Number Theory

Learning Topics: 

Factors, multiples, GCF, LCM, prime and composite numbers, divisibility, exponents, and patterns with exponents.

This page lists the Learning Objectives for all 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 nth 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.