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U n t er r i ch t spl a n
M o re M o d e l ing F rac t io ns
Altersgruppe: 4 t h Gr ade
Virginia - Mathematics Standards of Learning (2009): 2.3 a
Virginia - Mathematics Standards of Learning (2016): 1.4 .b, 2.4 .a,
2.4 .b
Fairfax County Public Schools Program of Studies: 2.3 .a.1, 2.3 .a.4 ,
2.3 .a.5
Online-Ressourcen: B e ads and F r ac t i o ns
Opening
T eacher
present s
St udent s
pract ice
Class
discussion
5
12
14
12
4
min
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 fractions
P r ac t i c e using fractions to describe parts of a whole
L e ar n to represent fractions
De v e l o p different representations that satisfy the same
conditions
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Ope ni ng | 5 min
Display the following:
S ay: Use fractions to describe the beads on the necklace. What
fraction is round? What fraction is striped? Etc.
Possible responses: Two fifths of the beads are spotted. Three
fifths of the beads are striped. Three fifths of the beads are
round. Two fifths of the beads are square.
S ay: Now let’s use the fraction
in our description. How would
you describe the necklace using
in your description?
Possible responses: The number of round beads is greater than
. The number of square beads is less than
striped beads is greater than
less than
. The number of
. The number of spotted beads is
.
S ay: In today’s episode, you will be building necklaces to model
fractions.
T e ac he r pr e se nt s M at h game : B e ads and F r ac t i o ns M o de l F r ac t i o ns: L e v e l I I | 12 min
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Using Presentation Mode, present Matific ’s episode B e ads and
F r ac t i o ns - M o de l F r ac t i o ns: L e v e l I I to the class, using the
projector.
The goal of the episode is to determine which beads to place on a necklace
in order to model the correct fraction or fractions.
E x a m p le :
S ay: Please read the instructions.
The instructions say, “Make a necklace such that exactly
the beads are striped and exactly
of
of the beads are square.”
A sk: What beads are available to use to make the necklace?
There are 4 different kinds of beads. There is a spotted round
bead, a striped round bead, a spotted square bead, and a striped
square bead.
A sk: How many beads should we use total if we want to satisfy
both conditions?
A possible response: We should use 6 total beads.
A sk: Out of the 6 beads, how many should be striped?
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There should be 1 striped bead.
A sk: Out of the 6 beads, how many should be square? How do you
know?
There should be 4 square beads. We want
square. Four sixths is equal to
of the beads to be
.
A sk the students which beads to place on the string.
As the students make suggestions, move beads to the monster’s
right hand.
When the students are satisfied with the necklace, click
.
If the necklace is accurate, the episode will proceed to the next problem.
If the necklace is not accurate, the instructions will wiggle.
The episode will present a total of three problems. The second
problem will ask for a necklace where at least
round and at most
of the beads are
of the beads are square. The third problem
will ask for a necklace where exactly
of the beads are striped
and exactly
of the beads are round. With both problems,
encourage the students to discuss and debate the ways to meet
both conditions.
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S t ude nt s pr ac t i c e M at h game : B e ads and F r ac t i o ns M o de l F r ac t i o ns: L e v e l I I | 14 min
Have the students play B e ads and F r ac t i o ns - M o de l
F r ac t i o ns: L e v e l I I on their personal devices. Circulate,
answering questions as necessary.
C l ass di sc ussi o n | 12 min
S ay: Let’s consider the problem where we need to make a necklace
where exactly
the beads are round and
the beads are spotted.
There are many necklaces that we could make that satisfy these
conditions. First of all, we can change the number of total beads we
use. What is the fewest number of beads we can use? Why?
The fewest number of beads we can use is 2. In order to be able
to model
, we need an even number of beads.
S ay: If we use 2 beads, what are the options if we want exactly
the beads to be round and
the beads to be spotted?
We could use 1 round spotted bead and 1 square striped bead. Or
we could use 1 round striped bead and 1 square spotted bead.
