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Illustrative Math-Media4Math Alignment

 

 

Illustrative Math Alignment: Grade 6 Unit 2

Introducing Ratios

Lesson 7: Creating Double Number Line Diagrams

Use the following Media4Math resources with this Illustrative Math lesson.

Thumbnail Image Title Body Curriculum Topic
PercentsAndDoubleNumberLines--Example--01.png

Math Example: Percents with Double Number Lines: Example 1

Math Example: Percents with Double Number Lines: Example 1

Topic

Ratios, Proportions, Percents

Description

This example demonstrates how to find 50% of 250 using a double number line. The solution shows two parallel number lines: one ranging from 0 to 100% and the other from 0 to 250. By aligning 50% on the percentage line with its corresponding value on the numerical line, we can see that 50% of 250 is 125. This method visually represents the concept that 50% is equivalent to one-half of a quantity.

Ratios and Rates
PercentsAndDoubleNumberLines--Example--10.png

Math Example: Percents with Double Number Lines: Example 10

Math Example: Percents with Double Number Lines: Example 10

Topic

Ratios, Proportions, Percents

Description

This example demonstrates how to determine an unknown value using a double number line when given a part and its corresponding percentage, involving a decimal percentage. The image shows two number lines: one ranging from 0 to 100% and another from 0 to an unknown number x. The position 70 is marked on the second line, visually illustrating the process of finding x when 70 is 12.5% of x.

Ratios and Rates
PercentsAndDoubleNumberLines--Example--11.png

Math Example: Percents with Double Number Lines: Example 11

Math Example: Percents with Double Number Lines: Example 11

Topic

Ratios, Proportions, Percents

Description

This example demonstrates how to determine what percent one number is of another using a double number line. The image shows two parallel number lines: one ranging from 0 to 100% and another from 0 to 75, with 25 marked as an intermediate point. This visual representation helps students understand the relationship between the part (25) and the whole (75) in percentage terms.

Ratios and Rates
PercentsAndDoubleNumberLines--Example--12.png

Math Example: Percents with Double Number Lines: Example 12

Math Example: Percents with Double Number Lines: Example 12

Topic

Ratios, Proportions, Percents

Description

This example illustrates how to calculate what percent one number is of another using a double number line. The image depicts two parallel number lines: one spanning from 0 to 100% and another from 0 to 220, with 55 marked as an intermediate point. This visual representation helps students understand the relationship between the part (55) and the whole (220) in percentage terms.

Ratios and Rates
PercentsAndDoubleNumberLines--Example--13.png

Math Example: Percents with Double Number Lines: Example 13

Math Example: Percents with Double Number Lines: Example 13

Topic

Ratios, Proportions, Percents

Description

This example demonstrates how to determine what percent one number is of another using a double number line. The image shows two parallel number lines: one ranging from 0 to 100% and another from 0 to 495, with 99 marked as an intermediate point. This visual representation helps students understand the relationship between the part (99) and the whole (495) in percentage terms.

Ratios and Rates
PercentsAndDoubleNumberLines--Example--14.png

Math Example: Percents with Double Number Lines: Example 14

Math Example: Percents with Double Number Lines: Example 14

Topic

Ratios, Proportions, Percents

Description

This example illustrates how to calculate what percent one number is of another using a double number line. The image depicts two parallel number lines: one spanning from 0 to 100% and another from 0 to 396, with 198 marked at the midpoint. This visual representation helps students understand the relationship between the part (198) and the whole (396) in percentage terms.

Ratios and Rates
PercentsAndDoubleNumberLines--Example--15.png

Math Example: Percents with Double Number Lines: Example 15

Math Example: Percents with Double Number Lines: Example 15

Topic

Ratios, Proportions, Percents

Description

This example demonstrates how to determine what percent one number is of another using a double number line, particularly when dealing with more complex ratios. The image shows two parallel number lines: one ranging from 0 to 100% and another from 0 to 856, with 107 marked at an eighth of the way. This visual representation helps students understand the relationship between the part (107) and the whole (856) in percentage terms.

