Illustrative Math Alignment: Grade 7 Unit 2

Introducing Proportional Relationships

Lesson 14: Four Representations

Use the following Media4Math resources with this Illustrative Math lesson.

Title	Body	Curriculum Nodes
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	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	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	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	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 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 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 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 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 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	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	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	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	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	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	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	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	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	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	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	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	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	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	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	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	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	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	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	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	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
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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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