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U n t er r i ch t spl a n
F rac t io ns o n t he Numb e r Line
Altersgruppe: 4 t h Gr ade , 5 t h Gr ade
Texas - TEKS: G3 .3 .N O.B
Riverside USD Scope and Sequence: 3 .N F .2b [3 .8] , 4 .N F .1 [4 .6] ,
4 .N F .2 [4 .6]
Oklahoma Academic Standards Mathematics: 3 .N .3 .2, 3 .N .3 .4 ,
4 .N .2.1, 4 .N .2.2, 4 .N .2.8, 5 .N .2.4
Virginia - Mathematics Standards of Learning (2009): 4 .2a, 4 .2b
Common Core: 3 .N F .A .2b, 4 .N F .A .1, 4 .N F .A .2
Mathematics Florida Standards (MAFS): 3 .N F .1.2b, 4 .N F .1.1,
4 .N F .1.2
Alaska: 3 .N F .2b, 3 .N F .3 b, 4 .N F .1, 4 .N F .2
Minnesota: 4 .1.2.1, 5 .1.2.3 , 5 .1.2.4
Fairfax County Public Schools Program of Studies: 4 .2.a.2, 4 .2.a.3 ,
4 .2.a.4 , 4 .2.a.5 , 4 .2.a.6, 4 .2.b.1, 4 .2.b.2
Nebraska Mathematics Standards: M A .3 .1.1.g, M A .4 .1.1.d,
M A .4 .1.1.i , M A .4 .1.1.k, M A .4 .1.2.e
South Carolina: 3 .N S F .2b, 3 .N S F .2c , 4 .N S F .1, 4 .N S F .2,
4 .N S F .3 a, 4 .N S F .3 b, 4 .N S F .3 c , 4 .N S F .4 a, 4 .N S F .4 b,
4 .N S F .4 c
Indiana: 4 .C .6, 4 .N S .3 , 4 .N S .4
Georgia Standards of Excellence: M GS E 3 .N F .2b, M GS E 4 .N F .1,
M GS E 4 .N F .2
Virginia - Mathematics Standards of Learning (2016): 4 .2.b
Online-Ressourcen: A l l t he S ame t o M e
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Opening
T eacher
present s
St udent s
play
Class
discussion
6
12
12
12
5
min
min
min
min
min
Closing
ZIE L E :
E x pe r i e nc e a visual model for equivalent fractions
P r ac t i c e identifying fractional portions
L e ar n to compute equivalent fractions
De v e l o p algebra skills
Ope ni ng | 6 min
A sk the students to draw a figure that represents .
A possible response:
A sk one student to present her drawing to the class.
A sk: How does this represent ?
A possible response: The entire rectangle represents one whole.
The rectangle is divided into six equal pieces. Each piece is of
the entire rectangle. Shading three of the pieces represents .
A sk: What is another fraction we could use to describe the shaded
region? How do you know?
We could say that the shaded region represents . Half of the
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We could say that the shaded region represents . Half of the
entire rectangle has been shaded.
S ay: One half and are called 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. They name the same part of the whole.
Display the following:
Ask: Can we think of more than one way to name the portion that has
been shaded?
Three fourths and
portion.
are two different ways to name the shaded
Say: So and name the same part. They are equal. They are
equivalent fractions.
T e ac he r pr e se nt s A l l t he S ame t o M e - F r ac t i o ns o n t he
N umbe r L i ne | 12 min
Present Matific ’s episode A l l t he S ame t o M e - F r ac t i o ns o n
t he N umbe r L i ne to the class, using the projector.
The goal of the episode is to fill in the missing number(s) to make equivalent
fractions.
E x a m p le :
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S ay: Please read the instruction.
Students can read the instruction at the bottom of the screen.
S ay: A number line has been divided into parts to help us solve this
problem. Above the number line are small green dividers
representing one way to partition the line. Below the number line
there are small pink dividers representing another way to partition
the line. You will notice that the green and pink dividers sometimes
meet. This is where they are equivalent. Look at the blue pointer. It
is pointing at the two equivalent fractions for this problem. What is
the missing number in this problem?
Students can answer based on the episode.
Click on the
to enter the number that the students indicate.
If the answer is correct, the episode will proceed to a new problem.
