Math and Science Perfect Together

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Math and Science Perfect Together

• Workshop from ACETTC
• Presenter Kathleen Willson
• Email kathleen.willson_at_stockton.edu

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New Jersey Core Curriculum Content Standards

• http//www.state.nj.us/njded/cccs/index.html
• Mathematics
• Science
• ETTCs Math Science Resource
• http//ettc.stockton.edu/njssi

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What is a fractal?
FRACTALS

• fractals as processes or images that exhibit
  self-similarity

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Fractals often look like objects in nature.

• Ferns
• Flowers
• Landscapes
• Clouds
• Crystals
• Explosions

All have fractal features and are considered
fractals in nature.
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Flowers
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Computer generated Tree
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Crystals
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Trees
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Landscapes
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Explosions
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Fractals are often formed by what is called an
iterative process.
Which means you use a process over and over
again To get a complicated figure Lets take
a look at three common fractals..
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Kochs Snowflake
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Koch Snowflake directions
Step One Start with a large equilateral
triangle.
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Koch Snowflake directions
Step Two. Make a Star. 1. Divide one side of
the triangle into three parts and remove the
middle section. 2. Replace it with two lines
the same length as the section you removed. 3.
Do this to all three sides of the triangle.
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Koch Snowflake directions
Step Three Do it again and again to all segments
of polygon
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All the iterative processes together.
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Sierpinskis Triangle
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To create Sierpinskis Triangle
Step One Draw an equilateral triangle with
sides of 2 triangle lengths each. Connect the
midpoints of each side. How many equilateral
triangles do you now have? Shade out the triangle
in the center. Think of this as cutting a hole in
the triangle.
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To create Sierpinskis Triangle
Step Two Draw another equilateral triangle with
sides of 4 triangle lengths each. Connect the
midpoints of the sides and shade the triangle in
the center as before. Notice the three small
triangles that also need to be shaded out in each
of the three triangles on each corner - three
more holes.
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To create Sierpinskis Triangle

• OR
• Draw a large equilateral triangle.
• Draw the midpoint of each side.
• Connect Midpoints.
• Shade the middle triangle.
• Repeat the process with the un-shaded triangles.
  
• How far can you get

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Jurassic Park Fractal
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Jurassic Park Fractal

• Step One
• We are going to start with a narrow strip of
  paper, let's say approximately 1" by 11".
  Construction paper works really well because it
  has a little more stiffness.
• Step Two
• Take the strip in both hands, fold the paper over
  end-to-end, right hand onto left, and crease.
• Now fold it again in the same way, right onto
  left, and crease, and
• again, right onto left and crease, and
• again right onto left and crease.
• You have folded it four times in all, right?

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Jurassic Park Fractal
Step Four Lay the paper on its edge. Crease all
the folds as right angles. Then rotate it until
it matches up with the figure below. Be sure to
find the closed-up square. See? You did it! It's
the same shape!
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Jurassic Park Fractal
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THE RULES

• The middle entry in the table is always a right.
• The entries to the left of the middle are the
  entries of the table before.
• 3. The entries to the right of the middle are
  opposites of the ones to the left.

