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Illustrative Math-Media4Math Alignment

 

 

Illustrative Math Alignment: Grade 6 Unit 3

Unit Rates and Percentages

Lesson 8: More about Constant Speed

Use the following Media4Math resources with this Illustrative Math lesson.

Thumbnail Image Title Body Curriculum Nodes
Closed Captioned Video: Algebra Applications: Inequalities, Segment 1: Hybrid Cars Closed Captioned Video: Algebra Applications: Inequalities, 1 Closed Captioned Video: Algebra Applications: Inequalities, Segment 1: Hybrid Cars

With the increasing demand worldwide for cars, the cost of gasoline continues to rise. The need for fuel-efficient cars makes hybrids a current favorite. An examination of the equations and inequalities that involve miles per gallon (mpg) for city and highway traffic reveals important information about hybrid cars and those with gasoline-powered engines. Students use the Graphs and Geometry features of the TI-Nspire.

Applications of Equations and Inequalities and Inequalities
Closed Captioned Video: Ratios and Rates: Converting Measurement Units Closed Captioned Video: Ratios and Rates: Converting Measurement Units Closed Captioned Video: Ratios and Rates: Converting Measurement Units

Video Tutorial: Ratios and Rates: Converting Measurement Units. In this video, we show how to use conversion rates to convert from one unit of measurement to another. Students are shown how to create a conversion rate.

Ratios and Rates
Closed Captioned Video: Ratios and Rates: Rates and Slopes of Lines Closed Captioned Video: Ratios and Rates: Rates and Slopes of Lines Closed Captioned Video: Ratios and Rates: Rates and Slopes of Lines

Video Tutorial: Ratios and Rates: Rates and Slopes of Lines. In this video we connect the concept of rate of change for a set of linear data to the concept of slope. We use the slope formula to find the rate of change.

Ratios and Rates
Closed Captioned Video: Ratios and Rates: Rates from Data Closed Captioned Video: Ratios and Rates: Rates from Data Closed Captioned Video: Ratios and Rates: Rates from Data

Video Tutorial: Ratios and Rates: Rates from Data. In this video, we look at linear data sets that can be used to find the rate of change.

Ratios and Rates
Closed Captioned Video: Ratios and Rates: Ratios as Decimals Closed Captioned Video: Ratios and Rates: Ratios as Decimals Closed Captioned Video: Ratios and Rates: Ratios as Decimals

Video Tutorial: Ratios and Rates: Ratios as Decimals. In this video, students explore ratios whose terms are decimals. Students are shown techniques for simplifying these types of ratios in ;the context of solving real-world ratio problems.

Ratios and Rates
Closed Captioned Video: Ratios, Proportions, and Percents: Calculating Percents Closed Captioned Video: Ratios, Proportions, and Percents: Calculating Percents Closed Captioned Video: Ratios, Proportions, and Percents: Calculating Percents

Video Tutorial: Ratios and Percents: Calculating Percents. In this video, students will see the relationship between ratios, proportions, and percents. A percent formula is derived and used to solve several real-world percent problems.

Ratios and Rates
Closed Captioned Video: Ratios: Unit Rates Closed Captioned Video: Ratios: Unit Rates Closed Captioned Video: Ratios: Unit Rates

What Are Ratios?

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

Ratios and Rates
Closed Captioned Video: Ratios: Visual Models for Ratios and Percents Closed Captioned Video: Ratios: Visual Models for Ratios and Percents Closed Captioned Video: Ratios: Visual Models for Ratios and Percents

What Are Ratios?

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

Ratios and Rates
Definition--Measures of Central Tendency--Average Speed Definition--Measures of Central Tendency--Average Speed Average Speed

Topic

Statistics

Definition

Average speed is the total distance traveled divided by the total time taken.

Description

This concept finds application in areas such as physics, transport, and everyday scenarios like calculating travel time. For example, if a car travels 300 km in 3 hours, the average speed is Average Speed = 300 km / 3 hours = 100 km/h. Understanding average speed is key in mathematics as it helps contextualize rate and distance problems in real-life situations.

Data Analysis
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--Converting Units Definition--Ratios, Proportions, and Percents Concepts--Converting Units Converting Units

Topic

Ratios, Proportions, and Percents

Definition

Converting units involves changing a measurement from one unit to another using a conversion factor.

Description

Converting units is essential in various fields such as science, engineering, and everyday life. It involves using ratios and proportions to switch between different measurement systems, such as converting inches to centimeters or gallons to liters.

