Two-fifths or .
A sk : How much is
plus ?
Because the numerator counts the number of parts, all we have to
do is to add the numerators. So, two-fifths plus one-fifth are
three-fifths, just as two tomatoes plus one tomato are three
tomatoes.
S ay : Today we will play with solving problems. Consider:
1. When we approach a problem, we need to think about and plan our
steps. If we are in a hurry, and start answering without thinking, we may
get stuck.
2. In the case we do not know how to start, it is important not to stay
stuck in front of the problem, but try to start in some direction. If we
succeed it is wonderful, if not at least we know what is the wrong
direction (which we didn't know until we tried).
T e ac he r pr e se nt s M at h game : T ank Up - A dd- S ubt r ac t
F r ac t i o ns: L e v e l I | 12 min
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Present Matific ’s episode T a n k Up - A d d - S u b t r a c t F r a c t io n s : L e v e l I
to the class, using the projector, on the Preset mode.
This episode practices problem solving in the context of fraction addition
and subtraction. You have to drive your car home. You start with a full tank.
Each block consumes a fixed fraction of your gas tank. Each gas station on
the way provides you with a certain fraction of a gas tank. You have to plan
your route, passing through gas stations so that you don’t run out of gas.
E x a m p le :
S ay : In this game we need to get the car (from the lower-left
corner), home (to the upper-right corner). Along the way there are
gas stations, and it is written on each station the amount of gas it
will add to our car, if we pass through it. At the left side of the
screen we see the fuel gauge of the car. In this case the car is full
(because the red needle is on 'F'), and the tank is divided into 3. So,
each block driven consumes
of the tank.
Demonstrate one ride of the car (click once on an arrow, no matter in what
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direction) and show the fuel gauge is down by
'restart'.
, now the tank is
full. Press
S ay : We have to go home without running out of gas.
S ay : Let's start driving up, in order to pass through the
station.
Drive the car up so it passes through the
tank
tank station.
S ay : Pay attention that in this ride we lost of the tank, and as
soon as we arrived at the gas station the tank filled, so the tank is
full again.
Drive the car up so it passes through each of the
tank stations.
E x a m p le :
Demonstrate how starting to drive up will get the car stuck.
S ay : So, it is not a good plan to start driving up.
A sk : Who has a better idea in how to solve this problem?
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Try the solutions students suggest. Discuss the importance of the
preliminary planning.
We start driving right and up towards the 1 tank station. We pass
that station; continue to the right until we pass the
and eventually drive up until the end.
tank station
Demonstrate the solution.
S ay : Consider, that in order to solve the problem, we need to plan
the moves we will do, ahead of the trip. If we go out without
planning, there is good chance we will stuck in the middle, of the
trip without gas.
Present the next question.
E x a m p le :
S ay : Again we need to get the car home, and again each ride uses
tank of gas. Let's think of the right route be f o r e we move the car.
A sk : How would we find the right way?
There are some points we should pay attention to:
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1. If we don’t drive back, the way will take 9 blocks, no matter what way we
choose to drive.
2. The only thing that changes on the way is the gas we fill.
3. Through the gas stations on the right, the amount of gas we can fill is
twice the full tank ( + + + + + = 2). Through the gas stations on
the up and then right, the amount of gas we can fill is one and two-thirds
of a tank ( + + =
). We need to travel 9 blocks, so we need 3 full
tanks. So if we start with full tank, we need another 2 tanks in order to
complete the drive.
A sk : So what is the right way?
If we will drive up we will stuck. So, we need to drive to the right,
through all the
tank stations.
Demonstrate the solution.
S t ude nt s pr ac t i c e M at h game : T ank Up - A dd- S ubt r ac t
F r ac t i o ns: L e v e l I | 12 min
Have students play T a n k Up - A d d - S u b t r a c t F r a c t io n s : L e v e l I on
their personal devices.
Circulate among them answering questions.
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M at h P r ac t i c e : P r o bl e m S o l v i ng W o r kshe e t | 8 min
Invite two students to play a game.
S ay : Let's play a game! The purpose of the game is to be the first to
reach the number 5. The game starts when the the sum is 0. In every
turn a student picks a number from a third, either two thirds or onethird, and add it to the total sum. The first to reach 5 is the winner.
Play the game a few times, with different students. It is possible to change
the numbers (for example to reach the number 4 by using quarters, two
quarters, three quarters and one-quarter).
S ay : Notice how important it is to plan our steps from the
beginning. If I say the number 4 or more, my opponent will say 5 and
win. But, if I will say the number three and two-thirds I will win,
because my opponent will have to say the number 4.
According to the level of the class, you could discuss the strategy of winning
this game. Who says the number three and two-thirds is the winner, so who
says the number two and one-third is the winner, so who says the number
one is the winner. Eventually, who starts the game and says one is the winner
(of course if he acts according to the winning strategy).
M at h W o r kshe e t P r ac t i c e : A ddi ng F r ac t i o ns - S ame
De no mi nat o r | 4 min
Have students work on the following worksheets:
1. A d d in g F r a c t io n s - S a m e De n o m in a t o r .
2. A d d in g F r a c t io n s w it h Un k n o w n s - S a m e De n o m in a t o r .
Circulate among them answering their questions.
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C l o si ng | 1 min
S ay : Today we have learned three important principles in solving
problems:
1. When we try to solve a problem, we need to think ahead and plan our
steps.
2. Sometimes a problem has more than one solution.
3. In the case where we do not know how to start, it is important not to
get stuck in front of the problem, but try to start in some direction. If we
succeed it is wonderful, if not at least we know what the wrong direction
(which we didn't know unless we try) is.
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