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### Arithme-Tic-Toc

6-8, 9-12

Students will be introduced to modular arithmetic by first examining a five-hour analog clock and its mathematical properties. Then students will investigate patterns and relationships that exist in 12-hour addition and multiplication clock tables. ### Impact of a Superstar

9-12

In this activity, students will use the Illuminations Line of Best Fit Interactive
to plot the data from two teams during the 2004‑05 NBA season. In
particular, students will look at the data for total points and minutes
played by each of the starters on the Los Angeles Lakers and Detroit
Pistons. The data suggest that Laker Kobe Bryant is an outlier—he
scores more points per minutes than his teammates, which is part of why
some sportswriters have described him as "selfish." But through further
investigation, students will also notice that Piston Ben Wallace is
also an outlier, because he scores fewer points than his teammates.### 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.### Walk the Plank

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.

### Dirt Bike Dilemma

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.### Seeing Music

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.### Check That Digit

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.### Number Representations

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.

### 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.### Escape from the Tomb

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?