For example, to convert 5 miles to kilometers, knowing that 1 mile is approximately 1.60934 kilometers, you multiply 

5 × 1.60934 = 8.0467 kilometers

Ratios and Rates
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--Equivalent Ratios Definition--Ratios, Proportions, and Percents Concepts--Equivalent Ratios Equivalent Ratios

Topic

Ratios, Proportions, and Percents

Definition

Equivalent ratios are ratios that express the same relationship between quantities.

Description

Equivalent ratios are fundamental in understanding proportions and scaling in mathematics. They represent the same relationship between quantities, even though the numbers themselves may differ. This concept is crucial in various applications, such as cooking, map reading, and creating models.

For instance, the ratios 2:3 and 4:6 are equivalent because they both simplify to the same ratio when reduced.

Ratios and Rates
Definition--Ratios, Proportions, and Percents Concepts--Part-to-Part Ratios Definition--Ratios, Proportions, and Percents Concepts--Part-to-Part Ratios Part-to-Part Ratios

Topic

Ratios, Proportions, and Percents

Definition

Part-to-part ratios compare different parts of a whole to each other.

Description

Part-to-part ratios are used to compare different parts of a whole, providing a way to understand the relationship between different components. This type of ratio is essential in fields such as statistics, biology, and economics.

For example, if a class has 10 boys and 15 girls, the part-to-part ratio of boys to girls is 10:15, which simplifies to 2:3.

Ratios and Rates
Definition--Ratios, Proportions, and Percents Concepts--Part-to-Whole Ratios Definition--Ratios, Proportions, and Percents Concepts--Part-to-Whole Ratios Part-to-Whole Ratios

Topic

Ratios, Proportions, and Percents

Definition

Part-to-whole ratios compare one part of a whole to the entire whole. These ratios are more commonly known as fractions.

Description

Part-to-whole ratios are used to compare a part of a whole to the entire whole, providing insights into the composition of a dataset or population. This type of ratio, more commonly referred to as fractions, is widely used in statistics, finance, and everyday decision-making.

Ratios and Rates
Definition--Ratios, Proportions, and Percents Concepts--Percent Definition--Ratios, Proportions, and Percents Concepts--Percent Percent

Topic

Ratios, Proportions, and Percents

Definition

A percent is a ratio that compares a number to 100.

Description

Percentages are a fundamental concept in mathematics, representing a ratio out of 100. They are used in various applications, including finance, statistics, and everyday calculations such as discounts and interest rates.

For example, if you score 45 out of 50 on a test, your percentage score is 

(45/50) × 100 = 90%

Percents
Definition--Ratios, Proportions, and Percents Concepts--Percent Decrease Definition--Ratios, Proportions, and Percents Concepts--Percent Decrease Percent Decrease

Topic

Ratios, Proportions, and Percents

Definition

Percent decrease measures the reduction in value expressed as a percentage of the original value.

Description

Percent decrease is used to quantify the reduction in value over time, expressed as a percentage of the original value. It is commonly used in finance, economics, and everyday scenarios such as price reductions and weight loss.

For example, if the price of a jacket drops from $80 to $60, the percent decrease is calculated as 

(80 − 60)/80 × 100 = 25%.

Percents
Definition--Ratios, Proportions, and Percents Concepts--Percent Increase Definition--Ratios, Proportions, and Percents Concepts--Percent Increase Percent Increase

Topic

Ratios, Proportions, and Percents

Definition

Percent increase measures the growth in value expressed as a percentage of the original value.

Description

Percent increase is used to quantify the growth in value over time, expressed as a percentage of the original value. It is commonly used in finance, economics, and everyday scenarios such as salary increases and population growth.

For example, if the price of a stock rises from \$50 to \$75, the percent increase is calculated as 

(75 − 50)/50 × 100 = 50%

Percents
Definition--Ratios, Proportions, and Percents Concepts--Percent of a Number Definition--Ratios, Proportions, and Percents Concepts--Percent of a Number Percent of a Number

Topic

Ratios, Proportions, and Percents

Definition

Percent of a number involves calculating the amount represented by a certain percentage of that number.

Description

Understanding percentages is crucial for working with finances, statistics, and data analysis. For instance, to find 20% of 50, multiply 50 by 0.20, resulting in 10. Likewise, it's important for everyday scenarios, such as calculating discounts during shopping.

Percents
Definition--Ratios, Proportions, and Percents Concepts--Percent of an Unknown Definition--Ratios, Proportions, and Percents Concepts--Percent of an Unknown Percent of an Unknown

Topic

Ratios, Proportions, and Percents

Definition

Percent of an unknown refers to solving for an unknown quantity when given a percentage of that quantity.

