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U n t er r i ch t spl a n
Cal c ul at ing Are a o f Trap e zo id s
Altersgruppe: 3 r d Gr ade , 4 t h Gr ade
Virginia - Mathematics Standards of Learning (2009): 3 .10b, 3 .9d
Virginia - Mathematics Standards of Learning (2016): 3 .8.b, 4 .7
Fairfax County Public Schools Program of Studies: 3 .10.b.1, 3 .9.d.1,
3 .9.d.2
Online-Ressourcen: S hape s o n t he Gr i d
Opening
T eacher
present s
St udent s
pract ice
Class
discussion
8
10
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 aligning polygons with a grid to determine area
P r ac t i c e finding area of triangles and quadrilaterals
L e ar n multiple strategies for finding area of a trapezoid
De v e l o p the area formula for a trapezoid
Ope ni ng | 8 min
Display the following po l ygo ns . Ask students to find their areas in their
notebooks.
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When the students are done working, share. A sk : What is the area of the
triangle? How did you find it?
We can find area of a triangle by multiplying the base times the height and
dividing by 2. If we multiply 2 by 4 and divide by 2, we get 4 square units.
The area of the triangle is 4 square units.
A sk : How can we find the area of the pe nt ago n ?
Responses may vary. A possible response: We can think of the pentagon
as a square with a triangle on top. We can find the area of the square and
the triangle and then add them.
A sk : What is the area of this pentagon? How do you know?
The pentagon has area 20 square units. We multiply 4 by 4 to get the area
of the square, 16. We already know that the area of the triangle is 4. The
area of the pentagon is the sum of these areas. Sixteen plus 4 is 20.
S ay : Today we are going to look at area of a t r ape z o i d . There are multiple
ways to find the area of a trapezoid. One way is to divide the trapezoid into
parts, and then add the areas of each of the parts. Before we begin today’s
episode, let’s talk about trapezoids for a minute.
Display the following:
S ay : When we talk about trapezoids, many of us picture something like this.
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But this is a special type of trapezoid known as an i so sc e l e s t r ape z o i d .
We could also have a trapezoid that looks like this.
Display the following:
A sk : What makes the first trapezoid different from the second?
In the first trapezoid, the sides that are not par al l e l are equal in length.
S ay : Correct. In an isosceles trapezoid, the non-parallel sides are equal in
length.
T e ac he r pr e se nt s M at h game : S hape s o n t he Gr i d - A r e a:
T r ape z o i ds | 10 min
Using Preset Mode, present Matific ’s episode S hape s o n t he Gr i d A r e a: T r ape z o i ds to the class, using the projector.
The goal of the episode is to find the area of trapezoids by using a grid under the
polygon.
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S ay : Please read the question.
The question asks, “What is the area of the square?”
A sk : How can we determine the area of the square?
We can rotate the square and move it to align it with the grid behind it.
Move the square so that it is aligned with the grid.
A sk : How can we find its area?
We can count the small squares of the grid to find its area.
A sk : What is the area of this square?
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 three questions. The second question
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will ask for the area of a rectangle, and the third will ask for the area of a
trapezoid. Encourage the students to find the area of the trapezoid in more
than one way.
S t ude nt s pr ac t i c e M at h game : S hape s o n t he Gr i d - A r e a:
T r ape z o i ds | 12 min
Have the students play S hape s o n t he Gr i d - A r e a: T r ape z o i ds on
their personal devices. Circulate, answering questions as necessary.
C l ass di sc ussi o n | 14 min
Display the following:
Ask the students to turn to a partner to brainstorm all the different methods
that could be used to find the area of this trapezoid.
When they are done discussing their methods, share. Ask different students
for their methods until all the different strategies have been presented.
Responses will vary. Possible methods include: 1. Divide the trapezoid
into a 3 by 4 rectangle and two 1 by 4 triangles. Find the area of each and
add. 2. Draw a line from the top left corner to the base. Remove the
triangle formed on the left. Reflect and rotate it and attach it to the right
side of the figure. Find the area of the resulting 4 by 4 square. 3. Draw a 4
by 5 rectangle around the trapezoid. Find the area of the rectangle.
Subtract the area of the two triangles that are within the rectangle but
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outside of the trapezoid.
