Illustrative Math Alignment: Grade 7 Unit 7

Expressions, Equations, and Inequalities

Lesson 9: Dealing with Negative Numbers

Use the following Media4Math resources with this Illustrative Math lesson.

Title	Body	Curriculum Topic
Math Example: Solving Quadratic Equations with Algebra Tiles--Example 1	Math Example: Solving Quadratic Equations with Algebra Tiles Topic Solving Equations Description In this example, we explore solving the quadratic equation x2 + 2x + 1 = 0 using algebra tiles. The visual representation shows how to rearrange the equation into (x + 1)2 = 0, demonstrating the power of algebra tiles in simplifying complex equations. By arranging the tiles, students can physically see the relationship between the terms and understand how they combine to form a perfect square trinomial.	Quadratic Equations and Functions
Math Example: Solving Quadratic Equations with Algebra Tiles--Example 2	Math Example: Solving Quadratic Equations with Algebra Tiles Topic Solving Equations Description This example illustrates the process of solving the quadratic equation x2+ 4x + 4 = 0 using algebra tiles. The visual representation demonstrates how to rearrange the equation into (x + 2)2 = 0, showcasing the power of algebra tiles in simplifying and solving quadratic equations. By arranging the tiles, students can physically see how the terms combine to form a perfect square trinomial, making the solution process more intuitive.	Quadratic Equations and Functions
Math Example: Solving Quadratic Equations with Algebra Tiles--Example 3	Math Example: Solving Quadratic Equations with Algebra Tiles Topic Solving Equations Description This example demonstrates the process of solving the quadratic equation x2 + 6x + 9 = 0 using algebra tiles. The visual representation shows how to rearrange the equation into (x + 3)2 = 0, illustrating the power of algebra tiles in simplifying and solving quadratic equations with larger coefficients. By arranging the tiles into a square, students can physically see how the terms combine to form a perfect square trinomial, making the solution process more intuitive and accessible.	Quadratic Equations and Functions
Math Example: Solving Quadratic Equations with Algebra Tiles--Example 4	Math Example: Solving Quadratic Equations with Algebra Tiles--Example 4 Topic Solving Equations Description In this example, we explore solving the quadratic equation x2 - 2x + 1 = 0 using algebra tiles. The visual representation demonstrates how to arrange the tiles into a perfect square, effectively transforming the equation into (-x + 1)2 = 0. This method showcases the versatility of algebra tiles in handling equations with both positive and negative terms, as well as illustrating the completing the square technique.	Quadratic Equations and Functions
Math Example: Solving Quadratic Equations with Algebra Tiles--Example 5	Math Example: Solving Quadratic Equations with Algebra Tiles--Example 5 Topic Solving Equations Description This example demonstrates the process of solving the quadratic equation x2 - 4x + 4 = 0 using algebra tiles. The visual representation shows how to arrange the tiles to form a perfect square, illustrating the completing the square method. By organizing the tiles, students can physically see how the terms combine to form the expression (-x + 2)2 = 0, making the solution process more intuitive and accessible.	Quadratic Equations and Functions
Math Example: Solving Quadratic Equations with Algebra Tiles--Example 6	Math Example: Solving Quadratic Equations with Algebra Tiles--Example 6 Topic Solving Equations Description This example illustrates the process of solving the quadratic equation x2 - 6x + 9 = 0 using algebra tiles. By modeling tiles on both sides of the equation, students can visually understand the principle of maintaining equality while manipulating the equation. The tiles are arranged into a square to form a perfect square trinomial, demonstrating the completing the square method in a tangible way.	Quadratic Equations and Functions
Math Example: Solving Quadratic Equations with Algebra Tiles--Example 7	Math Example: Solving Quadratic Equations with Algebra Tiles--Example 7 Topic Solving Equations Description This example demonstrates the process of solving the quadratic equation x2 + 3x + 2 = 0 using algebra tiles. The visual representation shows how to arrange the tiles into a rectangle, illustrating the factoring method for solving quadratic equations. By organizing the tiles in this way, students can physically see how the terms combine to form the factored expression (x + 2)(x + 1) = 0, making the solution process more intuitive and accessible.	Quadratic Equations and Functions
Math Example: Solving Quadratic Equations with Algebra Tiles--Example 8	Math Example: Solving Quadratic Equations with Algebra Tiles--Example 8 Topic Solving Equations Description This example illustrates the process of solving the quadratic equation x2 + 5x + 6 = 0 using algebra tiles. The visual representation demonstrates how to arrange the tiles into a rectangle, showcasing the factoring method for solving quadratic equations. By organizing the tiles in this manner, students can physically see how the terms combine to form the factored expression (x + 3)(x + 2) = 0, making the solution process more concrete and understandable.	Quadratic Equations and Functions
