Illustrative Math Alignment: Grade 7 Unit 4

Proportional Relationships and Percentages

Lesson 3: Revisiting Proportional Relationships

Use the following Media4Math resources with this Illustrative Math lesson.

Title	Body	Curriculum Nodes
Math Clip Art--Ratios, Proportions, Percents--Rates 02	Math Clip Art--Ratios, Proportions, Percents--Rates 02 Topic Ratios, Proportions, and Percents Description The image depicts a gas station with the formula Rate = a / b, where b ≠ 0, defining rate as a ratio of two different units. It introduces the formal definition of rates, providing a foundation for subsequent examples that apply this definition in real-world contexts. Ratios, Proportions, and Percents focuses on understanding and applying the concept of rates, which are comparisons of two quantities with different units.	Ratios and Rates
Math Clip Art--Ratios, Proportions, Percents--Rates 03	Math Clip Art--Ratios, Proportions, Percents--Rates 03 Topic Ratios, Proportions, and Percents Description The image shows a car at a gas station with the formula Speed = Distance / Time, explaining speed as a specific example of rate. It connects the abstract concept of rates to a concrete example (speed), making the topic relatable and easier to understand. Ratios, Proportions, and Percents focuses on understanding and applying the concept of rates, which are comparisons of two quantities with different units.	Ratios and Rates
Math Clip Art--Ratios, Proportions, Percents--Rates 04	Math Clip Art--Ratios, Proportions, Percents--Rates 04 Topic Ratios, Proportions, and Percents Description The image highlights a gasoline pump with the formula Rate = Dollars / Gallon, illustrating the cost of gasoline as an example of rate. It applies the concept of rates to another common scenario, reinforcing the idea of rates in daily life and extending understanding from speed to cost per unit. Ratios, Proportions, and Percents focuses on understanding and applying the concept of rates, which are comparisons of two quantities with different units.	Ratios and Rates
Math Clip Art--Ratios, Proportions, Percents--Rates 05	Math Clip Art--Ratios, Proportions, Percents--Rates 05 Topic Ratios, Proportions, and Percents Description The image depicts a car with the formula Fuel Efficiency Rate = Miles / Gallon, explaining how fuel efficiency is measured as a rate. It introduces a third example of rates, connecting to environmental and economic considerations, and further solidifying understanding. Ratios, Proportions, and Percents focuses on understanding and applying the concept of rates, which are comparisons of two quantities with different units.	Ratios and Rates
Math Clip Art--Ratios, Proportions, Percents--Rates 06	Math Clip Art--Ratios, Proportions, Percents--Rates 06 Topic Ratios, Proportions, and Percents Description The image shows a fruit market with the formula Rate = Dollars / Pound, illustrating the cost of fruits and vegetables per unit weight. It expands the application of rates to another familiar scenario, demonstrating versatility in its use across contexts. Ratios, Proportions, and Percents focuses on understanding and applying the concept of rates, which are comparisons of two quantities with different units.	Ratios and Rates
Math Clip Art--Ratios, Proportions, Percents--Rates 07	Math Clip Art--Ratios, Proportions, Percents--Rates 07 Topic Ratios, Proportions, and Percents Description The image shows a carton of eggs priced at $4 a dozen, defining a unit rate where b = 1, expressed as whole numbers or decimals. It introduces the concept of unit rates, a special type of rate, laying the groundwork for calculations in subsequent images. Ratios, Proportions, and Percents focuses on understanding and applying the concept of rates, which are comparisons of two quantities with different units.	Ratios and Rates
Math Clip Art--Ratios, Proportions, Percents--Rates 08	Math Clip Art--Ratios, Proportions, Percents--Rates 08 Topic Ratios, Proportions, and Percents Description The image features lemons priced at $2.50 for 5, with the calculation Unit Rate = 2.50 / 5 = 0.50 per lemon. It provides a step-by-step calculation of unit rates, reinforcing the concept introduced earlier with practical application. Ratios, Proportions, and Percents focuses on understanding and applying the concept of rates, which are comparisons of two quantities with different units.	Ratios and Rates
