Illustrative Math Alignment: Grade 6 Unit 1

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

Fractions

Definition

A unit fraction is a fraction where the numerator is 1 and the denominator is a positive integer.

Description

A unit fraction is a fundamental concept in the study of fractions and plays a crucial role in understanding more complex fractional operations. It represents one part of a whole that has been divided into equal parts. For example, the unit fraction 1/4 means one part of a whole that is divided into four equal parts.

Topic

Fractions

Definition

Equivalent fractions are fractions that represent the same part of a whole, even though they may have different numerators and denominators.

Description

Equivalent fractions are fundamental in understanding the concept of fractions in mathematics. They are fractions that, although they may look different, actually represent the same value. For example, the fractions 1/2 and 2/4 are equivalent because they both represent the same portion of a whole. This concept is crucial for various mathematical operations and problem-solving techniques.

Topic

Fractions

Definition

A unit fraction is a fraction where the numerator is 1 and the denominator is a positive integer.

Description

A unit fraction is a fundamental concept in the study of fractions and plays a crucial role in understanding more complex fractional operations. It represents one part of a whole that has been divided into equal parts. For example, the unit fraction 1/4 means one part of a whole that is divided into four equal parts.

Topic

Fractions

Definition

Equivalent fractions are fractions that represent the same part of a whole, even though they may have different numerators and denominators.

Description

Equivalent fractions are fundamental in understanding the concept of fractions in mathematics. They are fractions that, although they may look different, actually represent the same value. For example, the fractions 1/2 and 2/4 are equivalent because they both represent the same portion of a whole. This concept is crucial for various mathematical operations and problem-solving techniques.

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.

Topic

Fractions

Definition

The numerator is the top number in a fraction, representing the number of parts being considered out of the whole.

Description

In the realm of fractions, the numerator plays a crucial role. It is the number above the fraction bar, indicating how many parts of the whole are being counted. For instance, in the fraction 3/4, the numerator is 3, which means three parts out of a total of four parts are being considered. Understanding the numerator is fundamental to grasping the concept of fractions, as it directly affects the value and representation of the fraction.

Topic

Fraction Concepts

Definition

Fraction bars are visual representations of fractions that use rectangular bars divided into equal parts to illustrate fractional quantities.

Description

Fraction bars are essential tools in understanding and visualizing fractions, playing a crucial role in developing fraction concepts. These visual aids consist of rectangular bars divided into equal parts, with each part representing a unit fraction of the whole. The image showcases three fraction bar types illustrating halves, thirds, and sixths, clearly demonstrating how the denominator determines the number of equal parts in each bar.

Topic

Fractions

Definition

The denominator is the bottom number in a fraction that indicates into how many equal parts the whole is divided.

Description

In the context of fractions, the denominator plays a crucial role in understanding the size and division of the whole. It represents the total number of equal parts that make up a whole. For instance, in the fraction 3/4, the denominator is 4, indicating that the whole is divided into four equal parts. The numerator, which is 3 in this example, tells us how many of those parts are being considered.

Topic

Fractions

Definition

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

Description

The concept of the Greatest Common Factor (GCF) is crucial in the study of fractions. It is used to simplify fractions to their lowest terms, making them easier to work with and understand. When two or more fractions have the same GCF, it means they share a common factor that can be used to reduce each fraction to its simplest form. This process is essential for performing operations such as addition, subtraction, multiplication, and division of fractions.

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.

Topic

Fractions

Definition

The denominator is the bottom number in a fraction that indicates into how many equal parts the whole is divided.

Description

In the context of fractions, the denominator plays a crucial role in understanding the size and division of the whole. It represents the total number of equal parts that make up a whole. For instance, in the fraction 3/4, the denominator is 4, indicating that the whole is divided into four equal parts. The numerator, which is 3 in this example, tells us how many of those parts are being considered.

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.

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.

Topic

Fractions

Definition

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

Description

The concept of the Greatest Common Factor (GCF) is crucial in the study of fractions. It is used to simplify fractions to their lowest terms, making them easier to work with and understand. When two or more fractions have the same GCF, it means they share a common factor that can be used to reduce each fraction to its simplest form. This process is essential for performing operations such as addition, subtraction, multiplication, and division of fractions.

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.

Topic

Fractions

Definition

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

Description

The concept of the Greatest Common Factor (GCF) is crucial in the study of fractions. It is used to simplify fractions to their lowest terms, making them easier to work with and understand. When two or more fractions have the same GCF, it means they share a common factor that can be used to reduce each fraction to its simplest form. This process is essential for performing operations such as addition, subtraction, multiplication, and division of fractions.

Topic

Fractions

Definition

A fraction is in its simplest form when the numerator and denominator have no common divisor other than 1.

