Module 3

Codes are often used in word games and mathematical puzzles, but they have many other uses too. Governments and military organizations use codes to communicate in secret. Websites use codes and passwords to keep banking and financial information secure. Braille is a type of code that enables the blind to read.

 

Computers use a binary or hexadecimal code to convert words into information the computer can understand. Can you guess what the message is in the following hexadecimal code?

 

69 20 6c 6f 76 65 20 6d 61 74 69

 

The same message is written in a different code below. Now can you guess what it is?

 

R olev nzgs

 

In this module you will calculate the number of codes or passwords you can create given certain specifications. You will also learn about the role that order plays in arrangements and selections.

 

In this module you will investigate the following question: How are counting methods used to solve problems involving codes and passwords?

 

To investigate the module question, you will focus on the lessons and questions in the table.

 

Lesson	Topic	Lesson Questions
1	Fundamental Counting Principle	How can you use the fundamental counting principle to determine the number of outcomes in a given problem?
		What is factorial notation, and when is it used to solve problems?
2	Factorial Notation	How many arrangements of n distinct objects are present when they are arranged into a sequence containing all n objects?
		How are algebraic expressions involving factorial notation simplified?
3	Problems Involving Permutations	How can you determine the number of permutations when not all objects need to be arranged or when some of the objects are identical?
4	Solving Problems That Involve Combinations	What are the similarities and differences between permutation and combination problems?
		How are problems involving combinations solved?
5	Solving Probability Problems That Involve Permutations and Combinations	What strategies can be used to solve probability problems that involve permutations and combinations?

 

In Part 1 of Module 3 Project: Math Mystery, you will use the knowledge you have gained in this module to recover a stolen diamond and save a princess's jewels. In Part 2 you will create your own math mystery.