Illustrative Math Alignment: Grade 6 Unit 3

Unit Rates and Percentages

Lesson 14: Solving Percentage Problems

Use the following Media4Math resources with this Illustrative Math lesson.

Title	Body	Curriculum Nodes
Math Example--Math of Money--Calculating Tax--Example 4	Math Example--Math of Money--Calculating Tax--Example 4 Topic The Math of Money Description What is the tax due on a $999 purchase when the sales tax rate is 8%? The example shows how to apply the formula Tax Due = Cost * Tax Rate. Calculating tax is a fundamental skill in understanding financial literacy. This example and others like it help illustrate how percentages are applied in real-world scenarios, such as shopping and services. Seeing multiple worked-out examples allows students to recognize patterns and reinforce their understanding of applying formulas consistently in various contexts. It ensures they can adapt to different numbers and situations.	Percents
Math Example--Math of Money--Calculating Tax--Example 5	Math Example--Math of Money--Calculating Tax--Example 5 Topic The Math of Money Description What is the tax due on a $999.99 purchase when the sales tax rate is 9%? The example shows how to apply the formula Tax Due = Cost * Tax Rate. Calculating tax is a fundamental skill in understanding financial literacy. This example and others like it help illustrate how percentages are applied in real-world scenarios, such as shopping and services. Seeing multiple worked-out examples allows students to recognize patterns and reinforce their understanding of applying formulas consistently in various contexts. It ensures they can adapt to different numbers and situations.	Percents
Math Example--Math of Money--Calculating Tax--Example 6	Math Example--Math of Money--Calculating Tax--Example 6 Topic The Math of Money Description What is the tax due on a $1250 purchase when the sales tax rate is 6.5%? The example shows how to apply the formula Tax Due = Cost * Tax Rate. Calculating tax is a fundamental skill in understanding financial literacy. This example and others like it help illustrate how percentages are applied in real-world scenarios, such as shopping and services. Seeing multiple worked-out examples allows students to recognize patterns and reinforce their understanding of applying formulas consistently in various contexts. It ensures they can adapt to different numbers and situations.	Percents
Math Example--Math of Money--Calculating Tax--Example 7	Math Example--Math of Money--Calculating Tax--Example 7 Topic The Math of Money Description What is the tax due on a $1399 purchase when the sales tax rate is 7.5%? The example shows how to apply the formula Tax Due = Cost * Tax Rate. Calculating tax is a fundamental skill in understanding financial literacy. This example and others like it help illustrate how percentages are applied in real-world scenarios, such as shopping and services. Seeing multiple worked-out examples allows students to recognize patterns and reinforce their understanding of applying formulas consistently in various contexts. It ensures they can adapt to different numbers and situations.	Percents
Math Example--Math of Money--Calculating Tax--Example 8	Math Example--Math of Money--Calculating Tax--Example 8 Topic The Math of Money Description What is the tax due on a $1575.50 purchase when the sales tax rate is 8.5%? The example shows how to apply the formula Tax Due = Cost * Tax Rate. Calculating tax is a fundamental skill in understanding financial literacy. This example and others like it help illustrate how percentages are applied in real-world scenarios, such as shopping and services. Seeing multiple worked-out examples allows students to recognize patterns and reinforce their understanding of applying formulas consistently in various contexts. It ensures they can adapt to different numbers and situations.	Percents
Math Example--Math of Money--Calculating Tax--Example 9	Math Example--Math of Money--Calculating Tax--Example 9 Topic The Math of Money Description What is the tax due on a $1999.99 purchase when the sales tax rate is 9.5%? The example shows how to apply the formula Tax Due = Cost * Tax Rate. Calculating tax is a fundamental skill in understanding financial literacy. This example and others like it help illustrate how percentages are applied in real-world scenarios, such as shopping and services. Seeing multiple worked-out examples allows students to recognize patterns and reinforce their understanding of applying formulas consistently in various contexts. It ensures they can adapt to different numbers and situations.	Percents
