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U n t er r i ch t spl a n
M ul t ip l y F rac t io ns b y a Who l e
Numb e r
Altersgruppe: 4 t h Gr ade , 5 t h Gr ade
Virginia - Mathematics Standards of Learning (2009): 6.4 , 6.6a
Virginia - Mathematics Standards of Learning (2016): 6.5 .a
Fairfax County Public Schools Program of Studies: 6.4 .a.2, 6.6.a.1
Online-Ressourcen: W ho l e s and P ar t s
T eacher
present s
St udent s
pract ice
Class
discussion
Mat h
Worksheet
5
8
12
10
10
min
min
min
min
min
Opening
M at h Obj e c t i v e s
E x pe r i e nc e a visual model for multiplying and simplifying
fractions.
P r ac t i c e convert improper fraction to mixed number.
L e ar n to multiply a fraction by a whole number.
De v e l o p algebra skills.
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Ope ni ng | 5 min
A sk : Four children ate three slices of pizza each. How many slices
of pizza did the children eat?
All together, the children ate twelve slices of pizza.
A sk : Four children each ate
did the children eat?
of a pizza. How many trays of pizza
If each child ate , four children ate 4x3, or
of a pizza.
Present 12 slices of pizza on the board:
A sk : How many pizzas are there in
We can see that
are
, or
?
pizzas.
R e mi nd the class: A n i mpr o pe r f r ac t i o n is a fraction in which
the top number is larger than (or equal to) the bottom number. A
mi x e d numbe r is a whole number and a proper fraction combined.
T e ac he r pr e se nt s M at h game : W ho l e s and P ar t s - | 8 min
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Using Preset mode, present Matific ’s episode W h o le s a n d Pa r t s - to the
class, using the projector.
This episode allows the students to practice the multiplication of fractions
by whole numbers and the conversion between improper fractions and mixed
numbers, aided by concrete representations. The goal is to evaluate a
multiplication sentence. You can model a whole using either a disc or a
rectangle, and use the tools at your disposal.
E x a m p le :
S ay : Please read the instructions at the bottom of the screen.
S ay: We want to multiply a fraction by a whole number. First we
write a fraction in the form of : We take one unit, divide it into
three equal sized pieces (the denominator), and dispose of one
piece in order to keep two colored pieces (the numerator).
E x a m p le :
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S ay : Now we take the replication tool and duplicate this form five
times.
E x a m p le :
S ay : Now, in order to find out how many thirds we have, we count
the colored pieces.
A sk : How many thirds do we have?
We have ten thirds, or written mathematically:
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After we have solved this problem and found the improper fraction, we are
asked to convert it to a mixed number.
E x a m p le :
S ay: Please read the instructions at the bottom of the screen.
S ay : We need to convert the improper fraction
to a mixed
number. We take all the forms and rearrange them. We move the
colored pieces from one rectangle onto the other, in order to fill all
the units with colored pieces with some left over.
E x a m p le :
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A sk the students for the answer.
The answer is
because we have three whole units and one
colored piece out of three.
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 - | 12 min
Have students play W h o le s a n d Pa r t s - on their personal devices.
Circulate among them answering their questions.
C l ass di sc ussi o n | 10 min
Discuss any challenges the students faced while working individually.
Ask the class for responses as to how they dealt with any common issues
their classmates brought up.
S ay : Now that we have practiced multiplying fractions by whole
numbers by looking at shapes, we can see what steps are required.
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A sk: How do we multiply fractions by whole numbers?
We multiply the whole number by the numerator, and keep the
denominator the same.
S ay : Let’s multiply
× 4.
Have the students solve it in their notebooks. When they have finished
working, they should share their answers with one another.
We multiply the whole number by the numerator: 4 × 4 = 16, and we keep the
denominator the same. So the answer is
.
A sk: Why does it make sense that the denominator does not change
in multiplication?
The numerator counts the number of pieces the whole is divided
into. For example, in the problem
× 4 , the fraction tells us there
are four ninths. Now 4 × 4 = 16. And in this case,16 ninths
.
A sk : How do we convert an improper fraction into a mixed number?
We check how many times the numerator can by divided by the
denominator. The answer becomes the whole part of the mixed
number. The remainder is the numerator of the fraction part of
the mixed number, and the denominator stays the same.
S ay : Let’s convert
into a mixed number.
Have the students solve it in their notebooks. When they have finished, they
should share their answers.
16 can be divided by 9 once, so the whole part of the mixed number is 1. The
remainder is 7 so the numerator of the fraction part of the mixed number is 7,
and the denominator remains 9. So the answer is:
.
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M at h W o r kshe e t P r ac t i c e : M ul t i pl yi ng F r ac t i o ns by W ho l e
N umbe r s - Uni t F r ac t i o ns | 10 min
Have the students work on the following worksheets:
1. M u lt ip ly in g F r a c t io n s b y W h o le N u m b e r s - Un it F r a c t io n s .
2. M u lt ip ly in g F r a c t io n s b y W h o le N u m b e r s - Un it F r a c t io n s
w it h Un k n o w n s .
3. M u lt ip ly in g F r a c t io n s B y W h o le N u m b e r s - M u lt ip ly in g A n d
S im p lif y in g .
Some students may be ready to advance to M u lt ip ly in g F r a c t io n s B y
W h o le N u m b e r s - F in d in g Un k n o w n s .
Circulate among the students answering questions as necessary.
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