Illustrative Math Alignment: Grade 6 Unit 3

Unit Rates and Percentages

Lesson 17: Painting a Room

Use the following Media4Math resources with this Illustrative Math lesson.

Title	Body	Curriculum Nodes
Math Clip Art--Ratios, Proportions, Percents--Percents 05	Math Clip Art--Ratios, Proportions, Percents--Percents 05 Topic Ratios, Proportions, and Percents Description The image illustrates the concept of how fractions such as 3/4 and 3/5 convert to percents (75% and 60%) using shaded 10 x 10 grids. It expands on this idea by showing the concept of percents using a visual and tangible representation, reinforcing the idea of 100 as the base for comparison.	Percents
Math Clip Art--Ratios, Proportions, Percents--Percents 06	Math Clip Art--Ratios, Proportions, Percents--Percents 06 Topic Ratios, Proportions, and Percents Description The image illustrates the concept of connecting coins (1¢, 5¢, 10¢, 25¢) to their percent values of a dollar (1%, 5%, 10%, 25%). It expands on this idea by establishing a real-world application of percents, showing their utility in everyday contexts like money. The topic of Ratios, Proportions, and Percents explores fundamental math concepts by using practical examples. This collection aids in visualizing the connection between different mathematical forms such as ratios, percents, and fractions, making abstract concepts more accessible to students.	Percents
Math Clip Art--Ratios, Proportions, Percents--Percents 07	Math Clip Art--Ratios, Proportions, Percents--Percents 07 Topic Ratios, Proportions, and Percents Description The image illustrates percentages as fractions with a denominator of 100, such as 10% = 10 / 100, 15% = 15 / 100, and so on. It expands on this idea by showing how percents relate to fractions, reinforcing their equivalency and further grounding the concept. The topic of Ratios, Proportions, and Percents explores fundamental math concepts by using practical examples. This collection aids in visualizing the connection between different mathematical forms such as ratios, percents, and fractions, making abstract concepts more accessible to students.	Percents
Math Clip Art--Ratios, Proportions, Percents--Percents 08	Math Clip Art--Ratios, Proportions, Percents--Percents 08 Topic Ratios, Proportions, and Percents Description The image illustrates how to convert 1/4 to a percent using the proportion method: (1 / 4 = x / 100), solving for x = 25%. and expands on this idea by showing that provides a step-by-step method to convert fractions to percents, introducing proportional reasoning. The topic of Ratios, Proportions, and Percents explores fundamental math concepts by using practical examples. This collection aids in visualizing the connection between different mathematical forms such as ratios, percents, and fractions, making abstract concepts more accessible to students.	Percents
Math Clip Art--Ratios, Proportions, Percents--Percents 09	Math Clip Art--Ratios, Proportions, Percents--Percents 09 Topic Ratios, Proportions, and Percents Description The image illustrates the concept of converting a fraction to a percent using proportions, with 2/5 converting to 40%. and expands on this idea by showing that reinforces the proportion method with another example, building understanding through repetition. The topic of Ratios, Proportions, and Percents explores fundamental math concepts by using practical examples. This collection aids in visualizing the connection between different mathematical forms such as ratios, percents, and fractions, making abstract concepts more accessible to students.	Percents
Math Clip Art--Ratios, Proportions, Percents--Percents 10	Math Clip Art--Ratios, Proportions, Percents--Percents 10 Topic Ratios, Proportions, and Percents Description The image illustrates the concept of converting fractions to percents, dividing 5 by 8 to get 62.5% and expands on this idea by showing an alternative method for conversion, allowing for flexibility in approaches. The topic of Ratios, Proportions, and Percents explores fundamental math concepts by using practical examples. This collection aids in visualizing the connection between different mathematical forms such as ratios, percents, and fractions, making abstract concepts more accessible to students.	Percents
Math Clip Art--Ratios, Proportions, Percents--Percents 11	Math Clip Art--Ratios, Proportions, Percents--Percents 11 Topic Ratios, Proportions, and Percents Description The image illustrates the concept of the general equation for percents: a% * x = y, using the example 10% * 50 = 5. It emphasizes the three components of a percent equation: the percent, a base number, and the result, and expands on this idea by showing that establishes the foundational equation for solving percent problems, serving as a gateway to explore specific types of percent equations.	Percents
