Illustrative Math Alignment: Grade 6 Unit 1

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 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 serves as the title card for a series on mixed numbers. It displays the text "Mixed Numbers" in a clear, prominent font. The background may include subtle mathematical elements or fraction-related graphics to set the context for the following images in the series.

This introductory image sets the stage for the subsequent images, preparing students for an exploration of mixed numbers, which combine whole numbers and fractions. It provides a clear, concise title that immediately informs viewers about the specific fraction concepts they'll be studying.

Topic

Fractions

Description

This image shows the graph of 1 1/4 on a number line. It displays a number line with whole numbers marked, and a point clearly indicated at 1 1/4, which would be halfway between 1 and 1 1/2.

This representation helps students visualize where mixed numbers fall on a number line, reinforcing their understanding of how mixed numbers relate to whole numbers and fractions. It provides a concrete way to see that 1 1/4 is more than 1 but less than 2.

Teachers can use this image to discuss how mixed numbers can be located on a number line and to reinforce the concept that mixed numbers represent values between whole numbers.

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 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 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 shows another variation with these fractions: 1/4, 3/8, 5/12, and 15/16, emphasizing that proper fractions are less than 1. It displays visual models for each fraction, clearly showing that the shaded portion is less than the whole in each case.

This representation further reinforces the concept of proper fractions, showing examples with increasingly larger denominators. It helps students understand that even as fractions get closer to 1, they remain proper fractions as long as the numerator is less than the denominator.

Topic

Fractions

Description

This image serves as the title card for a series on proper and improper fractions. It displays the text "Proper and Improper Fractions" in a clear, prominent font. The background may include subtle mathematical elements or fraction-related graphics to set the context for the following images in the series.

This introductory image sets the stage for the subsequent images, preparing students for an exploration of the differences between proper and improper fractions. It provides a clear, concise title that immediately informs viewers about the specific fraction concepts they'll be studying.

Topic

Fractions

Description

This image is a variation of the previous one, now showing visual models for 10/10 and 10/9. It displays rectangular visual representations: one divided into 10 parts with all 10 parts shaded, and another pair of rectangles divided into 9 parts with 10 parts shaded.

This representation helps students understand that improper fractions include fractions equal to one whole (like 10/10) as well as those greater than one whole (like 10/9). It reinforces the concept that improper fractions have numerators greater than or equal to their denominators.

Topic

Fractions

Description

This image shows a/b for any whole number a and b, with b not equal to zero. It displays the fraction a/b with labels or explanations indicating that a and b can be any whole numbers, but b cannot be zero.

This representation introduces students to the general form of a fraction and the important rule that the denominator cannot be zero. It helps students understand that fractions can represent a wide range of values and prepares them for working with variables in algebraic fractions.

Topic

Fractions

Description

This image introduces the concept of improper fractions, stating that a fraction a/b is improper if a is greater than or equal to b. It displays the fraction a/b with a visual or textual explanation indicating that when the numerator is greater than or equal to the denominator, the fraction is improper.

This representation helps students understand the definition of improper fractions and how they differ from proper fractions. It sets the stage for exploring fractions that represent one whole or more than one whole.

Topic

Fractions

Description

This image presents a variation of the previous concept, now using rectangular models to show proper fractions: 1/3, 4/6, 4/9, and 7/12. It displays four rectangles, each divided into the appropriate number of sections with the corresponding number of sections shaded to represent each fraction.

Topic

Fractions

Description

This image is a variation of the previous one, now showing that for a proper fraction, a < b. It displays the fraction a/b again, but with an additional note or visual indicator that the numerator (a) is less than the denominator (b).

This representation introduces the concept of proper fractions, helping students understand that when the numerator is less than the denominator, the fraction represents a part of a whole that is less than one.

Topic

Fractions

Description

This image provides visual models of improper fractions using rectangular models for 6/5 and 16/12. It shows two rectangles: one divided into 5 parts with 6 parts shaded (extending beyond the original rectangle), and another divided into 12 parts with 16 parts shaded.

This representation helps students visualize improper fractions and understand that they represent more than one whole. It demonstrates how improper fractions can be represented visually, even when they exceed one complete unit.