Description

In mathematics, fractions represent parts of a whole. A fraction is composed of a numerator (the top number) and a denominator (the bottom number). Simplifying a fraction means reducing it to its simplest form, where the numerator and denominator have no common factors other than 1. For example, the fraction 4/8 can be simplified to 1/2 by dividing both the numerator and the denominator by their greatest common divisor, which is 4.

Topic

Fractions

Definition

Fraction models are visual representations used to illustrate the concept of fractions, showing parts of a whole.

Description

Fraction models play a crucial role in understanding and teaching fractions. These models provide a visual representation that helps students grasp the idea of parts of a whole, which is fundamental in fraction concepts. There are several types of fraction models, including area models, set models, and number lines.

Topic

Fractions

Definition

The denominator is the bottom number in a fraction that indicates into how many equal parts the whole is divided.

Description

In the context of fractions, the denominator plays a crucial role in understanding the size and division of the whole. It represents the total number of equal parts that make up a whole. For instance, in the fraction 3/4, the denominator is 4, indicating that the whole is divided into four equal parts. The numerator, which is 3 in this example, tells us how many of those parts are being considered.

Topic

Fractions

Definition

The numerator is the top number in a fraction, representing the number of parts being considered out of the whole.

Description

In the realm of fractions, the numerator plays a crucial role. It is the number above the fraction bar, indicating how many parts of the whole are being counted. For instance, in the fraction 3/4, the numerator is 3, which means three parts out of a total of four parts are being considered. Understanding the numerator is fundamental to grasping the concept of fractions, as it directly affects the value and representation of the fraction.

Topic

Fractions

Definition

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

Description

The concept of the Greatest Common Factor (GCF) is crucial in the study of fractions. It is used to simplify fractions to their lowest terms, making them easier to work with and understand. When two or more fractions have the same GCF, it means they share a common factor that can be used to reduce each fraction to its simplest form. This process is essential for performing operations such as addition, subtraction, multiplication, and division of fractions.

Topic

Fractions

Definition

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

Description

The concept of the Greatest Common Factor (GCF) is crucial in the study of fractions. It is used to simplify fractions to their lowest terms, making them easier to work with and understand. When two or more fractions have the same GCF, it means they share a common factor that can be used to reduce each fraction to its simplest form. This process is essential for performing operations such as addition, subtraction, multiplication, and division of fractions.

Topic

Fractions

Definition

The numerator is the top number in a fraction, representing the number of parts being considered out of the whole.

Description

In the realm of fractions, the numerator plays a crucial role. It is the number above the fraction bar, indicating how many parts of the whole are being counted. For instance, in the fraction 3/4, the numerator is 3, which means three parts out of a total of four parts are being considered. Understanding the numerator is fundamental to grasping the concept of fractions, as it directly affects the value and representation of the fraction.

This cheat sheet gathers together a number of resources on the topic of fractions. See the descriptions and links below. Each link takes you to a collection of resources around that topic. The middle column indicates the number of resources available and the third column takes you to page on Media4Math where those resources can be found.

Subscribers can download the PDF version of this cheat sheet.

Topic

Ratios and Fractions

Description

In many scenarios, ratios are expressed using whole numbers, yet there are instances, like in recipes, where fractions play a significant role. This example illustrates a ratio involving fractions and demonstrates how to convert it into a ratio with whole numbers. Students will engage in understanding the process of converting these fractions to whole numbers, enhancing their comprehension of ratios and their practical applications such as cooking or mixing. The focus is on the fundamental skill of fraction conversion and applying it in a ratio context.

Topic

Ratios and Fractions

Description

In many scenarios, ratios are expressed using whole numbers, yet there are instances, like in recipes, where fractions play a significant role. This example illustrates a ratio involving fractions and demonstrates how to convert it into a ratio with whole numbers. Students will engage in understanding the process of converting these fractions to whole numbers, enhancing their comprehension of ratios and their practical applications such as cooking or mixing. The focus is on the fundamental skill of fraction conversion and applying it in a ratio context.

Topic

Ratios and Fractions

Description

In many scenarios, ratios are expressed using whole numbers, yet there are instances, like in recipes, where fractions play a significant role. This example illustrates a ratio involving fractions and demonstrates how to convert it into a ratio with whole numbers. Students will engage in understanding the process of converting these fractions to whole numbers, enhancing their comprehension of ratios and their practical applications such as cooking or mixing. The focus is on the fundamental skill of fraction conversion and applying it in a ratio context.

Topic

Ratios and Fractions

Description

In many scenarios, ratios are expressed using whole numbers, yet there are instances, like in recipes, where fractions play a significant role. This example illustrates a ratio involving fractions and demonstrates how to convert it into a ratio with whole numbers. Students will engage in understanding the process of converting these fractions to whole numbers, enhancing their comprehension of ratios and their practical applications such as cooking or mixing. The focus is on the fundamental skill of fraction conversion and applying it in a ratio context.

