Here are some examples of Anamorphic Art. Click here
Friday, November 21, 2008
Wednesday, November 19, 2008
Well, probably!
The instructions for this activity are found in the Holt Cooperative Learning Activities book for section 5.8.
The object is to design probability games (e.g. dartboards) with specific requirements. Then, pick a game where the object is to land within a certain area/ number (examples: corn hole/ bean bag toss, darts, yahtzee...). Find probabilities of accuracy or winning if all cases are equal. (For cornhole, this would be landing in the hole; for darts, landing in the correct number field; for yahtzee, getting six of the same number...) Why does calculating an empirical probability not necessarily predict the outcome for these games? (Why are they not solely dependent on probability?)
Completion of this project requires:
1. Game sheet with correct probabilities according to specifications.
a. Use of color (markers, colored pencils) on the sheet
2. Game information
a. Correctly calculated probabilities
b. Explanation of why a theoretical probability does not necessarily predict a game's outcome.
The object is to design probability games (e.g. dartboards) with specific requirements. Then, pick a game where the object is to land within a certain area/ number (examples: corn hole/ bean bag toss, darts, yahtzee...). Find probabilities of accuracy or winning if all cases are equal. (For cornhole, this would be landing in the hole; for darts, landing in the correct number field; for yahtzee, getting six of the same number...) Why does calculating an empirical probability not necessarily predict the outcome for these games? (Why are they not solely dependent on probability?)
Completion of this project requires:
1. Game sheet with correct probabilities according to specifications.
a. Use of color (markers, colored pencils) on the sheet
2. Game information
a. Correctly calculated probabilities
b. Explanation of why a theoretical probability does not necessarily predict a game's outcome.
Tuesday, November 18, 2008
Math-atouille
Make models to show why some (two, to be exact) triangle congruence shortcuts do not necessarily create congruent triangles. Present the examples on sheets of paper or on posterboard.
In addition, look up the Triangle Inequality theorem. Create models to demonstrate why the Triangle Inequality theorem must be true. (Show what happens if it is not true.) Your work will be displayed in the room.
Completion of this project requires:
1. Model or diagram of non-valid triangle congruencies (label the attempted "shortcut" to congruent triangles.) Two shortcuts with counterexamples means there will be at least four triangles presented.
a. Triangles can be on paper or posterboard. Creation suggestions - uncooked linguine noodles!
2. Model or diagram of the Triangle Inequality theorem: any two sides of a triangle must be greater than the length of the third side. Three triangles must be modeled for this. (Creation suggestion is STILL linguine noodles!)
a. the third side longer than the sum of the other two side lengths
b. the third side's length equal to the sum of the other two side lengths
c. the third side's length less than the sum of the other two side lengths
In addition, look up the Triangle Inequality theorem. Create models to demonstrate why the Triangle Inequality theorem must be true. (Show what happens if it is not true.) Your work will be displayed in the room.
Completion of this project requires:
1. Model or diagram of non-valid triangle congruencies (label the attempted "shortcut" to congruent triangles.) Two shortcuts with counterexamples means there will be at least four triangles presented.
a. Triangles can be on paper or posterboard. Creation suggestions - uncooked linguine noodles!
2. Model or diagram of the Triangle Inequality theorem: any two sides of a triangle must be greater than the length of the third side. Three triangles must be modeled for this. (Creation suggestion is STILL linguine noodles!)
a. the third side longer than the sum of the other two side lengths
b. the third side's length equal to the sum of the other two side lengths
c. the third side's length less than the sum of the other two side lengths
Wheelchair accessibility
Find a wheelchair ramp in Grand Rapids or your neighborhood. Measure the length of the ramp along with the maximum height.
Look up the Americans with Disabilities Act and find information regarding wheelchair ramps. What is the maximum slope? What types of facilities are required to have wheelchair access? Why do some ramps have turns?...Along with other noteworthy information from the act.