Topic

Fractions

Description

This image shows 1/4 with labels for numerator and denominator. It displays the fraction 1/4 with the number 1 clearly labeled as the numerator and the number 4 labeled as the denominator.

This representation helps students understand the basic structure of a fraction, identifying the roles of the numerator and denominator. It reinforces the concept that the numerator represents the number of parts being considered, while the denominator represents the total number of equal parts the whole is divided into.

Topic

Fractions

Description

This image provides examples of proper fractions shown as circular fractions: 1/2, 2/4, 3/6, and 4/8. It displays four circles, each divided into the appropriate number of sections with the corresponding number of sections shaded to represent each fraction.

This visual representation helps students see that these fractions, while written differently, all represent proper fractions (less than one whole). It reinforces the concept of proper fractions and introduces the idea of equivalent fractions.

Topic

Fractions

Description

This example demonstrates simplifying the fraction 4/10 by finding the greatest common divisor (GCD), which is 2. The simplified form is 2/5. This teaches students about recognizing common factors and reducing fractions to their simplest form.

For a complete collection of math examples related to Simplifying Fractions click on this link: Math Examples: Simplifying Fractions Collection.

Topic

Fractions

Description

In this example, the concept of simplifying the fraction 3/6 is demonstrated. The goal is to show students how to find the greatest common divisor (GCD) of the numerator and denominator. By dividing both by 3, the fraction simplifies to its simplest form, 1/2. This activity promotes skills in fraction manipulation and the understanding of equivalent fractions.

For a complete collection of math examples related to Simplifying Fractions click on this link: Math Examples: Simplifying Fractions Collection.

Topic

Fractions

Description

This example demonstrates simplifying the fraction 6/10 by finding the GCD, which is 2. The simplified form is 3/5. This teaches students about recognizing common factors and reducing fractions to their simplest form.

For a complete collection of math examples related to Simplifying Fractions click on this link: Math Examples: Simplifying Fractions Collection.

Topic

Fractions

Description

This example focuses on strategies for simplifying the fraction 2/6. Students learn to find the GCD of 2 and 6, which is 2, to reduce the fraction to its simplified form, 1/3. The activity not only sharpens their division skills but also develops their understanding of equivalent fractions, allowing them to visualize how different fractions can represent the same value while fostering critical thinking about numerators and denominators.

Topic

Fractions

Description

This example illustrates the simplification of 4/6. Students learn to identify the GCD, which is 2, allowing them to reduce the fraction to 2/3. This practice strengthens their skills in division and enhances their understanding of number relationships, vital for more complex fraction concepts.

For a complete collection of math examples related to Simplifying Fractions click on this link: Math Examples: Simplifying Fractions Collection.

Topic

Fractions

Description

Focusing on the fraction 2/8, this example highlights the process of finding the GCD, which is 2. Through division, students simplify the fraction to 1/4. This exercise reinforces their skills in problem-solving and critical thinking regarding fractions.

For a complete collection of math examples related to Simplifying Fractions click on this link: Math Examples: Simplifying Fractions Collection.

Topic

Fractions

Description

Here, the fraction 3/9 is presented. Students are encouraged to find the GCD, noted as 3, allowing them to reduce to 1/3, showcasing critical skills in fraction simplification and equivalent identification.

For a complete collection of math examples related to Simplifying Fractions click on this link: Math Examples: Simplifying Fractions Collection.

Topic

Fractions

Description

This example demonstrates simplifying the fraction 8/10 by finding the GCD, which is 2. The simplified form is 4/5. This teaches students about recognizing common factors and reducing fractions to their simplest form.

For a complete collection of math examples related to Simplifying Fractions click on this link: Math Examples: Simplifying Fractions Collection.

Topic

Fractions

Description

This example demonstrates simplifying the fraction 4/12 by finding the GCD, which is 4. The simplified form is 1/3. This teaches students about recognizing common factors and reducing fractions to their simplest form.

For a complete collection of math examples related to Simplifying Fractions click on this link: Math Examples: Simplifying Fractions Collection.

