Use the following Media4Math resources with this Illustrative Math lesson.
Thumbnail Image | Title | Body | Curriculum Nodes |
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Definition--Ratios, Proportions, and Percents Concepts--Scale Drawing | Scale DrawingTopicRatios, Proportions, and Percents DefinitionA scale drawing is a representation of an object or structure with dimensions proportional to the actual object or structure. DescriptionScale drawings are essential in fields like architecture, engineering, and cartography, where accurate representations of large objects or areas are needed. For example, an architect might create a scale drawing of a building where 1 inch on the drawing represents 10 feet in reality. This allows for detailed planning and visualization without needing a full-sized model. |
Proportions | |
Definition--Ratios, Proportions, and Percents Concepts--Scale Factor | Scale FactorTopicRatios, Proportions, and Percents DefinitionA scale factor is a number that scales, or multiplies, some quantity. DescriptionScale factors are used in various applications, such as resizing images, models, and maps. For instance, if a model car is built at a scale factor of 1:24, it means the model is 1/24th the size of the actual car. This concept is crucial in fields requiring accurate scaling, such as architecture and engineering. |
Proportions | |
Definition--Ratios, Proportions, and Percents Concepts--Similar Figures | Similar FiguresTopicRatios, Proportions, and Percents DefinitionSimilar figures are figures that have the same shape but may differ in size; their corresponding angles are equal, and their corresponding sides are proportional. DescriptionSimilar figures are fundamental in geometry and are used in various real-world applications, such as creating scale models and maps. For example, two triangles are similar if their corresponding angles are equal and their sides are in proportion. This concept is essential for understanding geometric relationships and solving problems involving shapes and sizes. |
Proportions | |
Definition--Ratios, Proportions, and Percents Concepts--Solving Proportions | Solving ProportionsTopicRatios, Proportions, and Percents DefinitionSolving proportions involves finding the value of a variable that makes two ratios equal. DescriptionSolving proportions is a key skill in algebra and is used in various applications, such as scaling recipes, converting units, and solving real-world problems. For example, if you know that 2/3 = x/6 you can solve for x by cross-multiplying to get 2 * 6 = 3 * x leading to x = 4 |
Proportions | |
Definition--Ratios, Proportions, and Percents Concepts--The Constant of Proportionality | The Constant of ProportionalityTopicRatios, Proportions, and Percents DefinitionThe constant of proportionality is the constant value that relates two proportional quantities. DescriptionThe constant of proportionality is a fundamental concept in mathematics, particularly in linear relationships and direct variation. For example, in the equation y = kx, k is the constant of proportionality that relates y and x. This concept is crucial in fields like physics, where it is used to describe relationships such as speed (distance/time). |
Proportions | |
Definition--Ratios, Proportions, and Percents Concepts--The Golden Ratio | The Golden RatioTopicRatios, Proportions, and Percents DefinitionThe Golden Ratio is a special number approximately equal to 1.618, often denoted by the Greek letter φ (phi), which appears in various aspects of art, architecture, and nature. |
Applications of Ratios, Proportions, and Percents and Ratios and Rates | |
Definition--Ratios, Proportions, and Percents Concepts--The Golden Ratio | The Golden RatioTopicRatios, Proportions, and Percents DefinitionThe Golden Ratio is a special number approximately equal to 1.618, often denoted by the Greek letter φ (phi), which appears in various aspects of art, architecture, and nature. |
Applications of Ratios, Proportions, and Percents and Ratios and Rates | |
Definition--Ratios, Proportions, and Percents Concepts--The Percent One Number Is of Another | The Percent One Number Is of AnotherTopicRatios, Proportions, and Percents DefinitionThe percent one number is of another is a way to express one number as a percentage of another number. DescriptionUnderstanding how to express one number as a percentage of another is crucial in various real-world applications, such as calculating discounts, tax, and interest rates. For example, if you want to find out what percentage 25 is of 200, you divide 25 by 200 and multiply by 100, resulting in 12.5%. |
Percents | |
Definition--Ratios, Proportions, and Percents Concepts--Unit Rate | Unit RateTopicRatios, Proportions, and Percents DefinitionA unit rate is a comparison of any two separate but related measurements when one of the measurements is reduced to a single unit. DescriptionUnit rates are commonly used in everyday life, such as calculating speed (miles per hour), cost per item, or efficiency (miles per gallon). For example, if a car travels 300 miles on 10 gallons of gas, the unit rate is 30 miles per gallon. |
Ratios and Rates | |
