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U n t er r i ch t spl a n
Po l y g o ns Trans f o rmat io ns Enl arg e me nt
Altersgruppe: 4 t h Gr ade , 5 t h Gr ade
Virginia - Mathematics Standards of Learning (2009): 4 .11a, 4 .11b
Virginia - Mathematics Standards of Learning (2016): 5 .14 .a
Fairfax County Public Schools Program of Studies: 4 .11.a.1,
4 .11.b.1, 4 .11.b.2
Online-Ressourcen: Qui c k o n t he Dr aw
Opening
T eacher
present s
St udent s
pract ice
Class
discussion
Mat h
Pract ice
8
12
min
min
10
3
10
2
min
min
min
min
Closing
M at h Obj e c t i v e s
E x pe r i e nc e working with a grid.
P r ac t i c e enlargement of geometric shapes according to a
certain scale factor.
L e ar n about scale and proportion.
De v e l o p an acquaintance with different geometrical shapes.
Ope ni ng | 8 min
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Draw a grid on the board.
E x a m p le :
S ay : This is a grid. It is similar to a fishing net which is composed
of horizontal and vertical lines. The distance between each two
adjacent lines is equal. On this grid we can draw points, lines, and
every geometric shape we want, placing them in a specific position
on the plane.
Draw 2 adjacent points, each on a point of intersection, of the grid.
E x a m p le :
A sk : What is the distance between the points?
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Answers may vary. We can not know the distance between the
points, we can just say that the distance is 1 unit unit ( we don't
know how much every unit length is, for example in cm).
Draw a line segment that connects the points.
S ay : Now we know that the length of the line segment is 1 unit .
Add another 2 points on the grid, and make a square.
E x a m p le :
A sk : What shape did we get? How do you know?
The shape is a square, because all the edges are equal and all the
angles are both right and equal.
S ay : Consider that we can create a geometric shape in a specific
position. First we draw the vertices, then connect them with line
segments. We don't have to draw the vertices on points of
intersection, but it helps when we talk about distances, length, and
so on.
Create a copy of the square that is enlarged by a scale factor of 2.
E x a m p le :
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A sk : Is there a connection between the squares?
The left square is 2 times larger than the right one. Each edge of
the right square is 1 unit long, and each edge of the left square is
2 units long.
T e ac he r pr e se nt s M at h game : - | 12 min
Using Preset Mode on the projector, present Matific ’s episode - to the class.
This episode practices scaling a geometric shape by a given factor. In each
question, a shape is drawn on a grid (e.g., a triangle or a rectangle). The task
is to created a scaled copy of that shape (e.g., larger by a factor of 2) by
clicking vertices on the grid.
E x a m p le :
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S ay : We have a grid. In each question, a shape is drawn on a grid,
and we are being asked to create a copy of the shape that is
enlarged by a given scale factor. When we click on the grid a point
is being made. When we make another point, a line between the
points will be made.
Click on the grid and make a point. Next, click on the grid in a different place
and make a line.
S ay : When we click on the grid again, we create a triangle. When we
click again we create a quadrangular, and so on. We can delete an
existing point by clicking on it.
Click again and make a triangle. Afterwards click again and make a
quadrangular. Afterwards click on one of the points and delete it.
Click on the reset button
.
S ay: Please read the instructions at the bottom of the screen.
Students can read the instructions.
S ay : We need to create a copy of the shape that is enlarged by a
scale factor of 2.
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A sk : What is the shape on the grid? How do you know?
The shape is a rectangle, a quadrilateral with 4 right angles.
S ay : In order to create a copy of the rectangle, that is enlarged by a
scale factor of 2, we need to multiply each edge by 2.
A sk : What is the length of the rectangle?
4 units .
A sk : What is the width of the rectangle?
2 units.
S ay : In order to create a copy of the rectangle, that is enlarged by a
scale factor of 2, we need to create a rectangle with lengths of 8
units and width of 4 units.
Create a rectangle with a length of 8 units and width of 4 units.
E x a m p le :
Click on
and present the next question.
E x a m p le :
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S ay: Please read the instructions at the bottom of the screen.
Students can read the instructions.
A sk : What is the given shape? How do you know?
A triangle, a shape with 3 edges, 3 vertices, and 3 angles.
A sk : How would we create a copy of the triangle that is enlarged by
a scale factor of 3?
We draw a triangle where each of its edges is multiply by 3.
A sk : What is the length of each edge?
The lower edge is 4 units long. We do not know the other lengths
of the edges.
S ay : When we don't know the edge lengths, we have to look at the
other lengths of the shape. For example, in our case, we can see
that the distance between the upper vertex and the lower edge
there are 3 units lengths. Also, the vertical distance between the
lower-right vertex and the upper vertex is 1 unit, and the vertical
distance between the upper vertex and the lower-left vertex is 3
units. This information will help us to create the enlarged copy.