Math Clip Art--Ratios, Proportions, Percents--Percents 12	Math Clip Art--Ratios, Proportions, Percents--Percents 12 Topic Ratios, Proportions, and Percents Description The image illustrates the concept of how to solve the question 'what is 15% of 250?' using the equation a% * x = y, with calculations explicitly shown as 15 * 2.5 = 37.5. and expands on this idea by showing that provides a clear, step-by-step example to apply the general percent equation, enhancing comprehension through practical application.	Percents
Math Clip Art--Ratios, Proportions, Percents--Percents 13	Math Clip Art--Ratios, Proportions, Percents--Percents 13 Topic Ratios, Proportions, and Percents Description The image illustrates the concept of solving '150 is 30% of what number?' using the same equation a% * x = y and algebraic manipulation to find x = 500 and expands on this idea by showing that explains how to rearrange the percent equation to solve for different variables, expanding on problem-solving strategies.	Percents
Math Clip Art--Ratios, Proportions, Percents--Percents 14	Math Clip Art--Ratios, Proportions, Percents--Percents 14 Topic Ratios, Proportions, and Percents Description The image illustrates solving the problem 'what percent of 90 is 45?' using the equation a% * x = y, and algebraically finding a% = 50% and expands on this idea by showing that demonstrates how to find the percent in percent equations, further developing flexibility in solving percent-related problems.	Percents
Math Clip Art--Ratios, Proportions, Percents--Percents 15	Math Clip Art--Ratios, Proportions, Percents--Percents 15 Topic Ratios, Proportions, and Percents Description The image summarizes the three types of percent equations in a table format, highlighting the unknown variable in each scenario (percent, part, or whole) and expands on this idea by providing a comprehensive overview and categorization of percent problems, solidifying the framework introduced in earlier examples.	Percents
Math Clip Art--Ratios, Proportions, Percents--Proportions 01	Math Clip Art--Ratios, Proportions, Percents--Proportions 01 Topic Ratios, Proportions, and Percents Description This image showcases the concept of proportions using a dynamic visual of a runner in action framed within a golden ratio spiral. The proportion is represented algebraically as a/b = c/d, linking visual and mathematical representations. It introduces proportions conceptually and visually, setting the foundation for the subsequent examples.	Proportions
Math Clip Art--Ratios, Proportions, Percents--Proportions 02	Math Clip Art--Ratios, Proportions, Percents--Proportions 02 Topic Ratios, Proportions, and Percents Description This image illustrates proportions using two equivalent ratios, represented by measuring cups and cupcakes. It simplifies proportions to relatable everyday examples. It connects proportions to practical examples, emphasizing the real-world relevance. Proportions are a foundational concept in mathematics, connecting ratios to real-world applications. Examples like those in this collection help students visualize and reason about proportional relationships in meaningful contexts, solidifying their understanding.	Proportions
Math Clip Art--Ratios, Proportions, Percents--Proportions 03	Math Clip Art--Ratios, Proportions, Percents--Proportions 03 Topic Ratios, Proportions, and Percents Description This image uses coins to demonstrate proportions. The image compares groups of quarters and nickels to highlight equivalent ratios (3:1 and 6:2). It solidifies the concept of equivalent ratios through another real-life example, reinforcing the idea. Proportions are a foundational concept in mathematics, connecting ratios to real-world applications. Examples like those in this collection help students visualize and reason about proportional relationships in meaningful contexts, solidifying their understanding.	Proportions
Math Clip Art--Ratios, Proportions, Percents--Proportions 04	Math Clip Art--Ratios, Proportions, Percents--Proportions 04 Topic Ratios, Proportions, and Percents Description This image demonstrates proportions through a scale model example, comparing the height and width ratios of the Eiffel Tower in two scales. It highlights the application of proportions in scaling and models, bridging abstract and practical understanding. Proportions are a foundational concept in mathematics, connecting ratios to real-world applications. Examples like those in this collection help students visualize and reason about proportional relationships in meaningful contexts, solidifying their understanding.	Proportions
