Just want to show this video to you; it's connected to what we have been investigating and learning about; at the same time, this is going to be the basis of our unit inquiry for the grade 7s (hey, grade 8s, feel free to give this a try as well!)
Grade 7s:
Give it a try (and several other video by the same author) and consider this following question:
How can you 'prove' that this method does create a REGULAR pentagon? (using what you know about polygons and their unique characteristics?) Please respond by leaving your comments below.
____________________________________________________________________________
When you are done; please visit this webpage about Tiling (a plane) in real life:
Reflect on:
- What are three key ideas in this article?
- What are two new (or something you sort of knew, but now confirmed) learnings?
- Find one example, similar to the examples shown in this article, and bring it to class with you.
Happy learning to all!
This method does create a regular pentagon because the end result of this activity corresponds with the characteristics of a regular pentagon. A regular pentagon is a 5-sided polygon with all sides and angles equal.
ReplyDeleteThis figure has the following of a regular pentagon...:
5-SIDED POLYGON...CHECK!
ALL SIDES EQUAL...CHECK!
ALL ANGLES EQUAL...CHECK!
Therefore, this method does indeed create a REGULAR pentagon because it creates a pentagon that is constructed in such a manner that matches the characteristics of a regular pentagon.
How can you 'prove' that this method does create a REGULAR pentagon?
ReplyDeleteIt corresponds with all the features such as angles and equal sides and etc.
How can you 'prove' that this method does create a REGULAR pentagon?
ReplyDeletePolygons are any 2D shape that has 3 or more sides. Some specific characteristics of a regular polygons is that it has 5 equal sides, 5 angles(4 obtuse and 1 acute)You can prove that this method does create a regular pentagon because it corresponds with the characteristic of a pentagon as listed above. Some of these characteristics can be angles(size),dimensions etc.
To know whether a regular pentagon, there are always some characteristics and attributes that match the shape.A regular pentagon should always be classified as a regular polygon. As you can see Polygons are 2-dimensional shapes. They are made of straight lines, and the shape is "closed" (all the lines connect up). So a Pentagon would have some common characteristics which can correspond with a regular pentagon. So that way you can easily classify as. Some are:
ReplyDelete- 5 sides
- 5 vertices
- 5 lines of symmetry
- 4 obtuse angle
- 1 acute angle
REFLECTION
ReplyDelete1. WHAT ARE 3 KEY IDEAS IN THIS ARTICLE?
-One of the ideas in this article is that for the regular polygon to tessellate it all depends on the size of the internal angles.
2. WHAT ARE 2 NEW LEARNING?
- I learned that there are only 3 specific regular polygons that can tessellate:triangles, squares, and regular hexagons
-Another thing that I learned was that tessellations are used all around the world as a form of art.
3. FIND ONE EXAMPLE AND BRING IT TO CLASS WITH YOU.
(Shared on GAPPS)
~Shalindree~
What are three key ideas in this article?
ReplyDelete1. For regular polygons to tessellate and leave no gaps at each common point, the interior angles must divide exactly into 360°.
2. Regular tessellations are made up of regular polygons of the same size and shape. Regular polygons have all their sides the same length and angles the same size. Only three regular polygons tessellate: equilateral triangles, squares and hexagons.
3. When tiling, it is important that the shape of the tile when repeated should cover the whole surface or plane without any gaps or overlaps.
What are two new (or something you sort of knew, but now confirmed) learnings?
1. One new learning is that all interior angles have to divide exactly into 360.
2. I also learned that tessellations could be constructed with patterns, not just with regular polygons.
Find one example, similar to the examples shown in this article, and bring it to class with you.
1. Soccer Ball
What are three key ideas in this article.
ReplyDeleteThe three main shapes that they use to tile a plain. Which are equilateral triangle, square, and regular hexagon. This is because the shapes that they use to tile a plain need to equal 360* degrees no more or less. They also can not leave any space, because of that no other regular shape can be used because it will leave space and will not equal 360* degrees.
What are two new learning's that you have learned.
Why these three shapes are used. Now it is confirmed to me that it is because they have to equal 360 degrees and can not leave any space.
