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U n t er r i ch t spl a n
So l ving R at io Pro b l e ms
Altersgruppe: 6t h Gr ade
Virginia - Mathematics Standards of Learning (2009): 6.1
Virginia - Mathematics Standards of Learning (2016): 6.1, 6.12.a,
6.12.b, 6.12.c , 6.12.d
Fairfax County Public Schools Program of Studies: 6.1.a.1,
6.1.a.10, 6.1.a.2, 6.1.a.3 , 6.1.a.4 , 6.1.a.5 , 6.1.a.6, 6.1.a.7
Online-Ressourcen: Out o f P r o po r t i o n
Opening
T eacher
present s
St udent s
pract ice
Mat h
Pract ice
5
12
15
10
5
min
min
min
min
min
M at h Obj e c t i v e s
E x pe r i e nc e a visual model for ratios
P r ac t i c e using a tape diagram
L e ar n to solve equivalent ratios
De v e l o p proportional reasoning
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Closing
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Ope ni ng | 5 min
Have students work in pairs. Present them with the following
question:
Rachel discovers that by mixing 4 teaspoons of blue paint with 3 teaspoons
of green paint, she obtains the perfect color for her painting. She wants to
create a larger batch. How could Rachel mix larger amounts of paint to create
the same shade?
After the pairs have worked for a few minutes, share. Ask for
students to name a possible ratio of paints.
Possible solutions: 8 teaspoons of blue with 6 teaspoons of
green, 4 cups of blue with 3 cups of green, etc.
Write all solutions on the board, without editing.
Pick a correct solution on the board. Ask: Who agrees with this
solution? How do you know it is correct?
The solution should be equivalent to 4:3, such as 8:6, 12:9, 2:1.5,
etc. They are e q ui v al e nt r at i o s because when they are in
si mpl e st f o r m, they are equal.
Leave the work on the board for the closing discussion.
T e ac he r pr e se nt s M at h game : Out o f P r o po r t i o n - R at i o s:
L e v e l I | 12 min
Using Presentation Mode, present Matific ’s episode Out o f
P r o po r t i o n - R at i o s: L e v e l I to the class, using the projector.
The goal of the episode is to use a tape diagram to solve ratio problems.
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E x a m p le :
S ay: Please read the problem at the bottom of the episode.
The problem says, “There are 6 bears in the zoo. How many zebras
are in the zoo?”
S ay: Please read the sentence just below the t ape di agr am .
The sentence says, “In the city zoo, there are 5 zebras for every 2
bears.”
S ay: Now let’s look at the tape diagram. Why are the rectangles on
the top of length 5 and the rectangles on the bottom of length 2?
The ratio of zebras to bears is 5 to 2. So the rectangles for the
zebras have length 5 and the rectangles for the bears have length
2.
A sk: Why are there 3 rectangles of length 2?
There are 3 rectangles of length 2 to represent the 6 bears.
A sk: Why are there 3 rectangles of length 5?
There are 3 rectangles of length 5 because there are 3 rectangles
of length 2. Each time we place a rectangle in the bear row, we
must place a rectangle in the zebra row, in order to keep the ratio
of zebras to bears correct.
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A sk: How many zebras are in the zoo?
Click on the
to enter the students answer.
If the answer is correct, the episode will proceed to the next problem.
If the answer is incorrect, the problem will wiggle.
The episode will present a total of three problems. In the second
problem, one rectangle of length 4 and one of length 3 will appear
on the tape diagram. You will have to place more rectangles on the
tape diagram yourself. Turn the wheel
to adjust the length of
the rectangle. In the third problem, no rectangles will appear. Use
the wheel to place them yourself.
S t ude nt s pr ac t i c e M at h game : Out o f P r o po r t i o n - R at i o s:
L e v e l I | 15 min
Have the students play Out o f P r o po r t i o n - R at i o s: L e v e l I
and Out o f P r o po r t i o n - R at i o s: L e v e l I I on their personal
devices. Point out to the students that some questions ask about a
component within the ratio and some ask for the total. Circulate,
answering questions as necessary.
M at h P r ac t i c e : R at i o P r o bl e ms W o r kshe e t | 10 min
Display the following problems. Have students work independently.
1. In a math class, there are 6 students writing in pencil for every 2 students
using pen.
1. If there are 18 students using pencil, how many students are using
pens?
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2. If there are 18 students using pencil, how many total students are in the
class?
3. In simplest form, what is the ratio of students using pencils to total
students?
2. On a highway, there are 7 cars for every 2 trucks.
1. If 10 trucks pass, how many cars pass?
2. If 6 trucks pass, how many total vehicles pass?
3. In simplest form, what is the ratio of cars to total vehicles?
4. In simplest form, what is the ratio of total vehicles to cars?
5. In simplest form, what is the ratio of trucks to total vehicles?
3. On a field trip, there are 10 students for every teacher.
1. If there are 30 students, how many teachers are there?
2. If there are 5 teachers, how many students are there?
3. If there are 5 teachers, how many people are there total on the trip?
Review solutions. Discuss any questions the students may have.
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C l o si ng | 5 min
Return to the opening question about Rachel’s paints.
A sk: Are all solutions correct? How do we know? Are there any
answers we should cross off?
In each correct solution, the ratio of blue to green paint should be
4:3.
A sk: How many possible answers are there to Rachel’s paint
problem? How do you know?
There are an infinite number of solutions because there are an
infinite number of ratios equivalent to 4:3. (Some solutions are
more practical than others.)
Hand out a small sheet of paper. Ask students to write their own
ratio problem on the paper.
Collect the papers to review later.
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