Illustrative Math Alignment: Grade 6 Unit 1

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 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 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 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 shows the next fraction in the sequence: 4/6. It displays a rectangular model divided into six parts with four parts shaded, representing 4/6. It may also include the numerical process of multiplying both the numerator and denominator of 2/3 by 2 to get 4/6.

This representation helps students understand how to create equivalent fractions by multiplying both the numerator and denominator by the same number. It provides both a visual and potentially numerical explanation of the process.

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 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 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 starts a short sequence focusing on equivalent fractions of 1/5. It shows a rectangular model divided into five equal parts with one part shaded, representing 1/5.

This representation introduces students to the concept of fifths and sets the stage for exploring equivalent fractions with a denominator of 5. It provides a clear visual model for students to understand what 1/5 looks like.

Teachers can use this image to begin a discussion about fractions with a denominator of 5 and to prepare students for generating equivalent fractions.

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 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 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.

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 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 serves as the title card for a series on fractions in simplest form. It likely displays the text "Fractions in Simplest Form" 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 equivalent fractions and the process of simplifying 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 continues from the previous one, showing how common factors divide out when simplifying fractions. It likely displays the process of simplifying 2/4 to 1/2 with a focus on the common factor of 2, possibly using visual elements like circles or arrows to show how the common factor is removed from both the numerator and denominator.

This representation helps students understand the mathematical principle behind simplifying fractions. It visually demonstrates that we're dividing both the numerator and denominator by the same number, which doesn't change the fraction's value.

Topic

Fractions

Description

This image is a variation of the previous one, showing how to simplify 2/4. It displays the process of simplifying 2/4 to 1/2, using notation to show the division of both the numerator and denominator by their greatest common factor (2 in this case).

This representation helps students understand the process of simplifying fractions. It visually demonstrates that simplifying a fraction doesn't change its value, but expresses it in its lowest terms.

Teachers can use this image to explain the process of simplifying fractions and to reinforce the concept of equivalent fractions.

Topic

Fractions

Description

This image is a variation of the previous one, now showing the equivalence of 3/12 and 1/4 on number lines. It displays two number lines, one marked from 0 to 1 with 12 equal divisions and a point at 3/12, and another marked from 0 to 1 with 4 equal divisions and a point at 1/4.

This representation further reinforces the concept of equivalent fractions using number lines. It helps students visualize how fractions with different denominators can represent the same value.

Topic

Fractions

Description

This image shows fraction number lines demonstrating the equivalence of 6/12 and 1/2. It displays two number lines, one marked from 0 to 1 with 12 equal divisions and a point at 6/12, and another marked from 0 to 1 with 2 equal divisions and a point at 1/2.

This representation introduces a new model for understanding equivalent fractions and fraction simplification. It helps students visualize fractions on a linear scale and reinforces the concept that equivalent fractions occupy the same point on a number line.

Topic

Fractions

Description

This final image in the series shows how to reduce fractions numerically, demonstrating the simplification of 4/8, 8/12, 5/10, and 3/15. It displays these fractions and their simplified forms, with visual cues to show the simplification process.

This representation shifts from visual models to a more abstract, numerical approach to simplifying fractions. It helps students apply the concepts they've learned to a variety of fractions, reinforcing the process of finding common factors and dividing both the numerator and denominator.

Topic

Fractions

Description

This image presents rectangular fraction models showing the equivalence of 3/6 and 1/2. It displays two rectangles side by side, one divided into six equal parts with three parts shaded (representing 3/6), and the other divided into two equal parts with one part shaded (representing 1/2).

This visual representation helps students understand equivalent fractions using a different model than the circular ones previously shown. It reinforces the concept that fractions can be simplified while maintaining their value.

Topic

Fractions

Description

This image shows equivalent circular fraction models for 2/4 and 1/2. It displays two circles side by side, one divided into four equal parts with two parts shaded (representing 2/4), and the other divided into two equal parts with one part shaded (representing 1/2).

This visual representation helps students understand that fractions can be equivalent even when written differently. It introduces the concept of simplifying fractions by showing that 2/4 and 1/2 represent the same portion of a whole.

Topic

Fractions

Description

This image is a variation showing the equivalence of 6/8 and 3/4. It displays two circular fraction models side by side, one divided into eight parts with six shaded (representing 6/8), and the other divided into four parts with three shaded (representing 3/4).

This visual representation helps students see that 6/8 and 3/4 represent the same portion of a whole, reinforcing the concept of equivalent fractions. It also provides another example of simplifying fractions, this time with a different common factor.

Topic

Fractions

Description

This image is another variation, now demonstrating the equivalence of 4/12 and 1/3 on number lines. It shows two number lines, one marked from 0 to 1 with 12 equal divisions and a point at 4/12, and another marked from 0 to 1 with 3 equal divisions and a point at 1/3.

This representation continues to build on the concept of equivalent fractions using number lines. It helps students visualize how fractions with different denominators can represent the same value, even when the relationship isn't as immediately obvious as in previous examples.