All regular polygons have all sides equal. They also have 5 sides/vertices. This pentagon also has all sides equal and 5 equal sides/vertices.
ReplyDeleteTHE OTHER ONE ABOUT THE REFLECTION FOR TILING THE PLAIN THAT IS ANONYMOUS IS MINE.
I can prove that this method creates a regular pentagon by actually folding a piece of paper into the pentagon they show and then measuring the angles because they should all be equal. If they are equal, it reassures me that the pentagon is a regular pentagon. Also there should be 5 lines of symmetry thus again reassuring me that this is a regular pentagon. one last thing that confirms my theory is that all the sides and angles are equal. There are also vertices for each edge.
ReplyDeleteWhat are three key ideas in this article?
ReplyDelete- Regular polygons
- Internal angles
- Regular tessellations
What are two new (or something you sort of knew, but now confirmed) learnings?
- I learned that a regular tessellation is one made up of regular polygons of the same size and shape. [Regular polygons have all their sides the same length and angles the same size.] Only three regular polygons tessellate: equilateral triangles, squares and hexagons.
- In the tilings where the shapes meet. At these points the sum of the angles must add up to 360°. This is the case for equilateral triangles, squares and hexagons.
Find one example, similar to the examples shown in this article, and bring it to class with you.
http://www.tatasteelconstruction.com/file_source/Images/Construction/Reference/tessellations.jpg
This link has examples of many different tessellations.
What are three key ideas in this article?
ReplyDelete- Regular polygons
- Internal angles
- Regular tessellations
What are two new (or something you sort of knew, but now confirmed) learnings?
- I learned that a regular tessellation is one made up of regular polygons of the same size and shape. [Regular polygons have all their sides the same length and angles the same size.] Only three regular polygons tessellate: equilateral triangles, squares and hexagons.
- In the tilings where the shapes meet. At these points the sum of the angles must add up to 360°. This is the case for equilateral triangles, squares and hexagons.
Find one example, similar to the examples shown in this article, and bring it to class with you.
http://www.tatasteelconstruction.com/file_source/Images/Construction/Reference/tessellations.jpg
This link have examples of many different tessellations.
Three key ideas:
ReplyDelete- When tiling it is important that the shape of the tile when repeated should cover the whole surface or plane without any gaps or overlaps. A repeating pattern is then formed and in mathematics we call a tiling like this a tessellation.
- If we try and tessellate with these shapes and not allow overlaps there are always gaps when we try and fit two or more together.
- Semi-regular tessellations can be created by using two regular polygons repeatedly to tile the surface or plane, for example an octagon and a square.
Two new learnings:
- The first new learning that I discovered was that regular polygons have all their sides the same length and angles the same size and only three regular polygons tessellate which are equilateral triangles, squares and hexagons.
- My second new learning that I have discovered was that other regular polygon as their internal angles do not divide exactly into 360°.
The three key ideas in this article is that you can usually use one shape (rectangle)and turn it into another shape (pentagon), you can tell an irregular polygon because it has different angles and different side lengths, A regular pentagon is almost equal in every way (E.g parallel lines, side lengths, angles, etc...)
ReplyDeleteTwo new learning's are that most regular polygons have identical side lengths and angles, and that irregular polygons have many differences than regular polygons from different side lengths to different angles.
How can you prove this method does create a regular pentagon?
ReplyDeleteA equal pentagon has 5 identical side, 5 vertices, equal angles, 5 lines of symmetry. and have no parallel lines. Using a rectangle we made a pentagon by first making an irregular pentagon. We can determine that it is a irregular pentagon because it has only one line of symmetry, no parallel lines, 2 pairs of identical sides, and 5 vertices. By folding it in half from one point to another (diagonal from each other) we can make it as shown in the video. Then we fold away the two excess half pentagons at the side of the irregular pentagon. This method will create the identical sides. and create equal angles; all the attributes that make a equal pentagon.
Reflection
What are the 3 key ideas in this article?
I think the 3 key ideas are how tessellation is used in many real life aspects such as art, architecture, etc. The key math idea is how the attributes of the polygons (angle, length, etc.) can also affect the tessellation. Also it shows that in the social aspect it shows how the concept of tessellation is very essential skill for pursuing a certain career.
