Illustrative Math Alignment: Grade 7 Unit 9

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.

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.

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.

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.

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.

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.

Topic

Math of Money

Description

This example demonstrates compound interest calculation for a $1000 investment at a 2.5% interest rate over 5 years, compounded annually. Using the formula A = P(1 + r/n)nt, where P is the principal amount, r is the interest rate, n is the number of times interest is compounded per year, and t is the number of years, the final amount is calculated to be $1131.41.

Topic

Math of Money

Description

This example calculates compound interest for a $1000 investment at a 5% interest rate over 5 years, compounded monthly. Using the formula A = P(1 + r/n)nt, where P = 1000, r = 0.05, n = 12, and t = 5, the final amount is $1283.61.

Compound interest is a key concept in financial mathematics that shows how investments grow over time. This example highlights monthly compounding, demonstrating the impact of more frequent compounding on returns. Understanding these differences helps students apply compound interest in real-world financial scenarios.

Topic

Math of Money

Description

This example calculates compound interest for a $1000 investment at a 5% interest rate over 5 years, compounded daily. The formula $$A = P(1 + r/n)nt is used with P = 1000, r = 0.05, n = 365, and t = 5, resulting in an amount of $1284.00.

Understanding compound interest is crucial for financial literacy. This example demonstrates daily compounding and its effect on investment growth compared to other frequencies. By exploring various scenarios, students learn how different compounding intervals influence financial outcomes.

Topic

Math of Money

Description

This example calculates compound interest for a $1000 investment at a 5% interest rate over 5 years, compounded continuously. Using the formula A = Pert, where P = 1000, r = 0.05, and t = 5, the final amount is $1284.03.

Compound interest is a fundamental concept in finance, illustrating how investments grow exponentially over time. This example highlights continuous compounding, which shows the impact of applying interest at every possible moment. Understanding these differences helps students apply compound interest in real-world financial scenarios.

Topic

Math of Money

Description

This example calculates compound interest for a $1000 investment with an interest rate of 2.5% over 10 years, compounded annually. Using the formula A = P(1 + r/n)nt, where P = 1000, r = 0.025, n = 1, and $$t = 10, the final amount is $1280.08.

Understanding compound interest is crucial for financial literacy. This example demonstrates annual compounding and its effect on investment growth compared to other frequencies. By exploring various scenarios, students learn how different compounding intervals influence financial outcomes.

Topic

Math of Money

Description

This example calculates compound interest for a $1000 investment with a 2.5% interest rate, compounded semi-annually over 10 years. Using the formula A = P(1 + r/n)nt, where P = 1000, r = 0.025, n = 2, and t = 10, the final amount is $1282.04.

Understanding compound interest is essential for financial literacy. This example demonstrates semi-annual compounding and its effect on investment growth compared to other frequencies. By exploring various scenarios, students learn how different compounding intervals influence financial outcomes.

Topic

Math of Money

Description

This example calculates compound interest for a $1000 investment with a 2.5% interest rate, compounded quarterly over 10 years. Using the formula A = P(1 + r/n)nt, where P = 1000, r = 0.025, n = 4, and t = 10, the final amount is $1283.03.

Understanding compound interest is crucial for financial literacy. This example demonstrates quarterly compounding and its effect on investment growth compared to other frequencies. By exploring various scenarios, students learn how different compounding intervals influence financial outcomes.

Topic

Math of Money

Description

This example calculates compound interest for a $1000 investment with a 2.5% interest rate, compounded monthly over 10 years. Using the formula A = P(1 + r/n)nt, where P = 1000, r = 0.025, n = 12, and t = 10, the final amount is $1283.18.

Understanding compound interest is crucial for financial literacy. This example demonstrates monthly compounding and its effect on investment growth compared to other frequencies. By exploring various scenarios, students learn how different compounding intervals influence financial outcomes.

Topic

Math of Money

Description

This example demonstrates compound interest calculation for a $1000 investment at a 2.5% interest rate over 10 years, compounded daily. Using the formula A = P(1 + r/n)nt, with P = 1000, r = 0.025, n = 365, and t = 10, the result is $1284.01.

Understanding compound interest is essential for financial literacy. This example demonstrates daily compounding and its effect on investment growth compared to other frequencies. By exploring various scenarios, students learn how different compounding intervals influence financial outcomes.

Topic

Math of Money

Description

This example illustrates compound interest for a $1000 investment at a 2.5% interest rate over 10 years with continuous compounding. The formula for continuous compounding is A = Pert. With P = 1000, r = 0.025, and t = 10, the amount is calculated as $1284.03.

Understanding compound interest is crucial for financial literacy. This example demonstrates continuous compounding and its effect on investment growth compared to other frequencies. By exploring various scenarios, students learn how different compounding intervals influence financial outcomes.

Topic

Math of Money

Description

This example shows how to calculate compound interest for a $1000 investment with a 5% annual interest rate over 10 years, compounded annually. The formula used is A = P(1 + r/n)nt. Given P = 1000, r = 0.05, n = 1, and t = 10, the calculation yields $1628.89.

Understanding compound interest is essential for financial literacy. This example demonstrates annual compounding and its effect on investment growth compared to other frequencies. By exploring various scenarios, students learn how different compounding intervals influence financial outcomes.

