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U n t er r i ch t spl a n
Cl as s if y , Co mp o s e and
De c o mp o s e Po l y g o ns
Altersgruppe: 3 r d Gr ade , 4 t h Gr ade
Virginia - Mathematics Standards of Learning (2009): 2.16, 3 .14 ,
4 .12a
Virginia - Mathematics Standards of Learning (2016): 3 .12.a,
3 .12.b, 3 .12.c
Fairfax County Public Schools Program of Studies: 2.16.a.6,
3 .14 .a.7 , 4 .12.a.1, 4 .12.a.2
Online-Ressourcen: C ut , P ast e and F i gur e
Opening
T eacher
present s
St udent s
pract ice
Mat h
Pract ice
8
10
20
7
min
min
min
min
M at h Obj e c t i v e s
E x pe r i e nc e composing polygons by cutting, pasting, and
rotating other shapes
P r ac t i c e classifying polygons
L e ar n composing and decomposing polygons
De v e l o p an acquaintance with polygons with different
attributes and when displayed in different orientations
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Ope ni ng | 8 min
Prepare and bring to the class samples of triangles, rectangles, trapezoids,
parallelograms, rhombuses, pentagons, and hexagons (few samples from
each shape with different attributes including sizes, colors, and regular or
irregular polygons).
Note: Trapezoid has two accepted definitions, a quadrilateral with exactly
one pair of parallel sides or a quadrilateral with at least one pair of parallel
sides. Please refer to your standards or assessment guidelines for the
accepted definition.
S ay : Today we will identify different geometric shapes, and we will
compose and decompose new shapes.
Show the class one of the triangles.
A sk : Who knows what shape this is?
A triangle.
A sk : How do we know this is a triangle?
Triangle has 3 sides.
A sk : How many vertices does the triangle have?
The triangle has 3 vertices.
Show another triangle, in a different size and a different color, and hold it in a
different direction.
A sk : What shape this is?
A triangle.
A sk : How do we know this shape is also a triangle?
A triangle has 3 sides and 3 vertices.
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S ay : Pay attention that the color, the style, the size or the direction
of the shape has nothing to do with the type of the shape. The type
of the shape is determined only by the essential properties of the
shape, such as the number of sides or the number of vertices.
Draw the table on the board. Fill in the line of the triangle with the students.
Show a rectangle, asking the students to identify the name and its attributes.
Continue discussing the sample shapes, filling in the chart, and fill it along
with the progress of the lesson.
A sk : Do you see a connection between the number of sides and the
number of vertices?
Yes. in a polygon, the number of sides is as the number of
vertices.
S ay : How do we identify and name polygons?
By the number of its sides or by the number of its vertices.
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After you have filled in the chart:
A sk : How can we distinguish between a rectangle, a trapezoid and a
parallelogram? They both have the same number of sides and the
same number of vertices.
Add another column to the table so we can distinguish between different
quadrilateral.
E x a m p le :
Add the attributes to every quadrilateral. Give the students time to complete
the chart as a whole class, in small groups, or in pairs.
T e ac he r pr e se nt s mat h game : C ut , P ast e and F i gur e C o mpo si t i o n P uz z l e s: L e v e l I | 10 min
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Using Preset Mode, present Matific’s episode C u t , Pa s t e a n d F ig u r e C o m p o s it io n Pu z z le s : L e v e l I to the class using the projector.
This episode practices the classification of polygons and the composition
and decomposition of shapes from given ones. Cut or glue a given shape in
order to make a specified shape.
E x a m p le :
A sk : On the screen there are 2 shapes. What is the shape on the
right?
Triangle.
A sk : How many sides to the triangle?
3 sides.
Point on the triangle’s sides.
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A sk : How many vertices to the triangle?
The triangle has 3 vertices.
Point on the triangle’s vertices.
A sk : What is the left shape?
Rectangle.
A sk : How many sides and vertices to the triangle?
4 sides and 4 vertices.
Point on the rectangle’s sides and vertices.
A sk : What is the unique property that designate rectangle from all
other quadrilaterals?
All its angles are right or 90°.
Demonstrate how each shape can be rotated.
Illustrate how to use the glue tool: drag the triangle on the rectangle without
rotating it (in a way that won't create trapezoid) until two of their sides are
aligned together. Move the triangles rag the glue and drop it over the two
aligned sides. The two shapes will be glued to each other, forming a new
shape.
E x a m p le :
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Note: When the edges are not properly aligned, the glue cannot be applied.
Remind the students that they can always start over by clicking the reset
button
.
S ay : Please read the instructions at the bottom of the screen.
Students can read the instructions.
A sk : What are the attributes of a trapezoid?
Trapezoid is a quadrilateral (and those with 4 sides and 4
vertices) with at least one pair of parallel sides.
Glue one of the short sides of the rectangle with one of the short sides of
the triangle.
A sk : What shape is this? How do we know?
This is a trapezoid - a quadrilateral with at least one pair of parallel
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sides.
Click on
.
Show students the next question.
E x a m p le :
A sk : What is this shape?
Pentagon.
A sk : How many sides and vertices has the pentagon?
Pentagon has 5 sides and 5 vertices.
Illustrate how to use the scissors tool: dragging the scissors close to a
vertex marks all the possible cuts that can be made from that vertex, as
dotted lines. To choose a particular cut, hover over one of the dotted lines,
and drop the scissors.
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Click 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 make 3 triangles. We drag the scissors to one of
the vertices and cut a triangle.
Drag the scissors and cut one triangle. Ask the students to name the shapes
that are left.
S t ude nt s pr ac t i c e mat h game : C ut , P ast e and F i gur e C o mpo si t i o n P uz z l e s: L e v e l I | 20 min
Have students play C u t , Pa s t e a n d F ig u r e - C o m p o s it io n Pu z z le s :
L e v e l I and C u t , Pa s t e a n d F ig u r e - C o m p o s it io n Pu z z le s : L e v e l
I I on their personal devices.
Circulate, answering questions as necessary.
M at h P r ac t i c e : Ge o me t r i c al S hape s - C o mpo se and
De c o mpo se P o l ygo ns W o r kshe e t | 7 min
Discuss any challenges the students faced while working individually.
Hand each student 3 square shaped sheets, and ask them to create 2
congruent (equal-sized) triangles from each sheet.
After students are done (each student has 6 triangles), ask them to work
individually or with a partner to compose new shapes: a triangle, a rectangle,
a parallelogram, a trapezoid and a hexagon.
E x a m p le :
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Because there are more options of composing, you can challenge the
students to find other ways to compose the requested shapes. After
students are done, have students share the shapes they made.
Challenge students to work with a partner to create a six-pointed star. They
may work together to use two sets of shapes. As students work, encourage
them to "think outside the box", prompting them that they may overlap the
triangles.
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