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U n t er r i ch t spl a n
Id e nt if y ing and F o rming Po l y g o ns
Altersgruppe: 2nd Gr ade
Texas - TEKS: G2.8.GM .C , G3 .6.GM .B
Riverside USD Scope and Sequence: 2.G.1 [2.6]
Oklahoma Academic Standards Mathematics: 2.GM .1.1, 2.GM .1.4 ,
2.N .2.6
Virginia - Mathematics Standards of Learning (2009): 1.12, 1.13 ,
2.16
Common Core: 2.G.A .1
Mathematics Florida Standards (MAFS): 2.G.1.1
Alaska: 2.G.1
Minnesota: 3 .3 .1.2, 3 .3 .2.2, 4 .3 .1
Fairfax County Public Schools Program of Studies: 1.12.a.2,
1.12.a.3 , 1.12.a.6, 1.13 .a.1, 1.13 .a.4 , 2.16.a.5 , 2.16.a.6
Nebraska Mathematics Standards: M A .2.3 .1.a, M A .2.3 .1.d
South Carolina: 2.G.1, 3 .G.1, 4 .G.2
Indiana: 3 .G.2, 4 .G.5 , 5 .G.2
Georgia Standards of Excellence: M GS E 2.G.1
Virginia - Mathematics Standards of Learning (2016): 1.11.a
Online-Ressourcen: C ut , P ast e and F i gur e
T eacher
present s
St udent s
pract ice
Class
discussion
10
8
10
12
min
min
min
min
Opening
M at h Obj e c t i v e s
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P r ac t i c e identifying a shape based on its attributes
L e ar n to create a shape based on its attributes or its name
De v e l o p more comfort with identifying and composing
shapes
Ope ni ng | 10 min
Prepare several cut-outs of differing sizes, colors, and styles for
each of the following shapes: triangles, quadrilaterals, pentagons,
hexagons, heptagons, and octagons.
Examples of shapes of different styles for quadrilaterals are
squares and rectangles.
Additionally, you may wish to create some convex polygons and
some concave polygons.
You may decide not to call out the shapes as being “convex” or
“concave,” but it is important not to limit the possibilities to
only convex shapes.
Essentially, the focus should be on attributes (the number of
sides, angles, or vertices) that describe all shapes in a given
category.
Hold up each shape, one at a time, and ask the class: Does anyone
know what kind of shape this is?
As this may be the first time some of your students are
classifying pentagons, hexagons, or octagons, be sure to follow
each correct answer with a follow-up question. e.g., How do we
know that this is a triangle?
Try to coax responses that include some mention of traits,
such as the number of edges.
Be sure to note that color, size, and style have no bearing on
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the determination of the type of shape.
Depending on the shape you show, you may get some more
specific responses than intended at this moment.
For example, if you show a rectangle, the general classification
of quadrilateral is sufficient. If your students identify the shape
as a rectangle, support this claim, then ask what kind of shape a
rectangle is.
You may wish to use a phrase such as “family of shapes.” e.g.,
a rectangle is in the quadrilateral family.
Although counting the number of sides for each shape may be an
easy process for your students to lean on, include some mention of
vertices and angles (internal).
For example, if your class correctly identifies a hexagon and
gives the reason that it has 6 sides, continue by asking how many
vertices that same shape has.
Try to develop a connection between the number of vertices
and the number of sides for polygons, so that your students
expand their options for identifying shapes.
Do the same with the number of angles.
Now when your class identifies a shape and gives a reason, you can
ask: How else could we know that this is a ___?
Ideally, your class will start to use each attribute roughly equally.
Once you feel your class can identify each type of shape based on
its attributes, in general terms, move on to the episode for this
lesson.
T e ac he r pr e se nt s M at h game : C ut , P ast e and F i gur e P o l ygo ns f r o m T r i angl e s | 8 min
Present Matific ’s episode C ut , P ast e and F i gur e - P o l ygo ns
f r o m T r i angl e s to the class, using the projector. The goal of this
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episode is to compose triangles in order to form polygons with
specified attributes.
Each screen starts with only two items: triangles and glue.
The triangles can be moved and rotated.
When edges are aligned, the triangles can be glued together by
dragging the glue to the shared edge.
E x a m p le :
In the example above, the specified attribute for the final polygon is
that it has 8 vertices.
Ask your class to identify what type of shape will have 8 vertices.
The edges of the triangles must be congruent in order to glue them
together.
Note that some edges will seem close, but the composite figure
must be created from the given triangles and have smooth edges.
E x a m p le :
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Above, the functionality for rotating is shown. Clicking on a shape
will bring up the arrows, and subsequently dragging will rotate the
shape about its center.
If a shape is rotated near another shape, the shapes may be
automatically aligned, provided the sides are very close to
matching up.
Continue to translate and rotate the triangles (and subsequent
composite shapes), then glue the sides together.
Gluing as you go may lose sight of the fact that all of the
composite shapes originated from triangles; however, it does
give you the chance to call out the different types of shapes
(triangle, quadrilateral, pentagon, etc.).
Below, the figure has been formed and glued as desired, yielding a
polygon with 8 vertices.
Note that this is a concave polygon, which is why having shapes
of various styles was a key element of the opening.
E x a m p le :
In the example below, 3 triangles were given. Composing 2 of those
can form a quadrilateral (as desired), but the goal is to use all of the
available triangles.
Thus, this configuration is not sufficient. The third triangle must
be included in the final composite shape.
Again, be careful to orient this triangle correctly, as it is possible
to simply form a larger triangle here.
E x a m p le :
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Along the way, continue calling out shapes by their names.
Also inquire about the attributes of the intermediate composite
shapes you are forming.
Even though a question may focus on vertices, include some
mention of edges and angles.
S t ude nt s pr ac t i c e M at h game : C ut , P ast e and F i gur e P o l ygo ns f r o m T r i angl e s | 10 min
Have the students play C ut , P ast e and F i gur e - P o l ygo ns
f r o m T r i angl e s their personal devices.
Circulate, answering questions. Continue to encourage the unique
strategies your students attempt to use, such as seeing if the
largest simple shape will fit in the composite shape, then moving on
to the next largest simple shape, and so on.
Encourage the use of rotations. Your students may rule out a
simple shape simply because it does not have the correct
configuration at first.
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C l ass di sc ussi o n | 12 min
Check in with your class to make sure they are confident in
identifying polygons based on attributes.
Have your class work in groups of 2 or 3. Your students will be
drawing shapes based on either the name or a given attribute.
Have one student draw at a time. The other student(s) should be
checking the final shape and discussing whether the shape
satisfies the given condition.
Do a quick walk-around to check that the small groups are
working together to decide if each shape is correct or if it needs
revisions.
Examples of the conditions for the shape that you can give to your
students are:
A pentagon
A polygon with 6 edges
A polygon with 4 angles
Continue until each student has had a chance to draw a couple of
times, and the class seems to have a firm grasp of drawing shapes
based on the attribute or name given.
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