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Illustrative Math-Media4Math Alignment

 

 

Illustrative Math Alignment: Grade 6 Unit 3

Unit Rates and Percentages

Lesson 17: Painting a Room

Use the following Media4Math resources with this Illustrative Math lesson.

Thumbnail Image Title Body Curriculum Nodes
Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 5 Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 5 Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 5

Topic

Ratios, Proportions, and Percents

Description

This example demonstrates solving for c in a proportion where a = 9, b = 4, and d = 12. We set up the proportion 9 / 4 = c / 12 and solve for c, resulting in c = 27. This problem shows how to find an unknown value in the numerator of a proportion.

Proportions
Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 6 Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 6 Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 6

Topic

Ratios, Proportions, and Percents

Description

This example illustrates solving for c in a proportion where a = 8, b = 3, and d is expressed as x + 3. We set up the equation 8 / 3 = c / (x + 3) and solve for c, resulting in the expression c = (8(x + 3)) / 3. This problem demonstrates how to handle algebraic expressions in the denominator of a proportion.

Proportions
Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 7 Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 7 Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 7

Topic

Ratios, Proportions, and Percents

Description

This example demonstrates solving for d in a proportion where a = 12, b = 5, and c = 48. We set up the proportion 12 / 5 = 48 / d and solve for d, resulting in d = 20. This problem shows how to find an unknown value in the denominator of a proportion when all other values are known.

Proportions
Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 8 Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 8 Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 8

Topic

Ratios, Proportions, and Percents

Description

This example illustrates solving for d in a proportion where a = 11, b = 5, and c is expressed as x - 4. We set up the equation 11 / 5 = (x - 4) / d and solve for d, resulting in the expression d = (5(x - 4)) / 11. This problem demonstrates how to handle algebraic expressions in the numerator of a proportion.

Proportions
Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 9 Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 9 Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 9

Topic

Ratios, Proportions, and Percents

Description

This example demonstrates solving a proportion problem using similar triangles. Two triangles are shown, with one having sides of 3 and 4, and the other having sides of 6 and x. The problem requires finding the length of side x by setting up a proportion based on the similar triangles: 3 / 4 = 6 / x. Solving this equation leads to x = 8.

Proportions
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
MATH EXAMPLES--Teacher's Guide: Solving Equations with Percents MATH EXAMPLES--Teacher's Guide: Solving Equations with Percents MATH EXAMPLES--Teacher's Guide: Solving Equations with Percents

What Are Percents?

Percents Are a Type of Fraction
Solving Percent Equations
Math in the News: Issue 100--Late Night TV Ratings Math in the News: Issue 100--Late Night TV Ratings Math in the News: Issue 100--Late Night TV Ratings

July 2014. In this issue of Math in the News we look at the mathematics of the Nielsen Ratings. This provides an excellent application of ratios, proportions, and percents.

This is part of the Math in the News collection. To see the complete collection, click on this link. Note: The download is a PPT file.

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Data Analysis
MITN Math in the News: Issue 121--NFL Concussion Statistics Math in the News: Issue 121 | NFL Concussion Statistics

February 2023. In this issue of Math in the News we look at NFL statistics for the number of concussions. The NFL now tracks concussion, and this is an opportunity to analyze this data and draw conclusions.

—PRESS PREVIEW TO SEE THE SLIDE SHOW— This is part of the Math in the News collection. To see the complete collection, click on this link.

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Applications of Ratios, Proportions, and Percents
Math in the News: Issue 96--The California Drought Math in the News: Issue 96--The California Drought Math in the News: Issue 96--The California Drought

July 2015. This edition of Math in the News focuses on the severe drought currently taking place in California, and how it has impacted the water resources available to the state. In this edition, students will see how to use percentages given to determine actual amounts, and to determine percents out of a whole.

This is part of the Math in the News collection. To see the complete collection, click on this link. Note: The download is a PPT file.

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Applications of Ratios, Proportions, and Percents and Proportions
Math in the News: Issue 96--The California Drought Math in the News: Issue 96--The California Drought Math in the News: Issue 96--The California Drought

July 2015. This edition of Math in the News focuses on the severe drought currently taking place in California, and how it has impacted the water resources available to the state. In this edition, students will see how to use percentages given to determine actual amounts, and to determine percents out of a whole.

This is part of the Math in the News collection. To see the complete collection, click on this link. Note: The download is a PPT file.

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Applications of Ratios, Proportions, and Percents and Proportions
Math in the News: Issue 99--What Is Bitcoin? Math in the News: Issue 99--What Is Bitcoin? Math in the News: Issue 99--What Is Bitcoin?

May 2014. In this issue of Math in the News we explore Bitcoin. We look at how it's used for making purchases and how it differs from other currencies. This provides an opportunity to apply the concept of currency exchange.

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Applications of Ratios, Proportions, and Percents and Proportions
Paper-and-Pencil Quiz: Equations with Percents (Easy) Paper-and-Pencil Quiz: Equations with Percents (Easy) Paper-and-Pencil Quiz: Equations with Percents (Easy)

This is part of a collection of math quizzes on the topic of Equations with Percents.

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Quiz Library

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ary">click on this link.

