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U n t er r i ch t spl a n
Sub t rac t F rac t io ns Unl ike
De no minat o rs
Altersgruppe: 5 t h Gr ade
Texas - TEKS: G5 .3 .N O.H
Riverside USD Scope and Sequence: 5 .N F .1 [5 .3 ] , 5 .N F .2 [5 .3 ]
Oklahoma Academic Standards Mathematics: 5 .N .2.4 , 5 .N .3 .2,
5 .N .3 .3
Virginia - Mathematics Standards of Learning (2009): 3 .7 , 4 .5 b, 5 .6
Common Core: 5 .N F .A .1, 5 .N F .A .2
Mathematics Florida Standards (MAFS): 5 .N F .1.1, 5 .N F .1.2
Alaska: 5 .N F .1, 5 .N F .2, 5 .N F .A
Minnesota: 5 .1.3 , 5 .1.3 .1, 5 .1.3 .2, 5 .1.3 .4
Fairfax County Public Schools Program of Studies: 3 .7 .a.3 , 3 .7 .a.4 ,
3 .7 .a.6, 4 .5 .b.3 , 4 .5 .b.4 , 5 .6.a.3
Nebraska Mathematics Standards: M A .5 .1.2.h, M A .5 .2.3 .a
South Carolina: 5 .N S F .1, 5 .N S F .2
Indiana: 5 .A T .2, 5 .C .4
Georgia Standards of Excellence: M GS E 5 .N F .1, M GS E 5 .N F .2
Virginia - Mathematics Standards of Learning (2016): 3 .5 , 4 .5 .b,
4 .5 .c
Online-Ressourcen: P ut t he P ar t s T o ge t he r
Opening
T eacher
present s
St udent s
play
Act ivit y
5
12
15
10
5
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Closing
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ZIE L E :
Experience fractions on the number line
Practice making equivalent fractions
Learn to subtract fractions with unlike denominators
Develop an understanding of the need for common
denominators
Ope ni ng | 5 min
Display the following question.
How do you know that the following subtraction is incorrect?
A sk the students to write their answers in their notebooks.
When the students are done writing, share. Ask: How do you know
that the subtraction was done incorrectly?
Answers will vary depending on previous exposure to subtraction
of fractions. Some students may talk about the subtraction
algorithm and finding a common denominator. Others may explain
that is equal to 1, and it is impossible to start with , subtract a
positive number, and get an answer that is larger than . Still
others may draw representations of each fraction to show that
the answer is unreasonable.
S ay: Let’s remind ourselves of how to subtract fractions with the
same denominator. How do we subtract from ?
To subtract two fractions with the same denominator, we
subtract the numerators and keep the denominators the same.
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Here,
(or , after we simplify).
A sk: Why does it make sense that the denominator does not
change?
The denominator tells us the size of the piece. In this case, one
whole has been cut into 8 pieces. We are looking at , three of
those 8 pieces, and , one of those 8 pieces. When we subtract,
we take away one of those pieces from the three. That leaves us
with two of those pieces. The pieces are eighths, so we have .
Changing the denominator would mean that the size of the piece
has changed. (We can simplify to because quarter pieces are
twice the size of eighth pieces. So is equal to .)
S ay: Today’s episode looks at how we subtract fractions with
different denominators.
T e ac he r pr e se nt s P ut t he P ar t s T o ge t he r | 12 min
Present Matific ’s episode P ut t he P ar t s T o ge t he r - S ubt r ac t
F r ac t i o ns to the class, using the projector.
The goal of the episode is to subtract two fractions with unlike
denominators.
E x a m p le :
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S ay: Let’s watch the beginning of this episode very closely. Watch
the yellow hand that appears and what the hand does. Pay attention
to how one of the dials changes.
A sk: What subtraction problem are we being asked to solve?
Students can read the problem.
A sk: What did the yellow hand do along the number line?
The hand drew two segments along the number line, each one
representing a fraction. Then it moved the smaller segment to the
right until both segments were aligned on their right side.
A sk: Why would we want to align the segments on their right
sides?
Now we can see the difference in the length of the two segments
and find the answer to the subtraction problem.
S ay: The hand then turns one of the dials. Originally, the numbers on
each of the dials were the same as each of the denominators. Why
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would the episode change one of the dials?
When fractions have different denominators, the pieces are
different sizes. We cannot subtract them. We need to find a
smaller piece where multiple copies exactly fit inside each of the
larger pieces. Then we can subtract because all of the pieces are
the same size.
A sk: How do we find a piece that fits inside both denominators?
We find a common multiple of both denominators.
S ay: Yes, this is a c o mmo n de no mi nat o r . There are infinite
common denominators for a problem. Finding the smallest one
makes the calculations easier. So we look for the l o w e st
c o mmo n de no mi nat o r , or L C D .
Ask the students for the di f f e r e nc e in the problem.
Click on the
to enter the answer the students suggest.
If the answer is correct, the episode will proceed to the next problem.
If the answer is incorrect, the problem will wiggle.
The episode will present a total of five problems. The second
problem will have the dials correctly set, but you will need to draw
in the segments representing the fractions, align the segments on
their right, and change one dial to find the LCD. The remaining
problems will not have the dials correctly set.
S t ude nt s pl ay P ut t he P ar t s T o ge t he r | 15 min
Have the students play P ut t he P ar t s T o ge t he r - S ubt r ac t
F r ac t i o ns on their personal devices. Circulate, answering
questions as necessary.
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A c t i v i t y | 10 min
Display the following prompt:
Write a paragraph that explains why we need to use common denominators
when subtracting fractions.Feel free to add diagrams if they help.
Circulate, answering questions as necessary.
Collect the students’ papers, to display later.
A fraction’s denominator determines the size of the piece. For
example, here are diagrams of a circle cut into halves, thirds, and
fourths:
The larger the denominator is, the smaller the pieces are. When
we subtract, we need to subtract pieces that are the same size.
For example, if a problem reads
, we are looking at a piece
this size
and subtracting a piece this size
. It is
difficult to determine the difference. However, when we find a
common denominator, it is easy to see the answer. One half is
equal to , and is equal to . So we see that when we start with
and we subtract
, we are left with
, . We had 3
pieces, subtracted 2, and were left with 1. Since it takes 6 of
those pieces to make a whole, they are called sixths, and our
answer is .
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C l o si ng | 5 min
Display the following diagram.
Ask: What subtraction problem is being represented by this
diagram?
The problem is
.
Ask a student to come to the board and draw a representation of
the same problem without a number line. The student should draw
the fractions as parts of a whole.
-
=
A sk: What is the LCD for this problem?
The LCD is 12.
A sk: How do we use the LCD to find the answer?
We rewrite and using 12 as our denominator. We know that
and
. Now we can subtract:
. So the answer is
.
S ay: How do we know our answer is reasonable based on the
number line and the parts of a circle?
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Both the number line and the parts of a circle show that the
answer is just over . Seven twelfths is just over one half ( ), so
our answer is reasonable.
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