Math Clip Art--Ratios, Proportions, Percents--Rates 09	Math Clip Art--Ratios, Proportions, Percents--Rates 09 Topic Ratios, Proportions, and Percents Description The image illustrates the cost of 5 pounds of ground beef at $15.75, with the calculation Unit Rate = 15.75 / 5 = 3.25 per pound. It demonstrates another example of calculating unit rates, solidifying the learner's ability to perform similar calculations. Ratios, Proportions, and Percents focuses on understanding and applying the concept of rates, which are comparisons of two quantities with different units.	Ratios and Rates
Math Clip Art--Ratios, Proportions, Percents--Rates 10	Math Clip Art--Ratios, Proportions, Percents--Rates 10 Topic Ratios, Proportions, and Percents Description The image shows a runner covering 8 miles in 1.25 hours, with the calculation Speed = 8 / 1.25 = 6.4 miles/hour. It reinforces the speed example from earlier, providing another opportunity to apply the concept of rates to motion. Ratios, Proportions, and Percents focuses on understanding and applying the concept of rates, which are comparisons of two quantities with different units.	Ratios and Rates
Math Clip Art--Ratios, Proportions, Percents--Ratios 01	Math Clip Art--Ratios, Proportions, Percents--Ratios 01 Topic Ratios, Proportions, and Percents Description This image establishes the mathematical foundation for understanding ratios with an iconic example. Ratios, Proportions, and Percents is a fundamental concept in mathematics that helps students understand proportional reasoning, scaling, and comparative analysis. These examples provide a bridge between abstract mathematical principles and real-world applications, helping students grasp the utility of ratios.	Ratios and Rates
Math Clip Art--Ratios, Proportions, Percents--Ratios 02	Math Clip Art--Ratios, Proportions, Percents--Ratios 02 Topic Ratios, Proportions, and Percents Description Definition of a ratio as a relationship between two quantities using sports balls. It introduces the concept of ratios in an accessible and relatable way. Ratios, Proportions, and Percents is a fundamental concept in mathematics that helps students understand proportional reasoning, scaling, and comparative analysis. These examples provide a bridge between abstract mathematical principles and real-world applications, helping students grasp the utility of ratios.	Ratios and Rates
Math Clip Art--Ratios, Proportions, Percents--Ratios 03	Math Clip Art--Ratios, Proportions, Percents--Ratios 03 Topic Ratios, Proportions, and Percents Description Visual example of ratios using soccer balls and basketballs, expressed as 5:2, 5 to 2, and 5 / 2. Illustrates how ratios can be represented in multiple formats. Ratios, Proportions, and Percents is a fundamental concept in mathematics that helps students understand proportional reasoning, scaling, and comparative analysis. These examples provide a bridge between abstract mathematical principles and real-world applications, helping students grasp the utility of ratios.	Ratios and Rates
Math Clip Art--Ratios, Proportions, Percents--Ratios 04	Math Clip Art--Ratios, Proportions, Percents--Ratios 04 Topic Ratios, Proportions, and Percents Description A table summarizing different ratios derived from the group of balls, e.g., soccer to baseball or soccer to basketball. Shows how to systematically calculate and organize ratios from a dataset. Ratios, Proportions, and Percents is a fundamental concept in mathematics that helps students understand proportional reasoning, scaling, and comparative analysis. These examples provide a bridge between abstract mathematical principles and real-world applications, helping students grasp the utility of ratios.	Ratios and Rates
Math Clip Art--Ratios, Proportions, Percents--Ratios 05	Math Clip Art--Ratios, Proportions, Percents--Ratios 05 Topic Ratios, Proportions, and Percents Description Simplification of ratios in the table, e.g., 4 / 2 becomes 2 / 1. Highlights the importance of simplifying ratios for clarity and consistency. Ratios, Proportions, and Percents is a fundamental concept in mathematics that helps students understand proportional reasoning, scaling, and comparative analysis. These examples provide a bridge between abstract mathematical principles and real-world applications, helping students grasp the utility of ratios.	Ratios and Rates
