Geometry and Matrices Hands On Activity
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Transcript of Geometry and Matrices Hands On Activity
THE REASON YOU MIGHT ACTUALLY WANT TO LEARN THIS STUFF
BY CHRISTINE LAUBER
Geometry and MatricesHands On Activity
National Standards Materials
Geometry 9 – 12 Apply transformations and use symmetry to
analyze mathematical situations understand and represent translations, reflections,
rotations, and dilations of objects in the plane by using sketches, coordinates, vectors, function notation, and matrices;
use various representations to help understand the effects of simple transformations and their compositions.
Numbers and Operations 9 – 12 Understand meanings of operations and how
they relate to one another develop an understanding of properties of, and
representations for, the addition and multiplication of vectors and matrices;
Compute fluently and make reasonable estimates develop fluency in operations with real numbers, vectors, and matrices, using mental computation or paper-and-pencil calculations for simple cases and technology for more-complicated cases.
Quarter size sheets of graph paper
Graphing calculatorComputer
Animation Activity Packet
PowerPoint presentation with examples
Computer Animation
Computer Animation
First cartoons were all produced by hand.
Each slight movement required a new picture to be
drawn.
Today, computers have taken over!?
Can you name some of the computer
animated films you have seen?
What are the components of motion?
Think of how we move shapes on the
Cartesian Plane.
Translation
Rotation
Reflection
Dilation
In t
he b
egin
nin
g…
.
The first step any animator needs to do is create a simple representation of their character.
On your graph paper,
create a simple picture that
involves 5-10 points and is
NOT symmetrical.
My image will be of a kite in
the sky.
My matrix looks like this.
In order to create the picture in my TI calculator, I need to translate my matrix
into L1 and L2.
Reflects over the y-axis
Reflects over the x-axis
Rotates counterclockwise 56° Reflects over the y =
x axis
Now, change your image to a 3xn matrix by adding a last row of all 1’s
Slides 2 to the right
Slides 2 down
Slides 2 right and 3 down
Reflects over the y = x axis then slides 2 right
What about rotating the image?
Who thinks they have an idea of how to rotate the image?
Cos (5) -Sin (5)Sin (5) Cos (5)
-2.6896, 1.9924, .8716, -5.9772 7.7952, .1743, -9.9619, -.5229
-.5804, 1.9696, -1.7365, -5.90888.2258, -.3473, -9.8481, 1.0419
Cos (10) Sin (10)-Sin (10) Cos (10)