Math Clip Art--Ratios, Proportions, Percents--Proportions 05	Math Clip Art--Ratios, Proportions, Percents--Proportions 05 Topic Ratios, Proportions, and Percents Description This image shows proportionality between dimes and pennies using equivalent ratios (1:4 and 3:12). Mathematical steps verify proportionality. It introduces proportional reasoning and calculation steps to ensure clarity in identifying proportional relationships. Proportions are a foundational concept in mathematics, connecting ratios to real-world applications. Examples like those in this collection help students visualize and reason about proportional relationships in meaningful contexts, solidifying their understanding.	Proportions
Math Clip Art--Ratios, Proportions, Percents--Proportions 06	Math Clip Art--Ratios, Proportions, Percents--Proportions 06 Topic Ratios, Proportions, and Percents Description This image presents proportional triangles, with side lengths maintaining equivalent ratios (2:3:4 and 6:9:12). It demonstrates geometric applications of proportions, extending the concept to shapes and measurements. Proportions are a foundational concept in mathematics, connecting ratios to real-world applications. Examples like those in this collection help students visualize and reason about proportional relationships in meaningful contexts, solidifying their understanding.	Proportions
Math Clip Art--Ratios, Proportions, Percents--Proportions 07	Math Clip Art--Ratios, Proportions, Percents--Proportions 07 Topic Ratios, Proportions, and Percents Description This image contrasts proportionality with non-proportional groups of coins (dimes and nickels). Ratios differ, clarifying when proportions do not exist. It explains non-proportionality to deepen understanding of proportional relationships. Proportions are a foundational concept in mathematics, connecting ratios to real-world applications. Examples like those in this collection help students visualize and reason about proportional relationships in meaningful contexts, solidifying their understanding.	Proportions
Math Clip Art--Ratios, Proportions, Percents--Proportions 08	Math Clip Art--Ratios, Proportions, Percents--Proportions 08 Topic Ratios, Proportions, and Percents Description This image poses a question about proportional triangles, asking for the missing value (x) to maintain proportionality. It introduces problem-solving involving proportions, encouraging engagement and application. Proportions are a foundational concept in mathematics, connecting ratios to real-world applications. Examples like those in this collection help students visualize and reason about proportional relationships in meaningful contexts, solidifying their understanding.	Proportions
Math Clip Art--Ratios, Proportions, Percents--Proportions 09	Math Clip Art--Ratios, Proportions, Percents--Proportions 09 Topic Ratios, Proportions, and Percents Description This image solves the posed proportion problem by finding the value of x using equivalent ratios (x/6 = 7/3). It breaks down the process of solving proportions, reinforcing mathematical reasoning. Proportions are a foundational concept in mathematics, connecting ratios to real-world applications. Examples like those in this collection help students visualize and reason about proportional relationships in meaningful contexts, solidifying their understanding.	Proportions
Math Clip Art--Ratios, Proportions, Percents--Proportions 10	Math Clip Art--Ratios, Proportions, Percents--Proportions 10 Topic Ratios, Proportions, and Percents Description This image demonstrates proportionality in coins by calculating the number of nickels required for proportional groups (2/5 = 6/x). It closes the sequence with a real-world problem, consolidating the topic and providing a practical application. Proportions are a foundational concept in mathematics, connecting ratios to real-world applications. Examples like those in this collection help students visualize and reason about proportional relationships in meaningful contexts, solidifying their understanding.	Proportions
Math Clip Art--Ratios, Proportions, Percents--Rates 01	Math Clip Art--Ratios, Proportions, Percents--Rates 01 Topic Ratios, Proportions, and Percents Description The image shows a hurdler jumping over a hurdle, with an overlay of the golden ratio (1.618). It introduces the concept of rates by visually showing motion and proportions. This image sets the stage for understanding rates as a mathematical relationship and connects to the idea of proportion and efficiency, aligning with rates' use in describing relationships. 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 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

Illustrative Math Alignment: Grade 6 Unit 3

Unit Rates and Percentages

Lesson 17: Painting a Room

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