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Illustrative Math-Media4Math Alignment

 

 

Illustrative Math Alignment: Grade 7 Unit 7

Expressions, Equations, and Inequalities

Lesson 8: Reasoning about Solving Equations (Part 2)

Use the following Media4Math resources with this Illustrative Math lesson.

Thumbnail Image Title Body Curriculum Topic
Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 20 Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 20 Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 20

Topic

Linear Functions

Description

This example demonstrates the conversion of the linear equation -14x - 35y = 0 from standard form to slope-intercept form. The process involves isolating y and dividing by its coefficient, resulting in y = -2/5 x. This transformation clearly reveals the slope and y-intercept of the line.

 Standard Form
Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 21 Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 21 Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 21

Topic

Linear Functions

Description

This example showcases the transformation of the linear equation 28x - 21y = 0 from standard form to slope-intercept form. The process involves isolating y and dividing by its coefficient, resulting in y = 4/3 x. This step-by-step solution clearly reveals the slope and y-intercept of the line.

 Standard Form
Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 22 Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 22 Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 22

Topic

Linear Functions

Description

This example illustrates the conversion of the linear equation -13x + 39y = 0 from standard form to slope-intercept form. The solution involves isolating y and dividing by its coefficient, resulting in y = 1/3 x. This process clearly reveals the slope and y-intercept of the line.

 Standard Form
Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 3 Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 3 Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 3

Topic

Linear Functions

Description

This example showcases the transformation of the linear equation 5x - 2y = 12 from standard form to slope-intercept form. The process involves isolating y and dividing by its coefficient, resulting in y = 2.5x - 6. This step-by-step solution clearly reveals the slope and y-intercept of the line.

 Standard Form
Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 4 Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 4 Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 4

Topic

Linear Functions

Description

This example demonstrates the conversion of the linear equation -6x + 10y = 20 from standard form to slope-intercept form. The solution process involves isolating y and dividing by its coefficient, resulting in y = 0.6x + 2. This transformation clearly reveals the slope and y-intercept of the line.

 Standard Form
Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 5 Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 5 Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 5

Topic

Linear Functions

Description

This example illustrates the process of converting the linear equation -9x - 15y = -45 from standard form to slope-intercept form. The solution involves rearranging the equation to isolate y, resulting in y = 3/5 x + 3. This transformation clearly reveals the slope and y-intercept of the line.

 Standard Form
Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 6 Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 6 Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 6

Topic

Linear Functions

Description

This example demonstrates the conversion of the linear equation -8x - 12y = 25 from standard form to slope-intercept form. The process involves manipulating the equation to solve for y, yielding y = -2/3 x - 25/12. This transformation clearly reveals the slope and y-intercept of the line.

 Standard Form
Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 7 Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 7 Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 7

Topic

Linear Functions

Description

This example illustrates the transformation of the linear equation -2x + 16y = -36 from standard form to slope-intercept form. The solution process involves solving for y, resulting in y = 1/8 x - 9/4. This step-by-step conversion clearly reveals the slope and y-intercept of the line.

 Standard Form
Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 8 Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 8 Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 8

Topic

Linear Functions

Description

This example showcases the conversion of the linear equation -7x + 21y = 63 from standard form to slope-intercept form. The process involves rearranging the equation to isolate y, resulting in y = 1/3 x + 3. This transformation clearly reveals the slope and y-intercept of the line.

 Standard Form
Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 9 Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 9 Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 9

Topic

Linear Functions

Description

This example demonstrates the process of converting the linear equation 10x - 28y = 56 from standard form to slope-intercept form. The solution involves isolating y and dividing by its coefficient, resulting in y = (5/14)x - 2. This transformation clearly reveals the slope and y-intercept of the line.

 Standard Form
Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 1 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 1 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 1

This is part of a collection of math examples that focus on linear function concepts.

 Point-Slope Form and Slope-Intercept Form
Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 10 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 10 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 10

This is part of a collection of math examples that focus on linear function concepts.