Those are the only 2 options.
S ay: Let’s use 4 beads instead. How many options exist if we use 4
beads and we want exactly
the beads to be round and
beads to be spotted? What are the options?
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There are 3 options:
1. 2 round striped beads and 2 square spotted beads,
2. 1 round striped bead, 1 round spotted bead, 1 square striped bead, and 1
square spotted bead, or
3. 2 round spotted beads and 2 square striped beads.
S ay: Let’s use 6 beads instead. How many options exist if we use 6
beads and we want exactly
the beads to be round and
beads to be spotted? What are the options?
the
There are now 4 options:
1. 3 round striped beads and 3 square spotted beads,
2. 2 round striped beads, 1 round spotted bead, 2 square spotted beads, and
1 square striped bead,
3. 1 round striped bead, 2 round spotted beads, 2 square striped beads, and 1
square spotted bead, or
4. 3 round spotted beads and 3 square striped beads.
S ay: We can further complicate the problem by using the phrase “at
least”. Let’s consider the problem where we need to make a
necklace where at least
the beads are round and exactly
the
beads are spotted. Let’s start with 2 total beads. How many options
exist if we use 2 beads and we want at least
round and exactly
options?
the beads to be
the beads to be spotted? What are the
There are 3 options:
1. 1 round spotted bead and 1 square striped bead,
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2. 1 round striped bead and 1 square spotted bead, or
3. 2 round beads, where 1 is spotted and the other is striped.
S ay: Let’s use 4 beads instead. How many options exist if we use 4
beads and we want at least
the beads to be round and exactly
the beads to be spotted? What are the options?
There are 6 options:
1. 2 round spotted beads and 2 square striped beads,
2. 1 round spotted bead, 1 round striped bead, 1 square spotted bead, and 1
square striped bead,
3. 2 round striped beads and 2 square spotted beads,
4. 2 round spotted beads, 1 round striped bead, and 1 square striped bead,
5. 1 round spotted bead, 2 round striped beads, and 1 square spotted bead, or
6. 4 rounds beads, where 2 are spotted and 2 are striped.
S ay: Now let’s use 6 beads. How many options exist if we use 6
beads and we want at least
the beads to be round and exactly
the beads to be spotted? What are the options?
There are 10 options:
1. 3 round spotted beads and 3 square striped beads,
2. 2 round spotted beads, 1 round striped bead, 1 square spotted bead, and 2
square striped beads,
3. 1 round spotted bead, 2 round striped beads, 2 square spotted beads, and
1 square striped bead,
4. 3 round striped beads and 3 square spotted beads,
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5. 3 round spotted beads, 1 round striped bead, and 2 square striped beads,
6. 2 round spotted beads, 2 round striped beads, 1 square spotted bead, and
1 square striped bead,
7. 1 round spotted bead, 3 round striped beads, and 2 square spotted beads,
8. 3 round spotted beads, 2 round striped beads, and 1 square striped beads,
9. 2 round spotted beads, 3 round striped beads, and 1 square spotted bead,
or
10. 6 rounds beads, where 3 are spotted and 3 are striped.
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C l o si ng | 4 min
S ay: Suppose the episode asked us to make a necklace where
exactly
of the beads are striped and exactly
of the beads are
round. What is the first decision we need to make?
We need to decide who many total beads to use in the necklace.
A sk: What is the fewest number of beads we could use?
The fewest beads we could use is 4.
S ay: Let’s use 4 beads. What is the next decision we need to make?
We need to decide if we want to satisfy both conditions
simultaneously (i.e., use round striped beads) or separately (i.e.,
use round spotted beads and square striped ones).
S ay: Suppose we use round striped beads. Which beads do we
place on the necklace?
We use 1 round striped bead, 1 square striped bead, and 2 square
spotted beads.
S ay: Suppose we do not use any round striped beads. Then which
beads do we place on the necklace?
We use 1 round spotted bead, 2 square striped beads, and 1
square spotted bead.
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