Definition--Ratios, Proportions, and Percents Concepts--Visual Models for Percents | Visual Models for PercentsTopicRatios, Proportions, and Percents DefinitionVisual models for percents are diagrams or illustrations that represent percentages to help visualize and understand them. DescriptionVisual models for percents are useful tools in various fields, such as education, finance, and statistics, to represent data and make it more comprehensible. For example, pie charts and bar graphs are common visual models that help illustrate percentages and proportions effectively. |
Percents | |
Definition--Ratios, Proportions, and Percents Concepts--Visualizing Equivalent Ratios | Visualizing Equivalent RatiosTopicRatios, Proportions, and Percents DefinitionVisualizing equivalent ratios involves using diagrams or models to show that two ratios are equivalent. DescriptionVisualizing equivalent ratios is important in fields such as mathematics and engineering, where understanding proportional relationships is crucial. For example, using a double number line or a ratio table can help illustrate that the ratios 2:3 and 4:6 are equivalent. |
Ratios and Rates | |
Definition--Ratios, Proportions, and Percents Concepts--Visualizing Ratios | Visualizing RatiosTopicRatios, Proportions, and Percents DefinitionVisualizing ratios involves using diagrams or models to represent and understand the relationship between two quantities. DescriptionVisualizing ratios is essential in various fields, such as mathematics, science, and economics, where understanding the relationship between quantities is crucial. For example, using a bar model or a double number line can help illustrate the ratio of 3:4. |
Ratios and Rates | |
Desmos Activity: Slope As Rate of Change | Desmos Activity: Slope As Rate of Change Use this activity to explore slope as a rate of change. In this Desmos activity, the slope of the line is the rate (cost per pound) for purchasing fruit. Students manipulate the slider for m to see the impact on the cost. |
Slope and Ratios and Rates | |
Desmos Activity: Slope As Rate of Change | Desmos Activity: Slope As Rate of Change Use this activity to explore slope as a rate of change. In this Desmos activity, the slope of the line is the rate (cost per pound) for purchasing fruit. Students manipulate the slider for m to see the impact on the cost. |
Slope and Ratios and Rates | |
Formulas--Converting Celsius to Fahrenheit | Formulas--Converting Celsius to Fahrenheit
The formula for the Converting Celsius to Fahrenheit. This is part of a collection of math formulas. To see the complete collection of formulas, click on this link. Note: The download is a JPG file.Related ResourcesTo see resources related to this topic click on the Related Resources tab above. |
Applications of Ratios, Proportions, and Percents, Proportions and Ratios and Rates | |
Formulas--Converting Days to Hours | Formulas--Converting Days to Hours
The formula for Converting Days to Hours. This is part of a collection of math formulas. To see the complete collection of formulas, click on this link. Note: The download is a JPG file.Related ResourcesTo see resources related to this topic click on the Related Resources tab above. |
Applications of Ratios, Proportions, and Percents, Proportions and Ratios and Rates | |
Formulas--Converting Days to Minutes | Formulas--Converting Days to Minutes
The formula for Converting Days to Minutes. This is part of a collection of math formulas. To see the complete collection of formulas, click on this link. Note: The download is a JPG file.Related ResourcesTo see resources related to this topic click on the Related Resources tab above. |
Applications of Ratios, Proportions, and Percents, Proportions and Ratios and Rates | |
Formulas--Converting Days to Seconds | Formulas--Converting Days to Seconds
The formula for Converting Days to Seconds. This is part of a collection of math formulas. To see the complete collection of formulas, click on this link. Note: The download is a JPG file.Related ResourcesTo see resources related to this topic click on the Related Resources tab above. |
Applications of Ratios, Proportions, and Percents, Proportions and Ratios and Rates | |
Formulas--Converting Degrees to Radians | Formulas--Converting Degrees to Radians
The formula for Converting Degrees to Radians. This is part of a collection of math formulas. To see the complete collection of formulas, click on this link. Note: The download is a JPG file.Related ResourcesTo see resources related to this topic click on the Related Resources tab above. |
Applications of Ratios, Proportions, and Percents, Proportions and Ratios and Rates | |
Formulas--Converting Fahrenheit to Celsius | Formulas--Converting Fahrenheit to Celsius
The formula for Converting Fahrenheit to Celsius. This is part of a collection of math formulas. To see the complete collection of formulas, click on this link. Note: The download is a JPG file.Related ResourcesTo see resources related to this topic click on the Related Resources tab above. |
Applications of Ratios, Proportions, and Percents, Proportions and Ratios and Rates | |
Formulas--Converting Hours to Minutes | Formulas--Converting Hours to Minutes
