Illustrative Math Alignment: Grade 6 Unit 1

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

Ratios, Proportions, and Percents

Description

The image illustrates the concept of an introductory image that visually connects percents with proportions, showcasing a grid and a formula (a / b = c / d) next to a hurdler and a large percent sign. The golden ratio a / b = 1.618 is also present, symbolizing relationships, and expands on this idea by showing that serves as a thematic and conceptual introduction to percents by emphasizing proportional relationships and the idea of ratios.

Topic

Ratios, Proportions, and Percents

Description

The image illustrates the concept of fractions with different denominators: 1/4, 2/5, 5/6, and 5/8, each depicted as shaded portions of circles. and expands on this idea by showing that highlights the challenge of comparing fractions with different denominators, setting up the need for a common framework such as percents.

Topic

Ratios, Proportions, and Percents

Description

The image illustrates the concept of and expands on the previous image by comparing and ordering the fractions using inequality symbols: 1/4 < 2/5 < 5/8 < 5/6. This image expands on this idea by emphasizing the difficulty of comparing fractions and transitions to the rationale for using percents as a standard for comparison.

Topic

Ratios, Proportions, and Percents

Description

The image illustrates the concept of converting the fractions 1/4, 2/5, 5/6, and 5/8 into percents (25%, 40%, 83.33%, 62.5%) with their corresponding pie diagrams. It expands on this idea by showing that introduces percents as an easier method for comparing fractions by representing them with a common denominator of 100.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

Topic

Fractions

Topic

Fractions

Topic

Fractions

Topic

Fractions

Topic

Fractions

Topic

Fractions

Topic

Fractions

Topic

Fractions

Topic

Fractions

Topic

Fractions

Topic

Fractions

Topic

Fractions

Topic

Fractions

Topic

Fractions

Topic

Fractions

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.