9-12
In this lesson students will calculate terms of a geometric sequence to determine frequencies of the chromatic scale. They will then compare sine waves to see and hear the trigonometry behind harmonious and dissonant note combinations.
9-12
This lesson introduces students to a common and practical use of modular arithmetic. First the barcode system is examined, specifically UPC and ISBN bar coding. Then, students will discover the applications of modular arithmetic as applied to credit card numbers.
9-12
Students learn about the repeated subtraction and repeated division methods for converting a decimal number
N to a numeral in base
b, provided
b
is an integer other than ‑1, 0, or 1. Students also learn about the
Fibonacci representation, which is a method for representing a numeral
as a sum of Fibonacci numbers. The Fibonacci representation will be
useful in later lessons in this unit when exploring Nim games.
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.
9-12
Students are presented with a problem: two bowls are suspended from the ceiling by springs. One bowl is lower than the other. In one bowl, you can only place marbles; in the other bowl, you can only place bingo chips. How many items must be placed in each bowl so that the heights of the bowls are the same?
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.
9-12
In this lesson, students will use right triangle trigonometry to develop the law of sines.
9-12
In this lesson, students use right triangle trigonometry and the Pythagorean theorem to develop the law of cosines.
9-12
In static nim, the set of possible move sizes remains the same during the play of the game. In various versions of dynamic nim, the rules are such that the maximum number of counters that can be removed on each turn changes as the game is played. This maximum can depend on the current size of the pile, the number of counters removed on the previous play, or the move number of the game. In this lesson, students will explore the second type, where each move determines the maximum move size of the next move.
9-12
In this lesson, students consider the costs of owning a car and ways to lessen those costs. In particular, highway and city mileage are considered, and optimal mileage is calculated using fuel consumption versus speed data.
