# Number Theory

**Learning Objectives** for all Number Theory lessons in Unit 3

**Factors and Greatest Common Factors**

The student will be able to:

- Define factor, whole number, counting number, remainder, quotient and greatest common factor.
- Connect the whole-number dimensions of a rectangular garden to finding factors.
- Identify and list all factors of a given whole number.
- Determine the greatest common factor of two or more whole numbers.
- Describe the procedure for finding the greatest common factor of two or more whole numbers.
- Recognize the difference between a common factor and the greatest common factor of two or more whole numbers.
- Apply factoring concepts and procedures to complete five interactive exercises.

**Multiples and Least Common Multiples**

The student will be able to:

- Define multiple and least common multiple.
- Identify and list the set of multiples for a given whole number.
- Determine the least common multiple of two or more whole numbers.
- Recognize that the set of multiples for a given whole number is infinite.
- Describe the procedure for finding the least common multiple of two or more whole numbers.
- Recognize the difference between a common multiple and the least common multiple of two or more whole numbers.
- Apply multiple concepts and procedures to complete five interactive exercises.

**Prime and Composite Numbers**

The student will be able to:

- Define prime, composite and inclusive.
- Determine if a given whole number is prime or composite by finding all of its factors.
- Describe the procedure for determining if a whole number is prime or composite.
- Identify and list all prime numbers within a given range of whole numbers.
- Recognize that the number one is neither prime nor composite.
- Explain why a given number is prime or composite using full sentences.
- Apply prime and composite concepts and procedures to complete five interactive exercises.

**Divisibility Tests**

The student will be able to:

- Define divisibility test.
- Restate divisibility tests for 2, 3, 4, 5, 6, 8, 9 and 10.
- Perform a single divisibility test on a given whole number.
- Perform several divisibility tests on a given whole number.
- Choose and perform divisibility tests to determine if a number is prime or composite.
- Recognize the need for divisibility tests when working with large, whole numbers.
- Choose and perform divisibility tests to complete five interactive exercises.

**Exponents**

The student will be able to:

- Define base and exponent.
- Discover the need for exponential notation when writing a product of many factors.
- Recite and write numbers in exponential form.
- Indicate if a number is written in exponential form, factor form or standard form.
- Restate the rules for a base with an exponent of zero and one.
- Convert numbers between exponential form, factor form and standard form.
- Apply exponential concepts to complete five interactive exercises.

**Pattern and Exponents**

The student will be able to:

- Define powers.
- Identify the rule for a pattern of numbers by examining a list of powers.
- Predict the next number in the list of powers for a given a number.
- Given a base raised to the
*n*th power, determine the standard form of that base raised to the*n*+1 power using a single multiplication. - Evaluate five interactive exercises with word problems.
- Analyze each word problem to identify the given information.
- Formulate a strategy for solving each problem.
- Apply advanced exponential concepts to solve problems.

**Practice Exercises**

The student will be able to:

- Examine ten interactive exercises for all topics in this unit.
- Determine which concepts and procedures are needed to complete each practice exercise.
- Compute answers by applying procedures, and by predicting the next number in a sequence.
- Self-assess knowledge and skills acquired from this unit.

**Challenge Exercises**

The student will be able to:

- Evaluate ten interactive exercises with word problems for all topics in this unit.
- Analyze each word problem to identify the given information.
- Formulate a strategy for solving each problem.
- Apply strategies to solve routine and non-routine problems.
- Synthesize all information presented in this unit.
- Connect number theory to the real world.
- Develop problem-solving skills.

**Solutions**

The student will be able to:

- Examine the solution for each exercise presented in this unit.
- Identify which solutions need to be reviewed.
- Compare solutions to completed exercises.
- Identify and evaluate incorrect answers.
- Amend and label original answers.
- Identify areas of strength and weakness.
- Decide which concepts and procedures need to be reviewed from this unit.