Topic

Fractions

Description

This image is a variation of the previous one, but now using thirds. It shows a circle divided into three equal parts, each labeled 1/3, with an equation showing 1/3 + 1/3 + 1/3 = 1.

This representation builds on the previous example, helping students understand that the principle of unit fractions adding to a whole applies to different denominators. It reinforces the concept of fraction addition and the relationship between unit fractions and the whole.

Teachers can use this image to extend students' understanding of adding unit fractions and to discuss patterns they might notice as the denominator changes.

Topic

Fractions

Description

This image demonstrates that the sum of unit fractions from a circular fraction is 1, using halves as an example. It shows a circle divided into two equal parts, each labeled 1/2, with an equation showing 1/2 + 1/2 = 1.

This visual representation helps students understand that unit fractions can be added together to form a whole. It reinforces the concept of fraction addition and the relationship between unit fractions and the whole.

Teachers can use this image to introduce or reinforce the concept of adding fractions, particularly unit fractions, and to discuss the meaning of a "whole" in fraction terms.

Topic

Fractions

Description

This image is another variation, now using fourths. It shows a circle divided into four equal parts, each labeled 1/4, with an equation showing 1/4 + 1/4 + 1/4 + 1/4 = 1.

This representation continues to build on the previous examples, further reinforcing the concept that unit fractions add up to a whole, regardless of the denominator. It helps students see the pattern forming as the number of unit fractions increases.

Teachers can use this image to further extend students' understanding of adding unit fractions and to encourage them to predict what might happen with other denominators.

Topic

Fractions

Description

This image is a variation of the previous ones in the series, now using fifths. It shows a circle divided into five equal parts, each labeled 1/5, with an equation showing 1/5 + 1/5 + 1/5 + 1/5 + 1/5 = 1.

This representation continues the pattern established in the previous images, further reinforcing the concept that unit fractions add up to a whole, regardless of the denominator. It helps students solidify their understanding of the relationship between unit fractions and the whole.

Topic

Fractions

Description

This image is a variation of the previous one, but now using thirds. It shows a circle divided into three equal parts, each labeled 1/3, with an equation showing 1/3 + 1/3 + 1/3 = 1.

This representation builds on the previous example, helping students understand that the principle of unit fractions adding to a whole applies to different denominators. It reinforces the concept of fraction addition and the relationship between unit fractions and the whole.

Teachers can use this image to extend students' understanding of adding unit fractions and to discuss patterns they might notice as the denominator changes.

Topic

Fractions

Description

This image is a variation of the previous one, showing that halves have 2 unit fractions, thirds have 3 unit fractions, fourths have 4 unit fractions, and fifths have 5 unit fractions. It displays circular fraction models for each, with all sections labeled to show the number of unit fractions that make up each whole.

This representation helps students understand the relationship between the denominator of a unit fraction and the number of those unit fractions needed to make a whole. It reinforces the concept that the denominator indicates how many equal parts the whole is divided into.

Topic

Fractions

Description

This image is a variation of the previous ones in the series, now using fifths. It shows a circle divided into five equal parts, each labeled 1/5, with an equation showing 1/5 + 1/5 + 1/5 + 1/5 + 1/5 = 1.

This representation continues the pattern established in the previous images, further reinforcing the concept that unit fractions add up to a whole, regardless of the denominator. It helps students solidify their understanding of the relationship between unit fractions and the whole.

Topic

Fractions

Description

This image is a variation of the previous ones in the series, now using fifths. It shows a circle divided into five equal parts, each labeled 1/5, with an equation showing 1/5 + 1/5 + 1/5 + 1/5 + 1/5 = 1.

This representation continues the pattern established in the previous images, further reinforcing the concept that unit fractions add up to a whole, regardless of the denominator. It helps students solidify their understanding of the relationship between unit fractions and the whole.

Topic

Fractions

Description

This image provides examples of various unit fractions using circular fraction models. It includes representations of halves, thirds, fourths, and fifths. Each circle is likely divided into the appropriate number of sections, with one section highlighted to represent the unit fraction.

This visual comparison helps students understand different unit fractions and how they relate to their respective wholes. It allows for a direct comparison of the size of different unit fractions.

Topic

Fractions

Description

This image is another variation, now using fourths. It shows a circle divided into four equal parts, each labeled 1/4, with an equation showing 1/4 + 1/4 + 1/4 + 1/4 = 1.

This representation continues to build on the previous examples, further reinforcing the concept that unit fractions add up to a whole, regardless of the denominator. It helps students see the pattern forming as the number of unit fractions increases.

Teachers can use this image to further extend students' understanding of adding unit fractions and to encourage them to predict what might happen with other denominators.

Topic

Fractions

Description

This image is another variation, now using fourths. It shows a circle divided into four equal parts, each labeled 1/4, with an equation showing 1/4 + 1/4 + 1/4 + 1/4 = 1.

This representation continues to build on the previous examples, further reinforcing the concept that unit fractions add up to a whole, regardless of the denominator. It helps students see the pattern forming as the number of unit fractions increases.

Teachers can use this image to further extend students' understanding of adding unit fractions and to encourage them to predict what might happen with other denominators.

