Illustrative Math Alignment: Grade 8 Unit 3

This tutorials provides a summary of the properties of one-step equations. Note: The download is a PDF version of this tutorial.

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An equation shows a relationship between two quantities. The download is a PDF.

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To see the complete library of Instructional Resources , click on this link.

This tutorial provides an overview of two-step equations. Note: The download is a PDF version of this tutorial.

Library of Instructional Resources

To see the complete library of Instructional Resources , click on this link.

An equation shows a relationship between two quantities. Note: The download is a PDF.

Library of Instructional Resources

To see the complete library of Instructional Resources , click on this link.

This slide show shows what a system of equations is.

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Library of Instructional Resources

To see the complete library of Instructional Resources , click on this link.

Review key vocabulary on the topic of equations with this interactive and printable crossword puzzle.

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Review key vocabulary on the topic of equations with this interactive and printable crossword puzzle.

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Use this math game to review true equations, false equations, and conditional equations. The game provides feedback.

Use this math game to review one-step equations. Students are shown four equations and are asked to correctly label the equation with drag-and-drop. The game provides feedback.

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Use this math game to review two-step equations. Students are shown four equations and are asked to correctly label the equation with drag-and-drop. The game provides feedback.

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Review key vocabulary on the topic of equations with this interactive and printable word search puzzle.

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This is part of a collection of math clip art images that model numbers and expressions using algebra tiles.

This is part of a collection of math clip art images that model numbers and expressions using algebra tiles.

This is part of a collection of math clip art images that model numbers and expressions using algebra tiles.

This is part of a collection of math clip art images that model numbers and expressions using algebra tiles.

This is part of a collection of math clip art images that model numbers and expressions using algebra tiles.

This is part of a collection of math clip art images that model numbers and expressions using algebra tiles.

Topic

Inequalities

Description

This example demonstrates how to graph the linear inequality y > 2x + 3. The graph shows a dashed line representing the equation y = 2x + 3, with the region above the line shaded to indicate where the inequality holds true. The use of a dashed line signifies that points on the line itself are not included in the solution set.

Topic

Inequalities

Description

This example illustrates the graphing of the linear inequality y ≤ 3x + 2. The graph features a solid line representing the equation y = 3x + 2, with the area below the line shaded to indicate the region where the inequality is satisfied. The solid line signifies that points on the line are included in the solution set.

Topic

Inequalities

Description

This example demonstrates the graphing of the linear inequality y ≤ -2x + 1. The graph shows a solid line representing the equation y = -2x + 1, with the region below the line shaded to indicate where the inequality holds true. The solid line signifies that points on the line are included in the solution set.

Topic

Inequalities

Description

This example illustrates the graphing of the linear inequality y ≤ -3. The graph features a solid horizontal line at y = -3, with the region below this line shaded to represent the solution set of the inequality. The use of a solid line indicates that points on the line itself are included in the solution.

Topic

Inequalities

Description

This example illustrates the graphing of the linear inequality y > -3x + 1. The graph features a dashed line representing the equation y = -3x + 1, with the area above the line shaded to indicate the region where the inequality is satisfied. The dashed line signifies that points on the line are not part of the solution set.

Topic

Inequalities

Description

This example demonstrates the graphing of the linear inequality y > -1. The graph shows a dashed horizontal line at y = -1, with the region above this line shaded to represent the solution set of the inequality. The use of a dashed line indicates that points on the line itself are not included in the solution.

Topic

Inequalities

Description

This example illustrates the graphing of the linear inequality y < x - 2. The graph features a dashed line representing the equation y = x - 2, with the area below the line shaded to indicate the region where the inequality holds true. The dashed line signifies that points on the line are not included in the solution set.

Topic

Inequalities

Description

This example demonstrates the graphing of the linear inequality y < -3x + 4. The graph shows a dashed line representing the equation y = -3x + 4, with the region below the line shaded to indicate where the inequality holds true. Quadrants II and III are predominantly shaded, illustrating the solution set of this inequality.

