Illustrative Math Alignment: Grade 7 Unit 2

Introducing Proportional Relationships

Lesson 10: Introducing Graphs of Proportional Relationships

Use the following Media4Math resources with this Illustrative Math lesson.

Title	Body	Curriculum Nodes
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
Math Example--Ratios and Rates--Example 22	Math Example--Ratios and Rates--Example 22 Topic Ratios and Rates Description This example explores unit conversion, specifically converting the height of the Statue of Liberty from feet to miles. The image depicts the Statue of Liberty, providing a tangible reference for the mathematical problem. Understanding unit conversions, especially between widely different scales like feet and miles, is important in various fields such as geography, engineering, and urban planning. This example showcases how to use a conversion factor to change units, demonstrating the practical application of division and multiplication in real-world measurement scenarios.	Ratios and Rates
Math Example--Ratios and Rates--Example 23	Math Example--Ratios and Rates--Example 23 Topic Ratios and Rates Description This example focuses on unit conversion, specifically converting the height of columns from inches to feet. The image shows columns, providing a visual context for the mathematical problem. Understanding unit conversions between inches and feet is crucial in many practical applications, including construction, interior design, and everyday measurements. 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
Math Example--Ratios and Rates--Example 24	Math Example--Ratios and Rates--Example 24 Topic Ratios and Rates Description This example explores unit conversion in a sports context, specifically converting a quarterback's pass distance from yards to feet. The image shows a silhouette of a quarterback throwing a football, providing a real-world scenario for the mathematical problem. Understanding unit conversions between yards and feet is crucial in many sports, especially American football. This example demonstrates how to use a conversion factor to change units, illustrating the practical application of multiplication in sports-related measurement scenarios.	Ratios and Rates
Math Example--Ratios and Rates--Example 25	Math Example--Ratios and Rates--Example 25 Topic Ratios and Rates Description This example focuses on unit conversion in a geographic context, specifically converting the distance between San Antonio and Austin from miles to feet. The image shows a map of the route between these two Texas cities, providing a real-world scenario for the mathematical problem. Understanding unit conversions between miles and feet is important in various fields, including geography, transportation, and urban planning. This example demonstrates how to use a conversion factor to change units, illustrating the practical application of multiplication in distance-related measurement scenarios.	Ratios and Rates
Math Example--Ratios and Rates--Example 26	Math Example--Ratios and Rates--Example 26 Topic Ratios and Rates Description This example focuses on time unit conversion, specifically converting hours to minutes in the context of a standardized test duration. The image shows a clock, providing a visual representation of time for the mathematical problem. Understanding time unit conversions is crucial in many aspects of daily life, including scheduling, time management, and test-taking. This example demonstrates how to use a conversion factor to change units, illustrating the practical application of multiplication in time-related scenarios.	Ratios and Rates
Math Example--Ratios and Rates--Example 27	Math Example--Ratios and Rates--Example 27 Topic Ratios and Rates Description This example explores time unit conversion, specifically converting hours and minutes to seconds in the context of baking a pie. The image shows a steaming pie, providing a real-world scenario for the mathematical problem. Understanding time unit conversions, especially when dealing with mixed units, is important in various fields such as cooking, manufacturing, and project management. This example demonstrates how to use conversion factors to change units, illustrating the practical application of multiplication in time-related scenarios.	Ratios and Rates
Math Example--Ratios and Rates--Example 28	Math Example--Ratios and Rates--Example 28 Topic Ratios and Rates Description This example focuses on time unit conversion in a sports context, specifically converting minutes and seconds to seconds for a horse race lap time. The image shows a horse, providing a visual context for the mathematical problem. Understanding time unit conversions is crucial in many sports, especially those involving racing and timed events. This example demonstrates how to use conversion factors to change units and add different time units, illustrating the practical application of multiplication and addition in sports-related time scenarios.	Ratios and Rates
Math Example--Ratios and Rates--Example 29	Math Example--Ratios and Rates--Example 29 Topic Ratios and Rates Description This example explores time unit conversion in an IT context, specifically converting seconds to minutes for user session duration. The image shows a computer tower, providing a real-world scenario for the mathematical problem. Understanding time unit conversions is crucial in many technological fields, especially in IT and user experience analysis. This example demonstrates how to use a conversion factor to change units, illustrating the practical application of division in time-related measurement scenarios. It also introduces the concept of mixed numbers in the result.	Ratios and Rates
Math Example--Ratios and Rates--Example 3	Math Example--Ratios and Rates--Example 3 Topic Ratios and Rates Description This example focuses on ratios using black and green socks. The image displays a collection of socks, and students are tasked with determining the ratio of black socks to green socks. The solution shows that there are 2 pairs of black socks and 6 pairs of green socks, resulting in a ratio of 2 : 6, which simplifies to 1 : 3.	Ratios and Rates