If the answer is incorrect, the instruction will wiggle.
For the second problem, the episode will present dials. The dials
will already be set to the denominators in the problem and the line
will already be partitioned correctly. However, the pointer will not
yet be in place.
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A sk: Where should we place the pointer on the number line?
Move the pointer as the students indicate.
S ay: Now we can answer the problem. What is the missing number?
Students can answer based on the episode.
Click on the
to enter the number that the students indicate.
If the answer is correct, the episode will proceed to a new problem.
If the answer is incorrect, the instruction will wiggle.
For the rest of the problems, the dials will not be properly set. Each
dial represents the de no mi nat o r of each fraction, or the number
of partitions on the number line. You will need to turn the dial to
adjust the partitions. Ask for students’ input in how to change the
dials in order to solve the problems.
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The episode will present a total of six problems.
S t ude nt s pl ay A l l t he S ame t o M e - F r ac t i o ns o n t he
N umbe r L i ne | 12 min
Have the students play A l l t he S ame t o M e - F r ac t i o ns o n
t he N umbe r L i ne on their personal devices. Depending on time,
students may also proceed to the E q ui v al e nt F r ac t i o ns F i ndi ng Unkno w ns worksheets. Circulate, answering questions
as necessary.
C l ass di sc ussi o n | 12 min
S ay: Suppose the episode asked you to solve
the dials?
. How do you set
The dials control the number of partitions on the number line. So
each dial must be set to each denominator. So one dial should be
set to five and the other to 15.
A sk: Once you have the dials set at five and 15, how do you
determine the answer?
Look at the twelfth partition on the part of the line that is divided
into fifteenths. Then find how many fifths meet up with .
A sk: What is the answer for
?
Four is the missing number. Four fifths is equal to .
S ay: Suppose the episode asked you to solve
the dials?
. How do you set
One dial should be set to 16. Place the pointer on . Adjust the
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other dial until the fourth partition meets up with .
A sk: Once you have the dials set, how do you determine the
answer?
The number on the second dial is the answer.
A sk: What is the answer for
?
Eight is the missing number. Four eighths is equal to .
S ay: Suppose the episode asked you to solve
the dials?
. How do you set
Set the pink dial to any number greater than or equal to five.
Place the pointer on the fifth pink partition. Adjust the green dial
until the tenth green partition meets up with the fifth pink
partition.
A sk: Once you have the dials set, how do you determine the
answer?
The numbers on each dial are the answers.
A sk: What is the answer for
?
Responses may vary. A possible response: We can use six and 12
as the missing numbers. Five sixths is equal to .
A sk: How many answers are there to the problem
?
There are infinite answers. You can set the first denominator to
any number you want. Since it can be any number, there are infinite
ways to do this. The first denominator determines the second. In
this problem, the second denominator is always twice the first.
For example, if the first denominator is six, then the second is 12,
since
14, since
. If the first denominator is seven, then the second is
.
A sk: Did anyone find a way to solve the equivalent fraction problem
without using the dial? For example, how could we solve the
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problem
?
Responses may vary. Two possible responses:
1. In the fraction , the n u m e r a t o r is half the denominator. So that must
be true in the other fraction as well. Half of 20 is 10. So the numerator is
10, and the fraction is .
2. The denominator in the first fraction is four and in the second fraction is
20. So the denominator has been multiplied by five. So we must also
multiply the numerator by five. When we multiply two by five we get 10.
So the numerator is 10, and the second fraction is .
S ay: Complete the following problems:
S ay: Complete the following problems:
S ay: Let’s make a list.
Write the following on the board:
A sk: What patterns do you see?
Responses may vary. A possible response: In the list for , the
numerators increase by one each time and the denominators
increase by two each time. In the list for , the numerators
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increase by four each time and the denominators increase by five
each time. The original numerator determines what you count by
for the numerator, and the original denominator determines what
you count by for the denominator.
C l o si ng | 5 min
S ay: Define equivalent fractions.
Equivalent fractions are fractions that have the same value.
Hand out a small piece of paper. Ask the students to:
1. State two equivalent fractions.
2. Draw two figures that represent the fractions and demonstrate that
they are equal.
Collect the papers to review later.
A possible response:
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