Solving Percent Equations
Paper-and-Pencil Quiz: Equations with Percents (Hard) Paper-and-Pencil Quiz: Equations with Percents (Hard) Paper-and-Pencil Quiz: Equations with Percents (Hard)

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Quiz Library

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ary">click on this link.

Solving Percent Equations
Paper-and-Pencil Quiz: Equations with Percents (Medium) Paper-and-Pencil Quiz: Equations with Percents (Medium) Paper-and-Pencil Quiz: Equations with Percents (Medium)

This is part of a collection of math quizzes on the topic of Equations with Percents.

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ary">click on this link.

Solving Percent Equations
Video Definition 26--Fraction Concepts--Percent Video Definition 26--Fraction Concepts--Percent Video Definition 26--Fraction Concepts--Percent

This is part of a collection of math video definitions related to to the topic of fractions. Note: The download is an MP4 video.

Fractions and Mixed Numbers
Video Definition 27--Fraction Concepts--Percent Error Video Definition 27--Fraction Concepts--Percent Error Video Definition 27--Fraction Concepts--Percent Error

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Fractions and Mixed Numbers
Video Definition 28--Fraction Concepts--Percentage Video Definition 28--Fraction Concepts--Percentage Video Definition 28--Fraction Concepts--Percentage

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Fractions and Mixed Numbers
Video Definition 29--Fraction Concepts--Percentage Decrease Video Definition 29--Fraction Concepts--Percentage Decrease Video Definition 29--Fraction Concepts--Percentage Decrease

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Fractions and Mixed Numbers
Video Definition 30--Fraction Concepts--Percentage Increase Video Definition 30--Fraction Concepts--Percentage Increase Video Definition 30--Fraction Concepts--Percentage Increase

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Fractions and Mixed Numbers
Video Transcript: Algebra Applications: Variables and Equations, Segment 3: River Ratios Video Transcript: Algebra Applications: Variables and Equations, Segment 3: River Ratios Video Transcript: Algebra Applications: Variables and Equations, Segment 3: River Ratios

This is the transcript for the video of same title. Video contents: Why do rivers meander instead of traveling in a straight line? In going from point A to point B, why should a river take the circuitous route it does instead of a direct path? Furthermore, what information can the ratio of the river's length to its straight-line distance tell us? In this segment the geological forces that account for a river's motion are explained. In the process, the so-called Meander Ratio is explored. Students construct a mathematical model of a meandering river using the TI-Nspire. Having built the model, students then use it to generate data to find the average of many Meander Ratios. The results show that on average the Meander Ratio is equal to pi.

Applications of Equations and Inequalities and Applications of Ratios, Proportions, and Percents
Video Transcript: Application of Ratios: Roofs and Ramps Video Transcript: Application of Ratios: Roofs and Ramps Video Transcript: Application of Ratios: Roofs and Ramps

What Are Ratios?

A ratio is the relationship between two or more quantities among a group of items.

Applications of Ratios, Proportions, and Percents
Video Transcript: Percents: Applications of Percent -- Grade Video Transcript: Percents: Applications of Percent -- Grade Video Transcript: Percents: Applications of Percent -- Grade

This is the transcript that goes with the video segment entitled Video: Percents: Applications of Percent -- Grade.

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Percents
Video Transcript: Percents: Calculating Commissions and Tips Video Transcript: Percents: Calculating Commissions and Tips Video Transcript: Percents: Calculating Commissions and Tips

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Percents
Video Transcript: Percents: Calculating Tax Video Transcript: Percents: Calculating Tax Video Transcript: Percents: Calculating Tax

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Percents
Video Transcript: Percents: Calculating the Whole Given a Percent Video Transcript: Percents: Calculating the Whole Given a Percent Video Transcript: Percents: Calculating the Whole Given a Percent

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Percents
Video Transcript: Percents: Estimating Percents Video Transcript: Percents: Estimating Percents Video Transcript: Percents: Estimating Percents

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Percents
Video Transcript: Percents: Fraction-Percent Conversion Video Transcript: Percents: Fraction-Percent Conversion Video Transcript: Percents: Fraction-Percent Conversion

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Percents
Video Transcript: Percents: Multiple Percents Video Transcript: Percents: Multiple Percents Video Transcript: Percents: Multiple Percents

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Percents
Video Transcript: Percents: Percent Decrease Video Transcript: Percents: Percent Decrease Video Transcript: Percents: Percent Decrease

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Percents
Video Transcript: Percents: Percent Increase Video Transcript: Percents: Percent Increase Video Transcript: Percents: Percent Increase

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Percents
Video Transcript: Percents: Percent of a Difference Video Transcript: Percents: Percent of a Difference Video Transcript: Percents: Percent of a Difference

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Percents
Video Transcript: Percents: Percent of a Number Video Transcript: Percents: Percent of a Number Video Transcript: Percents: Percent of a Number

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Percents
Video Transcript: Percents: Percents and Multiples of Numbers Video Transcript: Percents: Percents and Multiples of Numbers Video Transcript: Percents: Percents and Multiples of Numbers

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Percents
Video Transcript: Percents: Probabilities and Percents Video Transcript: Percents: Probabilities and Percents Video Transcript: Percents: Probabilities and Percents

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Percents
Video Transcript: Percents: Simple Interest Video Transcript: Percents: Simple Interest Video Transcript: Percents: Simple Interest

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Percents