Illustrative Math Alignment: Grade 6 Unit 1

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 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 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 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 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, 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 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 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 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, 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 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 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 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 illustrates the unit fraction 1/4 both as a numerical fraction and as a circular fraction model. It shows the fraction 1/4 written out, alongside a circle divided into four equal parts with one part shaded or highlighted.

This representation helps students connect the abstract numerical concept of a unit fraction with a concrete visual model. It reinforces the understanding that a unit fraction has a numerator of 1 and represents one equal part of a whole divided into some number of equal parts.

Topic

Fractions

Description

This image demonstrates that a circular fraction for fourths is made up of four 1/4 sections. It shows a circle divided into four equal parts, with each part labeled as 1/4. This visual representation helps students understand that four unit fractions of 1/4 make up a whole.

This illustration is crucial for helping students grasp the concept of unit fractions and how they relate to the whole. It visually demonstrates that unit fractions are equal parts of a whole and that combining all the unit fractions results in 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 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 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 serves as the title card for a series on unit fractions. It displays the text "Unit Fractions" in a clear, prominent font. The background includes 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 unit fractions. It provides a clear, concise title that immediately informs viewers about the specific fraction concept they'll be studying.

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 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, 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 illustrates the unit fraction 1/4 both as a numerical fraction and as a circular fraction model. It shows the fraction 1/4 written out, alongside a circle divided into four equal parts with one part shaded or highlighted.

This representation helps students connect the abstract numerical concept of a unit fraction with a concrete visual model. It reinforces the understanding that a unit fraction has a numerator of 1 and represents one equal part of a whole divided into some number of equal parts.

Topic

Fractions

Description

This image demonstrates that a circular fraction for fourths is made up of four 1/4 sections. It shows a circle divided into four equal parts, with each part labeled as 1/4. This visual representation helps students understand that four unit fractions of 1/4 make up a whole.

This illustration is crucial for helping students grasp the concept of unit fractions and how they relate to the whole. It visually demonstrates that unit fractions are equal parts of a whole and that combining all the unit fractions results in the whole.

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 serves as the title card for a series on unit fractions. It displays the text "Unit Fractions" in a clear, prominent font. The background includes 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 unit fractions. It provides a clear, concise title that immediately informs viewers about the specific fraction concept they'll be studying.

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 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 illustrates the concept that in a fraction model all the fractional parts are the same size. This property is crucial for students to understand as they learn to understand fractions. The use of identical rectangular models allows students to see that 1/4 and 2/8 cover the same area, visually reinforcing their equivalence.

Teachers can use this image to introduce or reinforce the concept of equivalent fractions. It provides a visual representation that clearly shows how different fractions can represent the same portion of a whole.

Topic

Fractions

Description

This image analyzes the fraction 1/4 by clearly showing which part is the numerator and which is the denominator. It displays the fraction 1/4 with labels or arrows pointing to the 1 (numerator) and 4 (denominator), explaining what each number represents.

This breakdown is crucial for students to understand the components of a fraction. The numerator (1) represents the number of parts being considered, while the denominator (4) represents the total number of equal parts the whole is divided into.

Topic

Fractions

Description

This image serves as the title card for a series on the properties of fractions. It displays the text "Properties of Fractions" in a bold, eye-catching font. The background features a number of fraction models that demonstrate some of these properites.

This introductory image sets the stage for the subsequent images in the series, preparing students for an exploration of various fraction properties. It provides a clear, concise title that immediately informs viewers about the topic they'll be studying.

Topic

Fractions

Description

This image reinforces the concept that fraction parts must be the same size and shows what a circular fraction with unequal sectors would look like. It displays two circular models side by side: one correctly divided into equal sectors, and another incorrectly divided into unequal sectors.

This representation helps students understand the importance of equal parts in fractions. It visually demonstrates why fractions must be based on equal divisions of the whole to be valid.

Topic

Fractions

Description

This image is a variation of the previous one, now showing the fraction 2/4. It likely displays the numerical fraction 2/4 alongside a circular fraction model. The circular model would be divided into four equal sectors, with two sectors shaded to represent the numerator.