Math Example--Math of Money--Calculating Tips and Commissions--Example 1	Math Example--Math of Money--Calculating Tips and Commissions--Example 1 Topic The Math of Money Description Calculate a 15% tip on a $50 restaurant bill. The problem requires finding 15% of 50. To calculate the tip, multiply the cost (50) by the tip rate (0.15). Tip = 50 * 0.15 = 7.50. The answer is $7.50. In general, the topic 'The Math of Money' covers understanding the calculation of financial metrics like tips and commissions. Examples in this collection focus on real-world scenarios where these calculations are necessary, helping students grasp the mathematical principles involved.	Percents
Math Example--Math of Money--Calculating Tips and Commissions--Example 10	Math Example--Math of Money--Calculating Tips and Commissions--Example 10 Topic The Math of Money Description Calculate a 9.5% sales commission on a $350,999 sale. The problem requires finding 9.5% of 350,999. To calculate the commission, multiply the sale amount (350,999) by the commission rate (0.095). Commission = 350,999 * 0.095 ≈ 33,344.91. The answer is approximately $33,344.91.	Percents
Math Example--Math of Money--Calculating Tips and Commissions--Example 2	Math Example--Math of Money--Calculating Tips and Commissions--Example 2 Topic The Math of Money Description Calculate a 16% tip on a $55 restaurant bill. The problem requires finding 16% of 55. To calculate the tip, multiply the cost (55) by the tip rate (0.16). Tip = 55 * 0.16 = 8.8. The answer is $8.80. In general, the topic "The Math of Money" covers understanding the calculation of financial metrics like tips and commissions. Examples in this collection focus on real-world scenarios where these calculations are necessary, helping students grasp the mathematical principles involved.	Percents
Math Example--Math of Money--Calculating Tips and Commissions--Example 3	Math Example--Math of Money--Calculating Tips and Commissions--Example 3 Topic The Math of Money Description Calculate an 18% tip on a $75.50 restaurant bill. The problem requires finding 18% of 75.50. To calculate the tip, multiply the cost (75.50) by the tip rate (0.18). Tip = 75.50 * 0.18 = 13.59. The answer is $13.59. In general, the topic "The Math of Money" covers understanding the calculation of financial metrics like tips and commissions. Examples in this collection focus on real-world scenarios where these calculations are necessary, helping students grasp the mathematical principles involved.	Percents
Math Example--Math of Money--Calculating Tips and Commissions--Example 4	Math Example--Math of Money--Calculating Tips and Commissions--Example 4 Topic The Math of Money Description Calculate a 19.5% tip on a $49.99 restaurant bill. The problem requires finding 19.5% of 49.99. To calculate the tip, multiply the cost (49.99) by the tip rate (0.195). Tip = 49.99 * 0.195 Å 9.75. The answer is approximately $9.75. In general, the topic "The Math of Money" covers understanding the calculation of financial metrics like tips and commissions. Examples in this collection focus on real-world scenarios where these calculations are necessary, helping students grasp the mathematical principles involved.	Percents
Math Example--Math of Money--Calculating Tips and Commissions--Example 5	Math Example--Math of Money--Calculating Tips and Commissions--Example 5 Topic The Math of Money Description Calculate a 22.5% tip on a $159.99 restaurant bill. The problem requires finding 22.5% of 159.99. To calculate the tip, multiply the cost (159.99) by the tip rate (0.225). Tip = 159.99 * 0.225 ≈ 35.99. The answer is approximately $35.99. In general, the topic "The Math of Money" covers understanding the calculation of financial metrics like tips and commissions. Examples in this collection focus on real-world scenarios where these calculations are necessary, helping students grasp the mathematical principles involved.	Percents