Topic

Fractions

Description

This image is a variation of the previous one, showing that halves have 2 unit fractions, thirds have 3 unit fractions, fourths have 4 unit fractions, and fifths have 5 unit fractions. It displays circular fraction models for each, with all sections labeled to show the number of unit fractions that make up each whole.

This representation helps students understand the relationship between the denominator of a unit fraction and the number of those unit fractions needed to make a whole. It reinforces the concept that the denominator indicates how many equal parts the whole is divided into.

Topic

Fractions

Description

This image is a variation of the previous one, showing that halves have 2 unit fractions, thirds have 3 unit fractions, fourths have 4 unit fractions, and fifths have 5 unit fractions. It displays circular fraction models for each, with all sections labeled to show the number of unit fractions that make up each whole.

This representation helps students understand the relationship between the denominator of a unit fraction and the number of those unit fractions needed to make a whole. It reinforces the concept that the denominator indicates how many equal parts the whole is divided into.

Topic

Fractions

Description

This image demonstrates that the sum of unit fractions from a circular fraction is 1, using halves as an example. It shows a circle divided into two equal parts, each labeled 1/2, with an equation showing 1/2 + 1/2 = 1.

This visual representation helps students understand that unit fractions can be added together to form a whole. It reinforces the concept of fraction addition and the relationship between unit fractions and the whole.

Teachers can use this image to introduce or reinforce the concept of adding fractions, particularly unit fractions, and to discuss the meaning of a "whole" in fraction terms.

Topic

Fractions

Description

This image is a variation of the previous one, but now using thirds. It shows a circle divided into three equal parts, each labeled 1/3, with an equation showing 1/3 + 1/3 + 1/3 = 1.

This representation builds on the previous example, helping students understand that the principle of unit fractions adding to a whole applies to different denominators. It reinforces the concept of fraction addition and the relationship between unit fractions and the whole.

Teachers can use this image to extend students' understanding of adding unit fractions and to discuss patterns they might notice as the denominator changes.

Topic

Fractions

Description

This image provides a visual comparison of unit fractions 1/2, 1/3, 1/4, and 1/6, demonstrating that as the denominator increases, the value of the unit fraction decreases. It shows different unit fractions on a number line with a visual comparison of their lengths.

This representation helps students visualize the relative sizes of different unit fractions. It clearly illustrates that while each fraction represents one part, the size of that part decreases as the whole is divided into more pieces.

Topic

Fractions

Description

This image is a variation of the previous ones in the series, now using fifths. It shows a circle divided into five equal parts, each labeled 1/5, with an equation showing 1/5 + 1/5 + 1/5 + 1/5 + 1/5 = 1.

This representation continues the pattern established in the previous images, further reinforcing the concept that unit fractions add up to a whole, regardless of the denominator. It helps students solidify their understanding of the relationship between unit fractions and the whole.

Topic

Fractions

Description

This image is another variation, now using fourths. It shows a circle divided into four equal parts, each labeled 1/4, with an equation showing 1/4 + 1/4 + 1/4 + 1/4 = 1.

This representation continues to build on the previous examples, further reinforcing the concept that unit fractions add up to a whole, regardless of the denominator. It helps students see the pattern forming as the number of unit fractions increases.

Teachers can use this image to further extend students' understanding of adding unit fractions and to encourage them to predict what might happen with other denominators.

Topic

Fractions

Description

This image demonstrates that the sum of unit fractions from a circular fraction is 1, using halves as an example. It shows a circle divided into two equal parts, each labeled 1/2, with an equation showing 1/2 + 1/2 = 1.

This visual representation helps students understand that unit fractions can be added together to form a whole. It reinforces the concept of fraction addition and the relationship between unit fractions and the whole.

Teachers can use this image to introduce or reinforce the concept of adding fractions, particularly unit fractions, and to discuss the meaning of a "whole" in fraction terms.

Topic

Fractions

Description

This image provides a visual comparison of unit fractions 1/2, 1/3, 1/4, and 1/6, demonstrating that as the denominator increases, the value of the unit fraction decreases. It shows different unit fractions on a number line with a visual comparison of their lengths.

This representation helps students visualize the relative sizes of different unit fractions. It clearly illustrates that while each fraction represents one part, the size of that part decreases as the whole is divided into more pieces.

Topic

Fractions

Description

This image provides a visual comparison of unit fractions 1/2, 1/3, 1/4, and 1/6, demonstrating that as the denominator increases, the value of the unit fraction decreases. It shows different unit fractions on a number line with a visual comparison of their lengths.

This representation helps students visualize the relative sizes of different unit fractions. It clearly illustrates that while each fraction represents one part, the size of that part decreases as the whole is divided into more pieces.

Topic

Fractions

Description

This image provides a visual comparison of unit fractions 1/2, 1/3, 1/4, and 1/6, demonstrating that as the denominator increases, the value of the unit fraction decreases. It shows different unit fractions on a number line with a visual comparison of their lengths.

This representation helps students visualize the relative sizes of different unit fractions. It clearly illustrates that while each fraction represents one part, the size of that part decreases as the whole is divided into more pieces.