Topic

Ratios and Fractions

Description

In many scenarios, ratios are expressed using whole numbers, yet there are instances, like in recipes, where fractions play a significant role. This example illustrates a ratio involving fractions and demonstrates how to convert it into a ratio with whole numbers. Students will engage in understanding the process of converting these fractions to whole numbers, enhancing their comprehension of ratios and their practical applications such as cooking or mixing. The focus is on the fundamental skill of fraction conversion and applying it in a ratio context.

Topic

Ratios and Fractions

Description

In many scenarios, ratios are expressed using whole numbers, yet there are instances, like in recipes, where fractions play a significant role. This example illustrates a ratio involving fractions and demonstrates how to convert it into a ratio with whole numbers. Students will engage in understanding the process of converting these fractions to whole numbers, enhancing their comprehension of ratios and their practical applications such as cooking or mixing. The focus is on the fundamental skill of fraction conversion and applying it in a ratio context.

Topic

Ratios and Fractions

Description

In many scenarios, ratios are expressed using whole numbers, yet there are instances, like in recipes, where fractions play a significant role. This example illustrates a ratio involving fractions and demonstrates how to convert it into a ratio with whole numbers. Students will engage in understanding the process of converting these fractions to whole numbers, enhancing their comprehension of ratios and their practical applications such as cooking or mixing. The focus is on the fundamental skill of fraction conversion and applying it in a ratio context.

Topic

Ratios and Fractions

Description

In many scenarios, ratios are expressed using whole numbers, yet there are instances, like in recipes, where fractions play a significant role. This example illustrates a ratio involving fractions and demonstrates how to convert it into a ratio with whole numbers. Students will engage in understanding the process of converting these fractions to whole numbers, enhancing their comprehension of ratios and their practical applications such as cooking or mixing. The focus is on the fundamental skill of fraction conversion and applying it in a ratio context.

Topic

Ratios and Fractions

Description

In many scenarios, ratios are expressed using whole numbers, yet there are instances, like in recipes, where fractions play a significant role. This example illustrates a ratio involving fractions and demonstrates how to convert it into a ratio with whole numbers. Students will engage in understanding the process of converting these fractions to whole numbers, enhancing their comprehension of ratios and their practical applications such as cooking or mixing. The focus is on the fundamental skill of fraction conversion and applying it in a ratio context.

Topic

Ratios and Fractions

Description

In many scenarios, ratios are expressed using whole numbers, yet there are instances, like in recipes, where fractions play a significant role. This example illustrates a ratio involving fractions and demonstrates how to convert it into a ratio with whole numbers. Students will engage in understanding the process of converting these fractions to whole numbers, enhancing their comprehension of ratios and their practical applications such as cooking or mixing. The focus is on the fundamental skill of fraction conversion and applying it in a ratio context.

Topic

Ratios and Fractions

Description

In many scenarios, ratios are expressed using whole numbers, yet there are instances, like in recipes, where fractions play a significant role. This example illustrates a ratio involving fractions and demonstrates how to convert it into a ratio with whole numbers. Students will engage in understanding the process of converting these fractions to whole numbers, enhancing their comprehension of ratios and their practical applications such as cooking or mixing. The focus is on the fundamental skill of fraction conversion and applying it in a ratio context.

Topic

Fractions

Description

This image is a variation of the previous one, now showing the conversion of 12/5 to 2 2/5. It displays the step-by-step process of dividing 12 by 5 to get 2 with a remainder of 2, which then becomes the numerator of the fractional part.

This representation builds on the previous example, helping students see how the process works with larger numbers. It reinforces the concept that the whole number part of a mixed number comes from how many times the denominator goes into the numerator.

Topic

Fractions

Description

This image shows a variation of the previous concept, now converting 3 3/8 to 27/8. It displays the step-by-step process of multiplying 3 by 8 to get 24, adding 3, and then writing 27 over 8.

This representation builds on the previous example, helping students see how the process works with larger mixed numbers. It reinforces the concept that the numerator of the resulting improper fraction will always be larger than the denominator when converting from a mixed number.

Topic

Fractions

Description

This image presents a variation with 2 1/3 graphed on the number line. It shows a number line with whole numbers marked, and a point clearly indicated at 2 1/3, which would be one-third of the way from 2 to 3.

This representation builds on the previous examples, helping students visualize a different mixed number on the number line. It reinforces the concept that mixed numbers can be located precisely between whole numbers and helps students understand how the fractional part determines the exact position.

Topic

Fractions

Description

This image shows the numerical manipulation of 7/5 and converting it to 1 2/5. It displays the step-by-step process of dividing 7 by 5 to get 1 with a remainder of 2, which then becomes the numerator of the fractional part.