Ratios and Rates
PercentsAndDoubleNumberLines--Example--02.png

Math Example: Percents with Double Number Lines: Example 2

Math Example: Percents with Double Number Lines: Example 2

Topic

Ratios, Proportions, Percents

Description

This example illustrates how to calculate 25% of 180 using a double number line. The solution presents two parallel number lines: one spanning from 0 to 100% and the other from 0 to 180. By aligning 25% on the percentage line with its corresponding value on the numerical line, we can determine that 25% of 180 is 45. This method visually demonstrates that 25% is equivalent to one-quarter of a quantity.

Ratios and Rates
PercentsAndDoubleNumberLines--Example--03.png

Math Example: Percents with Double Number Lines: Example 3

Math Example: Percents with Double Number Lines: Example 3

Topic

Ratios, Proportions, Percents

Description

This example demonstrates how to find 33 1/3% of 240 using a double number line. The solution displays two parallel number lines: one ranging from 0 to 100% and the other from 0 to 240. By aligning 33 1/3% on the percentage line with its corresponding value on the numerical line, we can see that 33 1/3% of 240 is 80. This method visually represents the concept that 33 1/3% is equivalent to one-third of a quantity.

Ratios and Rates
PercentsAndDoubleNumberLines--Example--04.png

Math Example: Percents with Double Number Lines: Example 4

Math Example: Percents with Double Number Lines: Example 4

Topic

Ratios, Proportions, Percents

Description

This example illustrates how to calculate 40% of 105 using a double number line. The solution presents two parallel number lines: one spanning from 0 to 100% and the other from 0 to 105. By aligning 40% on the percentage line with its corresponding value on the numerical line, we can determine that 40% of 105 is 42. This method visually demonstrates that 40% is equivalent to two-fifths of a quantity.

Ratios and Rates
PercentsAndDoubleNumberLines--Example--05.png

Math Example: Percents with Double Number Lines: Example 5

Math Example: Percents with Double Number Lines: Example 5

Topic

Ratios, Proportions, Percents

Description

This example demonstrates how to find 12.5% of 88 using a double number line. The solution shows two parallel number lines: one ranging from 0 to 100% and the other from 0 to 88. By aligning 12.5% on the percentage line with its corresponding value on the numerical line, we can see that 12.5% of 88 is 11. This method visually represents the concept that 12.5% is equivalent to one-eighth of a quantity.

Ratios and Rates
PercentsAndDoubleNumberLines--Example--06.png

Math Example: Percents with Double Number Lines: Example 6

Math Example: Percents with Double Number Lines: Example 6

Topic

Ratios, Proportions, Percents

Description

This example demonstrates how to solve for an unknown value using a double number line when given a percentage. The image features two parallel number lines: one ranging from 0 to 100% and another from 0 to an unknown value x. It visually illustrates the process of determining x when 75 is 50% of x.

Ratios and Rates
PercentsAndDoubleNumberLines--Example--07.png

Math Example: Percents with Double Number Lines: Example 7

Math Example: Percents with Double Number Lines: Example 7

Topic

Ratios, Proportions, Percents

Description

This example illustrates how to determine an unknown value using a double number line when given a part and its corresponding percentage. The image depicts two parallel number lines: one spanning from 0 to 100% and another from 0 to an unknown value x. It visually demonstrates the process of finding x when 120 is 25% of x.

Ratios and Rates
PercentsAndDoubleNumberLines--Example--08.png

Math Example: Percents with Double Number Lines: Example 8

Math Example: Percents with Double Number Lines: Example 8

Topic

Ratios, Proportions, Percents

Description

This example demonstrates how to find an unknown value using a double number line when given a part and its corresponding percentage, involving a fractional percentage. The image shows two parallel number lines: one ranging from 0 to 100% and another from 0 to an unknown value x. It visually illustrates the process of determining x when 125 is 33 1/3% of x.

Ratios and Rates
PercentsAndDoubleNumberLines--Example--09.png

Math Example: Percents with Double Number Lines: Example 9

Math Example: Percents with Double Number Lines: Example 9

Topic

Ratios, Proportions, Percents

Description

This example illustrates how to solve for an unknown value using a double number line when given a part and its corresponding percentage. The image shows two horizontal number lines: the top line ranges from 0 to 100%, and the bottom line ranges from 0 to an unknown number x. The 40% mark on the top line aligns with 220 on the bottom line, visually demonstrating the process of finding x when 220 is 40% of x.