What are the 2 new (or something you sort of knew, but now confirmed) learning?
One new learning was the concept tessellation. I knew how tessellation worked but I used to call it “tiling” or “quilting” and I never noticed how single tessellation can only be used by the following 4 polygons; equilateral triangle, square, rectangle, and regular hexagons..
Another new learning was that I never knew the fact that only polygons that have internal angles add up to 360 degrees are the only polygons with the ability to tessellate. I find this concept very interesting
Find one example, similar to the examples shown in the article and bring it to class with you.
(Example will be brought to class.)
How can you prove this method does create a regular pentagon?
ReplyDeleteA equal pentagon has 5 identical side, 5 vertices, equal angles, 5 lines of symmetry. and have no parallel lines. Using a rectangle we made a pentagon by first making an irregular pentagon.We can determine that it is a irregular pentagon because it has only one line of symmetry, no parallel lines, 2 pairs of identical sides, and 5 vertices. By folding it in half from one point to another (diagonal from each other) we can make it as shown in the video. Then we fold away the two excess half pentagons at the side of the irregular pentagon. This method will create the identical sides. and create equal angles; all the attributes that make a equal pentagon.
Reflection
What are the 3 key ideas in this article?
I think the 3 key ideas are how tessellation is used in many real life aspects such as art, architecture, etc. The key math idea is how the attributes of the polygons (angle, length, etc.) can also affect the tessellation. Also it shows that in the social aspect it shows how the concept of tessellation is very essential skill for pursuing a certain career.
What are the 2 new (or something you sort of knew, but now confirmed) learning?
One new learning was the concept tessellation. I knew how tessellation worked but I used to call it “tiling” or “quilting” and I never noticed how single tessellation can only be used by the following 4 polygons; equilateral triangle, square, rectangle, and regular hexagons..
Another new learning was that I never knew the fact that only polygons that have internal angles add up to 360 degrees are the only polygons with the ability to tessellate. I find this concept very interesting
Find one example, similar to the examples shown in the article and bring it to class with you.
(Example will be brought to class.)
Math reflection
ReplyDeleteWhat are three key ideas in this articles?
First idea is that I learned how to tessellate and tile a shape. It means I learned the terminology of what tessellating means. To me tessellating is a basic method to tile a plane (limited space given)with the given 2 dimensional polygon.
Second idea, I learned is to use tessellating in a real like application use which is tiling an actual floor or figuring out how you tessellated the floor (by giving the transformation.
Third idea I learned is that you can only tessellate the three shapes which are equilateral triangles, square and hexagon.
What are two new (or something you sort of knew, but now confirmed) learnings?
Mr. Huang I don't understand this question please can you reply and help me. Thanks
Find one example, similar to the examples shown in this article, and bring it to class with you.
One of the easiest tessleting examples are tiling your floor with the square tiles.
The tiles have the area of 4m squared each.
The floor have the area of 20m squared.
So you will basically need 5 tiles with 5 rows of 4 each in the same position.
You can prove this method by using a regular piece of 18" by 11" inch paper and fold it on opposite angles making an irregular pentagon like this...Please refer to the website below.
ReplyDeletehttp://etc.usf.edu/clipart/42600/42611/irregpent_42611_lg.gif
You can prove this method is real because you start with a 4 sided piece of paper. When you fold the piece of paper in half it becomes an irregular pentagon. After folding the edges together to the middle in becomes a regular pentagon. You can also prove that this method is real because the paper has all right angles and when you fold the paper diagonally there is one right angles
ReplyDelete~Shalindree~
I think the polygon is a regular pentagon because since this shape could be made out of a rectangular piece of paper, it would be a regular shape. This is because if a piece of paper is a rectangle, it has parallel lines on the opposing side meaning it is equal. Pentagons are equal and can be the same no matter how ever you rotate it. To check if your correct you could use a ruler, protractor etc. This would help you verify because you know that when you measure the angles and length of each side, you could tell what the actual measurements are on an actual pentagon.
