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U n t er r i ch t spl a n
M o re Are a and Pe rime t e r
(M e t e rs )
Altersgruppe: 4 t h Gr ade
Virginia - Mathematics Standards of Learning (2009): 3 .9d, 5 .8a,
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.2, 5 .8.a.3 , 5 .8.a.4 , 5 .8.a.7 , 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
14
12
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 solve the following problem by working in their
notebooks: Find the perimeter and area of this rectangle.
When the students are done working, share. Ask: What is the
perimeter of the rectangle? How do you know?
The rectangle is 6 units by 4 units. To find perimeter, we add the
lengths of the edges of the polygon. So here, we add 6 plus 4 plus
6 plus 4 and get 20 units. The perimeter is 20 units.
A sk: What is the area of the rectangle? How do you know?
The rectangle has area 24 square units. We can either count the
number of small squares to see that there are 24 of them, or we
can multiply the length by the width. If we multiply, we are
multiplying 6 by 4, so we get 24 square units.
A sk: Why in our answer to perimeter, we say 20 units, but in our
answer to area, we say 24 square units? Why are the units different?
For perimeter, we are asking for the total distance around the
shape. Distance is one-dimensional. So we just use units. For
area, we are asking how many small squares fit inside the shape.
The small squares are two-dimensional. So we use square units.
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 I I ( me t e r s) | 12 min
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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 I I ( me t e r s) to the class, using the projector.
The goal of the episode is to answer perimeter and area questions after
measuring a rectangular piece of land.
E x a m p le :
S ay: Please read the question.
The question asks, “How many meters of fence will you need to
surround the park?”
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: Why do we double the sum?
The rectangle has 4 sides. To get the perimeter, we need to add
all four sides. If we just add the length and the width, we have
found the combined distance of two of the four sides. Since the
opposite sides of a rectangle are equal, we can double the sum of
the length and the width to get the total distance around the
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rectangle.
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 meters 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 two are
perimeter problems, the third is an area problem, and the last three
are multi-step problems that alternate between perimeter and 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 I I ( me t e r s) | 14 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 I I
( me t e r s) 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 V
( me t e r s) on their personal devices. Circulate, answering
questions as necessary.
E x t e nsi o n M at h P r ac t i c e : P e r i me t e r and A r e a W o r kshe e t |
12 min
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Distribute the following problems. Have students work in pairs.
1. Consider the following rectangles:
a. Each rectangle has a perimeter of 28 meters and an area of 40 square
meters. When we place the rectangles next to each other, we get the
following larger rectangle. What is its perimeter and area?
b. How do the perimeter and area of this rectangle relate to the perimeter and
area of the two rectangles above? Why does this make sense?
2. Find the area of the shaded regions:
3. Find the area of the following shape in as many ways as possible. At least
one of the ways should include subtraction.
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When the students are done working, review solutions. Discuss any
questions the students may have.
C l o si ng | 3 min
A sk: True or False? The area of a polygon is the amount of space
inside the polygon.
True, the area of a polygon is the amount of space inside the
polygon.
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A sk: True or False? To find perimeter of a rectangle, add the length
and the width.
False. To find the perimeter of a rectangle, double the sum of the
length and the width.
A sk: True or False? If we combine two rectangles, the area of the
combined rectangle is equal to the sum of the areas of the two
smaller rectangles.
True, the area of two combined rectangles is equal to the sum of
the areas of the individual rectangles.
A sk: True or False? If we combine two rectangles, the perimeter of
the combined rectangle is equal to the sum of the perimeters of the
two smaller rectangles.
False. When we combine two rectangles, the outside edges of
the combined rectangle do not include all the edges of the
original two rectangles. Two of the edges of the smaller
rectangles do not appear in the larger rectangle because they are
in the middle of the larger rectangle and therefore are not
counted when calculating the perimeter.
Display the following two polygons:
A sk: How do the perimeters of these two polygons compare? How
do their areas compare? How do you know?
The perimeters of the two polygons are the same. Perimeter is the
distance around a shape. Here, we could move the horizontal lines
on the staircase up so that they are aligned with the top stair.
Likewise, we could move the vertical parts of the stairs left so that
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they aligned with the vertical part of the bottom stair. Moving the
parts does not alter their length, so the perimeter remains
unchanged. Once we move the parts, we can see that the figure on
the right looks identical to the figure on the left, so their
perimeters must be equal. The area of the square is larger than the
area of the staircase. If we move the entire staircase to its left
until it overlaps with the square, we can see that the staircase fits
inside the square and therefore takes up less space.
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