Components of a Vector

In this lesson, students manipulate a velocity vector to control the movement of a car in a game setting. Students learn that vectors are composed of two components: magnitude and direction.

Sums of Vectors and Their Properties

This example illustrates how using a dynamic geometrical representation can help students develop an understanding of vectors and their properties, as described in the Number and Operations Standard. Students manipulate a two vectors to control the movement of a plane in a game-like setting. Students extend their knowledge from the first lesson to further investigate the system of vectors.

Caesar Cipher

In this lesson, students will investigate the Caesar substitution cipher. Text will be encoded and decoded using inverse operations.

Vigenere Cipher

Following their introduction to the Caesar Cipher, students will now learn about the polyalphabetic Vigenere cipher. Text will be encoded and decoded using inverse operations.

Stacking Squares

This lesson prompts students to explore ways of arranging squares to represent equivalences involving square- and cube-roots. Students’ explanations and representations (with their various ways of finding these roots) form the basis for further work with radicals.

Armstrong Numbers

An Armstrong number is an n-digit number that is equal to the sum of the n^th powers of its digits. In this lesson, students will explore Armstrong numbers, identify all Armstrong numbers less than 1000, and investigate a recursive sequence that uses a similar process. Throughout the lesson, students will use spreadsheets or other technology.

Growth Rate

Given growth charts for the heights of girls and boys, students will use slope to approximate rates of change in the height of boys and girls at different ages. Students will use these approximations to plot graphs of the rate of change of height vs. age for boys and girls.

Arithme-Tic-Toc

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.

Check That Digit

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

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.