Math Example--Math of Money--Calculating Tips and Commissions--Example 6	Math Example--Math of Money--Calculating Tips and Commissions--Example 6 Topic The Math of Money Description Calculate a 5% sales commission on a $1000 sale. The problem requires finding 5% of 1000. To calculate the commission, multiply the sale amount (1000) by the commission rate (0.05). Commission = 1000 * 0.05 = 50. The answer is $50. In general, the topic "The Math of Money" covers understanding the calculation of financial metrics like tips and commissions. Examples in this collection focus on real-world scenarios where these calculations are necessary, helping students grasp the mathematical principles involved.	Percents
Math Example--Math of Money--Calculating Tips and Commissions--Example 7	Math Example--Math of Money--Calculating Tips and Commissions--Example 7 Topic The Math of Money Description Calculate a 6% sales commission on a $1200 sale. The problem requires finding 6% of 1200. To calculate the commission, multiply the sale amount (1200) by the commission rate (0.06). Commission = 1200 * 0.06 = 72. The answer is $72. In general, the topic "The Math of Money" covers understanding the calculation of financial metrics like tips and commissions. Examples in this collection focus on real-world scenarios where these calculations are necessary, helping students grasp the mathematical principles involved.	Percents
Math Example--Math of Money--Calculating Tips and Commissions--Example 8	Math Example--Math of Money--Calculating Tips and Commissions--Example 8 Topic The Math of Money Description Calculate a 7.5% sales commission on a $25,500 sale. The problem requires finding 7.5% of 25,500. To calculate the commission, multiply the sale amount (25,500) by the commission rate (0.075). Commission = 25,500 * 0.075 = 1912.50. The answer is $1,912.50. In general, the topic "The Math of Money" covers understanding the calculation of financial metrics like tips and commissions. Examples in this collection focus on real-world scenarios where these calculations are necessary, helping students grasp the mathematical principles involved.	Percents
Math Example--Math of Money--Calculating Tips and Commissions--Example 9	Math Example--Math of Money--Calculating Tips and Commissions--Example 9 Topic The Math of Money Description Calculate an 8.5% sales commission on a $125,500 sale. The problem requires finding 8.5% of 125,500. To calculate the commission, multiply the sale amount (125,500) by the commission rate (0.085). Commission = 125,500 * 0.085 = 10,667.50. The answer is $10,667.50.	Percents
Math Example--Math of Money--Simple Interest--Example 1	Math Example--Math of Money--Simple Interest--Example 1 Topic The Math of Money Description An investment of $1000 earns 10% interest. Calculate the total amount of the investment after applying simple interest. The solution uses the formula for simple interest: Total Amount = P * (1 + r). Substitute P = 1000 and r = 0.1 to get 1000 * (1 + 0.1) = 1000 * 1.1 = 1100. Thus, the total amount is $1100. Understanding the math of money concepts is crucial for students, as it forms the basis for financial literacy. Examples like this showcase the practical application of simple interest formulas, helping learners to connect theoretical knowledge with real-world scenarios.	Percents
Math Example--Math of Money--Simple Interest--Example 10	Math Example--Math of Money--Simple Interest--Example 10 Topic The Math of Money Description An investment of $50,999 earns 21.55% interest. Calculate the total amount of the investment after applying simple interest. Substitute P = 50999 and r = 0.2155 in the formula Total Amount = P * (1 + r) to get 50999 * (1 + 0.2155) = 50999 * 1.2155 ≈ 61,989.28. Thus, the total amount is approximately $61,989.28. Understanding the math of money concepts is crucial for students, as it forms the basis for financial literacy. Examples like this showcase the practical application of simple interest formulas, helping learners to connect theoretical knowledge with real-world scenarios.	Percents
Math Example--Math of Money--Simple Interest--Example 2	Math Example--Math of Money--Simple Interest--Example 2 Topic The Math of Money Description An investment of $5000 earns 5% interest. Calculate the total amount of the investment after applying simple interest. Using the formula Total Amount = P * (1 + r), substitute P = 5000 and r = 0.05. This gives 5000 * (1 + 0.05) = 5000 * 1.05 = 5250. Therefore, the total amount is $5250. Understanding the math of money concepts is crucial for students, as it forms the basis for financial literacy. Examples like this showcase the practical application of simple interest formulas, helping learners to connect theoretical knowledge with real-world scenarios.	Percents
