Lesson 1

Lesson 1: Fundamental Counting Principle

 

Focus

 

Prior to 1999, the area code for the province of Alberta was 403. In 1999, another area code (780) was added and became the area code for the northern part of the province. The southern half of the province retained the 403 area code. In September 2008, Alberta added another area code, 587, across the province. Adding another area code provides the potential for 9 000 000 more phone numbers. Can you think of why the province continues to need more phone numbers?

 

By the end of this lesson, you will be able to show that this change does indeed amount to 9 000 000 new phone numbers.

 

Graham/25113263/flickr

 

Historically, licence plates in Alberta have consisted of three letters followed by three digits. Because the province is getting short of licence-plate numbers, Alberta is now changing the format to three letters followed by four digits. In 1997, Ontario switched from three digits and three letters to four letters and three digits. Can you figure out how many new licence plates each of these scenarios will create?

 

Determining the number of ways in which something may occur is a branch of mathematics called combinatorics. Combinatorics is used in many ways: from designing a computer network to coding a garage door opener to determining the chances of winning the lottery.

 

Lesson Outcomes

 

At the end of this lesson you will be able to

• use the fundamental counting principle to solve problems
• use a new notation, called factorial notation, to determine numbers of arrangements of items

Lesson Questions

 

You will investigate the following questions:

• 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?

Assessment

Your assessment may be based on a combination of the following tasks:

• completion of the Lesson 1 Assignment (Download the Lesson 1 Assignment and save it in your course folder now.)
• course folder submissions from Try This and Share activities
• additions to Glossary Terms and Formula Sheet
• work under Project Connection

Self-Check activities are for your own use. You can compare your answers to suggested answers to see if you are on track. If you are having difficulty with concepts or calculations, contact your teacher.

 

Remember that the questions and activities you will encounter provide you with the practice and feedback you need to successfully complete this course. You should complete all questions and place your responses in your course folder. Your teacher may wish to view your work to check on your progress and to see if you need help.

 

Time

 

Each lesson in Mathematics 30-2 Learn EveryWare is designed to be completed in approximately two hours. You may find that you require more or less time to complete individual lessons. It is important that you progress at your own pace, based on your individual learning requirements.

 

This time estimation does not include time required to complete Going Beyond activities or the Module Project.