Illustrative Math Alignment: Grade 6 Unit 7

Video Tutorial: Percents: Multiple Percents. In this video, we investigate calculating the percent of a percent. Multiple calculations of a percent are investigated relative to a combined percent calculation.

This video is part of a series of videos that cover the topic of percents. This includes the definition of a percent, percent operations, and applications of percents. Each video includes real-world examples of using percents to solve specific problems. 

Video Tutorial: Percents: Percents and Multiples of Numbers. In this video, we explore the difference between percent growth and the multiple of a number. Several real-world examples are used to explore these differences.

This video is part of a series of videos that cover the topic of percents. This includes the definition of a percent, percent operations, and applications of percents. Each video includes real-world examples of using percents to solve specific problems. 

Topic

Factors and Multiples

Definition

Factors are numbers that divide another number without leaving a remainder, while multiples are the result of multiplying a number by an integer.

Description

Understanding factors and multiples is crucial in mathematics, particularly in number theory and algebra. Factors are the building blocks of numbers, representing the integers that can be multiplied together to produce another number. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12. Multiples, on the other hand, are the product of a number and any integer. For instance, the multiples of 5 include 5, 10, 15, 20, and so on.

Topic

Factors and Multiples

Definition

A common factor is a number that divides two or more numbers exactly without leaving a remainder.

Description

Common factors are integral to understanding the mathematical concepts of factors and multiples. They are the numbers that can divide two or more given numbers without leaving a remainder. For example, if you consider the numbers 12 and 18, their common factors are 1, 2, 3, and 6. This is because these numbers can divide both 12 and 18 exactly, with no remainder.

Topic

Factors and Multiples

Definition

A common multiple is a number that is a multiple of two or more numbers.

Description

In the context of factors and multiples, understanding common multiples is crucial for solving various mathematical problems, particularly those involving fractions, least common multiples (LCM), and algebraic expressions. A common multiple of a set of numbers is a number that each of the numbers in the set divides without leaving a remainder. For example, the common multiples of 4 and 6 include 12, 24, 36, and so on. The smallest of these, 12, is known as the least common multiple (LCM).

Topic

Factors and Multiples

Definition

A divisor is a number that divides another number evenly, leaving no remainder.

Description

In the context of factors and multiples, a divisor plays a crucial role in understanding the relationships between numbers. A divisor is essentially a factor of a given number, as it divides that number without leaving a remainder. This concept is fundamental to identifying factors and understanding divisibility rules.

Topic

Factors and Multiples

Definition

Factor pairs are sets of two numbers that, when multiplied together, produce a given number.

Description

Factor pairs play a crucial role in understanding the relationships between numbers and their factors. They are essential in various mathematical operations, particularly in algebra and number theory. Factor pairs help students visualize the multiplicative structure of numbers and provide a foundation for more advanced concepts such as prime factorization and divisibility rules.

Topic

Factors and Multiples

Definition

A factor tree is a graphical method used to break down a number into its prime factors.

Description

A factor tree is a visual representation that helps in identifying the prime factors of a given number. It starts with the original number at the top and branches downwards, breaking the number into its factors until all the branches end in prime numbers. This method is particularly useful in understanding the concept of prime factorization, which is the process of expressing a number as the product of its prime factors.

Topic

Factors and Multiples

Definition

Factoring algebraic expressions involves breaking down a polynomial into simpler components called factors that, when multiplied together, give the original polynomial.

Description

Factoring algebraic expressions is a fundamental concept in algebra that plays a crucial role in simplifying expressions, solving equations, and understanding polynomial functions. This process involves expressing a polynomial as a product of its factors, which are simpler polynomials or numbers. For instance, the polynomial x^2 - 5x + 6 can be factored into (x - 2)(x - 3).

Topic

Factors and Multiples

Definition

Factors are numbers that divide evenly into another number without leaving a remainder.

Description

Factors play a crucial role in understanding the fundamental properties of numbers and their relationships. In the context of factors and multiples, factors are the building blocks that, when multiplied together, create a given number. This concept is essential for various mathematical operations and problem-solving techniques.

Topic

Factors and Multiples

Definition

The Greatest Common Factor (GCF) is the largest number that divides two or more numbers without leaving a remainder.

Description

The concept of the Greatest Common Factor (GCF) is crucial in the study of factors and multiples. The GCF is used to simplify fractions, find common denominators, and solve problems involving ratios. Understanding the GCF helps in breaking down complex problems into simpler parts, making it easier to handle large numbers and perform arithmetic operations efficiently.

Topic

Factors and Multiples

Definition

The least common multiple (LCM) is the smallest number that is a multiple of two or more numbers.

Description

The concept of the least common multiple (LCM) is essential in the study of factors and multiples. The LCM of two or more numbers is the smallest number that is evenly divisible by all of the given numbers. This concept is particularly useful in various mathematical operations and problem-solving scenarios.

