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Illustrative Math-Media4Math Alignment

 

 

Illustrative Math Alignment: Grade 7 Unit 1

Scale Drawings

Lesson 13: Draw It to Scale

Use the following Media4Math resources with this Illustrative Math lesson.

Thumbnail Image Title Body Curriculum Nodes
Closed Captioned Video: Algebra Applications: Variables and Equations, Segment 3: River Ratios Closed Captioned Video: Algebra Applications: Variables and Equations, 3 Closed Captioned Video: Algebra Applications: Variables and Equations, Segment 3: River Ratios

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, Variables and Unknowns, Variable Expressions and Applications of Ratios, Proportions, and Percents
Closed Captioned Video: Ratios: Application of Ratios: Roofs and Ramps Closed Captioned Video: Ratios: Application of Ratios: Roofs and Ramps Closed Captioned Video: Ratios: Application of Ratios: Roofs and Ramps

What Are Ratios?

A ratio is the relationship between two or more quantities among a group of items. Let's look at an example.

Ratios and Rates and Applications of Ratios, Proportions, and Percents
Definition--Ratios, Proportions, and Percents Concepts--Calculating Tax Definition--Ratios, Proportions, and Percents Concepts--Calculating Tax Calculating Tax

Topic

Ratios, Proportions, and Percents

Definition

Calculating tax involves determining the percentage amount to be added to the base price of a product or service.

Description

Calculating tax is a fundamental application of percentages in real-world scenarios. When purchasing goods or services, the total cost is often the sum of the base price and the tax applied. Understanding how to calculate tax is essential for budgeting and financial literacy.

For example, if a product costs $50 and the tax rate is 8%, the tax amount is calculated as 

50 × 0.08 = 4

Therefore, the total cost is 

Applications of Ratios, Proportions, and Percents
Definition--Ratios, Proportions, and Percents Concepts--Calculating Tips Definition--Ratios, Proportions, and Percents Concepts--Calculating Tips Calculating Tips

Topic

Ratios, Proportions, and Percents

Definition

Calculating tips involves determining the amount of money to give as a gratuity based on a percentage of the total bill.

Description

Calculating tips is a common use of percentages in everyday life, particularly in service industries such as dining. Tips are usually calculated as a percentage of the total bill, and understanding how to compute this is important for both customers and service providers. 

For instance, if a meal costs $80 and you want to leave a 15% tip, the tip amount is calculated as 

80 × 0.15 = 12

Applications of Ratios, Proportions, and Percents
Definition--Ratios, Proportions, and Percents Concepts--Dimensional Analysis Definition--Ratios, Proportions, and Percents Concepts--Dimensional Analysis Dimensional Analysis

Topic

Ratios, Proportions, and Percents

Definition

Dimensional analysis is a method used to convert one unit of measurement to another using conversion factors.

Description

Dimensional analysis is a powerful tool in mathematics and science for converting units and solving problems involving measurements. It uses the principle of multiplying by conversion factors to ensure that units cancel out appropriately, leading to the desired unit.

For example, to convert 50 meters per second to kilometers per hour, you use the conversion factors  1 meter = 0.001 kilometers and 1 hour = 3600 seconds: 

Applications of Ratios, Proportions, and Percents
Definition--Ratios, Proportions, and Percents Concepts--Ratios in Simplest Form Definition--Ratios, Proportions, and Percents Concepts--Ratios in Simplest Form Ratios in Simplest Form

Topic

Ratios, Proportions, and Percents

Definition

Ratios in simplest form are ratios that have been reduced to their smallest whole number terms.

Description

Reducing ratios to their simplest form is similar to the process of simplifying fractions, making it easier to compare and interpret data. A ratio is in simplest form when the greatest common divisor of the terms is 1.

For example, the ratio 8:12 simplifies to 2:3 by dividing both terms by their greatest common divisor, 4. This skill is essential for solving problems involving proportions and understanding relationships between quantities.

Applications of Ratios, Proportions, and Percents
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
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

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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

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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

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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

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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
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
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
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.

Note: The download is a PPT file.

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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 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.

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
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: Ratios: Application of Ratios: Roofs and Ramps Video Transcript: Ratios: Application of Ratios: Roofs and Ramps Video Transcript: Ratios: 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
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
VIDEO: Algebra Applications: Variables and Equations, Segment 3: River Ratios. VIDEO: Algebra Applications: Variables and Equations, 3 VIDEO: Algebra Applications: Variables and Equations, Segment 3: River Ratios.

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.

This is part of a collection of videos from the Algebra Applications video series on the topic of Variables and Equations.

Applications of Equations and Inequalities, Variables and Unknowns, Variable Expressions and Applications of Ratios, Proportions, and Percents