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First we draw the lower edge.
A sk : What is the length of the lower edge, on the enlarged copy?
If the length of the lower edge, of the given shape, is 4 units, the
lower edge of the enlarged triangle would be 3 times 4, which is
12 units.
Mark 2 vertices so the distance between them is 12 units at the lower part of
the grid, in order to save a place for the rest of the triangle.
A s k: What is the distance between the upper vertex and the lower
edge, of the enlarged triangle?
If the distance between the upper vertex and the lower edge, in
the given triangle, is 3 units, the distance between the upper
vertex and the lower edge in the enlarged triangle would be 3
times 3, which is 9 units.
Show which horizontal line the upper vertex would be.
A sk : What should the horizontal distance between the upper vertex
and the lower-right vertex of the enlarged triangle be?
If the horizontal distance between the upper vertex and the
lower-right vertex of the given triangle is 1 unit, the distance
between the upper vertex to the lower-right vertex of the
enlarged triangle should be 3 times 1, which is 3 units.
Mark the upper vertex.
E x a m p le :
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S ay : Notice that all the lengths in these triangles save the same
proportion. Every matching segment in the small triangle would be 3
times larger in the large triangle. For example, in the small triangle
the horizontal distance between the upper vertex and the lower-left
vertex is 3 units, and the matching distance in the large triangle is 3
times larger or 9 unit lengths.
S t ude nt s pr ac t i c e M at h game : - | 10 min
Have students play - on their personal devices.
Circulate, answering questions as necessary.
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C l ass di sc ussi o n | 3 min
Discuss any challenges students faced while working individually.
Ask the class for responses regarding how they dealt with any common
issues their classmates brought up.
M at h P r ac t i c e : Gr i d - E nl ar ge me nt W o r kshe e t | 10 min
Hand each student a grid (see Printable Handout below).
Instruct the students to draw a square,in the lower-right corner of the grid,
where the edges are 1 unit long. While students are working, draw a grid on
the board so you can illustrate the answers.
Next instruct students to create a copy of the shape, that is enlarged by a
scale factor of 2, place it near the first square.
Then instruct students to create a copy of the first shape, that is enlarged by
a scale factor of 4, place it near the second square.
E x a m p le :
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After the students finish, share answers and ask students to repeat the
same thing process using triangles.
First demonstrate on the board how and where to place the first triangle.
E x a m p le :
Next, instruct students to create a copy of the triangle, that is enlarged by a
scale factor of 2, place it near the first triangle.
Then, instruct students to create a copy of the first triangle, that is enlarged
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by a scale factor of 4, place it near the second triangle.
E x a m p le :
A sk : How many times is the small square represented in the 2times enlarged copy?
The small square is reflected 4 times in its 2-times enlarged
copy.
For the students who are facing difficulties seeing the answer, it is possible
to cut the small square and see how many times it appears in the larger
squares.
A sk : How many times is the small square reflected in the 4-times
enlarged copy?
The small square is reflected 16 times in its 4-times enlarged
copy.
A sk : How many times is the small triangle represented in the 2times enlarged copy?
The small triangle appears 4 times in its 2-times enlarged copy.
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For the students who are facing difficulties seeing the answer, it is possible
to cut the small triangle and see how many times it enters the larger
triangles.
A sk : How many times is the small triangle present in the 4-times
enlarged copy?
The small triangle appears 16 times in the 4-times enlarged copy.
A sk : How many times is the small triangle present in the 2-times
enlarged copy?
The small triangle appears 4 times in the 2-times enlarged copy.
A sk : How many times is the medium square present in the big
square?
The medium square appears 4 times, in the big square.
A sk : How many times does the medium triangle appear in the big
triangle?
The medium triangle is evident 4 times in the big triangle.
A sk : Is there any pattern when enlarging a shape by a scale factor of
2? Of 4?
When enlarging a shape by a scale factor of 2 the small shape
enters the big shape 4 times (which means the area of the big
shape is 4 times larger than the area of the small shape). When
enlarging a shape by a scale factor of 4 the small shape enters
the big shape 16 times (which means the area of the big shape is
16 times larger than the area of the small shape).
Pr in t a b le H a n d o u t : G r id
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C l o si ng | 2 min
A sk : How can we make a scale copy of a shape?
Our goal would be to draw the vertices. After we draw the
vertices the shape is well-defined. So we take each segment in
the original shape and enlarge it by the desired scale factor.
A sk : What should we do if we don't know the edge lengths?
We have to look after other lengths of the shape.
A sk : How should we make a scale copy of a circle?
We should take the radius or the diameter of the circle and
enlarge it by the desired scale factor.
A sk : Can we reduce a shape by a certain scale factor?
We can reduce a shape by a certain scale just as we enlarge it. For
example, if we want to reduce a shape by a scale of half, we take
each segment in the original shape and reduce it by half.
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