Illustrative Math Alignment: Grade 7 Unit 4

Video Tutorial: Percents: Calculating Tax. In this video we look at using tax rates to calculate tax owed. The tax rates are written as percents and converted to decimals to calculate the tax.

This video is part of a series of videos that cover the topic of percents. This includes the definition of a percent, percent operations, and applications of percents. Each video includes real-world examples of using percents to solve specific problems. 

Video Tutorial: Percents: Percent Decrease. In this video, we look at the concept of percent decrease. The formula for calculating percent decrease is shown and used in the context of solving real-world problems.

This video is part of a series of videos that cover the topic of percents. This includes the definition of a percent, percent operations, and applications of percents. Each video includes real-world examples of using percents to solve specific problems. 

Video Tutorial: Percents: Percent Increase. In this video, we look at the concept of percent increase. The formula for calculating percent increase is shown and used in the context of solving real-world problems.

This video is part of a series of videos that cover the topic of percents. This includes the definition of a percent, percent operations, and applications of percents. Each video includes real-world examples of using percents to solve specific problems. 

Topic

Financial Literacy

Definition

Capital gains tax is a tax on the profit realized from the sale of a non-inventory asset.

Topic

Financial Literacy

Definition

Federal income tax is a tax levied by the government on the annual earnings of individuals, corporations, and other legal entities.

Topic

Financial Literacy

Definition

Income tax is a tax levied by governments on personal income.

Topic

Financial Literacy

Definition

State income tax is a tax levied by individual states on the income of residents and businesses operating within the state.

Topic

Financial Literacy

Definition

Tax is a mandatory financial charge imposed by a government on individuals or entities to fund public expenditures.

Description

Taxes are essential for funding government operations and public services, such as infrastructure, education, and healthcare. Understanding taxes is crucial for personal financial planning and compliance with legal obligations. In real-world applications, taxes influence spending, saving, and investment decisions. Math education helps students understand how taxes are calculated and their impact on net income. A teacher might explain, "Taxes are money you pay to the government, which helps fund services like schools and roads."

Topic

Financial Literacy

Definition

A tax credit is an amount that taxpayers can subtract directly from taxes owed to the government.

Topic

Financial Literacy

Definition

A tax deduction is an expense that can be subtracted from gross income to reduce the amount of income that is subject to tax.

Topic

Financial Literacy

Definition

Taxable income is the portion of an individual's or business's income that is subject to taxation after all deductions and exemptions are applied.

Topic

Ratios, Proportions, and Percents

Definition

Calculating tax involves determining the percentage amount to be added to the base price of a product or service.

Description

Calculating tax is a fundamental application of percentages in real-world scenarios. When purchasing goods or services, the total cost is often the sum of the base price and the tax applied. Understanding how to calculate tax is essential for budgeting and financial literacy.

For example, if a product costs $50 and the tax rate is 8%, the tax amount is calculated as 

50 × 0.08 = 4

Therefore, the total cost is 

In this Algebra Application, students study the life cycles of 13- and 17-year cicadas, as well as the populations of bird predators. Students develop a mathematical model using spreadsheets and investigate why the prime number life cycles help the cicadas. The math topics covered include: Mathematical modeling, Data gathering and analysis, Percent increase and decrease, Prime numbers and composites. This real world application of math concepts will engage your students.

Topic

Ratios, Proportions, and Percents

Description

The image introduces the concept of percent change with the formula: Percent Change = (New - Original) / Original * 100%. It establishes the formula as the foundation for understanding percent change throughout the sequence.

Math clip art provides a visual and engaging way to explore complex mathematical concepts such as percent change. These examples illustrate how numbers, fractions, and percentages are interconnected, helping to build students' numerical reasoning skills.

Topic

Ratios, Proportions, and Percents

Description

This image explains that percent increase measures the change from one number to a greater number. It provides context for when to apply the concept of percent increase in real-life scenarios.

Math clip art provides a visual and engaging way to explore complex mathematical concepts such as percent change. These examples illustrate how numbers, fractions, and percentages are interconnected, helping to build students' numerical reasoning skills.

Topic

Ratios, Proportions, and Percents

Description

This image highlights that the numerical increase is the difference between the new and original values. It adds clarity by breaking down the calculation into a numerical difference.

Math clip art provides a visual and engaging way to explore complex mathematical concepts such as percent change. These examples illustrate how numbers, fractions, and percentages are interconnected, helping to build students' numerical reasoning skills.