The formula for Converting Hours to Minutes. This is part of a collection of math formulas. To see the complete collection of formulas, click on this link. Note: The download is a JPG file.Related ResourcesTo see resources related to this topic click on the Related Resources tab above. |
Applications of Ratios, Proportions, and Percents, Proportions and Ratios and Rates | |
Formulas--Converting Hours to Seconds | Formulas--Converting Hours to Seconds
The formula for Converting Hours to Seconds. This is part of a collection of math formulas. To see the complete collection of formulas, click on this link. Note: The download is a JPG file.Related ResourcesTo see resources related to this topic click on the Related Resources tab above. |
Applications of Ratios, Proportions, and Percents, Proportions and Ratios and Rates | |
Formulas--Converting Minutes to Seconds | Formulas--Converting Minutes to Seconds
The formula for Converting Minutes to Seconds. This is part of a collection of math formulas. To see the complete collection of formulas, click on this link. Note: The download is a JPG file.Related ResourcesTo see resources related to this topic click on the Related Resources tab above. |
Applications of Ratios, Proportions, and Percents, Proportions and Ratios and Rates | |
Formulas--Converting Radians to Degrees | Formulas--Converting Radians to Degrees
The formula for Converting Radians to Degrees. This is part of a collection of math formulas. To see the complete collection of formulas, click on this link. Note: The download is a JPG file.Related ResourcesTo see resources related to this topic click on the Related Resources tab above. |
Applications of Ratios, Proportions, and Percents, Proportions and Ratios and Rates | |
Formulas--Converting Seconds to Days | Formulas--Converting Seconds to Days
The formula for Converting Seconds to Days. This is part of a collection of math formulas. To see the complete collection of formulas, click on this link. Note: The download is a JPG file.Related ResourcesTo see resources related to this topic click on the Related Resources tab above. |
Applications of Ratios, Proportions, and Percents, Proportions and Ratios and Rates | |
Formulas--Converting Seconds to Hours | Formulas--Converting Seconds to Hours
The formula for Converting Seconds to Hours. This is part of a collection of math formulas. To see the complete collection of formulas, click on this link. Note: The download is a JPG file.Related ResourcesTo see resources related to this topic click on the Related Resources tab above. |
Applications of Ratios, Proportions, and Percents, Proportions and Ratios and Rates | |
Formulas--Converting Seconds to Minutes | Formulas--Converting Seconds to Minutes
The formula for Converting Seconds to Minutes. This is part of a collection of math formulas. To see the complete collection of formulas, click on this link. Note: The download is a JPG file.Related ResourcesTo see resources related to this topic click on the Related Resources tab above. |
Applications of Ratios, Proportions, and Percents, Proportions and Ratios and Rates | |
Instructional Resource | Instructional Resource | Strategy Pack | Adding Fractions
Learn different strategies for adding fractions. The Strategy Packs provide alternate ways of solving the same problem, giving your students different approaches to the same problem. The goal of the Strategy Packs is to encourage your students to think strategically when solving math problems. —PRESS PREVIEW TO LAUNCH THE PRESENTATION— To see the complete collection of Instructional Resources, click on this link.Note: The download is a PPT file. |
Add and Subtract Fractions | |
Instructional Resource--Strategy Pack--Comparing Fractions | Instructional Resource | Strategy Pack | Comparing Fractions
Learn different strategies for comparing fractions. The Strategy Packs provide alternate ways of solving the same problem, giving your students different approaches to the same problem. The goal of the Strategy Packs is to encourage your students to think strategically when solving math problems. —PRESS PREVIEW TO LAUNCH THE PRESENTATION— To see the complete collection of Instructional Resources, click on this link.Note: The download is a PPT file. |
Compare and Order Fractions | |
Instructional Resource--Strategy Pack--One-Step Addition Equations | Instructional Resource | Strategy Pack | One-Step Addition Equations
Learn different strategies for solving one-step addition equations. The Strategy Packs provide alternate ways of solving the same problem, giving your students different approaches to the same problem. The goal of the Strategy Packs is to encourage your students to think strategically when solving math problems. —PRESS PREVIEW TO LAUNCH THE PRESENTATION— To see the complete collection of Instructional Resources, click on this link.Note: The download is a PPT file. |
Solving One-Step Equations | |
Instructional Resource--Strategy Pack--One-Step Multiplication Equations | Instructional Resource | Strategy Pack | One-Step Multiplication Equations
Learn different strategies for solving one-step multiplication equations. The Strategy Packs provide alternate ways of solving the same problem, giving your students different approaches to the same problem. The goal of the Strategy Packs is to encourage your students to think strategically when solving math problems. —PRESS PREVIEW TO LAUNCH THE PRESENTATION— To see the complete collection of Instructional Resources, click on this link.Note: The download is a PPT file. |