Math Example--Ratios and Rates--Example 30	Math Example--Ratios and Rates--Example 30 Topic Ratios and Rates Description This example focuses on time unit conversion in an IT context, specifically converting seconds to hours for user session duration. The image shows a computer tower, providing a real-world scenario for the mathematical problem.	Ratios and Rates
Math Example--Ratios and Rates--Example 31	Math Example--Ratios and Rates--Example 31 Topic Ratios and Rates Description This example focuses on temperature unit conversion, specifically converting Celsius to Fahrenheit for the boiling point of water. The image shows a beaker of boiling water, providing a visual context for the mathematical problem. Understanding temperature unit conversions is crucial in many scientific fields, including chemistry, physics, and meteorology. This example demonstrates how to use a conversion formula to change units, illustrating the practical application of mathematical equations in real-world temperature scenarios.	Ratios and Rates
Math Example--Ratios and Rates--Example 32	Math Example--Ratios and Rates--Example 32 Topic Ratios and Rates Description This example explores temperature unit conversion, specifically converting Fahrenheit to Celsius for the freezing point of water. The image shows icicles, providing a visual representation of the freezing temperature for the mathematical problem.	Ratios and Rates
Math Example--Ratios and Rates--Example 4	Math Example--Ratios and Rates--Example 4 Topic Ratios and Rates Description This example explores ratios using purple and red socks. The image shows a collection of socks, and students are asked to determine the ratio of purple socks to red socks. The solution reveals that there is 1 pair of purple socks and 4 pairs of red socks, resulting in a ratio of 1 : 4, which is already in its simplest form.	Ratios and Rates
Math Example--Ratios and Rates--Example 5	Math Example--Ratios and Rates--Example 5 Topic Ratios and Rates Description This example focuses on ratios using black and green socks among a variety of colored socks. The image displays pairs of socks in black, green, orange, yellow, blue, and red. Students are asked to determine the ratio of black socks to green socks. The solution shows that there are 2 pairs of black socks and 10 pairs of green socks, resulting in a ratio of 2 : 10, which simplifies to 1 : 5.	Ratios and Rates
Math Example--Ratios and Rates--Example 6	Math Example--Ratios and Rates--Example 6 Topic Ratios and Rates Description This example explores ratios using geometric shapes of different colors. The image displays various shapes in yellow, blue, red, and green. Students are asked to determine the ratio of circular shapes to yellow objects. The solution reveals that there are 2 circular shapes and 1 yellow object, resulting in a ratio of 2 : 1, which is already in its simplest form.	Ratios and Rates
Math Example--Ratios and Rates--Example 7	Math Example--Ratios and Rates--Example 7 Topic Ratios and Rates Description This example focuses on ratios using geometric shapes. The image displays various shapes in yellow, blue, red, and green. Students are asked to determine the ratio of triangles to quadrilaterals. The solution shows that there are 4 triangles and 6 quadrilaterals, resulting in a ratio of 4 : 6, which simplifies to 2 : 3.	Ratios and Rates
Math Example--Ratios and Rates--Example 8	Math Example--Ratios and Rates--Example 8 Topic Ratios and Rates Description This example explores ratios using geometric shapes and colors. The image displays various shapes in yellow, blue, red, and green. Students are asked to determine the ratio of octagons to blue shapes. The solution reveals that there are 2 octagons and 5 blue shapes, resulting in a ratio of 2 : 5, which is already in its simplest form.	Ratios and Rates
Math Example--Ratios and Rates--Example 9	Math Example--Ratios and Rates--Example 9 Topic Ratios and Rates Description This example introduces the concept of ratios in genetics using a Punnett square. The image shows genetic combinations for a flower's color, including RR, Rw, and ww, with corresponding images of red and white flowers. Students are asked to determine the ratio of different gene combinations.	Ratios and Rates
Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 1	Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 1 Topic Ratios, Proportions, and Percents Description This example demonstrates how to solve a proportion problem where two ratios a:b and c:d are proportional. Given the values b = 3, c = 4, and d = 6, we need to find the value of a. The proportion is set up as a / 3 = 4 / 6, which is then solved to find that a = 2.	Proportions
Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 1	Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 1 Topic Ratios, Proportions, and Percents Description This example demonstrates how to solve a proportion problem where two ratios a:b and c:d are proportional. Given the values b = 3, c = 4, and d = 6, we need to find the value of a. The proportion is set up as a / 3 = 4 / 6, which is then solved to find that a = 2.	Proportions
Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 10	Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 10 Topic Ratios, Proportions, and Percents Description This example illustrates solving a proportion problem using similar triangles with algebraic expressions. Two triangles are shown, one with sides of 6 and 9, and the other with sides of 2x and 2x + 9. The problem requires setting up a proportion: 6 / 9 = 2x / (2x + 9). Solving this equation leads to x = 9, which then allows us to find the side lengths of 18 and 27.	Proportions
Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 10	Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 10 Topic Ratios, Proportions, and Percents Description This example illustrates solving a proportion problem using similar triangles with algebraic expressions. Two triangles are shown, one with sides of 6 and 9, and the other with sides of 2x and 2x + 9. The problem requires setting up a proportion: 6 / 9 = 2x / (2x + 9). Solving this equation leads to x = 9, which then allows us to find the side lengths of 18 and 27.	Proportions
Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 11	Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 11 Topic Ratios, Proportions, and Percents Description This example demonstrates solving a proportion problem using similar right triangles. Two right triangles are shown, one with legs of 7 and 9, and the other with legs of 14 and x. The problem requires finding the length of side x by setting up a proportion based on the similar triangles: 7 / 9 = 14 / x. Solving this equation leads to x = 18.	Proportions
Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 11	Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 11 Topic Ratios, Proportions, and Percents Description This example demonstrates solving a proportion problem using similar right triangles. Two right triangles are shown, one with legs of 7 and 9, and the other with legs of 14 and x. The problem requires finding the length of side x by setting up a proportion based on the similar triangles: 7 / 9 = 14 / x. Solving this equation leads to x = 18.	Proportions
Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 12	Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 12 Topic Ratios, Proportions, and Percents Description This example illustrates solving a proportion problem using similar right triangles with algebraic expressions. Two right triangles are shown, one with legs of 5 and 8, and the other with legs of 2x and (2x + 6). The problem requires setting up a proportion: 5 / 8 = 2x / (2x + 6). Solving this equation leads to x = 5, which then allows us to find the side lengths of 10 and 16.	Proportions
Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 12	Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 12 Topic Ratios, Proportions, and Percents Description This example illustrates solving a proportion problem using similar right triangles with algebraic expressions. Two right triangles are shown, one with legs of 5 and 8, and the other with legs of 2x and (2x + 6). The problem requires setting up a proportion: 5 / 8 = 2x / (2x + 6). Solving this equation leads to x = 5, which then allows us to find the side lengths of 10 and 16.	Proportions
Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 13	Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 13 Topic Ratios, Proportions, and Percents Description This example demonstrates solving a proportion problem using similar right triangles with special angles (30°-60°-90°). Two triangles are shown, with the smaller one having sides of 6√3 and 6, and the larger one having sides of x and 12. The problem requires finding the length of side x by setting up a proportion: (6√3) / 6 = x / 12. Solving this equation leads to x = 12√3.	Proportions
Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 13	Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 13 Topic Ratios, Proportions, and Percents Description This example demonstrates solving a proportion problem using similar right triangles with special angles (30°-60°-90°). Two triangles are shown, with the smaller one having sides of 6√3 and 6, and the larger one having sides of x and 12. The problem requires finding the length of side x by setting up a proportion: (6√3) / 6 = x / 12. Solving this equation leads to x = 12√3.	Proportions
Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 14	Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 14 Topic Ratios, Proportions, and Percents Description This example illustrates solving a proportion problem using similar right triangles with special angles (30°-60°-90°) and algebraic expressions. Two triangles are shown, with the smaller one having sides of 16 and 8, and the larger one having sides of (3x + 4) and 2x. The problem requires setting up a proportion: 16 / 8 = (3x + 4) / 2x. Solving this equation leads to x = 4, which then allows us to find the side lengths of 8 and 16.	Proportions
Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 14	Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 14 Topic Ratios, Proportions, and Percents Description This example illustrates solving a proportion problem using similar right triangles with special angles (30°-60°-90°) and algebraic expressions. Two triangles are shown, with the smaller one having sides of 16 and 8, and the larger one having sides of (3x + 4) and 2x. The problem requires setting up a proportion: 16 / 8 = (3x + 4) / 2x. Solving this equation leads to x = 4, which then allows us to find the side lengths of 8 and 16.	Proportions
Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 15	Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 15 Topic Ratios, Proportions, and Percents Description This example demonstrates solving a proportion problem using similar right triangles. Two right triangles are shown, with the smaller one having sides of 4 and 3, and the larger one having sides of x and 12. The problem requires finding the length of side x by setting up a proportion: 4 / 3 = x / 12. Solving this equation leads to x = 16.	Proportions
Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 15	Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 15 Topic Ratios, Proportions, and Percents Description This example demonstrates solving a proportion problem using similar right triangles. Two right triangles are shown, with the smaller one having sides of 4 and 3, and the larger one having sides of x and 12. The problem requires finding the length of side x by setting up a proportion: 4 / 3 = x / 12. Solving this equation leads to x = 16.	Proportions

Illustrative Math Alignment: Grade 7 Unit 2

Introducing Proportional Relationships

Lesson 10: Introducing Graphs of Proportional Relationships

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