This representation helps students understand the mathematical process behind converting improper fractions to mixed numbers. It provides a clear, numerical approach to complement the visual models seen in previous images.

Teachers can use this image to explain the algorithm for converting improper fractions to mixed numbers and to reinforce the connection between division and fractions.

Topic

Fractions

Description

This image shows the numerical manipulation of converting 1 2/5 to 7/5. It displays the step-by-step process of multiplying the whole number by the denominator, adding the numerator, and then writing this over the original denominator.

This representation helps students understand the mathematical process behind converting mixed numbers to improper fractions. It provides a clear, numerical approach to complement the visual models seen in previous images.

Teachers can use this image to explain the algorithm for converting mixed numbers to improper fractions and to reinforce the connection between multiplication and fractions.

Topic

Fractions

Description

This image is a variation of the previous one, for 1 1/2, showing the whole number part on the number line and then the fractional part. It displays a number line with the whole number 1 clearly marked, and then shows how the additional 1/2 is added to reach the final position of 1 1/2.

This representation helps students understand how mixed numbers are constructed on a number line, breaking down the process into two steps: locating the whole number, then adding the fraction. It reinforces the concept that mixed numbers combine whole numbers and fractions.

Topic

Fractions

Description

This image shows the numerical manipulation of 7/5 and converting it to 1 2/5. It displays the step-by-step process of dividing 7 by 5 to get 1 with a remainder of 2, which then becomes the numerator of the fractional part.

This representation helps students understand the mathematical process behind converting improper fractions to mixed numbers. It provides a clear, numerical approach to complement the visual models seen in previous images.

Teachers can use this image to explain the algorithm for converting improper fractions to mixed numbers and to reinforce the connection between division and fractions.

Topic

Fractions

Description

This image shows the numerical manipulation of converting 1 2/5 to 7/5. It displays the step-by-step process of multiplying the whole number by the denominator, adding the numerator, and then writing this over the original denominator.

This representation helps students understand the mathematical process behind converting mixed numbers to improper fractions. It provides a clear, numerical approach to complement the visual models seen in previous images.

Teachers can use this image to explain the algorithm for converting mixed numbers to improper fractions and to reinforce the connection between multiplication and fractions.

Topic

Fractions

Description

This image presents rectangular models for 6/5 and 1 1/5. It shows two sets of rectangles: one modeling 6/5 and the other modeling 1 1/5.

This representation helps students visualize the relationship between improper fractions and mixed numbers. It demonstrates how an improper fraction like 6/5 can be expressed as a mixed number 1 1/5, showing that they represent the same quantity.

Teachers can use this image to discuss the conversion between improper fractions and mixed numbers, and to reinforce the concept that mixed numbers represent quantities greater than one whole.

Topic

Fractions

Description

This image presents rectangular models for 6/5 and 1 1/5. It shows two sets of rectangles: one modeling 6/5 and the other modeling 1 1/5.

This representation helps students visualize the relationship between improper fractions and mixed numbers. It demonstrates how an improper fraction like 6/5 can be expressed as a mixed number 1 1/5, showing that they represent the same quantity.

Teachers can use this image to discuss the conversion between improper fractions and mixed numbers, and to reinforce the concept that mixed numbers represent quantities greater than one whole.

Topic

Fractions

Description

This image shows a variation of the previous concept, now converting 3 3/8 to 27/8. It displays the step-by-step process of multiplying 3 by 8 to get 24, adding 3, and then writing 27 over 8.

This representation builds on the previous example, helping students see how the process works with larger mixed numbers. It reinforces the concept that the numerator of the resulting improper fraction will always be larger than the denominator when converting from a mixed number.

Topic

Fractions

Description

This image is a variation of the previous one, now showing the conversion of 12/5 to 2 2/5. It displays the step-by-step process of dividing 12 by 5 to get 2 with a remainder of 2, which then becomes the numerator of the fractional part.

This representation builds on the previous example, helping students see how the process works with larger numbers. It reinforces the concept that the whole number part of a mixed number comes from how many times the denominator goes into the numerator.

Topic

Fractions

Description

This image shows rectangular models demonstrating how 1 1/3 can be converted to 4/3, illustrating that a mixed number can also be written as an improper fraction. It displays one whole rectangle plus a third of another rectangle, alongside a model showing four thirds.

This representation helps students visualize the process of converting mixed numbers to improper fractions. It reinforces the idea that mixed numbers and improper fractions can represent the same quantity.

Topic

Fractions

Description

This image presents the mixed number 1 1/4 with the whole number part labeled and the fraction part clearly identified. It  shows the number 1 1/4 with arrows or labels pointing to the '1' as the whole number part and '1/4' as the fraction part.

This representation helps students understand the structure of mixed numbers, showing how they combine a whole number with a proper fraction. It provides a clear visual breakdown of the components of a mixed number.