Solving One-Step Equations | |
Instructional Resource--Strategy Pack--Percent of a Number | Instructional Resource | Strategy Pack | Percent of a Number
Learn different strategies for finding the percent of a number. The Strategy Packs provide alternate ways of solving the same problem, giving your students different approaches to the same problem. The goal of the Strategy Packs is to encourage your students to think strategically when solving math problems. —PRESS PREVIEW TO LAUNCH THE PRESENTATION— To see the complete collection of Instructional Resources, click on this link.Note: The download is a PPT file. |
Percents | |
Instructional Resource--Strategy Pack--The Number That Is a Given Percent of Another Number | Instructional Resource | Strategy Pack | The Number Whose Percent Is Another Number
Learn different strategies for finding the number that is a given percentage of another number. The Strategy Packs provide alternate ways of solving the same problem, giving your students different approaches to the same problem. The goal of the Strategy Packs is to encourage your students to think strategically when solving math problems. —PRESS PREVIEW TO LAUNCH THE PRESENTATION— To see the complete collection of Instructional Resources, click on this link.Note: The download is a PPT file. |
Percents | |
Instructional Resource--Strategy Pack--The Percent One Number Is of Another | Instructional Resource | Strategy Pack | The Percent One Number Is of Another
Learn different strategies for finding the percent one number is of another. The Strategy Packs provide alternate ways of solving the same problem, giving your students different approaches to the same problem. The goal of the Strategy Packs is to encourage your students to think strategically when solving math problems. —PRESS PREVIEW TO LAUNCH THE PRESENTATION— To see the complete collection of Instructional Resources, click on this link.Note: The download is a PPT file. |
Percents | |
Instructional Resource--Strategy Pack--The Slope of a Line | Instructional Resource | Strategy Pack | The Slope of a Line
Learn different strategies for finding the slope of a line. The Strategy Packs provide alternate ways of solving the same problem, giving your students different approaches to the same problem. The goal of the Strategy Packs is to encourage your students to think strategically when solving math problems. —PRESS PREVIEW TO LAUNCH THE PRESENTATION— To see the complete collection of Instructional Resources, click on this link.Note: The download is a PPT file. |
Slope | |
Instructional Resource | Instructional Resource | Using the Unit Circle to Generate Trig Functions (Desmos)
In this tutorial, learn how to use the unit circle to generate trigonometric functions. —Click on Preview to see the tutorial— |
Trigonometric Functions | |
Instructional Resource--Strategy Pack--Percent One Number Is of Another | Instructional Resource | Strategy Pack | The Percent One Number Is of Another Learn different strategies for finding the percent one number is of another. The Strategy Packs provide alternate ways of solving the same problem, giving your students different approaches to the same problem. The goal of the Strategy Packs is to encourage your students to think strategically when solving math problems. —PRESS PREVIEW TO LAUNCH THE PRESENTATION—To see the complete collection of Instructional Resources, click on this link.Note: The download is a PPT file. |
Percents | |
INSTRUCTIONAL RESOURCE: Algebra Application: Cicada Cycles | INSTRUCTIONAL RESOURCE: Algebra Application: Cicada Cycles
In this Algebra Application, students study the life cycles of 13- and 17-year cicadas, as well as the populations of bird predators. Students develop a mathematical model using spreadsheets and investigate why the prime number life cycles help the cicadas. The math topics covered include: Mathematical modeling, Data gathering and analysis, Percent increase and decrease, Prime numbers and composites. This real world application of math concepts will engage your students. |
Applications of Ratios, Proportions, and Percents, Percents and Numerical Expressions | |
INSTRUCTIONAL RESOURCE: Algebra Application: Linear Functions: Circumference vs. Diameter | INSTRUCTIONAL RESOURCE: Algebra Application: Linear Functions: Circumference vs. Diameter
In this Algebra Application, students study the direction between diameter and circumference of a circle. Through measurement and data gathering students analyze the line of best fit and explore ways of calculating pi. The math topics covered include: Mathematical modeling, Linear functions, Data gathering and analysis, Ratios, Direct variation. This is a great back-to-school activity for middle school or high school students. This is also a great crossover activity that ties algebra and geometry. |
Applications of Linear Functions, Applications of Ratios, Proportions, and Percents and Applications of Circles | |
INSTRUCTIONAL RESOURCE: Algebra Application: Why Are Wildfires So Dangerous? | INSTRUCTIONAL RESOURCE: Algebra Application: Why Are Wildfires So Dangerous?
