3-5
In this lesson, students will pretend to travel to the island of Ambergris Caye off the coast of Belize. Students will work together to complete the measurements needed for their scuba diving gear in preparation for the dives, and they will solve elapsed time problems.
3-5
Students will work in pairs on various measurement problems. They will complete linear conversions, find elapsed time, calculate a percentage, and analyze data from a chart.
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.
6-8, 9-12
When one end of a wooden board is placed on a bathroom scale and the
other end is suspended on a textbook, students can "walk the plank" and
record the weight measurement as their distance from the scale changes.
The results are unexpected— the relationship between the weight and
distance is linear, and all lines have the same
x‑intercept. This investigation leads to a real world occurrence of negative slope, examples of which are often hard to find.
6-8
Students explore the relationship between the lengths of the sides and diagonals of a square. Students will use their discoveries to predict the diagonal length of any square.
9-12
Students discover the algorithm for solving linear programming problems and gain conceptual understanding by solving a real-world problem and using graphing calculator applications.
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.
