2. Geometry (HS)

 
  1. Reasoning About Numbers, Systems and Quantitative Situations (L1)
  2. Calculation, Algorithms, and Estimation (L2)
  3. Mathematical Reasoning, Logic and Proof (L3)
  4. Figures and Their Properties (G1)
  5. Relationships Between Figures (G2)
  6. Transformations of Figures in the Plane (G3)

 

Additional Links to General Mathematics Sites

 

3. Mathematical Reasoning, Logic, and Proof(L3)

High School

  1. L3.1 Mathematical Reasoning
    1. Geometry from the land of the Incas - Pentagons & Pentagrams
      This dynamic geometry software provides an environment in which we can explore geometric relationships and make test conjectures. The site also has a section on Geometry Theorems and Problems and quizzes in other areas mathematics.
    2. Geometry from the land of the Incas - Platonic Solids
      This dynamic geometry software provides views of Platonic Solids. Great animation as the five shapes rotate to show a three dimensional view of each shape.
    3. Glencoe Mathematics
      You work as an architect for an architectural firm. The city in which your firm is located wants to construct a monument to honor the war veterans from your city. The monument needs to be a unique building with a maximum of 1000 square feet of interior floor space. They also want a unique, creative tile pattern to be used on the floor inside the monument. You need to present a design for this building to the others in your firm. Your proposal should be in a portfolio that contains a design for the building and a pattern to be used for tiling the floor inside the building. If you prefer, you can prepare a Web page with this information for the members of your firm to view.
    4. Glencoe Mathematics - "Geocaching" Sends Folks on a Scavenger Hunt
      You work for a national company that plans to market treasure hunts to radio stations, television stations, and other organizations in various cities. Your company will profit by selling these hunts to the organizations. You need to present a sample treasure hunt to your boss. You may select any city in the U.S., or the world, if you prefer. After your hunt has been designed, you need to prepare a portfolio including the map to be used, clues, questions, and answers. If you prefer, you can prepare a Web page with this information that others can view. Then customers for this product could view a sample treasure hunt.
    5. Rink Works
      This site is for mathematical reasoning with great puzzles, mind benders and logic activities.
    6. Rhombus Conjectures
      An activity that always students to discover the properties of a rhombus.  It provides a method to discover the properties using pencil and paper or geometer sketchpad.
    7. Sketchpad v.3 Gallery - Projectile Motion
      This sketch show the path of a projectile computed interactively. Buttons give you control over showing the focus and direction and over an illustration of how to find the focus of the parabolic path using light rays. An animation button allows you to animate a ball along the path. A Time Trace button shows dynamic locus of the balls at uniform time intervals. Requires the program Gometer's Sketchpad
  2. L3.2 Language and Laws of Logic
    1. Laws of classical logic
      The laws of classical logic are a small collection of fundamental sentences of propositional logic and Boolean algebra, from which may be derived all true sentences in both of these elementary formal systems.
    2. Now what does that mean?
      Logic is putting your thoughts in order. It's a way to think so that you come to right conclusions. Inferences are implications, and part of logic is recognizing what a statement implies and what it doesn't.
      A fallacy is a mistake.
    3. What are the 4 fundamental laws of logic?
      Explains the four basic laws of logic.
  3. L3.3 Proof
    1. Mathematical Proof
      In mathematics, a proof is a convincing demonstration that some mathematical statement is necessarily true, within the accepted standards of the field. A proof is a logically deduced argument, not an empirical one. That is, the proof must demonstrate that a proposition is true in all cases to which it applies, without a single exception. An unproven proposition believed or strongly suspected to be true is known as a conjecture.
    2. Spark Notes
      This is a great over all site. It has a good table of contents with topics and problems to follow. There are supplimental proof problems available to try.
    3. Wikibooks- Mathematical Proof
      Sometimes people read mathematical proofs and think they are reading a foreign language. This book describes the language used in a mathematical proof and also the different types of proofs used in math

 

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