S ay : Use one of these methods to find the area of the trapezoid. What is its
area?
The trapezoid has area 16 square units.
Display the following:
S ay : The methods that we can use to find the area of an isosceles trapezoid
don’t all apply when we are looking at a trapezoid where the l e gs are not
equal. What method that we used before are we unable to use with this
trapezoid?
We cannot easily turn this trapezoid into a rectangle. If we draw a line
from the top left corner down to the base, the triangle that is formed on
the left does not fit on the right side of the figure because the legs are
different lengths.
S ay : We can divide this trapezoid into a rectangle with triangles on either
side, or we can draw a rectangle around the trapezoid, find the area of the
rectangle, and then subtract the area that is not included.
Display the following:
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S ay : Let’s look at the diagram on the left. What is the area of each piece,
and what is the area of the trapezoid?
The triangle on the left has area 2 square units. The rectangle in the
middle has area 12 square units. The triangle on the right has area 4
square units. Altogether, that is 18 square units.
S ay : Let’s look at the diagram on the right. What is the area of the rectangle
and the triangles within the rectangle? What is the area of the trapezoid?
How do you know?
The rectangle is 4 by 6, so it has area 24 square units. The area of the
triangle on the left is 2 square units. The area of the triangle on the right
is 4 square units. To find the area of the trapezoid, we subtract the area
of both triangles from the area of the rectangle. So we subtract 2 and 4
from 24. Subtracting 6 from 24 gives 18. The area of the trapezoid is 18
square units.
S ay : We are able to use our knowledge of area of rectangles and triangles
to find the area of trapezoids. What are the formulas for area of rectangles
and area of triangles?
To find area of a rectangle, we multiply length by width. To find area of a
triangle, we multiply
times the base times the height.
S ay : Yes. Now we will turn our attention to finding a formula for the area of
trapezoids.
Distribute two pieces of paper and scissors to each student.
Display the following instructions. Ask the students to complete them.
1. Cut one piece of paper into two equal pieces.
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2. Cut a trapezoid out of one of the pieces.
3. Trace the trapezoid on the other piece of paper and then cut it out. You should now
have 2 identical trapezoids.
4. On a second piece of paper, place the two trapezoids side by side so that the edges
line up. Trace them. How many different shapes can you make?
When the students are done, ask a student to come to the front of the room
to share the finished shapes.
While the trapezoids may look different, there are 4 possible
configurations:
S ay : So we’ve formed two he x ago ns and two q uadr i l at e r al s . How will
this help us determine a formula for the area of a trapezoid?
We can use the quadrilaterals. Both quadrilaterals that we formed are
parallelograms. We know that the area of a parallelogram is base times
height. So the area of the trapezoid is going to be half that.
Display the following:
A sk : How do the dimensions of the parallelogram relate to the dimensions
of the trapezoid?
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The height of the parallelogram is equal to the height of the trapezoid.
The base of the parallelogram is equal to the sum of both bases of the
trapezoid.
S ay : Yes. Now we have the formula for the area of a trapezoid.
Display the following:
S ay : Let’s return to the trapezoid that we already looked at.
Display the following:
S ay : We already figured out that this trapezoid has area 18 square units.
Now let’s apply the formula to make sure we get the same answer. What is
the height of this trapezoid? What is the length of the bases?
The height is 4 units, and the bases are 6 units and 3 units.
S ay : Explain how to use the formula to calculate the area.
The formula for area of a trapezoid is times the sum of the bases times
the height. First, let’s add the bases. If we add 6 and 3, we get 9. Then we
multiply
times 9 times 4. That is 18 square units.
S ay : So we have verified again that the area of this trapezoid is 18 square
units. Let’s use the trapezoid area formula to find the area of another
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trapezoid.
Display the following:
A sk : What is the area of this trapezoid? Explain how you found your answer.
To find the area of the trapezoid, first we add the bases. When we add 6
and 12, we get 18. Then we multiply 18 by and by the height, 4. Half of 18
is 9. When we multiply 9 by 4, we get 36 square units, the area of this
trapezoid.
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C l o si ng | 3 min
Display the following:
Distribute a small piece of paper to each student.
Ask the students to use two different methods to find the area of the
displayed trapezoid.
Collect papers, to review later.
A possible response:
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