Illustrative Math Alignment: Grade 7 Unit 2
Introducing Proportional Relationships
Lesson 15: Using Water Efficiently
Use the following Media4Math resources with this Illustrative Math lesson.
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Closed Captioned Video: Algebra Applications: Linear Functions, Segment 2: Cycling | Closed Captioned Video: Algebra Applications: Linear Functions, Segment 2: Cycling
Linear Expressions, Equations, and FunctionsLinear Expressions |
Special Functions and Applications of Linear Functions |
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Closed Captioned Video: Algebra Applications: Linear Functions, Segment 2: Cycling | Closed Captioned Video: Algebra Applications: Linear Functions, Segment 2: Cycling
Linear Expressions, Equations, and FunctionsLinear Expressions |
Special Functions and Applications of Linear Functions |
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Closed Captioned Video: Algebra Applications: Linear Functions | Closed Captioned Video: Algebra Applications: Linear Functions
Linear Expressions, Equations, and FunctionsLinear Expressions |
Special Functions and Applications of Linear Functions |
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Closed Captioned Video: Algebra Applications: Linear Functions | Closed Captioned Video: Algebra Applications: Linear Functions
Linear Expressions, Equations, and FunctionsLinear Expressions |
Special Functions and Applications of Linear Functions |
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Closed Captioned Video: Algebra Applications: Linear Functions, 1 | Closed Captioned Video: Algebra Applications: Linear Functions, Segment 1: Introduction
Linear Expressions, Equations, and FunctionsLinear Expres |
Special Functions and Applications of Linear Functions |
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Closed Captioned Video: Algebra Applications: Linear Functions, 1 | Closed Captioned Video: Algebra Applications: Linear Functions, Segment 1: Introduction
Linear Expressions, Equations, and FunctionsLinear Expres |
Special Functions and Applications of Linear Functions |
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Closed Captioned Video: Algebra Applications: Linear Functions, 3 | Closed Captioned Video: Algebra Applications: Linear Functions, Segment 3: Oil Exploration
Linear Expressions, Equations, and FunctionsLinear Exp |
Special Functions and Applications of Linear Functions |
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Closed Captioned Video: Algebra Applications: Linear Functions, 3 | Closed Captioned Video: Algebra Applications: Linear Functions, Segment 3: Oil Exploration
Linear Expressions, Equations, and FunctionsLinear Exp |
Special Functions and Applications of Linear Functions |
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Closed Captioned Video: Algebra Applications: Linear Functions, 4 | Closed Captioned Video: Algebra Applications: Linear Functions, Segment 4: Exercise
Linear Expressions, Equations, and FunctionsLinear Expression |
Special Functions and Applications of Linear Functions |
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Closed Captioned Video: Algebra Applications: Linear Functions, 4 | Closed Captioned Video: Algebra Applications: Linear Functions, Segment 4: Exercise
Linear Expressions, Equations, and FunctionsLinear Expression |
Special Functions and Applications of Linear Functions |
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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 |
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Closed Captioned Video: Ratios: Application of Ratios: Roofs and Ramps | Closed Captioned Video: Ratios: Application of Ratios: Roofs and RampsWhat 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 |
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Definition--Ratios, Proportions, and Percents Concepts--Calculating Tax | Calculating TaxTopicRatios, Proportions, and Percents DefinitionCalculating tax involves determining the percentage amount to be added to the base price of a product or service. DescriptionCalculating 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 |
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Definition--Ratios, Proportions, and Percents Concepts--Calculating Tips | Calculating TipsTopicRatios, Proportions, and Percents DefinitionCalculating tips involves determining the amount of money to give as a gratuity based on a percentage of the total bill. DescriptionCalculating 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 |
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Definition--Ratios, Proportions, and Percents Concepts--Dimensional Analysis | Dimensional AnalysisTopicRatios, Proportions, and Percents DefinitionDimensional analysis is a method used to convert one unit of measurement to another using conversion factors. DescriptionDimensional 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 |
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Definition--Ratios, Proportions, and Percents Concepts--Ratios in Simplest Form | Ratios in Simplest FormTopicRatios, Proportions, and Percents DefinitionRatios in simplest form are ratios that have been reduced to their smallest whole number terms. DescriptionReducing 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 |
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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 |
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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 |
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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 |
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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 |
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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 |
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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 |
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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 |
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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 |
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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 |
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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 |
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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 |
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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 |
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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 |
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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 |
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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 |
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INSTRUCTIONAL RESOURCE: Algebra Application: Creating an Exercise Chart | INSTRUCTIONAL RESOURCE: Algebra Application: Creating an Exercise Chart
In this Algebra Application, students develop a linear mathematical model based on the maximum heart rate during exercise based on age. Using this model, students investigate heart rate for moderate and vigorous workouts. The math topics covered include: Mathematical modeling, Linear functions, Families of functions, Computational thinking. The culminating activity is for students to create a simple program (using either a spreadsheet or a programming language like Python) to develop an exercise chart. 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. |
Applications of Linear Functions and Slope-Intercept Form |
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INSTRUCTIONAL RESOURCE: Algebra Application: Creating an Exercise Chart | INSTRUCTIONAL RESOURCE: Algebra Application: Creating an Exercise Chart
In this Algebra Application, students develop a linear mathematical model based on the maximum heart rate during exercise based on age. Using this model, students investigate heart rate for moderate and vigorous workouts. The math topics covered include: Mathematical modeling, Linear functions, Families of functions, Computational thinking. The culminating activity is for students to create a simple program (using either a spreadsheet or a programming language like Python) to develop an exercise chart. 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. |
Applications of Linear Functions and Slope-Intercept Form |
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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 |
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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 |
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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 |
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INSTRUCTIONAL RESOURCE: Algebra Application: When Will Space Travel Be Affordable? | INSTRUCTIONAL RESOURCE: Algebra Application: When Will Space Travel Be Affordable?