Ratios and Rates
RatiosAndDoubleNumberLines--Example--01.png

Math Example: Ratios with Double Number Lines: Example 1

Math Example: Ratios with Double Number Lines: Example 1

Topic

Ratios

Description

This example demonstrates the use of double number lines to solve a ratio problem involving orange and lemon juice. The juice mixture uses a ratio of 2 parts orange juice to 1 part lemon juice. Given 6 cups of orange juice, students are asked to determine the amount of lemon juice needed. The solution involves aligning the double number lines at the amount of orange juice and reading the corresponding amount of lemon juice, which is 3 cups.

Ratios and Rates
RatiosAndDoubleNumberLines--Example--10.png

Math Example: Ratios with Double Number Lines: Example 10

Math Example: Ratios with Double Number Lines: Example 10

Topic

Ratios

Description

This example introduces a four-part ratio of 5:2:1:1 for orange, lemon, lime, and strawberry juice. Given 10 cups of orange juice, students need to determine the amounts of lemon, lime, and strawberry juice required. The solution shows that 4 cups of lemon juice and 2 cups each of lime and strawberry juice are needed to maintain the ratio.

Ratios and Rates
RatiosAndDoubleNumberLines--Example--02.png

Math Example: Ratios with Double Number Lines: Example 2

Math Example: Ratios with Double Number Lines: Example 2

Topic

Ratios

Description

This example builds upon the previous one, using the same ratio of 2 parts orange juice to 1 part lemon juice. However, in this case, students are given 4 cups of lemon juice and asked to determine the amount of orange juice needed. The solution involves aligning the double number lines at the amount of lemon juice and reading the corresponding amount of orange juice, which is 8 cups.

Ratios and Rates
RatiosAndDoubleNumberLines--Example--03.png

Math Example: Ratios with Double Number Lines: Example 3

Math Example: Ratios with Double Number Lines: Example 3

Topic

Ratios

Description

This example introduces a new ratio of 3 parts orange juice to 1 part lime juice. Students are given 9 cups of orange juice and asked to determine the amount of lime juice needed. The solution involves using a double number line to align at the amount of orange juice and find the corresponding amount of lime juice, which is 3 cups.

Ratios and Rates
RatiosAndDoubleNumberLines--Example--04.png

Math Example: Ratios with Double Number Lines: Example 4

Math Example: Ratios with Double Number Lines: Example 4

Topic

Ratios

Description

This example introduces a more complex ratio of 3 parts orange juice to 2 parts lime juice. Students are given 4 cups of lime juice and asked to determine the amount of orange juice needed. The solution involves using a double number line to align at the amount of lime juice and find the corresponding amount of orange juice, which is 6 cups.

Ratios and Rates
RatiosAndDoubleNumberLines--Example--05.png

Math Example: Ratios with Double Number Lines: Example 5

Math Example: Ratios with Double Number Lines: Example 5

Topic

Ratios

Description

This example introduces a three-part ratio of 2:1:1 for orange, lemon, and raspberry juice. Given 4 cups of orange juice, students need to determine the amounts of lemon and raspberry juice required. The solution shows that 2 cups each of lemon and raspberry juice are needed to maintain the ratio.

Ratios and Rates
RatiosAndDoubleNumberLines--Example--06.png

Math Example: Ratios with Double Number Lines: Example 6

Math Example: Ratios with Double Number Lines: Example 6

Topic

Ratios

Description

This example presents a three-part ratio of 3:2:2 for orange, lemon, and raspberry juice. Given 6 cups of lemon juice, students need to determine the amounts of orange and raspberry juice required. The solution shows that 9 cups of orange juice and 6 cups of raspberry juice are needed to maintain the ratio.

Ratios and Rates
RatiosAndDoubleNumberLines--Example--07.png

Math Example: Ratios with Double Number Lines: Example 7

This is part of a series of math examples that show how to solve ratio problems involving double number lines.

Note: The download is a PNG file.

