Saturday, June 20, 2015

Shapes



http://www.math-salamanders.com/images/printable-geometry-sheets-tessellation-regular-polygons.gif

How to Create a Tessellation


How to Create a Tessellation

The appearance of your tessellation should be neat! Your tessellation (pattern) should cover the ENTIRE page (no gaps or unintentional white spaces). You need to turn in the template figure you used to create your tessellation. Coloring should be in between the lines, and No wrinkled or torn projects! You must use a figure created using one of the nibbling methods.

What to do:
1.    Begin by creating a “template” using at least 1 of the nibbling methods. Be sure to label all the pieces.
2.    Once the template has been created, place your template at any of the four corners of your graph paper and trace your first figure. The squares on the graph paper should align with the original square you started with, and therefore your template may hang off the edge of the paper.
3.    Once your figure has been traced slide it or reflect it and trace your next figure (whether you reflect for slide it depends on the nibbling technique you used)
4.    Continue step 3 until the entire page is covered. All your figures on the paper should fit together so that it looks like a puzzle. Figures at the edge will only be partial images
5.    Once you have the page covered in your tessellation, begin to add color in the figure.
6.    Be creative and have fun with the project!

Creating Your Template:

Method 1- The nibbling technique for geometric transformations:
1.    Begin with a square and design from one corner of the square to an adjacent corner. (Do not draw diagonally). Do not stop halfway across!


2.    Cut on the design line, being sure to have 2 pieces when done -the nibble and the rest of the sheet. There should be no other pieces lying around. This is very important! No trimming allowed.


3.    Slide the nibble across the sheet to the opposite side and tape the straight edges together. (Do not attach it to an adjacent edge. Do not flip the nibble around. Do not overlap the edges when taping.) The corners of the piece and the nibble should match perfectly.


4.    Repeat the procedure for the other sides

Method 2- The Rotating and nibbling technique for geometric transformations:
1.    Begin with a rectangle and design from one corner of the rectangle to an adjacent corner. (Do not draw diagonally). Do not stop halfway across!



2.    Cut on the design line, being sure to have 2 pieces when done -the nibble and the rest of the sheet. There should be no other pieces lying around. This is very important! No trimming allowed.



3.    Instead of sliding the nibble, rotate the nibble at its end point to an adjacent side of their square (not an opposite side). Mark your point of rotation and tape the straight edges together. (Do not overlap the edges when taping.) The corners of the piece and the nibble should match perfectly.


4.    Repeat the procedure for the other sides

Creating a Tessellation Using Reflections:
1.    Select any figure you want to use as your pattern (can use a figure from the nibbling methods or a combination of both).
2.    Then reflect or “flip” the figure repeatedly vertically (over the y-axis).
3.    Once you have a row of “flips”, take that row and reflect it horizontally (over the x-axis)
4.    Continue Steps 2 and 3 until your paper is covered.

http://www.fuhsd.net/view/3198.pdf 


Tessellation Worksheet


Name:                                         

Tessellation Worksheet


1.    List 3 different objects in the world around you that have tessellating patterns.







2.    Try drawing each of these patterns















3.    How many types of regular tessellations are there? List them.








4.    How many semi-regular tessellations are there? List them.


















Tessellation Treasure Map


Name:                                           

Tessellation Treasure Map

Directions:
Ahoy matey! Captain Tessellation is guarding his treasure. He will only surrender to the most fearsome scallywag that sails the sea. Captain Tessellation claims that no pirate be fierce enough to complete this treasure map. Are you? Fill out each event and you may be the pirate who wins his booty. Good luck matey!  

Event 1: Answer the following questions
1.  What three rules must a regular tessellation follow?




 2.  How many degrees are at each vertex of a tessellation?



Event 2:  Take a screen shot (or print out and paste to this worksheet) the regular polygons that can be tessellated. Show more than just a few repeated shapes. Make it clear that you discovered the regular polygons that can be tessellated. 









Event 3: Answer the following questions
1.  What is a tessellation?





2.  Another word for tessellation is                                            

3.  What is a regular tessellation? Give an example.








 4.  What is a semi-regular tessellation? Give an example.









Event 4: Answer the following questions

1.  How many semi-regular tessellations are there? List them by their correct classification (i.e. 4.8.8).







2.  Explain why this image won't be a semi-regular tessellation?









3.   Explain why this image won't be a semi-regular tessellation?














Event 5: Name each of the semi-regular tessellations (i.e. 4.8.8)





Event 6: Take a screen shot (or print out and paste to this worksheet) at least two tessellations you made in Tessellation Town.





































Event 7: Answer the following questions

1.    What is the difference between Alhambra style tessellation and Escher style tessellation?









2.    Were all of the Alhambra tessellation “true” tessellations? Explain why or why not.









3.    Who did the tilling/tessellations in the Alhambra?







4.    Where is the Alhambra located?






Event 8: How did M.C. Escher impact the “tessellation world”? Give examples.












Event 9: Using the formula (360/n) prove whether or not these shapes can be tessellated. Show all mathematical work.

1.    Triangle = 60°





2.    Square = 90°





3.    Pentagon = 108°





4.    Hexagon = 120°





Unlock The Code:
Ahoy there buccaneer! Looks like you are almost done with your treasure hunt. Unlock this secret code and you will be the first scallywag to find out where Captain Tessellations treasure is located. But remembarrrr Captain Tessellation be guarding his precious treasure and he will let no pirate pass unless they have the completed treasure map and the three keys.

Directions:
Unlock the secret code at the bottom of this page. Answer the following multiple-choice questions. Each question corresponds to a blank space in the riddle below. The first question corresponds with the first space. The second question corresponds with the second blank space, and so on. Place the letter to your answer in the corresponding space to unlock Captain Tessellation’s secret message.

1.  M.C Escher was born in
A.  1959
B.  1856
C.  1898
D.  2009

2.  A tessellation is
J.   a type of shape
K.  a mathematical equation 
L.  a repeated pattern with no gaps or overlaps
M.  none of the above

3.  How many semi-regular tessellations are there?
A.  8
B.  29
C.  5
D.  15

4.  Which regular polygon tessellates?
P.  Triangle
Q.  Square
R.  Hexagon
S.  All of the above

5.  Which of the following is NOT a semi-regular tessellation?
R.  3.3.3.3.6
S.  4.8.4
T.  3.3.3.4.4
U. 4.8.8

6.  Each vertices of a tessellation is exactly
R.  360°
S.  90°
T.  180°
U.  270°

7.  What famous 14th century palace is renowned for its incorporation of intricate tessellated patterns?
M.  Windsor Castle
N.  Castle Frankenstein
O.  The Alhambra
P.  none of the above

8.  What is a polygon?
O.  any two-dimensional, closed shape with three straight sides or more
P.  any two-dimensional, closed shape with four straight sides or more
Q.  any two-dimensional, closed shape with exactly four straight sides
R.  any three- dimensional, closed shape with three straight sides or more

9.  Which of the following would NOT be an example of a Tessellation?
L.  a honeycomb
M.  a rack of billiard balls
N.  a grid
O.  all of these are examples of tessellations

If the treasure is what you seek to find then you must also keep in mind. Without the map and the three keys Captain Tessellation will tell you to leave. Make sure that you have it all. If you try to trick him then you will fall. You’ll walk the plank you’ll lose your head so don’t think you can trick him instead. But if you have completed all of the tasks then this is what Captain Tessellation asks, “Come visit my home it is pretty cool. You can find me located at your school. If you be lying get ready to meet your doom. If your not then look inside your                                                              ."