Description

Knowing how to find a percentage of an unknown variable is essential for solving equations in algebra. This concept appears in various situations, such as when determining discounts or portions of a total amount.

For instance, if 20% of an unknown number equals 15, you can set up the equation: 

0.20x = 15

Percents
Definition--Ratios, Proportions, and Percents Concepts--Percents as Decimals Definition--Ratios, Proportions, and Percents Concepts--Percents as Decimals Percents as Decimals

Topic

Ratios, Proportions, and Percents

Definition

Percents as decimals involve converting a percentage into its decimal representation.

Description

Converting percents to decimals is a key skill in mathematics, allowing students to perform calculations involving percentages more easily. To convert, divide the percent by 100.

For example, 75% as a decimal is 0.75, calculated by dividing 75 by 100. This conversion is useful in many contexts, such as finance, where calculations are conducted using decimal values. Mastering this concept enables students to approach real-world problems with greater confidence and accuracy.

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

Topic

Ratios, Proportions, and Percents

Definition

A proportion is an equation that states that two ratios are equal.

Description

Understanding proportions is essential in mathematics, as it is used to solve problems involving ratios and fractions. Proportions are commonly seen in real-world applications such as cooking, map measurements, and scale models.

To illustrate, if there are 2 apples for every 3 oranges, the proportion can be expressed as 2:3. Solving proportions involves finding and solving an equivalent ratio.

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

Topic

Ratios, Proportions, and Percents

Definition

Proportional refers to the relationship between two quantities where their ratio is constant.

Description

Proportional relationships are fundamental in mathematics and science, describing how one quantity changes in relation to another. This concept is used in various fields, including physics, economics, and engineering.

For example, if the speed of a car is proportional to the time it travels, doubling the time will double the distance covered. Understanding proportionality helps students solve complex problems and apply mathematical reasoning in real-world situations.

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

Topic

Ratios, Proportions, and Percents

Definition

A rate is a ratio that compares two quantities with different units.

Description

Rates are used to compare different quantities, such as speed (miles per hour) or price (cost per item). Understanding rates is essential for interpreting data and making informed decisions in various contexts, such as travel and budgeting.

For instance, if a car travels 60 miles in 2 hours, the rate is 30 miles per hour. Learning about rates helps students analyze real-world situations and apply mathematical reasoning to everyday problems.

Ratios and Rates
Definition--Ratios, Proportions, and Percents Concepts--Ratio Definition--Ratios, Proportions, and Percents Concepts--Ratio Ratio

Topic

Ratios, Proportions, and Percents

Definition

A ratio is a comparison of two quantities by division.

Description

Ratios are used to express the relationship between two quantities, providing a way to compare different amounts. They are fundamental in various fields, including mathematics, science, and finance.

For example, the ratio of 4 to 5 can be written as 4:5 or 4/5. Understanding ratios helps students analyze data, solve problems, and make informed decisions in real-world situations.

Ratios and Rates
Definition--Ratios, Proportions, and Percents Concepts--Ratios and Fractions Definition--Ratios, Proportions, and Percents Concepts--Ratios and Fractions Ratios and Fractions

Topic

Ratios, Proportions, and Percents

Definition

Ratios and fractions are both ways of comparing quantities, with fractions representing a part of a whole.

Description

Understanding the connection between ratios and fractions is crucial for solving problems involving proportions and scaling. Ratios can be expressed as fractions, providing a way to understand the relationship between quantities. A fraction is a part-whole ratio.

Ratios and Rates
Definition--Ratios, Proportions, and Percents Concepts--Ratios and Slope Definition--Ratios, Proportions, and Percents Concepts--Ratios and Slope Ratios and Slope

Topic

Ratios, Proportions, and Percents

Definition

The slope of a line is a ratio that represents the change in y over the change in x.

Description

Understanding the relationship between ratios and slope is essential for interpreting graphs and solving problems in algebra and geometry. The slope is a measure of how steep a line is, calculated as the ratio of the vertical change to the horizontal change between two points.

For example, if a line rises 2 units for every 3 units it runs horizontally, the slope is 2/3. This concept is crucial for understanding linear relationships and analyzing data in various fields.

Ratios and Rates
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--Ratios with Decimals Definition--Ratios, Proportions, and Percents Concepts--Ratios with Decimals Ratios with Decimals

Topic

Ratios, Proportions, and Percents

Definition

Ratios with decimals involve comparing two quantities where one or both of the quantities are represented as decimal numbers.

