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Geometry

Inequalities in Triangles

9-12
Students will use pasta to create models of triangles and non-triangles and investigate the relationship between the longest side of the triangle and the sum of the other two sides of the triangle. In addition, students will measure the sides and angles of a scalene triangle and investigate the relationship between the location of the largest angle and largest side in a triangle.
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Geometry

Static Nim

9-12
Static Nim is a one-pile game between two players. In this game, the maximum number of tokens that can be removed on each turn remains constant throughout the game. In this lesson, students will learn to represent the positions as the vertices of a directed graph and the moves as the edges of the graph. Also, they will learn that solving a game means finding a partition of the vertices into two sets such that three important properties are satisfied.
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Geometry

Power of Points

9-12
In many curricula, the Power of Points theorem is often taught as three separate theorems: the Chord-Chord Power theorem, the Secant-Secant Power theorem, and the Tangent-Secant Power theorem. Using a dynamic geometry applet, students will discover that these three theorems are related applications of the Power of Point theorem. They also use their discoveries to solve numerical problems.
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Geometry

Law of Sines

9-12
In this lesson, students will use right triangle trigonometry to develop the law of sines.
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Geometry

Law of Cosines

9-12
In this lesson, students use right triangle trigonometry and the Pythagorean theorem to develop the law of cosines.
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Geometry

Perplexing Parallelograms

9-12
A surprising result occurs when two line segments are drawn through a point on the diagonal of a parallelogram and parallel to the sides. From this construction, students are able to make various conjectures, and the basis of this lesson is considering strategies for proving (or disproving) one of those conjectures.
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Geometry

Inscribed and Circumscribed Polygons

9-12
By calculating the areas of regular polygons inscribed and circumscribed about a unit circle, students create an algorithm that generates the never-ending digits of π, a common curiosity among high school students.
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Geometry

Improving Archimedes' Method

9-12
Archimedes was the first mathematician to develop a converging series approximation to π. That highly influential discovery guided the development of calculus many hundreds of years later. However, his method only gives lower and upper boundaries that form intervals known to capture π, not a single numeric estimate of π. In this lesson, students ask, “Where is π located in those intervals?” They also discover an improvement to Archimedes' method that generates the infinite digits of π more efficiently and accurately.
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Geometry

Pieces of Proof

9-12
There is a leap to be made from understanding postulates and theorems in geometry to writing proofs using them.  This lesson offers an intermediate step, in which students put together the statements and reasons to build a formal proof.
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Geometry

Dividing a Town into Pizza Delivery Regions

9-12

Students will construct perpendicular bisectors, find circumcenters, calculate area, and use proportions to explore the following problem:

You are the owner of five pizzerias in the town of Squaresville. To ensure minimal delivery times, you devise a system in which customers call a central phone number and get transferred to the pizzeria that is closest to them. How should you divide the town into five regions so that every house receives delivery from the closest pizzeria? Also, how many people should staff each location based on coverage area?