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U n t er r i ch t spl a n
R e p re s e nt ing Bas ic R at io s
Altersgruppe: 6t h Gr ade
Virginia - Mathematics Standards of Learning (2009): 6.1, 6.2a
Virginia - Mathematics Standards of Learning (2016): 6.1, 6.2.a
Fairfax County Public Schools Program of Studies: 6.1.a.5 , 6.1.a.6,
6.2.a.1
Online-Ressourcen: B i r ds o n t he W i r e
Opening
T eacher
present s
St udent s
pract ice
Class
discussion
5
12
12
14
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 comparing quantities
P r ac t i c e representing ratios
L e ar n that different arrangements might have equivalent
ratios
De v e l o p proportional reasoning
Ope ni ng | 5 min
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A sk : What does the word r at i o mean?
A ratio is a comparison of two numbers, using division.
Display the following flowers:
A sk : What is the ratio of purple to red flowers?
The ratio of purple to red flowers is 3 to 2.
A sk : How do we write the ratio of 3 to 2?
There are three ways to write it: 3 to 2, 3:2, or
.
A sk : Would it be correct to say that the ratio of purple to red
flowers is 2 to 3?
No. The order of the problem is important. If the ratio of purple
to red flowers is 3 to 2, then there are more purple flowers. There
are 3 purple flowers for every 2 red ones. If the ratio of purple to
red flowers is 2 to 3, then there are more red flowers. There are 2
purple flowers for every 3 red ones.
Display the following flowers:
S ay : Sydney says that the ratio of purple to red flowers here is 6 to
2. Pat disagrees and says that it is 3 to 1. Who is correct?
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They are both correct. There are multiple ways to describe the
flowers using ratios. The ratio 3 to 1 says that there are 3 purple
flowers for every 1 red flower. That is true whether there is 1 red
flower (and 3 purple), 2 red flowers (and 6 purple), 10 red flowers
(and 30 purple), or any other possible combination where the
number of purple flowers is 3 times the number of red ones.
T e ac he r pr e se nt s M at h game : B i r ds o n t he W i r e - R at i o s:
L e v e l I | 12 min
Using Presentation Mode, present Matific ’s episode B ir d s o n t h e W ir e R a t io s : L e v e l I to the class, using the projector.
The goal of the episode is to practice ratios by placing birds on a wire in the
given ratio.
E x a m p le :
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S ay : Please read the instructions.
The instructions say, “Place birds on the wires so that the ratio of
blue birds to green birds is 1 to 3.”
A sk : What does a ratio of 1 to 3 mean?
It means that for every 1 blue bird, there are 3 green birds.
S ay : Yes. A ratio shows a comparison. So it is possible that there is
exactly 1 blue bird on the wires, but it is possible that there are
more. How many birds of each color should we place on the wires?
As the students make suggestions, move birds onto the wires.
When the students are satisfied with the birds, click
.
If the ratio is accurate, the episode will proceed to the next problem.
If the ratio is not accurate, the instructions will wiggle.
The episode will present a total of three problems. The final
problem will contain two ratios. All three colors of birds will need
to be moved onto the wires.
S t ude nt s pr ac t i c e M at h game : B i r ds o n t he W i r e - R at i o s:
L e v e l I | 12 min
Have the students play B i r ds o n t he W i r e - R at i o s: L e v e l I on
their personal devices. Circulate, answering questions as necessary.
C l ass di sc ussi o n | 14 min
S ay : Let’s consider the problem where we want to place the birds
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on the wire so that the ratio of blue birds to green birds is 4 to 3.
Display the following:
S ay : There is not just one solution to this problem. Why not?
A ratio compares two numbers. This ratio says that for every 4
blue birds, there are 3 green birds. If there are more than 4 blue
birds, then there are more than 3 green birds. In order for the ratio
to stay 4 to 3, each time we add 4 blue birds, we need to add 3
green birds.
S ay : So we can change the number of birds that we place on the
wire. What is the fewest number of birds we can use? Why?
The fewest number of birds that we can place is 7. The fewest
number of blue birds we can use is 4, and the fewest number of
green birds is 3. So altogether, that’s 7 birds.