Topic

Ratios, Proportions, and Percents

Description

This image demonstrates how numerical increase is represented as fractional change using the formula: (b - a) / a. It bridges numerical increase to fractional change, setting up for conversion to percent increase.

Math clip art provides a visual and engaging way to explore complex mathematical concepts such as percent change. These examples illustrate how numbers, fractions, and percentages are interconnected, helping to build students' numerical reasoning skills.

Topic

Ratios, Proportions, and Percents

Description

This image shows the formula for percent change as a fractional change expressed as a percentage: (b - a) / a * 100%. It reinforces the connection between fractional change and percent increase as part of the calculation process.

Math clip art provides a visual and engaging way to explore complex mathematical concepts such as percent change. These examples illustrate how numbers, fractions, and percentages are interconnected, helping to build students' numerical reasoning skills.

Topic

Ratios, Proportions, and Percents

Description

This image provides an example of a percent increase calculation from 8 to 10, resulting in 25%. It offers a practical example to illustrate how the formula is applied to real numbers.

Math clip art provides a visual and engaging way to explore complex mathematical concepts such as percent change. These examples illustrate how numbers, fractions, and percentages are interconnected, helping to build students' numerical reasoning skills.

Topic

Ratios, Proportions, and Percents

Description

This image reiterates the example calculation, emphasizing that the change from 8 to 10 is a 25% increase. It reinforces understanding by repeating the example with emphasis on the interpretation of the result.

Math clip art provides a visual and engaging way to explore complex mathematical concepts such as percent change. These examples illustrate how numbers, fractions, and percentages are interconnected, helping to build students' numerical reasoning skills.

Topic

Ratios, Proportions, and Percents

Description

This image defines percent decrease as the change from one number to a lesser number. It introduces the complementary concept of percent decrease to show both directions of percent change.

Math clip art provides a visual and engaging way to explore complex mathematical concepts such as percent change. These examples illustrate how numbers, fractions, and percentages are interconnected, helping to build students' numerical reasoning skills.

Topic

Ratios, Proportions, and Percents

Description

This image explains that numerical decrease is the difference between the new and original values. It mirrors the earlier explanation of numerical increase, ensuring consistency in presenting both cases.

Math clip art provides a visual and engaging way to explore complex mathematical concepts such as percent change. These examples illustrate how numbers, fractions, and percentages are interconnected, helping to build students' numerical reasoning skills.

Topic

Ratios, Proportions, and Percents

Description

This image demonstrates fractional change for a decrease using the formula: (b - a) / a. It completes the explanation of percent change by connecting numerical decrease to fractional representation.

Math clip art provides a visual and engaging way to explore complex mathematical concepts such as percent change. These examples illustrate how numbers, fractions, and percentages are interconnected, helping to build students' numerical reasoning skills.

Topic

Ratios, Proportions, and Percents

Description

This image explains that percent decrease represents fractional change expressed as a percentage: (b - a) / a * 100%. It extends the explanation to show how fractional change can be converted to percent decrease.

Math clip art provides a visual and engaging way to explore complex mathematical concepts such as percent change. These examples illustrate how numbers, fractions, and percentages are interconnected, helping to build students' numerical reasoning skills.

Topic

Ratios, Proportions, and Percents

Description

This image provides an example of a percent decrease calculation from 10 to 8, resulting in -20%. It offers a practical example illustrating the application of the formula to calculate percent decrease.

Math clip art provides a visual and engaging way to explore complex mathematical concepts such as percent change. These examples illustrate how numbers, fractions, and percentages are interconnected, helping to build students' numerical reasoning skills.

Topic

Ratios, Proportions, and Percents

Description

This image reiterates the example, emphasizing that the change from 10 to 8 represents a 20% decrease. It reinforces understanding by summarizing the example with focus on the final interpretation of the result.

Math clip art provides a visual and engaging way to explore complex mathematical concepts such as percent change. These examples illustrate how numbers, fractions, and percentages are interconnected, helping to build students' numerical reasoning skills.

Topic

The Math of Money

Description

What is the tax due on a $1000 purchase when the sales tax rate is 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.

Topic

The Math of Money

Description

What is the tax due on a $9999.99 purchase when the sales tax rate is 9.9%? 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.

Topic

The Math of Money

Description

What is the tax due on a $1500 purchase when the sales tax rate is 6%? 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.

Topic

The Math of Money

Description

What is the tax due on a $2550 purchase when the sales tax rate is 7%? 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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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

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.