Completion of this project requires:
1. Information about the wheelchair ramp - location, length, height.
2. Correct computation of the slope of the ramp.
3. Information from the Americans with Disabilities Act:
a. Maximum slope of a ramp and a reason for having a maximum slope.
b. Two other specific rules/ guidelines that you found interesting
c. One thing you learned from the Act
Look up the Americans with Disabilities Act and find information regarding wheelchair ramps. What is the maximum slope? What types of facilities are required to have wheelchair access? Why do some ramps have turns?...Along with other noteworthy information from the act.
Completion of this project requires:
1. Information about the wheelchair ramp - location, length, height.
2. Correct computation of the slope of the ramp.
3. Information from the Americans with Disabilities Act:
a. Maximum slope of a ramp and a reason for having a maximum slope.
b. Two other specific rules/ guidelines that you found interesting
c. One thing you learned from the Act
Monday, November 17, 2008
Pythagorus' Squires
For your enjoyment, click here!
Completion of this project requires:
1. Printed proof of the Pythagorean theorem NOT shown in class
2. A succinct but sufficient review of the printed proof, adding what you understand well and what you do not understand.
3. Link to an applet (a simple computer program)of a proof of the Pythagorean theorem (does not have to be the same as the proof for part 1.)
4. Three to five sentences on what you learned from the proof and the applet, along with why it was beneficial for you to complete this project.
Completion of this project requires:
1. Printed proof of the Pythagorean theorem NOT shown in class
2. A succinct but sufficient review of the printed proof, adding what you understand well and what you do not understand.
3. Link to an applet (a simple computer program)of a proof of the Pythagorean theorem (does not have to be the same as the proof for part 1.)
4. Three to five sentences on what you learned from the proof and the applet, along with why it was beneficial for you to complete this project.
Ol' Great-Grandpa Geometry
It has been said that geometry is the oldest math in the world. Present, in a brochure format, how geometry was developed and used in three different cultures. Informational brochure must be on an 8.5 x 11" sheet of paper folded into thirds.
Completing this project requires:
1. Brochure including:
a. Development of geometry around the world (general)
b. Information on three historical cultures and their use and development of geometry.
c. How geometry is used our culture today. (You will probably find it easiest to use and explain one in-depth example.)
2. Brochure Format has:
a. 8.5 x 11" sheet of paper folded into thirds
b. Organization and neatness
c. Multiple colors and at least three visual diagrams/pictures in addition to verbal explanations.
d. Title page (with brochure title, your name, illustration)
Completing this project requires:
1. Brochure including:
a. Development of geometry around the world (general)
b. Information on three historical cultures and their use and development of geometry.
c. How geometry is used our culture today. (You will probably find it easiest to use and explain one in-depth example.)
2. Brochure Format has:
a. 8.5 x 11" sheet of paper folded into thirds
b. Organization and neatness
c. Multiple colors and at least three visual diagrams/pictures in addition to verbal explanations.
d. Title page (with brochure title, your name, illustration)
Tessellations
Tessellation information is found on pages 154 and 196. A complete rubric is provided in class for the tessellation project.
Original tessellation (not traced or printed from a computer), either a translational tessellation or rotational tessellation. Ideal tessellations will include colors, have a more complicated, smaller-sized pattern, have extra detail to make a recognizable design (and a title!), and will be presented on an 8.5 x 11" sheet of plain paper.
Completing this project requires:
1. Colored 8.5 x 11 piece of plain paper
2. Pattern used (preferably 2.5" x 2.5" or smaller) taped to the back of the tessellation
Original tessellation (not traced or printed from a computer), either a translational tessellation or rotational tessellation. Ideal tessellations will include colors, have a more complicated, smaller-sized pattern, have extra detail to make a recognizable design (and a title!), and will be presented on an 8.5 x 11" sheet of plain paper.
Completing this project requires:
1. Colored 8.5 x 11 piece of plain paper
2. Pattern used (preferably 2.5" x 2.5" or smaller) taped to the back of the tessellation
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