Introduction to Geometry 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 many lines of symmetry does it have? 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 1 2 3 4 Sections

Geometry is Connected to Algebra! Paper Fold Folds 1 2 3 4 Sections 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 1 2 3 4 Area

Geometry is Connected to Algebra! Paper Fold Folds 1 2 3 4 Area 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!

1. This is a _____________Sequence. 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 1 2 3 4 Area 88 1. This is a _____________Sequence. In this case, the rate is (1/2) and the original area is ___________ 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 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 (What can you construct or create??) Goto the NIMS Geo Wiki to download and complete Reflection Journal

NIMS websites Mann’s homepage Olsen’s homepage NIMS 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