Transcript What can you construct or create?? - nimsgeometry2010

NIMS GEO.
June 14, 2010
Introduction to Geometry
Notecard Information
• Name
• Grades
• Favorite Geometry Shaper
What did the acorn Say
when he grew up?
• Gee, I’m a Tree
What is Geometry?
• Technical meaning
• Your definitions
Geometry
• Is all about
– Constructions
– (or Connections)
Geometry
• Start with a small set
• An initial criteria
• See what you can build, construct,
connect
• Physical and Mental Constructions
A simple sheet of paper
• What do you know?
• Where can you go?
• How can you show?
The paper
• Is what shape?
– How do you know?
• How many lines of symmetry does it
have?
– How do you show?
• What other properties does it have?
– Where can you go?
Paper Fold
Folds
0
Sections
1
1
2
3
4
Paper Fold
Folds
0
1
2
3
4
Sections
1
2
4
8
16
This is a Geometric Sequence.
These occur when you multiply by the same
rate each time.
In this case, that rate is 2 and the function
would be
Y = 1 * 2x
Where X is the number of Folds and Y is the
number of sections.
The value 1 represents the initial amount.
Geometry is Connected to Algebra!
Paper Fold
Folds
0
Area
1
1
2
3
4
Paper Fold
Folds
0
1
2
3
4
Area
1
1/2
1/4
1/8
1/16
This is a Geometric Sequence.
These occur when you multiply by the same
rate each time.
In this case, that rate is (1/2) and the function
would be
Y = 1 * (1/2)x
Where X is the number of Folds and Y is the
resulting area.
The value
Geometry is Connected to Algebra!
Paper Fold Extension
Suppose the original area of your paper was 88
square units. If you fold as before, fill in the
following table and answer the questions below
Folds
0
Area
88
1
2
3
4
1. This is a _____________Sequence.
2. In this case, the rate is (1/2) and the
original area is ___________
3. The function could be written as
Y = ______* (_____)x
Where X is the number of Folds and Y is the
resulting area.
Paper Fold Bonus
• Take any sheet of paper and fold as
we did in class (so that each fold is
the perpendicular bisector of the
previous fold) 8 times
• Bring in the folded paper and be able
to show me the folds and resulting
sections
You can learn (construct) a
lot from a sheet of paper
• You can also learn (constuct) a lot
from a notecard
• In this case, we are going to let our
notecard represent a plane
• A plane is a 2 dimensional flat shape
with infinite length and width
Building Blocks of Geometry
• Point
– No dimension, infinitely small
• Line
– 1 dimension (length),
• Plane
– 2 dimensions (length and width)
• Different geometries define or
represent these items differently!
• These all reside in Space (3 dimensions)
For Euclidean geometry
Our notecard represents a
plane
• Draw 3 noncollinear points on your
plane
• Draw three lines connecting each
pair of points
• Label the points A, B and C
What do we know?
•
•
•
•
•
Point, Line, Plane
Segments
Rays
Angles
Triangles…
Where Can we go?
• Vertical angles are equal
• Angles that form a linear pair are
supplementary
• Other triangle properties tomorrow
Hang on to this ‘plane’ notecard
How can we show?
• For vertical angles?
– Measure
– Trace and Place
– Fold?
What if we started with
a circle?
•
•
•
•
What can we construct?
What do we know?
What can we show?
How do we know?
Circle
• The set of all points in a plane
equidistant from a given point
• The common distance is called the
radius
• The given point is called the center
• Find the center of your circle…
• Where can we go……..
June 14 Assignments
Due June 15
1.
2.
3.
4.
5.
6.
7.
Complete Paper Fold extension (and bonus if you wish)
Read the Geometry, More than Shapes article
Read pages 5-6 in text and see if you can find a more
technical term for a truncated tetrahedron
Use your circle fold to complete questions on page 7 of
text—be able to describe (draw or show) 4 polygons with
the indicated areas
Complete you definitions tasks
Complete Activity 3.11 on page 127 in your text
A.
(What can you construct or create??)
Goto the NIMS Geo Wiki to download and complete
Reflection Journal
NIMS websites
• Mann’s homepage
– http://www.wiu.edu/users/mfrrm1/
• Olsen’s homepage
– http://www.wiu.edu/users/mfjro1/wiu/index.htm
• NIMS homepage
– http://www.riroe.com/nims/nims10.htm
• NIMS Geometry Wiki
– http://nimsgeometry2010.pbworks.com/
– Syllabus and reflection
– Daily notes and assignments
– Other resources—check regularly