Topic

Fractions

Description

This example demonstrates simplifying the fraction 10/12 by finding the GCD, which is 2. The simplified form is 5/6. This teaches students about recognizing common factors and reducing fractions to their simplest form.

For a complete collection of math examples related to Simplifying Fractions click on this link: Math Examples: Simplifying Fractions Collection.

Topic

Fractions

Description

In this case, the fraction 6/8 is shown, where the GCD is identified as 2. Simplifying the fraction leads to 3/4, a practical example that helps students master the concept of equivalent fractions and the importance of factoring in mathematics.

For a complete collection of math examples related to Simplifying Fractions click on this link: Math Examples: Simplifying Fractions Collection.

Topic

Fractions

Description

This example presents the fraction 4/8 and guides students to recognize that the GCD is 4. Simplifying to 1/2, this problem emphasizes the significance of understanding common factors in fractions, an essential skill in mathematics.

For a complete collection of math examples related to Simplifying Fractions click on this link: Math Examples: Simplifying Fractions Collection.

Topic

Fractions

Description

This example focuses on simplifying the fraction 2/10. By finding the GCD, which is 2, students simplify the fraction to 1/5. This activity reinforces their skills in recognizing common factors and understanding equivalent fractions.

For a complete collection of math examples related to Simplifying Fractions click on this link: Math Examples: Simplifying Fractions Collection.

Topic

Fractions

Description

This example demonstrates simplifying the fraction 2/12 by finding the GCD, which is 2. The simplified form is 1/6. This teaches students about recognizing common factors and reducing fractions to their simplest form.

For a complete collection of math examples related to Simplifying Fractions click on this link: Math Examples: Simplifying Fractions Collection.

Topic

Fractions

Description

This example demonstrates the concept of simplifying fractions, in which students are guided through the process of reducing a fraction to its simplest form. It emphasizes identifying the greatest common divisor (GCD) and dividing both the numerator and denominator by this value. Solving problems like this enhances skills in recognizing factors, understanding number properties, and executing division. This example is a crucial building block for understanding more complex fraction operations, establishing a solid foundation for students.

Topic

Fractions

Description

This example demonstrates simplifying the fraction 8/12 by finding the GCD, which is 4. The simplified form is 2/3. This teaches students about recognizing common factors and reducing fractions to their simplest form.

For a complete collection of math examples related to Simplifying Fractions click on this link: Math Examples: Simplifying Fractions Collection.

Topic

Fractions

Description

This example demonstrates the simplification of the fraction 6/9. Students identify the GCD as 3, simplifying the fraction to 2/3. This exercise enhances their understanding of division and equivalent fractions, essential for advanced mathematical concepts.

For a complete collection of math examples related to Simplifying Fractions click on this link: Math Examples: Simplifying Fractions Collection.

Topic

Fractions

Description

This example demonstrates simplifying the fraction 3/12 by finding the GCD, which is 3. The simplified form is 1/4. This teaches students about recognizing common factors and reducing fractions to their simplest form.

For a complete collection of math examples related to Simplifying Fractions click on this link: Math Examples: Simplifying Fractions Collection.

Topic

Fractions

Description

This example demonstrates simplifying the fraction 6/12 by finding the GCD, which is 6. The simplified form is 1/2. This teaches students about recognizing common factors and reducing fractions to their simplest form.

For a complete collection of math examples related to Simplifying Fractions click on this link: Math Examples: Simplifying Fractions Collection.

Topic

Fractions

Description

This image shows the final fraction in the sequence: 8/12. It displays a rectangular model divided into twelve parts with eight parts shaded, representing 8/12. It may also include the numerical process of multiplying both the numerator and denominator of 2/3 by 4 to get 8/12.

Topic

Fractions

Description

This image shows the final fraction in the sequence: 8/12. It displays a rectangular model divided into twelve parts with eight parts shaded, representing 8/12. It may also include the numerical process of multiplying both the numerator and denominator of 2/3 by 4 to get 8/12.

Topic

Fractions

Description

This image continues the sequence, now showing 3/15 with a rectangular model and the numerical process to generate this equivalent fraction. It displays a rectangle divided into 15 parts with three parts shaded, alongside the numerical process of multiplying both the numerator and denominator of 1/5 by 3 to get 3/15.