Math Example--Math of Money--Simple Interest--Example 3	Math Example--Math of Money--Simple Interest--Example 3 Topic The Math of Money Description An investment of $10,500 earns 12% interest. Calculate the total amount of the investment after applying simple interest. Apply the formula Total Amount = P * (1 + r). With P = 10500 and r = 0.12, calculate 10500 * (1 + 0.12) = 10500 * 1.12 = 11760. So, the total amount is $11760. Understanding the math of money concepts is crucial for students, as it forms the basis for financial literacy. Examples like this showcase the practical application of simple interest formulas, helping learners to connect theoretical knowledge with real-world scenarios.	Percents
Math Example--Math of Money--Simple Interest--Example 4	Math Example--Math of Money--Simple Interest--Example 4 Topic The Math of Money Description An investment of $999 earns 15% interest. Calculate the total amount of the investment after applying simple interest. Substitute P = 999 and r = 0.15 into the formula Total Amount = P * (1 + r), resulting in 999 * (1 + 0.15) = 999 * 1.15 = 1148.85. Therefore, the total amount is $1148.85. Understanding the math of money concepts is crucial for students, as it forms the basis for financial literacy. Examples like this showcase the practical application of simple interest formulas, helping learners to connect theoretical knowledge with real-world scenarios.	Percents
Math Example--Math of Money--Simple Interest--Example 5	Math Example--Math of Money--Simple Interest--Example 5 Topic The Math of Money Description An investment of $99.99 earns 7% interest. Calculate the total amount of the investment after applying simple interest. Using the formula Total Amount = P * (1 + r) with P = 99.99 and r = 0.07, compute 99.99 * (1 + 0.07) = 99.99 * 1.07 ≅ 106.99. The total amount is approximately $106.99. Understanding the math of money concepts is crucial for students, as it forms the basis for financial literacy. Examples like this showcase the practical application of simple interest formulas, helping learners to connect theoretical knowledge with real-world scenarios.	Percents
Math Example--Math of Money--Simple Interest--Example 6	Math Example--Math of Money--Simple Interest--Example 6 Topic The Math of Money Description An investment of $20,000 earns 5.5% interest. Calculate the total amount of the investment after applying simple interest. With P = 20000 and r = 0.055, use the formula Total Amount = P * (1 + r) to get 20000 * (1 + 0.055) = 20000 * 1.055 = 21,100. Therefore, the total amount is $21,100. Understanding the math of money concepts is crucial for students, as it forms the basis for financial literacy. Examples like this showcase the practical application of simple interest formulas, helping learners to connect theoretical knowledge with real-world scenarios.	Percents
Math Example--Math of Money--Simple Interest--Example 7	Math Example--Math of Money--Simple Interest--Example 7 Topic The Math of Money Description An investment of $25,550 earns 10.75% interest. Calculate the total amount of the investment after applying simple interest. Substitute P = 25550 and r = 0.1075 in Total Amount = P * (1 + r). This gives 25550 * (1 + 0.1075) = 25550 * 1.1075 = 26,955.25. So, the total amount is $26,955.25. Understanding the math of money concepts is crucial for students, as it forms the basis for financial literacy. Examples like this showcase the practical application of simple interest formulas, helping learners to connect theoretical knowledge with real-world scenarios.	Percents
Math Example--Math of Money--Simple Interest--Example 8	Math Example--Math of Money--Simple Interest--Example 8 Topic The Math of Money Description An investment of $999.99 earns 7.5% interest. Calculate the total amount of the investment after applying simple interest. Using P = 999.99 and r = 0.075 in Total Amount = P * (1 + r), calculate 999.99 * (1 + 0.075) = 999.99 * 1.075 = 1074.99. Thus, the total amount is approximately $1074.99. Understanding the math of money concepts is crucial for students, as it forms the basis for financial literacy. Examples like this showcase the practical application of simple interest formulas, helping learners to connect theoretical knowledge with real-world scenarios.	Percents
