1
U n t er r i ch t spl a n
Who l e s and Part s – F rac t io n
Ad d it io n Like De no minat o rs
Altersgruppe: 4 t h Gr ade
Virginia - Mathematics Standards of Learning (2009): 3 .7 , 4 .5 b,
4 .5 d
Virginia - Mathematics Standards of Learning (2016): 3 .5 , 4 .5 .b,
4 .5 .c
Fairfax County Public Schools Program of Studies: 3 .7 .a.4 , 3 .7 .a.6,
4 .5 .b.2, 4 .5 .b.3 , 4 .5 .b.4 , 4 .5 .d.1
Online-Ressourcen: W ho l e s and P ar t s
St udent s
pract ice
6
8
12
6
8
5
min
min
min
min
min
min
Opening
Class
discussion
Mat h
Worksheet
Pract ice
T eacher
present s
M at h Obj e c t i v e s
E x pe r i e nc e a visual model for adding fractions.
L e ar n to add fractions with like denominators.
De v e l o p an understanding of the need for common
denominators.
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Closing
2
Ope ni ng | 6 min
A s k students to draw a picture that illustrates
illustrates
and a picture that
.
When students are finished, ask one student to come to the board and draw
their picture.
The shapes may vary, but most students will probably draw a rectangle or a
circle:
A sk : How do we know that these pictures show
and
?
The rectangles are cut into 5 equal pieces. In the first picture,
two of the 5 pieces are colored, illustrating
, and in the second
picture one of the 5 pieces is colored, illustrating
.
For the next question, make sure that the whole in the two pictures is the
same.
S ay : Now let’s add and
.
Display the following:
S ay : We took the one colored piece from the second picture and
added it to the two colored pieces from the first picture, so we get
3 colored pieces.
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3
In this way students can see why
+
= .
Remind students that the numerator states how many pieces we are taking
out of the total number of equal pieces, or the denominator.
T e ac he r pr e se nt s M at h game : W ho l e s and P ar t s - A dd
F r ac t i o ns | 8 min
Using the Preset mode, on the projector, present Matific ’s episode W h o le s
a n d Pa r t s - A d d F r a c t io n s to the class.
This episode enables students to practice the addition of fractions with like
denominators, aided by concrete representations. The goal is to evaluate an
addition sentence. You can model a whole using either a disc or a rectangle,
and the tools at your disposal.
E x a m p le :
S ay: Please read the instructions at the bottom of the screen.
Students can read the instructions.
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S ay: We want to add fractions with like denominators. First we
make two forms of . We create a “unit” of either a rectangle or a
circle. The denominator is 3, so we need to divide the unit into 3
equal sized parts. The numerator is 2, so we need to remove 1 part,
and place it into the bin, leaving 2 parts. We can either do the same
again, or use the replication tool.
E x a m p le :
Move the colored pieces from one rectangle onto the other, so that the
colored pieces fill one rectangle, leaving what is left represented on the
second rectangle.
E x a m p le :
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5
A sk students for the sum.
The sum is or
, either answer is correct. Those two answers
are the same, because we can look at the answer as 4 colored
pieces, with each being equal to a third, or we can look at the
answer as 1 whole and 1 third.
S t ude nt s pr ac t i c e M at h game : W ho l e s and P ar t s - A dd
F r ac t i o ns | 12 min
Have students play W h o le s a n d Pa r t s - A d d F r a c t io n s on their
personal devices.
Circulate answering questions.
Advanced students can play other variants of this episode W h o le s a n d
Pa r t s - A d d M ix e d N u m b e r s or W h o le s a n d Pa r t s - M ix e d
N u m b e r A d d it io n .
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C l ass di sc ussi o n | 6 min
S ay : Using diagrams to represent fractions is a fantastic way to
visualize what is happening. Now that we have practiced adding
fractions by looking at colored pieces, we can see what steps are
required.
A sk : How do we add fractions with the same denominator?
We add the numerators and keep the denominator the same.
S ay: Give me an example of a fraction addition problem and its
answer.
Answers will vary.
A sk: Why does the denominator not change in the sum?
One way to respond is that the denominator tells us the overall
size, or total number of pieces. For example, in the problem
, the whole has been cut into 7 pieces. We are looking at
the 7 pieces, and
+
or 3 of
or 2 of the 7 pieces. When we add them
together we get 5 out of the 7 pieces, or . The denominator
does not change because it still requires 7 pieces to make a
whole. Another way to explain it is that the denominator counts
the number of pieces we divided the whole into. For example, in
the problem + the first fraction tells us there are 3 sevenths
and the second tells us that there are 2 sevenths. Now, 3 plus 2
are 5., giving us 5 sevenths.
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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 | 8 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 - Un it F r a c t io n s .
3. 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, answering questions as necessary.
C l o si ng | 5 min
A sk : A new student thinks that + = . How can you explain why
this answer is incorrect? How can you help that student arrive at
the correct answer?
A possible response: Adding
we simplify
, we get
to itself cannot result in . When
, which means
is equal to , so
plus
cannot equal . When we add fractions with like denominators,
we add the numerators and keep the denominator the same.
Therefore,
+
=
, which simplifies to
.
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