ReplyDeleteHow can you 'prove' that this method does create a REGULAR pentagon? (redo)
ReplyDeleteA equal pentagon has 5 identical side, 5 vertices, equal angles, 5 lines of symmetry. and have no parallel lines. Using a rectangle we made a pentagon by first making an irregular pentagon. We can determine that it is an irregular pentagon because it has only one line of symmetry, no parallel lines, 2 pairs of identical sides, and 5 vertices. By folding it in half from one point to another (diagonal from each other) we can make it as shown in the video. Then we fold away the two excess half pentagons that was created during the first fold making the irregular pentagon. The diagonal fold creates a wide angle at the side of the irregular pentagon; the unique attribute that makes the irregular pentagon. At the side of the irregular pentagon we fold them to create a more smaller angle. By determining the excess half pentagons at the side will create a more accurate identical side measurement and create equal angles; all the attributes that make a equal pentagon. This is proof on how it transformed from a rectangle into a proper regular pentagon.
I can prove that this video makes a regular pentagon because a regular pentagon has all equal sides and angles. We created a regular pentagon by first folding a regular piece of paper and folding one vertex to the opposing vertex (diagonally). Then fold the outside edges into the middle of the current figure. Then that should be a regular pentagon. I can prove that this is a regular pentagon because all the angles are approximately the same. With a rectangle you can easily tell that all the angles are the same without measuring them because all the angles are like this _|. All the angles in the regular pentagon look like this _/ or this \_ which then proves that this is a regular pentagon. An irregular pentagon would have uneven angles like this _\ and this \_.
ReplyDeleteA pentagon needs 5 vertices and 5 edges and this pentagon also has the same vertices and edges. This also has no right angles, but has obtuse angles. It has obtuse angle because all obtuse angles go outwards. It also has all same sides.
ReplyDeleteIf you make a big star on the pentagon and colour the inside and youll see that there are different equilateral triangles outside and if it was to be a iregualr pentagon this would not have bin possible. If you make another star in the middle You will get the same result
I can prove that this method does indeed create a regular pentagon because, by drawing a star in which the vertices meet at the vertices of the pentagon, it creates congruent triangles at the edges. When the triangles are congruent, this means that the bases of the triangles are equal. Therefore, each edge is equal, with a total of 5 sides equal. This is one of the unique characteristics of a regular pentagon. Also, when all sides are equal, all angles are equal, so identifying the angles would be unnecessary if you already know the side length. I conclude that this method does indeed create a regular pentagon because of congruent triangles within the pentagon, which visually represents equal edges.
ReplyDeleteWe can prove that this method of creating a regular pentagon is real because when I fold it the first it draws and crises into an irregular pentagon. After the second fold it turns into a proper regular pentagon. This is another proven example that states that this method is correct. Which we can also explain with the corresponding attributes and characteristics. o know whether a regular pentagon, there are always some characteristics and attributes that match the shape.A regular pentagon should always be classified as a regular polygon. As you can see Polygons are 2-dimensional shapes. They are made of straight lines, and the shape is "closed" (all the lines connect up). A Pentagon would have some common characteristics which can correspond with a regular pentagon. So that way you can easily classify as. Some are:
ReplyDelete- 5 sides
- 5 vertices
- 5 lines of symmetry
- 4 obtuse angle
- 1 acute angle
Another example that proves it is a true method is
We can prove that this method is correct because there are 2 proven ideas. One of the proven ideas are to know whether a regular pentagon, there are always some characteristics and attributes that match the shape.A regular pentagon should always be classified as a regular polygon. As you can see Polygons are 2-dimensional shapes. They are made of straight lines, and the shape is "closed" (all the lines connect up). So a Pentagon would have some common characteristics which can correspond with a regular pentagon. So that way you can easily classify as. Some are:
ReplyDelete- 5 sides
- 5 vertices
- 5 lines of symmetry
- 4 obtuse angle
- 1 acute angle
Second idea is that when you fold the rectangle piece of paper into a pentagon it makes the following crises. Which are the first fold can create a irregular pentagon. But after the second fold it creates the regular fold because of the equal sides and etc.