Ratios and Rates
RatiosAndDoubleNumberLines--Example--08.png

Math Example: Ratios with Double Number Lines: Example 8

Math Example: Ratios with Double Number Lines: Example 8

Topic

Ratios

Description

This example presents a three-part ratio of 4:3:2 for orange, lemon, and lime juice. Given 4 cups of lime juice, students need to determine the amounts of orange and lemon juice required. The solution shows that 8 cups of orange juice and 6 cups of lemon juice are needed to maintain the ratio.

Ratios and Rates
RatiosAndDoubleNumberLines--Example--09.png

Math Example: Ratios with Double Number Lines: Example 9

Math Example: Ratios with Double Number Lines: Example 9

Topic

Ratios

Description

This example features a three-part ratio of 5:2:1 for orange, lemon, and lime juice. Given 6 cups of lemon juice, students need to determine the amounts of orange and lime juice required. The solution demonstrates that 15 cups of orange juice and 3 cups of lime juice are needed to maintain the ratio.

Ratios and Rates
VideoTutorial--Ratios11Thumbnail.jpg

Video Tutorial: Ratios, Video 11

Video Tutorial: Ratios and Proportions: Solving Proportions

This is part of a collection of video tutorials on the topic of Ratios and Proportions. This series includes a complete overview of ratios, equivalent ratios, rates, unit rates, and proportions. The following section will provide additional background information for the complete series of videos.

What Are Ratios?

A ratio is the relationship between two or more quantities among a group of items. The purpose of a ratio is find the relationship between two or more items in the collection.

Let's look at an example.

Ratios and Rates
VideoTutorial--Ratios1Thumbnail.jpg

Video Tutorial: Ratios, Video 1

Video Tutorial: Ratios: What Are Ratios?

This is part of a collection of video tutorials on the topic of Ratios and Proportions. This series includes a complete overview of ratios, equivalent ratios, rates, unit rates, and proportions. The following section will provide additional background information for the complete series of videos.

What Are Ratios?

A ratio is the relationship between two or more quantities among a group of items. The purpose of a ratio is find the relationship between two or more items in the collection.

Let's look at an example.

Ratios and Rates
VideoTutorial--Ratios12Thumbnail.jpg

Video Tutorial: Ratios, Video 12

Video Tutorial: Ratios and Proportions: Scale Drawings

This is part of a collection of video tutorials on the topic of Ratios and Proportions. This series includes a complete overview of ratios, equivalent ratios, rates, unit rates, and proportions. The following section will provide additional background information for the complete series of videos.

What Are Ratios?

A ratio is the relationship between two or more quantities among a group of items. The purpose of a ratio is find the relationship between two or more items in the collection.

Let's look at an example.

Ratios and Rates
VideoTutorial--Ratios13Thumbnail.jpg

Video Tutorial: Ratios, Video 13

Video Tutorial: Ratios and Rates: Rates from Data

This is part of a collection of video tutorials on the topic of Ratios and Proportions. This series includes a complete overview of ratios, equivalent ratios, rates, unit rates, and proportions. The following section will provide additional background information for the complete series of videos.

What Are Ratios?

A ratio is the relationship between two or more quantities among a group of items. The purpose of a ratio is find the relationship between two or more items in the collection.

Let's look at an example.

Ratios and Rates
VideoTutorial--Ratios14Thumbnail.jpg

Video Tutorial: Ratios, Video 14

Video Tutorial: Ratios and Rates: Rates and Slopes of Lines

This is part of a collection of video tutorials on the topic of Ratios and Proportions. This series includes a complete overview of ratios, equivalent ratios, rates, unit rates, and proportions. The following section will provide additional background information for the complete series of videos.

What Are Ratios?

A ratio is the relationship between two or more quantities among a group of items. The purpose of a ratio is find the relationship between two or more items in the collection.

Let's look at an example.

Ratios and Rates
VideoTutorial--Ratios15Thumbnail.jpg

Video Tutorial: Ratios, Video 15

Video Tutorial: Ratios and Rates: Converting Measurement Units

This is part of a collection of video tutorials on the topic of Ratios and Proportions. This series includes a complete overview of ratios, equivalent ratios, rates, unit rates, and proportions. The following section will provide additional background information for the complete series of videos.