This representation helps students understand how the numerator changes while the denominator remains the same. It visually demonstrates that 2/4 is twice as much as 1/4, while still being part of the same whole.

Topic

Fractions

Description

This image demonstrates the concept that in a fraction model, the shaded region represent the fractional part. This property is essential for students to understand as they learn to order fractions and make comparisons in real-world scenarios. The rectangular model clearly shows that 3/4 covers more area than 1/4, making the comparison visually apparent.

Topic

Fractions

Description

This image compares the numerical fraction 1/4 with a circular fraction model of the same value. The circular model is divided into four equal sectors, with one sector shaded. The shaded region represents the numerator (1), while the total number of sectors represents the denominator (4).

This comparison helps students connect the abstract numerical representation of fractions with a more concrete visual model. It reinforces the concept that the numerator represents the parts being considered, while the denominator represents the total number of equal parts.

Topic

Fractions

Description

This image illustrates the fundamental concept that fractions represent parts of a whole. It displays a rectangle divided into four equal parts, with one part highlighted, demonstrating how the highlighted portion relates to the entire shape.

This basic principle is crucial for students to grasp as they begin working with fractions. The visual representation helps students connect the abstract fraction 1/4 with a concrete image of one out of four equal parts. By using a rectangular model, students are introduced to different ways of representing fractions beyond the common circular model.

Topic

Fractions

Description

This image shows examples of circular fractions for 1/2, 1/3, 1/5, and 1/6. It displays four circular models, each divided into the appropriate number of sectors, with one sector shaded in each.

This representation helps students visualize different unit fractions and understand how the size of each part changes as the denominator increases. It provides a clear visual comparison of these common fractions.

Teachers can use this image to discuss how the size of each part decreases as the denominator increases, even though in each case only one part is being considered.

Topic

Fractions

Description

This image is another variation, now showing the fraction 3/4. It likely displays the numerical fraction 3/4 alongside a circular fraction model. The circular model would be divided into four equal sectors, with three sectors shaded to represent the numerator.

This representation further reinforces how the numerator changes while the denominator remains constant. It visually demonstrates that 3/4 is three times as much as 1/4 and more than 2/4, while still being part of the same whole.

Topic

Fractions

Description

This image is a variation of the previous one, now showing examples of circular fractions for 2/3, 2/5, 3/6, and 5/8. It likely displays four circular models, each divided into the appropriate number of sectors, with the corresponding number of sectors shaded in each.

This representation helps students visualize different fractions and understand how the shaded portion changes as both the numerator and denominator vary. It provides a clear visual comparison of these fractions.

Topic

Fractions

Description

This image illustrates how to write 1/4 as a fraction. This representation helps students understand the basic concept of fractions - that they represent parts of a whole. The visual aids in connecting the abstract numerical representation (1/4) with a concrete image of one out of four equal parts.

Teachers can use this image to introduce or reinforce the concept of writing fractions. It provides a clear link between the visual representation and the numerical notation of fractions.

Teacher's Script: "This is how we write 1/4 as a fraction. What do you notice?"

Topic

Percents

Description

The video explores converting fractions to percents for simplified calculations. Examples include determining cargo contents, rose sales, and motorcycle proportions. Fraction-percent equivalence simplifies arithmetic and provides quick insights into ratios and totals. Applications include logistics, commerce, and urban planning.

Topic

Percents

Description

The video explores converting fractions to percents for simplified calculations. Examples include determining cargo contents, rose sales, and motorcycle proportions. Fraction-percent equivalence simplifies arithmetic and provides quick insights into ratios and totals. Applications include logistics, commerce, and urban planning.

Topic

Percents

Description

The video explores converting fractions to percents for simplified calculations. Examples include determining cargo contents, rose sales, and motorcycle proportions. Fraction-percent equivalence simplifies arithmetic and provides quick insights into ratios and totals. Applications include logistics, commerce, and urban planning.

Topic

Percents

Description

The video explores converting fractions to percents for simplified calculations. Examples include determining cargo contents, rose sales, and motorcycle proportions. Fraction-percent equivalence simplifies arithmetic and provides quick insights into ratios and totals. Applications include logistics, commerce, and urban planning.