Math Clip Art--Ratios, Proportions, Percents--Ratios 06	Math Clip Art--Ratios, Proportions, Percents--Ratios 06 Topic Ratios, Proportions, and Percents Description Application of ratios to geometric shapes (circles, triangles, hexagons) with a table of ratios. Extends the concept of ratios to other objects, demonstrating versatility. Ratios, Proportions, and Percents is a fundamental concept in mathematics that helps students understand proportional reasoning, scaling, and comparative analysis. These examples provide a bridge between abstract mathematical principles and real-world applications, helping students grasp the utility of ratios.	Ratios and Rates
Math Clip Art--Ratios, Proportions, Percents--Ratios 07	Math Clip Art--Ratios, Proportions, Percents--Ratios 07 Topic Ratios, Proportions, and Percents Description Simplified ratios in the table for geometric shapes. Reinforces the practice of simplifying ratios for better comprehension. Ratios, Proportions, and Percents is a fundamental concept in mathematics that helps students understand proportional reasoning, scaling, and comparative analysis. These examples provide a bridge between abstract mathematical principles and real-world applications, helping students grasp the utility of ratios.	Ratios and Rates
Math Clip Art--Ratios, Proportions, Percents--Ratios 08	Math Clip Art--Ratios, Proportions, Percents--Ratios 08 Topic Ratios, Proportions, and Percents Description Example of a three-term ratio (Red : Yellow : Blue = 6 : 4 : 3) using lollipops. Expands understanding of ratios to include three quantities. Ratios, Proportions, and Percents is a fundamental concept in mathematics that helps students understand proportional reasoning, scaling, and comparative analysis. These examples provide a bridge between abstract mathematical principles and real-world applications, helping students grasp the utility of ratios.	Ratios and Rates
Math Clip Art--Ratios, Proportions, Percents--Ratios 09	Math Clip Art--Ratios, Proportions, Percents--Ratios 09 Topic Ratios, Proportions, and Percents Description Three-term ratios applied to a recipe: Flour : Sugar : Milk = 3 : 2 : 1. Connects ratios to real-world applications, specifically in cooking. Ratios, Proportions, and Percents is a fundamental concept in mathematics that helps students understand proportional reasoning, scaling, and comparative analysis. These examples provide a bridge between abstract mathematical principles and real-world applications, helping students grasp the utility of ratios.	Ratios and Rates
Math Clip Art--Ratios, Proportions, Percents--Ratios 10	Math Clip Art--Ratios, Proportions, Percents--Ratios 10 Topic Ratios, Proportions, and Percents Description Fractions in ratios: Milk to Water = 1/4 : 1/2, simplified to 1 : 2. Demonstrates handling fractional ratios and simplifying them to whole numbers. Ratios, Proportions, and Percents is a fundamental concept in mathematics that helps students understand proportional reasoning, scaling, and comparative analysis. These examples provide a bridge between abstract mathematical principles and real-world applications, helping students grasp the utility of ratios.	Ratios and Rates
Math Clip Art--Ratios, Proportions, Percents--Ratios 11	Math Clip Art--Ratios, Proportions, Percents--Ratios 11 Topic Ratios, Proportions, and Percents Description Demonstrates equivalent ratios by simplifying fractions for Red:Green (4:2 to 2:1) and Strawberries:Lemons (6:3 to 2:1). Emphasizes the concept of equivalent ratios by showing how they simplify to the same value, reinforcing previous examples. Ratios, Proportions, and Percents is a fundamental concept in mathematics that helps students understand proportional reasoning, scaling, and comparative analysis. These examples provide a bridge between abstract mathematical principles and real-world applications, helping students grasp the utility of ratios.	Ratios and Rates
Math Clip Art--Ratios, Proportions, Percents--Scale Drawings and Scale Models 01	Math Clip Art--Ratios, Proportions, Percents--Scale Drawings and Scale Models 01 This is part of a collection of math clip art images that explain different aspects of ratios, proportions, and percents.	Proportions
Math Clip Art--Ratios, Proportions, Percents--Scale Drawings and Scale Models 02	Math Clip Art--Ratios, Proportions, Percents--Scale Drawings and Scale Models 02 This is part of a collection of math clip art images that explain different aspects of ratios, proportions, and percents.	Proportions
