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Illustrative Math-Media4Math Alignment

 

 

Illustrative Math Alignment: Grade 6 Unit 3

Unit Rates and Percentages

Lesson 9: Solving Rate Problems

Use the following Media4Math resources with this Illustrative Math lesson.

Thumbnail Image Title Body Curriculum Nodes
Definition--Ratios, Proportions, and Percents Concepts--Scale Drawing Definition--Ratios, Proportions, and Percents Concepts--Scale Drawing Scale Drawing

Topic

Ratios, Proportions, and Percents

Definition

A scale drawing is a representation of an object or structure with dimensions proportional to the actual object or structure.

Description

Scale 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 Definition--Ratios, Proportions, and Percents Concepts--Scale Factor Scale Factor

Topic

Ratios, Proportions, and Percents

Definition

A scale factor is a number that scales, or multiplies, some quantity.

Description

Scale 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 Definition--Ratios, Proportions, and Percents Concepts--Similar Figures Similar Figures

Topic

Ratios, Proportions, and Percents

Definition

Similar figures are figures that have the same shape but may differ in size; their corresponding angles are equal, and their corresponding sides are proportional.

Description

Similar 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 Definition--Ratios, Proportions, and Percents Concepts--Solving Proportions Solving Proportions

Topic

Ratios, Proportions, and Percents

Definition

Solving proportions involves finding the value of a variable that makes two ratios equal.

Description

Solving 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 Definition--Ratios, Proportions, and Percents Concepts--The Constant of Proportionality The Constant of Proportionality

Topic

Ratios, Proportions, and Percents

Definition

The constant of proportionality is the constant value that relates two proportional quantities.

Description

The 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 Definition--Ratios, Proportions, and Percents Concepts--The Golden Ratio The Golden Ratio

Topic

Ratios, Proportions, and Percents

Definition

The 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 Definition--Ratios, Proportions, and Percents Concepts--The Golden Ratio The Golden Ratio

Topic

Ratios, Proportions, and Percents

Definition

The 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 Definition--Ratios, Proportions, and Percents Concepts--The Percent One Number Is of Another The Percent One Number Is of Another

Topic

Ratios, Proportions, and Percents

Definition

The percent one number is of another is a way to express one number as a percentage of another number.

Description

Understanding 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 Definition--Ratios, Proportions, and Percents Concepts--Unit Rate Unit Rate

Topic

Ratios, Proportions, and Percents

Definition

A unit rate is a comparison of any two separate but related measurements when one of the measurements is reduced to a single unit.

Description

Unit 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 Definition--Ratios, Proportions, and Percents Concepts--Visual Models for Percents Visual Models for Percents

Topic

Ratios, Proportions, and Percents

Definition

Visual models for percents are diagrams or illustrations that represent percentages to help visualize and understand them.

Description

Visual 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 Definition--Ratios, Proportions, and Percents Concepts--Visualizing Equivalent Ratios Visualizing Equivalent Ratios

Topic

Ratios, Proportions, and Percents

Definition

Visualizing equivalent ratios involves using diagrams or models to show that two ratios are equivalent.

Description

Visualizing 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 Definition--Ratios, Proportions, and Percents Concepts--Visualizing Ratios Visualizing Ratios

Topic

Ratios, Proportions, and Percents

Definition

Visualizing ratios involves using diagrams or models to represent and understand the relationship between two quantities.

Description

Visualizing 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 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 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 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 Resources

To 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 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 Resources

To 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 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 Resources

To 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 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 Resources

To 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 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 Resources

To 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 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 Resources

To 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 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 Resources

To 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 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 Resources

To 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 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 Resources

To 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 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 Resources

To 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 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 Resources

To 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 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 Resources

To 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 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 Resources

To see resources related to this topic click on the Related Resources tab above.

Applications of Ratios, Proportions, and Percents, Proportions and Ratios and Rates
Strategy Packs 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
Strategy Packs 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
Strategy Packs 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
Strategy Packs 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
Strategy Packs 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
Strategy Pack 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
Strategy Pack 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
Strategy Pack 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
Math Tutorials 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
Strategy Pack 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 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 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? 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? 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 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 Resources

To 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 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 Resources

To see the complete library of Instructional Resources , click on this link.

Compare and Order Fractions and Find Equivalent Fractions
Interactive Math Game--DragNDrop Math--Arithmetic--Counting Strategies 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 Resources

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Counting
Math Clip Art: 3D Objects--Gear 1 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 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 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 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 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 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