In this Algebra Application, students examine the budding industry of commercial space travel. Using data from the Bureau of Transportation Statistics, students build a mathematical model from historical airfare data. This model is used to predict when commercial space travel will become affordable. This also includes a discussion of inflation-adjusted costs and the future value of money. Topics covered: Mathematical modeling, Linear regression, Exponential functions, The time value of money. |
Applications of Exponential and Logarithmic Functions, Applications of Linear Functions and Data Analysis |
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INSTRUCTIONAL RESOURCE: Algebra Application: When Will Space Travel Be Affordable? | INSTRUCTIONAL RESOURCE: Algebra Application: When Will Space Travel Be Affordable?
In this Algebra Application, students examine the budding industry of commercial space travel. Using data from the Bureau of Transportation Statistics, students build a mathematical model from historical airfare data. This model is used to predict when commercial space travel will become affordable. This also includes a discussion of inflation-adjusted costs and the future value of money. Topics covered: Mathematical modeling, Linear regression, Exponential functions, The time value of money. |
Applications of Exponential and Logarithmic Functions, Applications of Linear Functions and Data Analysis |
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INSTRUCTIONAL RESOURCE: Algebra Application: When Will Space Travel Be Affordable? | INSTRUCTIONAL RESOURCE: Algebra Application: When Will Space Travel Be Affordable?
In this Algebra Application, students examine the budding industry of commercial space travel. Using data from the Bureau of Transportation Statistics, students build a mathematical model from historical airfare data. This model is used to predict when commercial space travel will become affordable. This also includes a discussion of inflation-adjusted costs and the future value of money. Topics covered: Mathematical modeling, Linear regression, Exponential functions, The time value of money. |
Applications of Exponential and Logarithmic Functions, Applications of Linear Functions and Data Analysis |
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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 |
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Instructional Resource: Applications of Linear Functions: Circumference vs. Diameter | In this Slide Show, apply concepts of linear functions to the context of circumference vs. diameter. Note: The download is a PPT file. Related ResourcesTo see the complete collection of Tutorials on this topic, click on this link: https://bit.ly/3g0P3cN |
Applications of Linear Functions |
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Instructional Resource: Applications of Linear Functions: Cost vs. Time | In this Slide Show, apply concepts of linear functions to the context of cost vs. time data and graphs. Note: The download is a PPT file. Related ResourcesTo see the complete collection of Tutorials on this topic, click on this link: https://bit.ly/3g0P3cN |
Applications of Linear Functions |
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Instructional Resource: Applications of Linear Functions: Cricket Chirps | In this Slide Show, apply concepts of linear functions to the context of cricket chirps. Note: The download is a PPT file. Related ResourcesTo see the complete collection of Tutorials on this topic, click on this link: https://bit.ly/3g0P3cN |
Applications of Linear Functions |
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Instructional Resource: Applications of Linear Functions: Distance vs. Time | In this Slide Show, apply concepts of linear functions to the context of distance vs. time data and graphs. Note: The download is a PPT file. Related ResourcesTo see the complete collection of Tutorials on this topic, click on this link: https://bit.ly/3g0P3cN |
Applications of Linear Functions |
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Instructional Resource: Applications of Linear Functions: Hooke's Law | In this Slide Show, apply concepts of linear functions to the context of Hooke's law. Note: The download is a PPT file. Related ResourcesTo see the complete collection of Tutorials on this topic, click on this link: https://bit.ly/3g0P3cN |
Applications of Linear Functions and Proportions |
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Instructional Resource: Applications of Linear Functions: Hooke's Law | In this Slide Show, apply concepts of linear functions to the context of Hooke's law. Note: The download is a PPT file. Related ResourcesTo see the complete collection of Tutorials on this topic, click on this link: https://bit.ly/3g0P3cN |
Applications of Linear Functions and Proportions |
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Instructional Resource: Applications of Linear Functions: Momentum and Impulse | In this Slide Show, apply concepts of linear functions to the context of momentum and impulse. Note: The download is a PPT file. Related ResourcesTo see the complete collection of Tutorials on this topic, click on this link: https://bit.ly/3g0P3cN |
Applications of Linear Functions |
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Instructional Resource: Applications of Linear Functions: Perimeter of a Rectangle | In this Slide Show, apply concepts of linear functions to the context of rectangular perimeter. Note: The download is a PPT file. Related ResourcesTo see the complete collection of Tutorials on this topic, click on this link: https://bit.ly/3g0P3cN |
Applications of Linear Functions |
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Instructional Resource: Applications of Linear Functions: Saving Money | In this Slide Show, apply concepts of linear functions to the context of saving money. Note: The download is a PPT file. Related ResourcesTo see the complete collection of Tutorials on this topic, click on this link: https://bit.ly/3g0P3cN |
Applications of Linear Functions |
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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 ResourcesTo see the complete collection of Tutorials on this topic, click on this link: https://bit.ly/3g0P3cN |
Applications of Linear Functions |
