conics art for camt 2011
TRANSCRIPT
The Start of Something
BIG
CONICS Art Foldable
�Create a multifaceted foldable
�CONIC Art Practice
�Create Your Own CONICS Art
Start Something BIG..
� From the ziploc bag:� Take one full sheet
and one half sheet of cardstock
� You will also need to share the scissorsFirst, take the half
� Next take the full sheet
� First, fold it hotdog style and make a crease
� Open the fold and fold in the two edges towards the center
Foldable
� First, take the half sheet and fold it hotdog style
� Then cut along the crease and lay aside
towards the center crease—this will result in 3 parallel creases and 4 columns
� Repeat this process hamburger style—this will result in a table with 4 rows and 4 columns
� Take the full sheet (yellow) and fold in half hamburger (taco; horizontally) style
� Cut from the FOLDED edge along each of the 3 creases UP TO the vertical crease
Now cut and weave…
3 creases UP TO the vertical crease
� This will result in 3 slits in the middle of your paper
� Now weave the two strips alternately through the slits
� Center
� Radius
� Equation
� Tangent
� Axis of Symmetry
� Equation
� Direction
� Focus
� Directrix
� Center
� Equation
� Vertices
� Foci
� Co-vertices
� Center
� Equation
� Vertices
� Foci
� Co-vertices
� Asymptotes
� Center
� Radius
� Equation
� Tangent
� Axis of Symmetry
� Equation
� Direction
� Focus
� Directrix
The equation of a circle with
center (0,0) and
radius, r, is
x2 + y2 = r2
� Center
� Equation
� Vertices
� Foci
� Co-vertices
� Center
� Equation
� Vertices
� Foci
� Co-vertices
� Asymptotes
c2 = a2 – b2
c2 = a2 + b2
Tangent
HORIZONTAL VERTICAL
HORIZONTAL VERTICALHORIZONTAL VERTICAL
HORIZONTAL VERTICAL
� Center
� Radius
� Equation
� Tangent
� Axis of Symmetry
� Equation
� Direction
� Focus
� Directrix
� Center
� Equation
� Vertices
� Foci
� Co-vertices
� Center
� Equation
� Vertices
� Foci
� Co-vertices
� Asymptotes
c2 = a2 – b2
c2 = a2 + b2
HORIZONTAL VERTICAL
Now let’s try some CONIC art!
{ } ( )29111 xY −−= ,
�Take your calculator
�Go to the y= screen
�Type the following equations:
�
� You should see a smiley face on your calculator.
� Use Zoom 4:Zdecimal to see the design better
� The final step is to turn AxesOff Use
Note: These equations have been solved for y= from the standard form on the foldable. Most students use Green Globs to practice and refine their artwork in standard form
before solving for y=e.g. Y1 was: x2 + y2 = 9
�
�
�
�
). and .(. 51512522
≤≤−−= xxxY
{ } ( ) 1125111132
++−−= *)./)((, xY
{ } ( ) 1125111142
+−−−= *)./)((, xY
� The final step is to turn AxesOff Use the Format (2nd ZOOM, then scroll down to AxesOff)
{ } ( ) ). and ./(*)/(, 53534911152
≤≤−−−−= xxxY
� Use what you have learned and design your own CONIC Art
� You may use the foldable to design your own equations or just modify the dragonfly equations
Now it’s your turn…
� While you are working I will display some of my students’ works…