In this Algebra Application, students learn about wildfires and the measurement of air quality. The math topics covered include: Scientific notation, Rates, Density, Data Analysis. The specific focus of this investigation is the health hazards from wildfire smoke. This includes a discussion of air density, measurement in microns, and measurement of air quality. Links to various web sites, including the EPA's site, provide relevant background information and data. The culminating activity is a case study of the wildfires in the Lake Tahoe area. Students analyze historical data and make a recommendation on the air quality. This is a great back-to-school activity for middle school or high school students. A relevant real-world application allows them to review math concepts. |
Laws of Exponents and Applications of Ratios, Proportions, and Percents | |
INSTRUCTIONAL RESOURCE: Algebra Application: Why Are Wildfires So Dangerous? | INSTRUCTIONAL RESOURCE: Algebra Application: Why Are Wildfires So Dangerous?
In this Algebra Application, students learn about wildfires and the measurement of air quality. The math topics covered include: Scientific notation, Rates, Density, Data Analysis. The specific focus of this investigation is the health hazards from wildfire smoke. This includes a discussion of air density, measurement in microns, and measurement of air quality. Links to various web sites, including the EPA's site, provide relevant background information and data. The culminating activity is a case study of the wildfires in the Lake Tahoe area. Students analyze historical data and make a recommendation on the air quality. This is a great back-to-school activity for middle school or high school students. A relevant real-world application allows them to review math concepts. |
Laws of Exponents and Applications of Ratios, Proportions, and Percents | |
INSTRUCTIONAL RESOURCE: Tutorial: Strategies for Ordering Fractions | INSTRUCTIONAL RESOURCE: Tutorial: Strategies for Ordering Fractions
Learn various strategies for ordering fractions. These strategies include benchmark fractions, number lines, and equivalent fractions. Note: The download is a PDF file. This is part of a collection of math tutorials on a variety of math topics. To see the complete collection of these resources, click on this link.Library of Instructional ResourcesTo see the complete library of Instructional Resources , click on this link. |
Compare and Order Fractions and Find Equivalent Fractions | |
INSTRUCTIONAL RESOURCE: Tutorial: Strategies for Ordering Fractions | INSTRUCTIONAL RESOURCE: Tutorial: Strategies for Ordering Fractions
Learn various strategies for ordering fractions. These strategies include benchmark fractions, number lines, and equivalent fractions. Note: The download is a PDF file. This is part of a collection of math tutorials on a variety of math topics. To see the complete collection of these resources, click on this link.Library of Instructional ResourcesTo see the complete library of Instructional Resources , click on this link. |
Compare and Order Fractions and Find Equivalent Fractions | |
Interactive Math Game--DragNDrop--Counting Strategies | Interactive Math Game--DragNDrop Math--Arithmetic--Counting Strategies
In this drag-and-drop game, have students practice their Skip Counting and Counting On skills. This includes Skip Counting by 2's, 5's, and 10's. This game generates thousands of different combinations, offering an ideal opportunity for skill review in a game format. This is part of a collection of math games and interactives. To see the complete collection of the games, click on this link. Note: The download is the teacher's guide.Related ResourcesTo see additional resources on this topic, click on the Related Resources tab. |
Counting | |
Math Clip Art--3D Objects--Gear 1 | Math Clip Art--3D Objects--Gear 1
This collection of clip art images includes images of 3D figures and composite figures. |
Applications of Ratios, Proportions, and Percents and Proportions | |
Math Clip Art--3D Objects--Gear 2 | Math Clip Art--3D Objects--Gear 2
This collection of clip art images includes images of 3D figures and composite figures. |
Applications of Ratios, Proportions, and Percents and Proportions | |
Math Clip Art--3D Objects--Gear 3 | Math Clip Art--3D Objects--Gear 3
This collection of clip art images includes images of 3D figures and composite figures. |
Applications of Ratios, Proportions, and Percents and Proportions | |
Math Clip Art--Applications of Proportions--Exchange Rates 1 | Math Clip Art--Applications of Proportions--Exchange Rates 1 This is a collection of clip art images that show an application of proportional reasoning in the context of currency exchange rates. |
Ratios and Rates and Proportions | |
Math Clip Art--Applications of Proportions--Exchange Rates 1 | Math Clip Art--Applications of Proportions--Exchange Rates 1 This is a collection of clip art images that show an application of proportional reasoning in the context of currency exchange rates. |
Ratios and Rates and Proportions | |
Math Clip Art--Applications of Proportions--Exchange Rates 10 | Math Clip Art--Applications of Proportions--Exchange Rates 10 This is a collection of clip art images that show an application of proportional reasoning in the context of currency exchange rates. |
Ratios and Rates and Proportions |