Topic

Factors and Multiples

Definition

A multiple is a number that can be divided by another number without leaving a remainder.

Description

Multiples are fundamental in understanding the relationships between numbers in mathematics. They are particularly relevant when learning about factors and multiples, which are key concepts in elementary and middle school math curricula. A multiple of a number is obtained by multiplying that number by an integer. For example, the multiples of 5 include 5, 10, 15, 20, and so on.

Topic

Factors and Multiples

Definition

Multiples of 10 are the numbers that result from multiplying 10 by any whole number.

Description

Multiples of 10 play a significant role in understanding factors and multiples. These numbers are easily recognizable as they always end in zero and form a predictable pattern on the number line. In the context of factors and multiples, multiples of 10 serve as an excellent example to illustrate the concept of multiples in general.

Topic

Factors and Multiples

Definition

Multiples are the results obtained when a number is multiplied by an integer.

Description

In mathematics, understanding the concept of multiples is crucial, especially when dealing with factors and multiples. A multiple of a number is the product obtained when that number is multiplied by an integer. For example, the multiples of 3 include 3, 6, 9, 12, and so on. This concept is fundamental in various mathematical operations and problem-solving scenarios.

Topic

Factors and Multiples

Definition

Prime factorization is the process of breaking down a composite number into its prime factors.

Description

Prime factorization is a fundamental concept in the study of factors and multiples. It involves expressing a composite number as a product of prime numbers. For example, the number 60 can be factorized into 2 × 2 × 3 × 5. This process is crucial because it provides a unique representation of numbers, which is essential in various mathematical applications, including simplifying fractions, finding least common multiples (LCM), and greatest common divisors (GCD).

Topic

Factors and Multiples

Definition

Prime factors are the prime numbers that multiply together to give the original number.

Description

Prime factors are a fundamental concept in the study of factors and multiples. They are the building blocks of all numbers, as any integer greater than 1 can be expressed as a product of prime numbers. This process is known as prime factorization. For example, the prime factorization of 28 is 2 × 2 × 7, where 2 and 7 are prime numbers.

Topic

Factors and Multiples

Definition

Proper factors are the factors of a number excluding the number itself and 1.

Description

Proper factors play a significant role in the study of factors and multiples. Understanding proper factors is essential for grasping more complex mathematical concepts such as prime factorization, greatest common divisors, and least common multiples.

Topic

Factors and Multiples

Definition

Simplifying fractions involves reducing the fraction to its simplest form by dividing both the numerator and the denominator by their greatest common factor (GCF).

Topic

Factors and Multiples

Definition

An unknown factor is a value in a multiplication equation that needs to be determined to solve the equation.

Description

Factors and multiples are fundamental concepts in mathematics, particularly in number theory and arithmetic. Understanding these concepts is crucial for solving a wide range of mathematical problems, from basic arithmetic to more advanced topics such as algebra and number theory.

Factors of a number are the integers that can be multiplied together to produce that number. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12. These numbers can be paired in various ways to produce the product 12 (e.g., 2 x 6, 3 x 4).

Topic

Factors and Multiples

Definition

The Least Common Multiple (LCM) of two or more numbers is used to find the Least Common Denominator (LCD) when working with fractions.

Topic

Factors and Multiples

Definition

Visual models of multiples are graphical representations that help illustrate the concept of multiples and common multiples of numbers, making it easier to understand their relationships and properties.

Topic

Fractions

Definition

The Least Common Multiple (LCM) of two or more numbers is the smallest number that is a multiple of each of the numbers.

Description

The concept of the Least Common Multiple (LCM) is fundamental in the study of fractions. It is particularly useful when adding, subtracting, or comparing fractions. The LCM helps in finding a common denominator, which is essential for performing these operations with fractions.

This is part of a collection of images that cover key vocabulary on a variety of math topics.

Topic

Multiplication and Division

Definition

A multiple is the product of a number and a whole number.

Description

Multiples are numbers obtained by multiplying a given number by a whole number. For example, the multiples of 3 include 3, 6, 9, 12, and so on. Understanding multiples is crucial for solving problems involving patterns, sequences, and divisibility. They are used in various real-world applications, such as scheduling, where events occur at regular intervals, and in computer science for data organization. Teaching students about multiples helps them identify patterns in numbers and develop their mathematical reasoning skills.

This tutorial provides an overview of multiples and factors. This includes an exploration of generating multiples by skip-counting.

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In this Easter Egg hunt, students find the multiples of a given number from a group of eggs with numbers on them.

Note: The download is the teacher's guide.

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This is part of a collection of math video definitions related to the topics of Multiplication and Division, ideal for use in an early elementary classroom. Note: The download is an MP4 video.

This is part of a collection of math video definitions related to the topics of Multiplication and Division, ideal for use in an early elementary classroom. Note: The download is an MP4 video.

A table that lists all the multiples for the numbers 1-10.