Topic

Inequalities

Description

This example illustrates the graphing of the linear inequality y < 6. The graph features a horizontal dashed line at y = 6, with the region below this line shaded to represent the solution set of the inequality. Quadrants III and IV are entirely shaded, demonstrating where the inequality holds true.

Topic

Inequalities

Description

This example demonstrates the graphing of the linear inequality y ≥ 5x + 3. The graph shows a solid line representing the equation y = 5x + 3, with the region above the line shaded to indicate where the inequality holds true. Quadrants I and II are predominantly shaded, illustrating the solution set of this inequality. The use of a solid line signifies that points on the line are included in the solution.

Topic

Inequalities

Description

This example illustrates the graphing of the linear inequality y ≥ -2x - 1. The graph features a solid line representing the equation y = -2x - 1, with the area above the line shaded to indicate the region where the inequality is satisfied. Quadrants I and IV are predominantly shaded, demonstrating the solution set of this inequality. The solid line signifies that points on the line are included in the solution.

Topic

Inequalities

Description

This example demonstrates the graphing of the linear inequality y ≥ 2. The graph shows a solid horizontal line at y = 2, with the region above this line shaded to represent the solution set of the inequality. The use of a solid line indicates that points on the line itself are included in the solution.

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.

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%.

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.

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.

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%.

Topic

Solving Equations

Description

This math example demonstrates solving percent equations by asking "52.2 is what percent of 98.5?" The solution involves setting up the equation 98.5 * (x / 100) = 52.2, then solving for x to get x = 52.2 * (100 / 98.5), which is approximately 52.99%. This example introduces a scenario where both the numerator and denominator are decimal numbers, resulting in a percentage that is also close to the original numerator.

Topic

Solving Equations

Description

This math example focuses on solving percent equations by asking "68 is what percent of 320?" The solution involves setting up the equation 320 * (x / 100) = 68, then solving for x to get x = 68 * (100 / 320), which equals 21.25%. This example demonstrates how to calculate a percentage when dealing with whole numbers, resulting in a percentage that's less than 25%.

Topic

Solving Equations

Description

This math example demonstrates solving percent equations by asking "75.5 is what percent of 555.25?" The solution involves setting up the equation 555.25 * (x / 100) = 75.5, then solving for x to get x = 75.5 * (100 / 555.25), which is approximately 13.59%. This example introduces a scenario where both the numerator and denominator are decimal numbers, resulting in a percentage that's less than 15%.

Topic

Solving Equations

Description

This math example focuses on solving percent equations by asking "125 is what percent of 2?" The solution involves setting up the equation 2 * (x / 100) = 125, then solving for x to get x = 125 * (100 / 2), which equals 6250%. This example demonstrates how to calculate a percentage when the first number is significantly larger than the second, resulting in a percentage well over 100%.

Topic

Solving Equations

Description

This math example demonstrates solving percent equations by asking "300 is what percent of 3.5?" The solution involves setting up the equation 3.5 * (x / 100) = 300, then solving for x to get x = 300 * (100 / 3.5), which equals 8571.43%. This example introduces a scenario where the resulting percentage is extremely large, over 8000%, due to the first number being significantly larger than the small decimal base number.

Topic

Solving Equations

Description

This math example focuses on solving percent equations by asking "278 is what percent of 99?" The solution involves setting up the equation 99 * (x / 100) = 278, then solving for x to get x = 278 * (100 / 99), which equals 280.80%. This example demonstrates how to calculate a percentage when the first number is significantly larger than the second, resulting in a percentage greater than 200%.

Topic

Solving Equations

Description

This math example demonstrates solving percent equations by asking "300 is what percent of 75.5?" The solution involves setting up the equation 75.5 * (x / 100) = 300, then solving for x to get x = 300 * (100 / 75.5), which equals 397.35%. This example introduces a scenario where the resulting percentage is close to 400%, with the first number being significantly larger than the decimal base number.