Math Clip Art--Ratios, Proportions, Percents--Scale Drawings and Scale Models 03	Math Clip Art--Ratios, Proportions, Percents--Scale Drawings and Scale Models 03 This is part of a collection of math clip art images that explain different aspects of ratios, proportions, and percents.	Proportions
Math Clip Art--Ratios, Proportions, Percents--Scale Drawings and Scale Models 04	Math Clip Art--Ratios, Proportions, Percents--Scale Drawings and Scale Models 04 This is part of a collection of math clip art images that explain different aspects of ratios, proportions, and percents.	Proportions
Math Clip Art--Ratios, Proportions, Percents--Scale Drawings and Scale Models 05	Math Clip Art--Ratios, Proportions, Percents--Scale Drawings and Scale Models 05 This is part of a collection of math clip art images that explain different aspects of ratios, proportions, and percents.	Proportions
Math Clip Art--Ratios, Proportions, Percents--Scale Drawings and Scale Models 06	Math Clip Art--Ratios, Proportions, Percents--Scale Drawings and Scale Models 06 This is part of a collection of math clip art images that explain different aspects of ratios, proportions, and percents.	Proportions
Math Example--Ratios and Rates--Example 1	Math Example--Ratios and Rates--Example 1 Topic Ratios and Rates Description This math example focuses on understanding ratios using colored socks. The image displays a collection of red and blue socks, and students are asked to determine the ratio of red socks to blue socks. The solution demonstrates that there are 4 pairs of red socks and 4 pairs of blue socks, resulting in a ratio of 4 : 4, which simplifies to 1 : 1.	Ratios and Rates
Math Example--Ratios and Rates--Example 10	Math Example--Ratios and Rates--Example 10 Topic Ratios and Rates Description This example focuses on finding equivalent ratios using a collection of socks in various colors. The image shows socks arranged in rows, with black, green, white, and other colors present. Students are asked to find a ratio among three colors that is equivalent to 1 : 3 : 1.	Ratios and Rates
Math Example--Ratios and Rates--Example 11	Math Example--Ratios and Rates--Example 11 Topic Ratios and Rates Description This example focuses on finding equivalent ratios using a collection of socks in various colors. The image shows socks arranged in rows, with black, green, white, and other colors present. Students are asked to find a ratio among three colors that is equivalent to 1 : 4 : 1.	Ratios and Rates
Math Example--Ratios and Rates--Example 12	Math Example--Ratios and Rates--Example 12 Topic Ratios and Rates Description This example explores the concept of similar triangles using ratios. The image shows a right triangle with sides labeled as 9, 12, and 15 units. Students are asked to determine if this triangle is similar to a standard 3-4-5 Pythagorean triplet triangle. Understanding similar triangles is an important application of ratios in geometry. This example demonstrates how ratios can be used to compare the sides of triangles and determine similarity. By scaling the sides of a known triangle (3-4-5) and comparing them to the given triangle, students can see how ratios maintain proportionality in similar shapes.	Ratios and Rates
Math Example--Ratios and Rates--Example 13	Math Example--Ratios and Rates--Example 13 Topic Ratios and Rates Description This example focuses on verifying the similarity of triangles using ratios. The image shows a right triangle with sides labeled 25, 60, and 65 units. Students are guided through a step-by-step process to determine if this triangle is similar to a 5-12-13 right triangle.	Ratios and Rates
Math Example--Ratios and Rates--Example 14	Math Example--Ratios and Rates--Example 14 Topic Ratios and Rates Description This example explores the concept of special right triangles using ratios. The image shows a right triangle with sides labeled 3, 3 2 2 , and 6 units. Students are guided through a step-by-step process to verify if this triangle is similar to a 30°-60°-90° triangle.	Ratios and Rates
Math Example--Ratios and Rates--Example 15	Math Example--Ratios and Rates--Example 15 Topic Ratios and Rates	Ratios and Rates
