Number Theory

Number Theory

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.

Order your CD today for Home or School

Mathgoodies CD  OR  Mathgoodies CD

Complete Curriculum  |  Educator's Guide  |  Main CD Page