Topic

Math of Money

Description

This example illustrates the calculation of compound interest for a $1000 investment at a 2.5% interest rate over 5 years, compounded semi-annually. The formula A = P(1 + r/n)nt is applied with P = 1000, r = 0.025, n = 2, and t = 5. The final amount after 5 years is $1132.27.

Topic

Math of Money

Description

This example calculates compound interest for a $1000 investment with a 5% interest rate, compounded twice a year over 10 years. The formula used is A = P(1 + r/n)nt. Given P = 1000, r = 0.05, n = 2, and t = 10, the calculation results in $1638.62.

Understanding compound interest is crucial for financial literacy. This example demonstrates semi-annual compounding and its effect on investment growth compared to other frequencies. By exploring various scenarios, students learn how different compounding intervals influence financial outcomes.

Topic

Math of Money

Description

This example calculates compound interest for a $1000 investment with a 5% interest rate over 10 years, compounded quarterly. Using the formula A = P(1 + r/n)nt, with P = 1000, r = 0.05, n = 4, and t = 10, the result is $1643.62.

Understanding compound interest is essential for financial literacy. This example demonstrates quarterly compounding and its effect on investment growth compared to other frequencies. By exploring various scenarios, students learn how different compounding intervals influence financial outcomes.

Topic

Math of Money

Description

This example presents the calculation of compound interest for a $1000 investment with a 5% interest rate over 10 years, compounded monthly. Using the formula A = P(1 + r/n)nt, with P = 1000, r = 0.05, n = 12, and t = 10, the final amount is $1647.67.

Understanding compound interest is crucial for financial literacy. This example demonstrates monthly compounding and its effect on investment growth compared to other frequencies. By exploring various scenarios, students learn how different compounding intervals influence financial outcomes.

Topic

Math of Money

Description

This example illustrates calculating compound interest for a $1000 investment with a 5% interest rate over 10 years, compounded daily. Using the formula A = P(1 + r/n)nt, with P = 1000, r = 0.05, n = 365.25, and t = 10, the result is $1648.65.

Understanding compound interest is essential for financial literacy. This example demonstrates daily compounding and its effect on investment growth compared to other frequencies. By exploring various scenarios, students learn how different compounding intervals influence financial outcomes.

Topic

Math of Money

Description

This example shows calculating compound interest for a $1000 investment with a 5% interest rate, compounded continuously over 10 years. The formula used is A = Pert. Given P = 1000, r = 0.05, and t = 10, the calculation results in $1648.72.

Understanding compound interest is crucial for financial literacy. This example demonstrates continuous compounding and its effect on investment growth compared to other frequencies. By exploring various scenarios, students learn how different compounding intervals influence financial outcomes.

Topic

Math of Money

Description

This example demonstrates the calculation of compound interest for a $1000 investment at a 2.5% interest rate over 5 years, compounded quarterly. The formula A = P(1 + r/n)nt is used, where P = 1000, r = 0.025, n = 4, and t = 5. The resulting amount after 5 years is $1132.71.

Topic

Math of Money

Description

This example illustrates the calculation of compound interest for a $1000 investment at a 2.5% interest rate over 5 years, compounded monthly. The formula A = P(1 + r/n)nt is applied with P = 1000, r = 0.025, n = 12, and t = 5. The final amount after 5 years is $1132.78.

Topic

Math of Money

Description

This example demonstrates the calculation of compound interest for a $1000 investment at a 2.5% interest rate over 5 years, compounded daily. The formula A = P(1 + r/n)nt is used, where P = 1000, r = 0.025, n = 365.25, and t = 5. The resulting amount after 5 years is $1133.14.

Topic

Math of Money

Description

This example demonstrates the calculation of compound interest for a $1000 investment at a 2.5% interest rate, compounded continuously over 5 years. Using the formula A = P•ert, where P = 1000, r = 0.025, and t = 5, the final amount is calculated as $1133.15.

Topic

Math of Money

Description

This example calculates compound interest for a $1000 investment with a 5% annual interest rate over 5 years, compounded annually. Using the formula A = P(1 + r/n)nt, where P = 1000, r = 0.05, n = 1, and t = 5, the final amount is $1276.28.

Compound interest is essential in understanding how investments grow over time. This example emphasizes annual compounding and its effects on investment returns. By examining different compounding frequencies, students can appreciate how often interest is applied impacts overall growth.

Topic

Math of Money

Description

This example calculates compound interest for a $1000 investment with a 5% interest rate, compounded semi-annually over 5 years. Using the formula A = P(1 + r/n)nt, where P = 1000, r = 0.05, n = 2, and t = 5, the final amount is $1280.08.

Compound interest is fundamental in financial mathematics, illustrating how investments grow over time. This example highlights semi-annual compounding, showing how different frequencies impact returns. Understanding these variations helps students grasp the practical applications of compound interest in real-life scenarios.

Topic

Math of Money

Description

This example illustrates calculating compound interest for a $1000 investment at a 5% interest rate, compounded quarterly over 5 years. The formula A = P(1 + r/n)nt is used with P = 1000, r = 0.05, n = 4, and t = 5, resulting in an amount of $1282.04.

Understanding compound interest is key to financial literacy, showing how investments can grow exponentially. This example demonstrates quarterly compounding and its influence on returns. By examining different compounding intervals, students gain insight into the effects on financial growth.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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%.

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.

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%.

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.