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Unit Plan
Cut the Knot

Cut the Knot: Existence of the Orthocenter

For Students 9th - 10th
This site defines the altitude of a triangle and gives the standard notation for altitudes of a triangle. The site then goes to list several proofs involving altitudes and orthocenters.
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Graphic
Cut the Knot

Cut the Knot: The Floor Function

For Students 9th - 10th
This site explains the floor function [x] notation (also known as the greatest integer function). The site contains several examples and graphs to help understand the concept. There is also an advanced exercise using the floor function...
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Activity
Cut the Knot

Cut the Knot: Proof Without Words

For Students 9th - 10th
This site explains the method of proof using diagrams. The site gives some history of methods of proof and how it has changed through time. The site gives numerous examples of proofs without words and a practice exercise to be worked on...
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Activity
Cut the Knot

The Game of Hex

For Students 9th - 10th
Play against a basic or an advanced competitor the game of hex, a race from one side of a patterned board to the other. This game cannot end in a tie, and it is addictive!
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Handout
Cut the Knot

Cut the Knot!: Analogues and Generalization of the Pythagorean Theorem

For Students 9th - 10th
This site discusses the theorems and other findings which are directly related to the fundamental Pythagorean theorem. Be sure to click on the link to information on Pythagorean theorem to find several proofs of the theorem.
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Handout
Cut the Knot

Cut the Knot!: Recipes for the "Average Value" of a Function

For Students 9th - 10th
Site explains a "recipe" for finding the average value of a function using summations.
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Unit Plan
Cut the Knot

Cut the Knot!: Fundamental Theorem of Algebra

For Students 9th - 10th Standards
Contains a summary of the fundamental theorem of algebra as it pertains to integrals.
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Unit Plan
Cut the Knot

Cut the Knot!: Remarks on Proving the Fundamental Theorem of Algebra

For Students 9th - 10th Standards
Contains relevant information regarding to the fundamental theorem of algebra.
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Website
Cut the Knot

Cut the Knot!: Proofs in Mathematics

For Students 9th - 10th Standards
This site provides an explanation of mathematical proofs. It also has links to different types of proofs.