Display the following:
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S ay : Of course, we could add birds. As you said, every time we add 4
blue birds, we need to add 3 green birds. So instead of 4 blue birds,
let’s say we place 8 blue birds on the wires. Then how many green
birds should be on the wires to keep the ratio the same?
With 8 blue birds, we need 6 green birds to keep the ratio the
same.
Display the following:
A sk : If we continue the pattern, what numbers would be in the next
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3 rows of the table?
T
​ he next row would have 12 blue birds and 9 green birds. The
fourth row would have 16 blue birds and 12 green birds. The fifth
row would have 20 blue birds and 15 green birds.
Display the following:
A sk : What patterns do you notice within the table?
Responses may vary. Possible responses may include: Numbers
on the left increase by 4. Numbers on the right increase by 3. The
number on the right is always of the number on its left. If we
add two rows of the table, we get another row. If we multiply one
row of the table by a number, we get another row.
Display the following:
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S ay : Suppose we skipped some rows in the table. How many green
birds should we place on the wires if we place 44 blue birds on the
wires, if we want to keep the ratio 4 to 3? How can we figure it
out?
Responses may vary. Possible responses include: To get 44 blue
birds, we have multiplied the 4 original birds by 11. So we need to
multiply the 3 original green birds by 11 also, to keep the ratio the
same. Three times 11 is 33, so we need 33 green birds. Another
way to do the calculation would be to notice that the row after
20 blue birds and 15 green birds would be 24 blue birds and 18
green birds. Then we could add these two rows together (20 and
24 to get 44 blue birds, and 15 and 18 to get 33 green birds).
S ay : Let’s consider a new problem. Suppose we want to place the
birds on the wire so that the ratio of blue birds to green birds is 3
to 7. What is the fewest number of birds we can use? Why?
T
​ he fewest number of birds we can use is 10. We need 3 blue
birds and 7 green birds, for a total of 10 birds.
A sk : If we didn’t use 10 birds, what is the next fewest number of
birds we can use? Why?
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The next fewest number of birds we can use is 20. Each time we
add 3 blue birds, we add 7 green birds. So we can have 6 blue
birds and 14 green birds (for a total of 20 birds) and still have a
ratio of 3 to 7.
Display the following:
A sk : If we continue the pattern, what numbers would be in the next
2 rows of the table?
The next row would have 9 blue birds and 21 green birds. The
fourth row would have 12 blue birds and 28 green birds.
Display the following:
S ay : Suppose we skipped some rows in the table. Keeping the ratio
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the same, how many blue birds should we place on the wires if we
place 56 green birds on the wires? How do you know?
We need 24 blue birds if there are 56 green birds. A possible
explanation: The ratio is 3 to 7. If we multiply the 7 by 8 to get
56, we need to multiply the 3 by 8 to get 24.
S ay : Keeping the ratio the same, how many green birds should we
place on the wires if we place 18 blue birds on the wires? How do
you know?
We need 42 green birds if there are 18 blue birds. A possible
explanation: The ratio is 3 to 7. If we multiply the 3 by 6 to get
18, we need to multiply the 7 by 6 to get 42.
S ay : Let’s consider a new problem. Suppose we want to place the
birds on the wire so that the ratio of blue birds to green birds is 4
to 6. What is the fewest number of birds we can use? Why?
The fewest number of birds we can use is 5. The ratio 4 to 6 is
the same as the ratio 2 to 3. For every 2 blue birds, we place 3
green birds. If we place 2 blue birds and 3 green birds, then we
have placed 5 total birds on the wires.
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C l o si ng | 4 min
Display the following:
A sk : What is the ratio of shaded to unshaded squares?
The ratio of shaded to unshaded squares is 5 to 4.
A sk : What is the ratio of unshaded to shaded squares?
The ratio of unshaded to shaded squares is 4 to 5.
A sk : What is the ratio of shaded to total squares?
The ratio of shaded to total squares is 5 to 9.
A sk a student to come to the board and draw a diagram that has
more shaded squares but where the ratio of shaded to unshaded
squares remains the same.
A possible response:
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