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U n t er r i ch t spl a n
Who l e s and Part s – M ake M ixe d
Numb e rs
Altersgruppe: 4 t h Gr ade , 5 t h Gr ade
Virginia - Mathematics Standards of Learning (2009): 3 .3 a, 3 .3 b,
3 .7
Virginia - Mathematics Standards of Learning (2016): 3 .2.a, 3 .2.b
Fairfax County Public Schools Program of Studies: 3 .3 .a.1, 3 .3 .b.1,
3 .3 .b.2, 3 .7 .a.3
Online-Ressourcen: W ho l e s and P ar t s
T eacher
present s
St udent s
pract ice
7
6
min
min
Opening
Class
discussion
Mat h
Pract ice
12
7
10
3
min
min
min
min
Closing
M at h Obj e c t i v e s
E x pe r i e nc e a visual model for mixed numbers.
P r ac t i c e representing mixed numbers.
L e ar n the meaning of the numerator and the denominator.
De v e l o p mixed numbers and improper fraction equivalencies.
Ope ni ng | 7 min
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A s k students to draw a picture illustrating .
When students are finished, ask one student to draw the picture.
The shape may vary, but most students will probably draw a rectangle or a
circle:
A sk: How do we know this picture represents ?
The object is cut into 5 equal pieces. Three of the 5 pieces are
colored – illustrating .
S ay: The de no mi nat o r , or bottom number, shows the total
number of pieces needed to make one whole. The nume r at o r , or
top number, shows the number of pieces we are considering.
A sk : So what does
mean?
It means we have 2 whole objects and part of a third. We have
of the third object. The picture represents what
looks like:
S ay: A number such as
, that combines a whole number with a
fraction, is called a mi x e d numbe r .
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A sk : Where might you see a mixed number?
Answers will vary. Possible responses: we see mixed numbers in
people’s ages, distances, recipes, time, weights, etc.
T e ac he r pr e se nt s M at h game : W ho l e s and P ar t s - M ake
M i x e d N umbe r s | 6 min
Present Matific ’s episode W h o le s a n d Pa r t s - M a k e M ix e d N u m b e r s
to the class, using the Preset mode, on the projector.
This episode introduces concrete representations of mixed numbers. You
have to create a given part of a whole. 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 create
units.
A sk: Looking only at the whole number part of the mixed number,
how many units should we take?
Move one unit of a rectangle.
E x a m p le :
A sk: Looking only at the fraction part of the mixed number, what do
the numerator and denominator tell us?
The numerator tells us how many pieces we are taking out of the
total number of equal pieces, the denominator.
Drag another unit, cut it into two equal pieces, and toss one part into the bin.
E x a m p le :
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S ay : When we represent a mixed number, first we represent the
whole part of the mixed number, and then we represent the fraction.
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 - M ake
M i x e d N umbe r s | 12 min
Have students play W h o le s a n d Pa r t s - M a k e M ix e d N u m b e r s on
their personal devices.
Circulate answering questions.
Students who finish Wholes and Parts can move on to play S a y C h e e s e M o d e l M ix e d N u m b e r s .
Copyright 2015 www.matific.com
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C l ass di sc ussi o n | 7 min
S ay: In this episode, we were building mixed numbers. First, we
represented the whole part and then the fraction part of the mixed
number. How else can we build the whole part of a mixed number?
We could use 2 half pieces, 3 thirds, 4 fourths, 5 fifths, etc., to
represents the whole.
A sk: What does this tell us about fractions, in which the numerator
is equal to the denominator?
When the numerator is equal to the denominator, the fraction is
equal to 1, or a whole.
A sk: So how many sevenths equal 1?
Seven-sevenths equal 1.
A sk: So how many elevenths equal 1?
Eleven-elevenths equal 1.
A sk: So how many hundredths equal 1?
One hundred-hundredths equal 1.
M at h P r ac t i c e : M i x e d N umbe r s R e pr e se nt at i o n W o r kshe e t
| 10 min
S ay : Let’s look at the mixed number
. We could represent the
whole with one unit and then represent the fraction with 2 pieces
sized each. Instead, let’s use only fifths. How many fifths do we
need to represent one whole?
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We need 5 fifths to represent one whole.
S ay: And we have 2 fifths, which represent the fraction. How many
fifths do we have altogether?
We have 7 fifths altogether.
Display:
S ay : This fraction,
, is called an i mpr o pe r f r ac t i o n which is a
fraction where the numerator is greater than, or equal to, the
denominator.
A sk: Now let’s consider
. If we only use fourths, how many
fourths do we need in order to show
? How do you know?
We need 7 fourths. With 4 fourths to represent the whole, plus 3
fourths to represent the fraction. Altogether, that’s 7 fourths.
Display:
A sk: Now let’s consider
. If we use only ninths, how many ninths
do we need to arrive at
? How can we represent
improper fraction? How do you know?
as an
We need 17 ninths. We need 9 ninths to represent the whole plus
8 ninths to represent the fraction. Altogether, that’s 17 ninths.
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Display:
A sk: Now let’s consider
. How can we represent this improper
fraction as a mixed number? How do you know?
The numerator is 11, which means there are 11 sixths. We take 6
sixths and represent it by one whole. Leaving 5 sixths.
Display:
A sk: Now let’s consider
. If we use only sevenths, how many
sevenths do we need to arrive at
? How do you know?
We need 17 sevenths. To represent the 2 whole values, we need 7
sevenths each. That’s 14 sevenths so far. Then we need 3
sevenths to represent the fraction. So that’s 17 sevenths
altogether.
Display:
S ay: Let’s consider
. How can we represent this improper
fraction as a mixed number? How do you know?
The numerator is 19, which means there are 19 eighths. Eighteighths is equal to one whole, so 19 eighths is equal to two
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wholes with a remainder of 3 eighths.
Show:
S ay : We have been writing the same number twice, once as a mixed
number and once as an improper fraction. What do you notice about
the equal numbers?
Answers will vary. Possible responses include:
1. When the whole number part of the mixed number is 1, the numerator in
the improper fraction is equal to the sum of the numerator and
denominator in the mixed number.
2. The denominator is the same in both the mixed number and the
improper fraction.
3. In the improper fraction, if we divide the numerator by the denominator,
we obtain the mixed number.
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C l o si ng | 3 min
A sk : What does the denominator represent?
The de no mi nat o r , or bottom number, shows the total number of
pieces needed to make one whole.
A sk : What does the numerator represent?
The nume r at o r , or top number, shows the number of pieces we
are considering.
A sk : So what does
mean?
It means we have 2 whole objects and part of a third. We have
of the third object.
A sk : How do we call such a number
?
A number such as
, that combines a whole number with a
fraction, is called a mi x e d numbe r .
Copyright 2015 www.matific.com