What Are Ratios?

A ratio is the relationship between two or more quantities among a group of items. The purpose of a ratio is find the relationship between two or more items in the collection.

Let's look at an example.

Ratios and Rates
VideoTutorial--Ratios16Thumbnail.jpg

Video Tutorial: Ratios, Video 16

Video Tutorial: Ratios, Proportions, and Percents: Calculating Percents

This is part of a collection of video tutorials on the topic of Ratios and Proportions. This series includes a complete overview of ratios, equivalent ratios, rates, unit rates, and proportions. The following section will provide additional background information for the complete series of videos.

What Are Ratios?

A ratio is the relationship between two or more quantities among a group of items. The purpose of a ratio is find the relationship between two or more items in the collection.

Let's look at an example.

Ratios and Rates
Video Tutorial: Ratios: Visual Models for Ratios and Percents

Video Tutorial: Ratios, Video 17

Video Tutorial: Ratios: Visual Models for Ratios and Percents

This is part of a collection of video tutorials on the topic of Ratios and Proportions. This series includes a complete overview of ratios, equivalent ratios, rates, unit rates, and proportions. The following section will provide additional background information for the complete series of videos.

What Are Ratios?

A ratio is the relationship between two or more quantities among a group of items. The purpose of a ratio is find the relationship between two or more items in the collection.

Let's look at an example.

Ratios and Rates
VideoTutorial--Ratios18Thumbnail.jpg

Video Tutorial: Ratios, Video 18

Video Tutorial: Ratios and Rates: Ratios as Decimals

This is part of a collection of video tutorials on the topic of Ratios and Proportions. This series includes a complete overview of ratios, equivalent ratios, rates, unit rates, and proportions. The following section will provide additional background information for the complete series of videos.

What Are Ratios?

A ratio is the relationship between two or more quantities among a group of items. The purpose of a ratio is find the relationship between two or more items in the collection.

Let's look at an example.

Ratios and Rates
VideoTutorial--Ratios19Thumbnail.jpg

Video Tutorial: Ratios, Video 19

Video Tutorial: Ratios: Application of Ratios: Roofs and Ramps

This is part of a collection of video tutorials on the topic of Ratios and Proportions. This series includes a complete overview of ratios, equivalent ratios, rates, unit rates, and proportions. The following section will provide additional background information for the complete series of videos.

What Are Ratios?

A ratio is the relationship between two or more quantities among a group of items. The purpose of a ratio is find the relationship between two or more items in the collection.

Let's look at an example.

Applications of Ratios, Proportions, and Percents and Proportions
VideoTutorial--Ratios2Thumbnail.jpg

Video Tutorial: Ratios, Video 2

Video Tutorial: Ratios: Ratios with Three Items

This is part of a collection of video tutorials on the topic of Ratios and Proportions. This series includes a complete overview of ratios, equivalent ratios, rates, unit rates, and proportions. The following section will provide additional background information for the complete series of videos.

What Are Ratios?

A ratio is the relationship between two or more quantities among a group of items. The purpose of a ratio is find the relationship between two or more items in the collection.

Let's look at an example.

Ratios and Rates
Video Tutorial: Rate of Change

Video Tutorial: Ratios, Video 20

Video Tutorial: Ratios and Rates: Rate of Change

This is part of a collection of video tutorials on the topic of Ratios and Proportions. This series includes a complete overview of ratios, equivalent ratios, rates, unit rates, and proportions. The following section will provide additional background information for the complete series of videos.

What Are Ratios?

A ratio is the relationship between two or more quantities among a group of items. The purpose of a ratio is find the relationship between two or more items in the collection.

Let's look at an example.

Point-Slope Form and Slope
VideoTutorial--Ratios3Thumbnail.jpg

Video Tutorial: Ratios, Video 3

Video Tutorial: Ratios: Fractional Ratios

This is part of a collection of video tutorials on the topic of Ratios and Proportions. This series includes a complete overview of ratios, equivalent ratios, rates, unit rates, and proportions. The following section will provide additional background information for the complete series of videos.