Math Example--Math of Money--Simple Interest--Example 9	Math Example--Math of Money--Simple Interest--Example 9 Topic The Math of Money Description An investment of $25,125 earns 10.55% interest. Calculate the total amount of the investment after applying simple interest. Using P = 25125 and r = 0.1055 in Total Amount = P * (1 + r), compute 25125 * (1 + 0.1055) = 25125 * 1.1055 ≈ 27,775.69. The total amount is approximately $27,775.69. Understanding the math of money concepts is crucial for students, as it forms the basis for financial literacy. Examples like this showcase the practical application of simple interest formulas, helping learners to connect theoretical knowledge with real-world scenarios.	Percents
Math Example--Percents--Equations with Percents: Example 1	Math Example--Percents--Equations with Percents: Example 1 Topic Solving Equations Description This math example focuses on solving percent equations, specifically asking "What is 5% of 8?" The solution involves converting 5% to its decimal form, 0.05, and then multiplying it by 8 to get the result of 0.4. This straightforward approach demonstrates how to tackle basic percent calculations efficiently.	Solving Percent Equations
Math Example--Percents--Equations with Percents: Example 10	Math Example--Percents--Equations with Percents: Example 10 Topic Solving Equations Description This math example demonstrates solving percent equations by asking "What is 170% of 9.5?" The solution involves converting 170% to its decimal equivalent, 1.7, and then multiplying it by 9.5 to obtain the result of 16.15. This example combines a percentage greater than 100% with a decimal base number, further illustrating the versatility of the percent-to-decimal conversion method in complex scenarios.	Solving Percent Equations
Math Example--Percents--Equations with Percents: Example 11	Math Example--Percents--Equations with Percents: Example 11 Topic Solving Equations Description This math example focuses on solving percent equations, specifically asking "What is 225.5% of 78?" The solution involves converting 225.5% to its decimal form, 2.255, and then multiplying it by 78 to arrive at the answer of 175.89. This example introduces a decimal percentage greater than 200% and a larger whole number as the base value, demonstrating the scalability and flexibility of the percent-to-decimal conversion method in complex scenarios.	Solving Percent Equations
Math Example--Percents--Equations with Percents: Example 12	Math Example--Percents--Equations with Percents: Example 12 Topic Solving Equations Description This math example demonstrates solving percent equations by asking "What is 400% of 92.8?" The solution involves converting 400% to its decimal equivalent, 4.0, and then multiplying it by 92.8 to obtain the result of 371.2. This example showcases how to handle percentages greater than 100% and their application to decimal numbers, illustrating the versatility of the percent-to-decimal conversion method in complex scenarios.	Solving Percent Equations
Math Example--Percents--Equations with Percents: Example 13	Math Example--Percents--Equations with Percents: Example 13 Topic Solving Equations Description This math example focuses on solving percent equations by asking "5 is what percent of 9?" The solution involves setting up the equation 9 * (x / 100) = 5, then solving for x to get x = 5 * (100 / 9), which is approximately 55.56%. This example introduces a new type of percent problem where students must find the percentage given two known values.	Solving Percent Equations
Math Example--Percents--Equations with Percents: Example 14	Math Example--Percents--Equations with Percents: Example 14 Topic Solving Equations Description This math example demonstrates solving percent equations by asking "6 is what percent of 2.3?" The solution involves setting up the equation 2.3 * (x / 100) = 6, then solving for x to get x = 6 * (100 / 2.3), which is approximately 260.87%. This example introduces a scenario where the resulting percentage is greater than 100% and involves a decimal base number.	Solving Percent Equations
