Number theory is an exciting area of mathematics, with many practical
applications. Some day, you may need to use factors to help you
build a yard with a specific area, or use multiples to solve a scheduling problem
at work. Many topics from elementary number theory are covered on Math Goodies. You have been
selected to explore these topics, and to apply your knowledge through critical
You will explore resources on Math Goodies to answer specific questions on number theory. The key to
learning in this WebQuest is to become engaged in finding information,
and to learn from what you have
found. These tasks will require a computer, access to the Internet, paper and pencil.
Familiarity with Math
Goodies is helpful, but not necessary.
Process Part I: Number Theory Unit and Worksheets
- Browse our instructional unit on Number Theory,
which covers factors, GCF, Multiples, LCM, prime and composite numbers,
divisibility tests and exponents.
- Complete all five exercises at the end of each core lesson in this unit.
- Complete our Worksheet on The
Sieve of Eratosthenes
Elementary Number Theory Questions
Answer each question, in order, and write down your answer
on paper in your own words. You may work alone or in groups.
- What is elementary number theory?
- Give an example of how can multiples help you with gardening? (You may
provide a specific example you
found on our site.)
- What is a factor?
- What is 1,729,463 raised to the zero power?
- Is 25 the same as 2 x 5? Explain why or why not using full sentences.
- What is the Fibonacci sequence? (Hint: It can be found on several pages.)
- Write the Fibonacci sequence on paper.
- What is the rule for this sequence? Write your answer using your own words.
- Is the number 31 prime or composite? Explain your answer.
- Is the number 747 prime or composite? Explain your answer.
- How did you arrive at your answer to questions 9 and question 10? What method did you use
- Why do we use divisibility tests?
- Which test(s) will determine if the number 876 is prime or
composite? Explain your answer.
- What is the Sieve of Eratosthenes?
- Find all prime numbers less than 100.
- What is the smallest prime number?
- Which prime number is even?
- What is an emirp?
- List all emirps between 1 and 100.
- Our instructional unit on Number Theory.
- Our worksheet on The Sieve of Eratosthenes.
- Switch your answers with a classmate or group member.
- Review each other's answers.
- Exchange ideas: Discuss what you have learned.
- Go through the answer key to our worksheet on The Sieve of Eratosthenes.
- Assess your ability to find information in this WebQuest.
- Assess your ability to learn from the information you found.
- Which tasks were easy for you?
- Which tasks did you struggle with?
Congratulations! You learned about topics in number theory and extended your
knowledge through critical thinking. You did this by embarking on a quest for information, and
by learning from the information you found.
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