This representation further reinforces the concept of generating equivalent fractions and helps students see the pattern emerging in the sequence.

Topic

Fractions

Description

This image serves as a summary slide showing the four equivalent fractions explored in the previous sequence: 1/5, 2/10, 3/15, and 4/20. It displays all four rectangular models side by side, clearly demonstrating their equivalence and reinforcing that this process can continue indefinitely.

This representation provides a comprehensive view of the equivalent fractions, allowing students to see the progression and pattern all at once. It reinforces the concept that these fractions, despite looking different, all represent the same amount.

Topic

Fractions

Description

This image presents a variation with rectangular models showing equivalent fractions: 1/3, 2/6, 3/9, and 4/12. It displays four rectangles side by side, each divided and shaded to represent these fractions.

This representation introduces a new model for understanding equivalent fractions. It helps students see that the concept of equivalent fractions applies across different visual representations and reinforces the pattern of multiplying both numerator and denominator by the same number.

Topic

Fractions

Description

This image serves as the title card for a series on equivalent fractions. It displays the text "Equivalent Fractions" in a clear, prominent font. The background may include subtle mathematical elements or fraction-related graphics to set the context for the following images in the series.

This introductory image sets the stage for the subsequent images, preparing students for an exploration of fractions that have the same value but are written differently. It provides a clear, concise title that immediately informs viewers about the specific fraction concepts they'll be studying.

Topic

Fractions

Description

This image completes the short sequence by showing 4/20 with a rectangular model and the numerical process to generate this equivalent fraction. It displays a rectangle divided into 20 parts with four parts shaded, alongside the numerical process of multiplying both the numerator and denominator of 1/5 by 4 to get 4/20.

This representation completes the pattern of equivalent fractions for 1/5 and reinforces the concept of generating equivalent fractions by multiplying both the numerator and denominator by the same number.

Topic

Fractions

Description

This image serves as a summary slide showing the four equivalent fractions explored in the previous sequence: 2/3, 4/6, 6/9, and 8/12. It displays all four rectangular models side by side, clearly demonstrating their equivalence.

Topic

Fractions

Description

This image serves as a summary slide showing the four equivalent fractions explored in the previous sequence: 2/3, 4/6, 6/9, and 8/12. It displays all four rectangular models side by side, clearly demonstrating their equivalence.

Topic

Fractions

Description

This image displays circular fraction models that are equivalent: 1/2, 2/4, 3/6, and 4/8. It shows four circles side by side, each divided and shaded to represent these fractions.

This visual representation expands on the previous image, showing multiple equivalent fractions. It helps students see the pattern in equivalent fractions and understand that as both the numerator and denominator are multiplied by the same number, the fraction's value remains the same.

Teachers can use this image to discuss patterns in equivalent fractions and to introduce the concept of simplifying and expanding fractions.

Topic

Fractions

Description

This image continues the sequence, now showing 6/9. It displays a rectangular model divided into nine parts with six parts shaded, representing 6/9. It may also include the numerical process of multiplying both the numerator and denominator of 2/3 by 3 to get 6/9.

This representation further reinforces the concept of generating equivalent fractions and helps students see the pattern emerging in the sequence.

Teachers can use this image to continue the discussion on equivalent fractions and to encourage students to predict the next fraction in the sequence.

Topic

Fractions

Description

This image starts a new sequence focusing on equivalent fractions of 2/3. It shows a rectangular fraction model divided into three equal parts with two parts shaded, representing 2/3.

This representation introduces students to a new fraction and sets the stage for exploring its equivalent forms. It provides a clear visual model for students to understand what 2/3 looks like.

Teachers can use this image to begin a discussion about fractions with a numerator greater than 1 and to prepare students for generating equivalent fractions of 2/3.

Topic

Fractions

Description

This image shows another variation with rectangular models demonstrating equivalent fractions: 1/4, 2/8, 3/12, and 4/16. It displays four rectangles side by side, each divided and shaded to represent these fractions.

This representation further reinforces the concept of equivalent fractions using a different set of fractions. It helps students see the pattern in creating equivalent fractions by multiplying both the numerator and denominator by the same number.