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Polygons With Personality Common Core 3.G.1, 2.G.1, 1.G.1, 1.G.2 Polygons Shapes

This ended up being one of those lessons that I’ll be giddy about doing every year. It was the perfect blend of academics and craftiness. It rolled math vocabulary and concepts, character traits, writing skills and cutting and pasting all into one. This Polygons with Personality Geometry Activity is included in Geometry Resources Bundle, which includes 100+ pages of games, activities, writing projects, visual aides, and more to help teach students about 2D Geometry.


We’ve been working with polygons during Math Workshop using all of the games, activities and printables in my shapes packet throughout the week so the students were familiar with the language and attributes. However, this activity would also be a great introduction to the unit as it has them looking at the attributes of various polygons.

I began by reviewing what character traits are. We discussed how they are based on what someone says or does and not on appearance. I revealed a chart that included columns headed with the letters T, S, P, H, O, R and together we listed one character trait that began with each of those letters. I told them that I picked those letters for a reason, but wouldn’t tell them why until later in the day. Their excitement and interest level grew with curiosity.

I gave them each a copy of the printable and challenged them to list 25 character traits that began with those letters in 15 minutes. I was amazed by their word choices (punctual, reluctant, rambunctious, sophisticated, etc.). We came together as a class and compiled the individual ideas into an anchor chart. We talked about the words and their meanings as I added them to the list.

I printed the polygon printables from my geometry packet onto plain paper and used the photocopier to make 3 of each in an assortment of colors using construction paper. I passed them out to my students along with a graphic organizer. They used the graphic organizer to list their shapes attributes along with places the shape can be found (i.e. a triangle can be a sail on a boat, a slice of pizza, etc). I opted to do this prior to reading the story because I wanted them to generate their own ideas and not just record the ones from the book. Using the graphic organizer and the story frame each of my friends composed two paragraphs.

After lunch I read, The Greedy Triangle by Marilyn Burns. I had cut 10 strips of paper and attached them to each other using metal brads. At the start of the story, I held 3 of them with the others folded in the back to form a triangle. As the story progressed and the triangle turned into a quadrilateral and then a pentagon and then a hexagon, etc. I revealed another side to form the new shape.

Afterwards we discussed why he was greedy and used details from the text to support that character trait. I then began gluing the polygon images from my packet onto our chart of words directly over the letters that were originally heading the columns. After a quick minilesson on alliteration (score another point for embedding state test review), each of my friends selected a character trait that began with the same letter as the polygon they had been writing about. They composed the final part of their writing piece by citing fictional actions to support the trait they selected.

The final (and crowd favorite) part of the project was bringing their shapes to life by adding eyes, mouths and other components.


anchor chart headers for a guided lesson

photos to help you visualize implementing this resource in your classroom

graphic organizer template for students to use to plan their story

5 differentiated final copy stationary that students can use to publish their writing

8 polygon printables for students to transform into characters


► This geometry resource helps you create a highly engaging hands-on learning experience for your students.

► This resource helps you facilitate an integrated math and literacy learning experience.

► It is aligned to the Common Core standards, so you can be confident that these are important concepts and skills for your grade level.

► It’s quick and easy to prep, which will save you lots of time as a teacher.

► The final products create a beautiful, colorful bulletin board wall display that students, colleagues, and administrators will admire.


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Polygons on TemariKai.com


  Stitching Shapes and

     Given that temari is so dependent
upon geometry, some discussion on basic polygon shapes might be in
order. Polygons are 2-dimensional shapes composed of straight lines, and
they are closed — that is all
the lines are connected. Polygon is a Greek word meaning many (poly)
angles (gon). If all of the sides are the same length and all of the
angles are equal, it’s a regular
polygon. If these conditions are not met, it’s an irregular polygon. If
the lines defining the shape do not cross over each other, it’s a simple polygon. If they do, it’s a
complex polygon. You will see
all types occurring in temari designs.

        The basic polygons that frequently
appear in temari designs are as follows:

Diamond Hishi or Ryou  菱 Simple, 4 sides, irregular
Triangle Sankaku   三角 Simple, 3 sides, either
Square Shikaku, Masu   四角 Simple 4 sides, regular
Five point star Hoshi   星かがり Complex
Pentagon Gokaku   五角 Simple, 5 sides, either
Hexagon Rokkaku, Lokkaku  
Simple, 6 sides, either
Octagon Hachikakkei   
Simple, 8 sides, either


        Understanding the Japanese: kaku   角   means corner. San means 3; thus, sankakku
is 3 corners, or triangle. (Another word for 3 is mitsu
as in mitsubishi. «Bishi» is
how «hishi» is pronounced, when written as mitsuhishi, so it has become
mitsubishi in English vernacular — and this means 3 diamonds.) Go
means 5, so gokakku is a
pentagon, 5 corners. Roku means
six; rokkaku is a 6 cornered
figure, or hexagon. (Another word for six is kikkou;
this is used in Mitsubane Kikkou
which is based on a 6 cornered center).