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Jurassic Park Fractal
RRLRRLLRLLRLLRR
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Can we code this??
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Even More fun!!
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Questions.On fractals more informationcan be
found on ETTCs website.http//ettc.stockton.edu
/njssi
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Stick Figures Rules K-81. Your groups goal is
to construct ONE figure which matches all the
clues. Work cooperatively to achieve this
goal.2. When it is time to begin open your
envelope and pass out clues to each member of the
group.3. When you believe you group has the
completed figure, get it checked for correctness
and proceed to next figure.4. YOU MAY NOT break
the sticks.5. First group to finish all
figures, or group with the most figures completed
when time is up WINS!
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Stick Figures Rules High School1. Your groups
goal is to construct ONE figure which matches all
the clues. Work cooperatively to achieve this
goal., but do not look at each others clues.2.
When it is time to begin open your envelope and
pass out clues to each member of the group, face
down.3. When you get your clue, you may look
only at your own clue. You may not look at
anyone elses. You may share your clue by
telling others whats on it, but you may not show
it to anyone else.4. When you believe you group
has the completed figure, get it checked for
correctness and proceed to next figure.5. YOU
MAY NOT break the sticks.6. First group to
finish all figures, or group with the most
figures completed when time is up WINS!
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Break!!10 MINUTES!!
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Tessellations
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Why Tessellations?
State of NJ - Core Curriculum Standards Mathematic
s - 4. 07 Geometric Properties Standard
State of NJ - Core Curriculum Standards Mathematic
s - 4. 11 Patterns Relationships
State of NJ - Core Curriculum Standards Science
5.5- Math and Science
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What is a tessellation?
Formal definition A careful juxtaposition of
elements into a coherent pattern sometimes called
a mosaic or tiling.
Simply put A tessellation is like a puzzle that
repeats a particular pattern.
For example
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In nature and life, they appear often
Honeycombs...
Mud flats...
In games, like checkers..
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Study of Science
X-ray Crystallography
This picture depicts the transformation of eight
points in an array to make a very small crystal
lattice, which tessellates.
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more science.
This image suggests the relationship between
tessellations, symmetry, and x-ray
crystallography.
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and even more science.
Hydrogen Peroxide, among other chemicals, has
this tessellating, crystal structure.
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The mathematics of the Regular Tessellation...

• A regular polygon tessellation is constructed
  from regular polygons.

• Regular polygons have equal sides and equal
  angles.

• The regular polygons must fill the plane at each
  vertex, with repeating patterns and no
  overlapping pieces.

Note this pentagon does not fit into the vertex
therefore it is not a regular tessellation.
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A famous mathematician, Kepler studied
tessellations and noted the regular tessellations
or (tilings) of the plane.
There are only three regular tessellations
one of triangles
one of squares
and one of hexagons.
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This is NOT a regular polygon tessellation, becaus
e...
vertex
The plane is not filled at the vertex, because
there is space left over.
space
A regular polygon tessellation, can be changed
using alterations to the sides of the polygon.
These alterations are called transformations.
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Three Common Transformations
1. Translation, which is a slide of one side of
the polygon.
2. Reflection, which is a flip or mirror image
of one side of the polygon.
3. Rotation, which is a turn of a side around
one vertex of the polygon.
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Translations - a slide
this side
the alteration
moves here
Get practice template and try creating a
translation.
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Lets try together.. a translation or slide.
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Reflections - mirror images
the alteration
flips here
Get practice template and try creating a
reflection.
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Lets try together.. a translation or slide.
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Reflections - mirror images
the alteration
flips here
Get practice template and try creating a
reflection.
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Lets try together.. a reflection, flip or
mirror image
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Rotations - turns
the alteration
here
rotates around this vertex
Get practice template and try creating a
rotation...
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Lets try together.. a rotation or turn
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Lets test your knowledge

• Quiz tessellations/ regular or not.
• Quiz What kind of transformation?

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Questions.On tessellations more
informationcan be found on ETTCs
website.http//ettc.stockton.edu/njssi
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BLOCK IT RULES Materials Patterns Blocks or
Shapes. Object of the Game TO total the most
amount of points. Hexagons 1 point Trapezoids
1/2 of a point Rhombi 1/4 of a point Triangles
1/6 of a point Number of Players 2 to 4 The
Play Each player needs 3 yellow hexagons, 3 red
trapezoids, 3 blue rhombi and 3 green triangles.
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• Whats in the BAG?
• Work together with partner, to decipher the clues
  and make
• Predictions out how many of each color are in the
  bag.
• When you have decided together look in the bag
  and check.
• Do each bag, and remember to use all clues to
  solve each bag.
• First, team with 6 correct bags most bags at end
  of time period wins.

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Thanks once again.. More informationcan be
found on ETTCs website.http//ettc.stockton.edu
/njssi