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U n t er r i ch t spl a n
Cal c ul at ing Are a o f R ig ht
Triang l e s
Altersgruppe: 3 r d Gr ade , 4 t h Gr ade
Virginia - Mathematics Standards of Learning (2009): 3 .10b, 3 .9d,
5 .8a
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, 5 .8.a.5
Online-Ressourcen: S hape s o n t he Gr i d
Opening
T eacher
present s
St udent s
pract ice
Mat h
Pract ice
5
12
12
15
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 right triangles with a grid to determine
their area
P r ac t i c e finding area of rectangles
L e ar n to calculate area of a right triangle
De v e l o p facility with comparing traits of different polygons
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Ope ni ng | 5 min
Display the following:
A sk : What is the area of this rectangle? How do you know?
This rectangle has area 20 square units. We can count the unit
squares inside the rectangle. There are 20 unit squares within the
rectangle.
Display the following:
S ay : It may be harder to determine the area of the right triangle
because some of the unit squares within it are incomplete.
However, if we compare this triangle to the rectangle we just
looked at, we will be able to determine its area.
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Display the following:
A sk : How does the triangle compare to the rectangle?
The triangle is half of the rectangle. If we draw a line segment
from the top left corner of the rectangle to the bottom right
corner, we would form the triangle.
S ay : We determined that the area of the rectangle is 20 square
units. What is the area of the triangle? How do you know?
The area of the triangle is 10 square units. The triangle is half the
size of the rectangle. Half of the rectangle’s area, 20, is 10 square
units.
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:
R i ght T r i angl e s | 12 min
Present Matific ’s episode S hape s o n t he Gr i d - A r e a: R i ght
T r i angl e s to the class, using the projector.
The goal of the episode is to find the area of right triangles by using a grid
under the polygon.
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S ay : Please read the question.
Students can respond based on the episode.
A sk : How can we determine its area?
We can rotate the shape and move it to align it with the grid
behind it. Then we can count the small squares of the grid to find
its area.
Move the polygon so that it is aligned with the grid.
A sk : What is the area of this polygon?
Click on the
to enter the students’ answer.
If the answer is correct, the episode will proceed to the next question.
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If the answer is incorrect, the question will wiggle.
The episode will present a total of six questions. Two of them will
ask for the area of a square or rectangle. The other four questions
will ask for the area of a right triangle.
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:
R i ght T r i angl e s | 12 min
Have the students play S hape s o n t he Gr i d - A r e a: R i ght
T r i angl e s on their personal devices. Circulate, answering
questions as necessary.
M at h P r ac t i c e : A r e a o f R i ght T r i angl e s W o r kshe e t | 15 min
Before class begins, prepare cutouts of squares and right triangles
in two different sizes each. (One large square, 3 large triangles, 6
small squares, and 14 small triangles per student will be more than
sufficient.) The edge of the larger square should be twice the edge
of the smaller square. The leg of the smaller triangle should equal
the edge of the smaller square. The leg of the larger triangle should
equal the edge of the larger square. For example:
Distribute rulers and copies of the four polygons.
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Ask the students to measure the edges of the squares and triangles
and calculate their areas.
When the students are done working, display a banner:
S ay : Now we’re going to use the polygons to make a banner.
Make available glue, paper, and more cutouts of the polygons.
Display the following instructions:
1. Using any of the cutouts you wish, make a banner by gluing the cutouts
onto a white piece of paper in the same shape as the displayed banner.
2. Add up the areas of the individual polygons in order to calculate the area of
the entire banner.
When the students are done working, review the areas of each
polygon.
Collect the banners, to display later.
A possible banner:
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The area of the entire banner is 14 times the size of the smaller
triangle.
If time allows, lead a discussion relating the areas of the smaller
polygons to the larger polygons. Students may be surprised to learn
that even though the edges of the larger polygons are twice the
edges of the smaller ones, the areas are 4 times the size.
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C l o si ng | 3 min
Distribute a small piece of graph paper to each student.
Display the following triangle and instructions:
Collect papers, to review later.
A possible response:
3. This triangle has a base of 6 units and a height of 4 units. To
find the area of a triangle, we multiply
height. When we multiply
times the base times the
by 6 by 4, we get 12.
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