Note: The download is a PDF file.

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A table that lists all the multiples for the numbers 1-20.

Note: The download is a PDF file.

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A table that lists all the multiples for the numbers 1-5.

Note: The download is a PDF file.

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In this set of 10 interactive flash cards add numbers with multiple digits. Press the Options button to decide how to display the flash cards. Press the Play button to auto-play the sequence of flash cards. Press Shuffle to change the order of the cards.

Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards.

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Quizlet Library

To see the complete Quizlet Flash Card Library, click on this Link to see the collection.

In this set of 10 interactive flash cards add numbers with multiple digits. Press the Options button to decide how to display the flash cards. Press the Play button to auto-play the sequence of flash cards. Press Shuffle to change the order of the cards.

Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards.

Related Resources

To see other resources related to this topic, click on the Resources tab above.

Quizlet Library

To see the complete Quizlet Flash Card Library, click on this Link to see the collection.

In this set of 10 interactive flash cards add numbers with multiple digits. Press the Options button to decide how to display the flash cards. Press the Play button to auto-play the sequence of flash cards. Press Shuffle to change the order of the cards.

Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards.

Related Resources

To see other resources related to this topic, click on the Resources tab above.

Quizlet Library

To see the complete Quizlet Flash Card Library, click on this Link to see the collection.

In this set of 10 interactive flash cards add numbers with multiple digits. Press the Options button to decide how to display the flash cards. Press the Play button to auto-play the sequence of flash cards. Press Shuffle to change the order of the cards.

Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards.

Related Resources

To see other resources related to this topic, click on the Resources tab above.

Quizlet Library

To see the complete Quizlet Flash Card Library, click on this Link to see the collection.

In this set of 10 interactive flash cards add numbers with multiple digits. Press the Options button to decide how to display the flash cards. Press the Play button to auto-play the sequence of flash cards. Press Shuffle to change the order of the cards.

Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards.

Related Resources

To see other resources related to this topic, click on the Resources tab above.

Quizlet Library

To see the complete Quizlet Flash Card Library, click on this Link to see the collection.

In this set of 10 interactive flash cards divide numbers by multiples of 10. Press the Options button to decide how to display the flash cards. Press the Play button to auto-play the sequence of flash cards. Press Shuffle to change the order of the cards.

Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards.

Related Resources

To see other resources related to this topic, click on the Resources tab above.

Quizlet Library

To see the complete Quizlet Flash Card Library, click on this Link to see the collection.

In this set of 10 interactive flash cards divide numbers by multiples of 10. Press the Options button to decide how to display the flash cards. Press the Play button to auto-play the sequence of flash cards. Press Shuffle to change the order of the cards.

Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards.

Related Resources

To see other resources related to this topic, click on the Resources tab above.

Quizlet Library

To see the complete Quizlet Flash Card Library, click on this Link to see the collection.

In this set of 10 interactive flash cards divide numbers by multiples of 10. Press the Options button to decide how to display the flash cards. Press the Play button to auto-play the sequence of flash cards. Press Shuffle to change the order of the cards.

Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards.

Related Resources

To see other resources related to this topic, click on the Resources tab above.

Quizlet Library

To see the complete Quizlet Flash Card Library, click on this Link to see the collection.

In this set of 10 interactive flash cards divide numbers by multiples of 10. Press the Options button to decide how to display the flash cards. Press the Play button to auto-play the sequence of flash cards. Press Shuffle to change the order of the cards.

Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards.

Related Resources

To see other resources related to this topic, click on the Resources tab above.

Quizlet Library

To see the complete Quizlet Flash Card Library, click on this Link to see the collection.

In this set of 10 interactive flash cards divide numbers by multiples of 10. Press the Options button to decide how to display the flash cards. Press the Play button to auto-play the sequence of flash cards. Press Shuffle to change the order of the cards.

Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards.

Related Resources

To see other resources related to this topic, click on the Resources tab above.

Quizlet Library

To see the complete Quizlet Flash Card Library, click on this Link to see the collection.

Subtract pairs of integers in this 20-flash card set. The integers are in the range -20 to 20.

Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards.

Related Resources

Subtract pairs of integers in this 20-flash card set. The integers are in the range -20 to 20.

Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards.

Related Resources

Subtract pairs of integers in this 20-flash card set. The integers are in the range -20 to 20.

Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards.

Related Resources

Subtract pairs of integers in this 20-flash card set. The integers are in the range -20 to 20.

Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards.

Related Resources

Subtract pairs of integers in this 20-flash card set. The integers are in the range -20 to 20.

Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards.

Related Resources

This is part of a collection of math video definitions related to the topics of primes and composites. Note: The download is an MP4 video.

This is part of a collection of math video definitions related to to the topic of fractions. Note: The download is an MP4 video.

This is the transcript that goes with the video segment entitled Video: Percents: Multiple Percents.

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