Description

Ratios with decimals are crucial in various real-world applications, particularly in financial calculations, engineering, and scientific measurements. For instance, when calculating financial ratios such as the price-to-earnings ratio, decimals are often involved. Understanding how to work with these ratios allows for more precise and meaningful comparisons.

Ratios and Rates
Definition--Ratios, Proportions, and Percents Concepts--Ratios with Fractions Definition--Ratios, Proportions, and Percents Concepts--Ratios with Fractions Ratios with Fractions

Topic

Ratios, Proportions, and Percents

Definition

Ratios with fractions compare two quantities where one or both of the quantities are fractions.

Description

Ratios with fractions are essential in various mathematical and real-world contexts, such as cooking, where ingredients are often measured in fractions. Understanding these ratios allows for accurate scaling of recipes or other measurements. For example, if a recipe calls for 1/2 cup of sugar to 1/4 cup of butter, the ratio is 1/2:1/4, which simplifies to 2:1 by multiplying both terms by 4.

Ratios and Rates
Definition--Ratios, Proportions, and Percents Concepts--Ratios with Percents Definition--Ratios, Proportions, and Percents Concepts--Ratios with Percents Ratios with Percents

Topic

Ratios, Proportions, and Percents

Definition

Ratios with percents involve comparing quantities where one or both of the quantities are expressed as percentages.

Description

Ratios with percents are widely used in various fields, including finance, statistics, and everyday life. For example, when comparing interest rates, growth rates, or discount rates, percentages are often used. Understanding these ratios allows for better financial decision-making and data analysis.

Ratios and Rates
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 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
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
PowerPointPresentations.jpg Instructional Resource: Applications of Linear Functions: Speed and acceleration

In this Slide Show, apply concepts of linear functions to the context of speed and acceleration.

Note: The download is a PPT file.

Related Resources

To see the complete collection of Tutorials on this topic, click on this link: https://bit.ly/3g0P3cN
Applications of Linear Functions
Math Clip Art--Applications of Linear and Quadratic Functions: Speed and Acceleration, Image1 Math Clip Art--Applications of Linear and Quadratic Functions: Speed and Acceleration 01 Math Clip Art--Applications of Linear and Quadratic Functions: Speed and Acceleration 01

Topic

Quadratics

Description

This image features a vintage car in motion with a blurred background, emphasizing speed. It serves as an introduction to the series on speed and acceleration in linear and quadratic functions. The image visually represents the concept of speed through motion blur, making it relatable for students learning about linear functions. By using this image, teachers can engage students with real-world applications of mathematical concepts.

Graphs of Linear Functions and Graphs of Quadratic Functions
Math Clip Art--Applications of Linear and Quadratic Functions: Speed and Acceleration, Image 2 Math Clip Art--Applications of Linear and Quadratic Functions: Speed and Acceleration 02 Math Clip Art--Applications of Linear and Quadratic Functions: Speed and Acceleration 02

Topic

Quadratics

Description

This image depicts a yellow car alongside a table that shows time in seconds and distance in feet, illustrating a constant speed of 88 ft/sec (60 mph). The table provides a clear example of how linear functions can represent constant speeds. Teachers can use this image to demonstrate the relationship between time, distance, and speed, reinforcing the concept of constant rates within linear functions.

Graphs of Linear Functions and Graphs of Quadratic Functions
Math Clip Art--Applications of Linear and Quadratic Functions: Speed and Acceleration, Image 3 Math Clip Art--Applications of Linear and Quadratic Functions: Speed and Acceleration 03 Math Clip Art--Applications of Linear and Quadratic Functions: Speed and Acceleration 03

Topic

Quadratics

Description

This image is a variation of the previous image that highlights the common difference as the rate of speed. It builds on the previous example by emphasizing how the common difference (88 ft/sec) serves as the rate in linear equations. This visual representation helps students grasp how mathematical differences translate into real-world speeds.

Graphs of Linear Functions and Graphs of Quadratic Functions
Math Clip Art--Applications of Linear and Quadratic Functions: Speed and Acceleration, Image 4 Math Clip Art--Applications of Linear and Quadratic Functions: Speed and Acceleration 04 Math Clip Art--Applications of Linear and Quadratic Functions: Speed and Acceleration 04

Topic

Quadratics

Description

This image presents a table with time in seconds and distance in feet, accompanied by a graph illustrating a linear relationship between time and distance. The constant increase of 88 feet per second is depicted as the slope of the Distance-vs-Time linear function graph. This visual aids students in understanding how linear functions can model real-world speed scenarios.

Graphs of Linear Functions and Graphs of Quadratic Functions