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U n t er r i ch t spl a n
Are a and Pe rime t e r (Imp e rial )
Altersgruppe: 4 t h Gr ade
Virginia - Mathematics Standards of Learning (2009): 3 .9d, 5 .8a,
5 .8b, 6.10c
Virginia - Mathematics Standards of Learning (2016): 4 .7 , 5 .8.a,
5 .8.b
Fairfax County Public Schools Program of Studies: 3 .9.d.1, 3 .9.d.2,
5 .8.a.1, 5 .8.a.2, 5 .8.a.3 , 5 .8.a.4 , 5 .8.a.7 , 5 .8.b.1, 5 .8.b.3 ,
6.10.c .1
Online-Ressourcen: F e nc e d I n
Opening
T eacher
present s
St udent s
pract ice
Ext ension
Mat h
Pract ice
6
12
12
14
3
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 real-world example of perimeter and area
P r ac t i c e measuring lengths
L e ar n to calculate perimeter and area
De v e l o p algebraic skills
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Ope ni ng | 6 min
A sk the students to define perimeter and area. They should write
their responses in their notebooks.
When the students are done writing, share.
A sk : What is the definition of perimeter?
Perimeter is the distance around a shape.
Ask: What is the definition of area?
Area is the amount of space inside a shape.
Display the following rectangle:
A sk : How can we find the perimeter of this rectangle?
We add 24 and 78 and double the result.
A sk : Why do we double?
We want the distance all the way around the rectangle. Adding 24
and 78 only gets us halfway around the rectangle.
A sk : How do we find the area of this rectangle?
We multiply 24 by 78.
A sk : What unit would we use for the perimeter of this rectangle?
We would use feet as the unit.
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A sk : What unit would we use for the area of this rectangle?
We would use square feet.
A sk : Why do we use square feet?
Area asks us how many small squares fit inside the rectangle.
Each square in this case is 1 foot by 1 foot. We are asking how
many 1 foot by 1 foot squares we can place inside the rectangle.
Thus, the unit is square feet.
T e ac he r pr e se nt s M at h game : F e nc e d I n - P e r i me t e r - A r e a:
L e v e l I ( yar ds) | 12 min
Present Matific ’s episode F e nc e d I n - P e r i me t e r - A r e a: L e v e l
I ( yar ds) to the class, using the projector.
The goal of the episode is to calculate perimeter and area after measuring a
rectangular piece of land.
E x a m p le :
S ay : Please read the question.
The question asks, “How many yards of fence will you need to
surround the park?”
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A sk : What are we being asked to find?
We are being asked to find the distance around the park, or the
perimeter of the park.
A sk : How can we figure out the perimeter?
We can measure the length and width of the park. Then we add
those two numbers together and double the sum.
A sk : What is the length of the horizontal side?
Students can answer based on the episode.
Move the tape measure to measure the vertical side.
A sk : What is the length of the vertical side?
Students can answer based on the episode.
A sk : How many yards of fence do we need?
Click on the
to enter the students’ answer.
If the answer is correct, the episode will proceed to the next question.
If the answer is incorrect, the question will wiggle.
The episode will present a total of six problems. The first four are
about perimeter and the last two are about area.
S t ude nt s pr ac t i c e M at h game : F e nc e d I n - P e r i me t e r A r e a: L e v e l I ( yar ds) | 12 min
Have the students play F e nc e d I n - P e r i me t e r - A r e a: L e v e l I
( yar ds) and F e nc e d I n - P e r i me t e r - A r e a: L e v e l I I ( yar ds)
on their personal devices. Circulate, answering questions as
necessary.
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E x t e nsi o n M at h P r ac t i c e : A r e a and P e r i me t e r W o r kshe e t |
14 min
Distribute graph paper.
Display the following problems. Have students work in groups of
four to solve.
On the graph paper:
1. draw all the rectangles you can find (whose length and width are whole
numbers) that have area:
a. 15 square units
b. 16 square units
c. 20 square units
d. 25 square units
2. find the perimeter of each of the rectangles you found in #1.
3. draw all the rectangles you can find (whose length and width are whole
numbers) that have perimeter:
a. 10 units
b. 11 units
c. 12 units
d. 16 units
4. find the area of each of the rectangles you found in #3.
Circulate, answering questions as necessary.
When the students are done working, ask: How many rectangles did
you find that have area 15? What are they?
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We found two rectangles. One is 1 unit by 15 units, and the other
rectangle is 3 units by 5 units.
A sk : How do you know that you have found all possible rectangles?
We used all the factors of 15. Fifteen has 4 factors: 1, 3, 5, and
15.
A sk : How many rectangles did you find that have area 16? What are
they?
There are three rectangles. One is 1 unit by 16 units, another is 2
units by 8 units, and the last is 4 units by 4 units.
A sk : What rectangles did you find that have area 20?
We found a rectangle that is 1 unit by 20 units, another that is 2
units by 10 units, and a third that is 4 units by 5 units.
A sk : What rectangles did you find that have area 25?
There are two rectangles – one is 1 unit by 25 units and the other
is 5 units by 5 units.
S ay : Let’s look at the perimeter of the rectangles you found.
Display the following table:
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A sk students for the perimeters of each rectangle and fill them
into the table.
A sk : If we know the area of a rectangle, do we know its perimeter?
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No. A rectangle with area 20 could have perimeter 42, 24, or 18
units.
A sk : How is it possible for us to have such different perimeters?
The rectangles in the table vary from really skinny and long to
square. The distance around these differently-shaped rectangles
varies.
S ay : Now let’s look at questions 3 and 4. Let’s make another table
and fill in.
Display the following table:
A sk students to fill in the table.
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A sk : Why could we not find any rectangles that have perimeter 11?
If the length and width of each rectangle must be a whole number,
then the perimeter cannot be odd. To find perimeter, we add the
length and the width and then double. When we double, we are
multiplying a whole number by 2. Multiplying a whole number by 2
gives an even number.
A sk : If we know the perimeter of a rectangle, do we know its area?
No. We saw that there are four possible rectangles with
perimeter 16. When we calculate the area of each, we get four
different areas.
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C l o si ng | 3 min
S ay: In this episode, we looked only at rectangles. Let’s close by
looking not only at rectangles but also at some other shapes.
Display the following shapes:
S ay : Here are a few ways to arrange nine squares with the edges
touching. So the area of each of the shapes is 9 square units. What
is the perimeter of each?
The first has a perimeter of 20 units. The second has a perimeter
of 12 units. The third has a perimeter of 18 units. The fourth has a
perimeter of 16 units.
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