Math Example--Ratios and Rates--Example 16	Math Example--Ratios and Rates--Example 16 Topic Ratios and Rates Description This example focuses on converting units of speed and calculating rates. The image shows a car and calculations for converting speed from miles per hour to feet per second, given the distance traveled in miles and time in minutes. Understanding unit conversions and rate calculations is crucial in many real-world applications, particularly in physics and engineering. This example demonstrates how to use ratios to convert between different units of speed, showcasing the practical application of mathematical concepts in everyday scenarios.	Ratios and Rates
Math Example--Ratios and Rates--Example 17	Math Example--Ratios and Rates--Example 17 Topic Ratios and Rates Description This example explores the concept of unit rates using the cost of gasoline. The image shows a red gasoline container, and students are asked to calculate the cost per gallon of gas given the total cost and volume. Understanding unit rates is a fundamental skill in mathematics with numerous real-world applications. This example demonstrates how to calculate a unit rate by dividing the total cost by the total quantity, illustrating the practical use of division in everyday scenarios like purchasing gasoline.	Ratios and Rates
Math Example--Ratios and Rates--Example 18	Math Example--Ratios and Rates--Example 18 Topic Ratios and Rates Description This example focuses on calculating unit rates in a restaurant context. The image shows a hamburger, and students are asked to determine the cost per pound of ground beef given the total cost and weight purchased. Understanding unit rates is essential in various real-world scenarios, particularly in business and economics. This example illustrates how to calculate a unit rate by dividing the total cost by the total quantity, demonstrating the practical application of division in a restaurant supply context.	Ratios and Rates
Math Example--Ratios and Rates--Example 19	Math Example--Ratios and Rates--Example 19 Topic Ratios and Rates Description This example explores the concept of flow rates using a backyard pool scenario. The image shows a backyard pool, and students are asked to calculate the rate of water flow in gallons per minute given the pool's capacity and the time taken to fill it. Understanding flow rates is important in various fields, including engineering and physics. This example demonstrates how to calculate a rate by dividing the total volume by the total time, illustrating the practical application of division in real-world scenarios involving fluid dynamics.	Ratios and Rates
Math Example--Ratios and Rates--Example 2	Math Example--Ratios and Rates--Example 2 Topic Ratios and Rates Description This example explores ratios using purple and black socks. The image shows a collection of socks, and students are asked to determine the ratio of purple socks to black socks. The solution reveals that there is 1 pair of purple socks and 2 pairs of black socks, resulting in a ratio of 1 : 2, which is already in its simplest form.	Ratios and Rates
Math Example--Ratios and Rates--Example 20	Math Example--Ratios and Rates--Example 20 Topic Ratios and Rates Description This example focuses on unit conversion using the height of the Statue of Liberty. The image shows the Statue of Liberty, and students are asked to convert its height from feet to inches. Understanding unit conversions is crucial in many fields, including science, engineering, and everyday life. This example demonstrates how to use a conversion factor to change units, illustrating the practical application of multiplication in real-world measurement scenarios.	Ratios and Rates
Math Example--Ratios and Rates--Example 21	Math Example--Ratios and Rates--Example 21 Topic Ratios and Rates Description This example focuses on unit conversion, specifically converting the height of the Statue of Liberty from feet to yards. The image shows the iconic Statue of Liberty, providing a real-world context for the mathematical problem. Understanding unit conversions is crucial in many fields, including engineering, science, and everyday life. This example demonstrates how to use a conversion factor to change units, illustrating the practical application of division and multiplication in real-world measurement scenarios.	Ratios and Rates

Illustrative Math Alignment: Grade 7 Unit 4

Proportional Relationships and Percentages

Lesson 3: Revisiting Proportional Relationships

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