Math Example--Percents--Equations with Percents: Example 15	Math Example--Percents--Equations with Percents: Example 15 Topic Solving Equations Description This math example focuses on solving percent equations by asking "9 is what percent of 38?" The solution involves setting up the equation 38 * (x / 100) = 9, then solving for x to get x = 9 * (100 / 38), which is approximately 23.68%. This example demonstrates how to calculate a percentage when the first number is smaller than the second, resulting in a percentage less than 100%.	Solving Percent Equations
Math Example--Percents--Equations with Percents: Example 16	Math Example--Percents--Equations with Percents: Example 16 Topic Solving Equations Description This math example demonstrates solving percent equations by asking "2 is what percent of 55.5?" The solution involves setting up the equation 55.5 * (x / 100) = 2, then solving for x to get x = 2 * (100 / 55.5), which is approximately 3.6036%. This example introduces a scenario where the resulting percentage is a small fraction, less than 5%, and involves a decimal base number.	Solving Percent Equations
Math Example--Percents--Equations with Percents: Example 17	Math Example--Percents--Equations with Percents: Example 17 Topic Solving Equations Description This math example focuses on solving percent equations by asking "8 is what percent of 120?" The solution involves setting up the equation 120 * (x / 100) = 8, then solving for x to get x = 8 * (100 / 120), which is approximately 6.67%. This example demonstrates how to calculate a percentage when dealing with larger whole numbers, resulting in a percentage less than 10%.	Solving Percent Equations
Math Example--Percents--Equations with Percents: Example 18	Math Example--Percents--Equations with Percents: Example 18 Topic Solving Equations Description This math example demonstrates solving percent equations by asking "3.5 is what percent of 350?" The solution involves setting up the equation 350 * (x / 100) = 3.5, then solving for x to get x = 3.5 * (100 / 350), which equals 1%. This example introduces a scenario where the resulting percentage is a whole number (1%) and involves a decimal number as the first value.	Solving Percent Equations
Math Example--Percents--Equations with Percents: Example 19	Math Example--Percents--Equations with Percents: Example 19 Topic Solving Equations Description This math example focuses on solving percent equations by asking "12 is what percent of 8?" The solution involves setting up the equation 8 * (x / 100) = 12, then solving for x to get x = 12 * (100 / 8), which equals 150%. This example demonstrates how to calculate a percentage when the first number is larger than the second, resulting in a percentage greater than 100%.	Solving Percent Equations
Math Example--Percents--Equations with Percents: Example 2	Math Example--Percents--Equations with Percents: Example 2 Topic Solving Equations Description This math example demonstrates solving percent equations by asking "What is 7% of 9.5?" The solution involves converting 7% to its decimal equivalent, 0.07, and then multiplying it by 9.5 to obtain the result of 0.665. This example builds upon the previous one by introducing a decimal number as the base value.	Solving Percent Equations
Math Example--Percents--Equations with Percents: Example 20	Math Example--Percents--Equations with Percents: Example 20 Topic Solving Equations Description This math example demonstrates solving percent equations by asking "32 is what percent of 1.5?" The solution involves setting up the equation 1.5 * (x / 100) = 32, then solving for x to get x = 32 * (100 / 1.5), which equals 2133.3%. This example introduces a scenario where the resulting percentage is significantly larger than 100% and involves a decimal base number less than 1.	Solving Percent Equations
Math Example--Percents--Equations with Percents: Example 21	Math Example--Percents--Equations with Percents: Example 21 Topic Solving Equations Description This math example focuses on solving percent equations by asking "48 is what percent of 55?" The solution involves setting up the equation 55 * (x / 100) = 48, then solving for x to get x = 48 * (100 / 55), which equals 87.27%. This example demonstrates how to calculate a percentage when the two numbers are relatively close in value, resulting in a percentage close to but less than 100%.	Solving Percent Equations

Illustrative Math Alignment: Grade 6 Unit 3

Unit Rates and Percentages

Lesson 14: Solving Percentage Problems

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