What Are Ratios?

A ratio is the relationship between two or more quantities among a group of items. The purpose of a ratio is find the relationship between two or more items in the collection.

Let's look at an example.

Ratios and Rates
VideoTutorial--Ratios4Thumbnail.jpg

Video Tutorial: Ratios, Video 4

Video Tutorial: Ratios: Ratios and Fractions

This is part of a collection of video tutorials on the topic of Ratios and Proportions. This series includes a complete overview of ratios, equivalent ratios, rates, unit rates, and proportions. The following section will provide additional background information for the complete series of videos.

What Are Ratios?

A ratio is the relationship between two or more quantities among a group of items. The purpose of a ratio is find the relationship between two or more items in the collection.

Let's look at an example.

Ratios and Rates
VideoTutorial--Ratios5Thumbnail.jpg

Video Tutorial: Ratios, Video 5

Video Tutorial: Ratios: Visual Models for Ratios

This is part of a collection of video tutorials on the topic of Ratios and Proportions. This series includes a complete overview of ratios, equivalent ratios, rates, unit rates, and proportions. The following section will provide additional background information for the complete series of videos.

What Are Ratios?

A ratio is the relationship between two or more quantities among a group of items. The purpose of a ratio is find the relationship between two or more items in the collection.

Let's look at an example.

Ratios and Rates
VideoTutorial--Ratios6Thumbnail.jpg

Video Tutorial: Ratios, Video 6

Video Tutorial: Ratios: Numerical Models for Ratios

This is part of a collection of video tutorials on the topic of Ratios and Proportions. This series includes a complete overview of ratios, equivalent ratios, rates, unit rates, and proportions. The following section will provide additional background information for the complete series of videos.

What Are Ratios?

A ratio is the relationship between two or more quantities among a group of items. The purpose of a ratio is find the relationship between two or more items in the collection.

Let's look at an example.

Ratios and Rates
VideoTutorial--Ratios7Thumbnail.jpg

Video Tutorial: Ratios, Video 7

Video Tutorial: Ratios: Equivalent Ratios

This is part of a collection of video tutorials on the topic of Ratios and Proportions. This series includes a complete overview of ratios, equivalent ratios, rates, unit rates, and proportions. The following section will provide additional background information for the complete series of videos.

What Are Ratios?

A ratio is the relationship between two or more quantities among a group of items. The purpose of a ratio is find the relationship between two or more items in the collection.

Let's look at an example.

Ratios and Rates
VideoTutorial--Ratios8Thumbnail.jpg

Video Tutorial: Ratios, Video 8

Video Tutorial: Ratios: Rates

This is part of a collection of video tutorials on the topic of Ratios and Proportions. This series includes a complete overview of ratios, equivalent ratios, rates, unit rates, and proportions. The following section will provide additional background information for the complete series of videos.

What Are Ratios?

A ratio is the relationship between two or more quantities among a group of items. The purpose of a ratio is find the relationship between two or more items in the collection.

Let's look at an example.

Ratios and Rates
VideoTutorial--Ratios9Thumbnail.jpg

Video Tutorial: Ratios, Video 9

Video Tutorial: Ratios: Unit Rates

This is part of a collection of video tutorials on the topic of Ratios and Proportions. This series includes a complete overview of ratios, equivalent ratios, rates, unit rates, and proportions. The following section will provide additional background information for the complete series of videos.

What Are Ratios?

A ratio is the relationship between two or more quantities among a group of items. The purpose of a ratio is find the relationship between two or more items in the collection.

Let's look at an example.

Ratios and Rates
VideoTutorial--Ratios10Thumbnail.jpg

Video Tutorial: Ratios, Video 10

Video Tutorial: Ratios and Proportions: What are Proportions?

This is part of a collection of video tutorials on the topic of Ratios and Proportions. This series includes a complete overview of ratios, equivalent ratios, rates, unit rates, and proportions. The following section will provide additional background information for the complete series of videos.

What Are Ratios?

A ratio is the relationship between two or more quantities among a group of items. The purpose of a ratio is find the relationship between two or more items in the collection.

Let's look at an example.

Ratios and Rates