 Point-Slope Form and Slope-Intercept Form
Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 11 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 11 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 11

This is part of a collection of math examples that focus on linear function concepts.

 Point-Slope Form and Slope-Intercept Form
Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 12 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 12 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 12

This is part of a collection of math examples that focus on linear function concepts.

 Point-Slope Form and Slope-Intercept Form
Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 13 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 13 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 13

This is part of a collection of math examples that focus on linear function concepts.

 Point-Slope Form and Slope-Intercept Form
Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 14 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 14 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 14

This is part of a collection of math examples that focus on linear function concepts.

 Point-Slope Form and Slope-Intercept Form
Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 15 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 15 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 15

This is part of a collection of math examples that focus on linear function concepts.

 Point-Slope Form and Slope-Intercept Form
Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 16 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 16 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 16

This is part of a collection of math examples that focus on linear function concepts.

 Point-Slope Form and Slope-Intercept Form
Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 17 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 17 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 17

This is part of a collection of math examples that focus on linear function concepts.

 Point-Slope Form and Slope-Intercept Form
Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 18 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 18 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 18

This is part of a collection of math examples that focus on linear function concepts.

 Point-Slope Form and Slope-Intercept Form
Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 19 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 19 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 19

This is part of a collection of math examples that focus on linear function concepts.

 Point-Slope Form and Slope-Intercept Form
Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 2 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 2 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 2

This is part of a collection of math examples that focus on linear function concepts.

 Point-Slope Form and Slope-Intercept Form
Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 20 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 20 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 20

This is part of a collection of math examples that focus on linear function concepts.

 Point-Slope Form and Slope-Intercept Form
Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 21 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 21 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 21

This is part of a collection of math examples that focus on linear function concepts.

 Point-Slope Form and Slope-Intercept Form
Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 22 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 22 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 22

This is part of a collection of math examples that focus on linear function concepts.

 Point-Slope Form and Slope-Intercept Form
Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 23 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 23 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 23

This is part of a collection of math examples that focus on linear function concepts.

 Point-Slope Form and Slope-Intercept Form
Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 24 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 24 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 24

This is part of a collection of math examples that focus on linear function concepts.

 Point-Slope Form and Slope-Intercept Form
Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 25 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 25 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 25

This is part of a collection of math examples that focus on linear function concepts.

 Point-Slope Form and Slope-Intercept Form
Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 26 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 26 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 26

This is part of a collection of math examples that focus on linear function concepts.

 Point-Slope Form and Slope-Intercept Form
Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 27 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 27 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 27

This is part of a collection of math examples that focus on linear function concepts.

 Point-Slope Form and Slope-Intercept Form
Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 28 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 28 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 28

This is part of a collection of math examples that focus on linear function concepts.

 Point-Slope Form and Slope-Intercept Form
Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 29 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 29 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 29

This is part of a collection of math examples that focus on linear function concepts.

 Point-Slope Form and Slope-Intercept Form
Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 3 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 3 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 3

This is part of a collection of math examples that focus on linear function concepts.

 Point-Slope Form and Slope-Intercept Form
Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 4 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 4 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 4

This is part of a collection of math examples that focus on linear function concepts.

 Point-Slope Form and Slope-Intercept Form
Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 5 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 5 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 5

This is part of a collection of math examples that focus on linear function concepts.

 Point-Slope Form and Slope-Intercept Form
Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 6 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 6 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 6

This is part of a collection of math examples that focus on linear function concepts.

 Point-Slope Form and Slope-Intercept Form
Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 7 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 7 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 7

This is part of a collection of math examples that focus on linear function concepts.

 Point-Slope Form and Slope-Intercept Form
Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 8 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 8 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 8

This is part of a collection of math examples that focus on linear function concepts.

 Point-Slope Form and Slope-Intercept Form
Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 9 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 9 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 9

This is part of a collection of math examples that focus on linear function concepts.

 Point-Slope Form and Slope-Intercept Form
Math Example--Percents-- Equations with Percents: Example 1 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 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 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 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 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 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 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 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 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 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 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