        When stitching polygons and
shapes, the things to concentrate on are keeping it symmetrical if it’s
a regular shape (side lengths equal and the shape symmetrical) and
making sure that the rounds are distinct — that is, they all appear
independent, rather than spiraling out from the center. Remember to
stretch the points on corners (stretching
the points refers to allowing space for the volume of the thread
as it turns corners). The more acute (smaller) the internal angle
(inside the shape), the sharper the corner becomes and the more the
stitch needs to be stretched. This correlates to the number of sides of
the polygon: the more sides it has, the less stretching is needed.
Without the correct positioning of the stitch, the threads will not lay
smoothly and form sharp, clear corners. Remember that each round of a
shape is just that — one distinct round. When placing the stitches, be
careful to maintain the individuality of each round rather than it
appearing to be a continuous path from the center. Shapes and polygons
can be stitched as either solids, or with open areas. The same standards
apply either way — work for sharp, clear corners and distinct rows.

Another major criteria for working polygons is how the last
stitch of the final row (either of a color or of the total
motif) is finished off. It’s so very easy to just «finish» the
stitch as you’ve been working all of the others — but, in doing
this, the thread rhythm is broken. It can be seen in the image
to the right that if this is done, the final overlap of the last
stitch is out of synch with the rest of the stitches. The row
began at Point 1; Points 2, 3, and 4 all have the thread
entering the stitch from the left and under. If the thread is
carried back to Point 1 and the needle inserted per usual, the
thread enters the stitch from the left but over.

In order to correct this reversal, and
in doing so maintain the correct lay so that all of the stitches
look the same, pass the needle under the starting thread prior
to taking the stitch. Informally, I refer to this as
«underpassing». It should also be noted that underpassing
applies in all cases, not just polygons. For example, the last
stitch of Uwagake Chidori should also be handled this way. The
goal is to not be able to tell where the last stitch is.

When coming to the last stitch, carry the thread under the
starting thread. Pull the thread through to normal tension, and
then insert the needle in the normal position to complete the


Very often, polygons are regular: the sides should be of equal
length & corner angles equal. This can be tricky especially
on open shapes. There are a few tricks for getting polygons to
be regular and equal and replicating them. This example is an
open shikaku, it but can be applied to any polygon. It’s easier
and more accurate to concentrate on diagonals through the center
of the shape rather than on the sides. It’s also easier and more
accurate to rely on relational distances for the dimensions. A
paper strip, or a hem gauge (the little ruler that sewers use to
set and repeat a distance, with the little slider on it) are
both handy to help. If using a hem gauge, it’s only for setting
a distance using the slider, however on smaller mari it becomes
less accurate.

Open shapes need to be symmetrical (usually). The easiest way
to achieve this is by using a paper strip. Determine the
distance of the diagonals (distance through the center) of the
shape. Mark a strip with the length, as well as the mid-point.
Place the mid-point on the center of the face and then place
pins for the corners. Repeat on all diagonals 
Check that the spacing is correct early on. This is most
easily done on small spaces with a paper strip. Mark the
diagonal and also the center. Check all diagonals for the same
length. This strip marking can also be used later on to
replicate the same size open shape elsewhere on the mari. If the
diagonals are equal, then the equal angles and equal side
lengths fall into place automatically.

             This is a TemariKai.com Printable Page; ©
2014, all rights reserved. Right click to print one copy for personal

Star (geometry)


Star is a type of flat non-convex polygons that does not have an unambiguous mathematical definition.

Star polygon

Star polygon is a polygon in which all sides and angles are equal, and whose vertices coincide with the vertices of a regular polygon. The sides of a star polygon can intersect. There are many star polygons or stars , among them a pentagram, a hexagram, two heptagrams, an octogram, a decagram, a dodecagram.

Star polygons can be obtained by simultaneously extending all sides of a regular polygon after they intersect at its vertices until their next intersection at the points that are the vertices of the star polygon. The resulting star polygon will be the star shape of the regular polygon from which it is derived. The vertices of the star polygon will be considered only the points at which the sides of this polygon converge, but not the points of intersection of these sides; the star shape of a given polygon has as many vertices as itself. This operation cannot be done with a regular triangle and a square, since after extension their sides no longer intersect; among regular polygons, only polygons with more than four sides have star shapes. The star shape of a regular pentagon (pentagon) is a pentagram.

In another way to get the star shape of a regular n -gon, each of its vertices is connected to m -th from it on a circle in a clockwise direction. The star obtained in this way is designated as {n/m} . In this case, the points of intersection of the sides with each other are not considered as vertices. Such a star has n vertices and n sides, just like a regular n gon.

The ratio of the radii of 2 circles of a regular star with the above construction option: external (on which the vertices of the angles of the rays of the star lie) and internal (on which the points of intersection of the sides of neighboring rays lie) is calculated by the formula:

cos ⁡ ( π n × m ) cos ⁡ ( π n × ( m − 1 ) ) {displaystyle {frac {cos left({frac {pi }{n}} imes m
ight)}{cos left({frac {pi }{n}} imes (m-1)

Stars can be connected (non-disintegrating single polygons), not being compounds of other regular or stellated polygons (as in the case of a pentagram), and can be disconnected , decomposing into several identical regular polygons or connected stars (an example of which is the star shape of a hexagon is a hexagram, which is a compound of two triangles).

A regular polygon can have several star shapes, the number of which depends on how many times its sides intersect each other after they are extended, an example of which is a heptagon that has 2 star shapes (two types of a seven-pointed star).

Two-dimensional discrete set of stars.
Magenta — convex polygons.
Green — connected stars {n/m} (where n and m are coprime numbers), see also Lissajous Figures.
Black stars are not connected {n/m} (where n and m are not coprime numbers).
Blue lines connect a polygon (a convex or connected star) with all non-connected stars that are connections (after rotation) of a different number of identical polygons, such as this one

Vertex-transitive polygon

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