Math Example: Solving Two-Step Equations of the Form ax + b = c--Example 1	Math Example: Solving Two-Step Equations of the Form ax + b = c--Example 1 Topic Solving Equations Description An example of solving a two-step equation involving multiplication and addition demonstrates solving the equation 2x + 3 = 7 by performing two inverse operations to isolate x. The operations shown are subtracting 3 from both sides and then dividing by 2. This example demonstrates how to isolate the variable by first undoing any addition or subtraction, followed by division to find the solution.	Solving Two-Step Equations
Math Example: Solving Two-Step Equations of the Form ax + b = c--Example 10	Math Example: Solving Two-Step Equations of the Form ax + b = c--Example 10 Topic Solving Equations Description An example of solving a two-step equation involving multiplication and addition involves solving -3x + (-12) = -42 by performing two inverse operations: addition and division to isolate x. This example demonstrates how to isolate the variable by first undoing any addition or subtraction, followed by division to find the solution.	Solving Two-Step Equations
Math Example: Solving Two-Step Equations of the Form ax + b = c--Example 2	Math Example: Solving Two-Step Equations of the Form ax + b = c--Example 2 Topic Solving Equations Description An example of solving a two-step equation involving multiplication and addition shows solving the equation 3x + 4 = 13 by using two inverse operations. The steps involve subtracting 4 and then dividing by 3. This example demonstrates how to isolate the variable by first undoing any addition or subtraction, followed by division to find the solution.	Solving Two-Step Equations
Math Example: Solving Two-Step Equations of the Form ax + b = c--Example 3	Math Example: Solving Two-Step Equations of the Form ax + b = c--Example 3 Topic Solving Equations Description An example of solving a two-step equation involving multiplication and addition involves solving the equation 2x + 4 = 8 using inverse operations. It shows subtraction and division to isolate x. This example demonstrates how to isolate the variable by first undoing any addition or subtraction, followed by division to find the solution.	Solving Two-Step Equations
Math Example: Solving Two-Step Equations of the Form ax + b = c--Example 4	Math Example: Solving Two-Step Equations of the Form ax + b = c--Example 4 Topic Solving Equations Description An example of solving a two-step equation involving multiplication and addition illustrates solving -4x + 5 = 25. It uses inverse operations by subtracting 5 and dividing by -4. This example demonstrates how to isolate the variable by first undoing any addition or subtraction, followed by division to find the solution. Solving equations is a foundational skill in algebra, involving steps to isolate the variable and solve for its value. This collection of examples illustrates different methods for solving two-step equations, reinforcing the importance of order in arithmetic operations.	Solving Two-Step Equations
Math Example: Solving Two-Step Equations of the Form ax + b = c--Example 5	Math Example: Solving Two-Step Equations of the Form ax + b = c--Example 5 Topic Solving Equations Description An example of solving a two-step equation involving multiplication and addition shows the solution to -7x + 6 = 48 by isolating x with inverse operations, including subtraction and division. This example demonstrates how to isolate the variable by first undoing any addition or subtraction, followed by division to find the solution.	Solving Two-Step Equations
Math Example: Solving Two-Step Equations of the Form ax + b = c--Example 6	Math Example: Solving Two-Step Equations of the Form ax + b = c--Example 6 Topic Solving Equations Description An example of solving a two-step equation involving multiplication and addition solves the equation 6x + (-2) = 34 by using inverse operations, specifically addition and division, to find the value of x. This example demonstrates how to isolate the variable by first undoing any addition or subtraction, followed by division to find the solution.	Solving Two-Step Equations
Math Example: Solving Two-Step Equations of the Form ax + b = c--Example 7	Math Example: Solving Two-Step Equations of the Form ax + b = c--Example 7 Topic Solving Equations Description An example of solving a two-step equation involving multiplication and addition solves 10x + (-6) = 54 by isolating x through inverse operations, including addition and division. This example demonstrates how to isolate the variable by first undoing any addition or subtraction, followed by division to find the solution. Solving equations is a foundational skill in algebra, involving steps to isolate the variable and solve for its value. This collection of examples illustrates different methods for solving two-step equations, reinforcing the importance of order in arithmetic operations.	Solving Two-Step Equations
Math Example: Solving Two-Step Equations of the Form ax + b = c--Example 8	Math Example: Solving Two-Step Equations of the Form ax + b = c--Example 8 Topic Solving Equations Description An example of solving a two-step equation involving multiplication and addition shows solving -x + (-5) = 71 by performing inverse operations to isolate x, using addition and division by -1. This example demonstrates how to isolate the variable by first undoing any addition or subtraction, followed by division to find the solution.	Solving Two-Step Equations
Math Example: Solving Two-Step Equations of the Form ax + b = c--Example 9	Math Example: Solving Two-Step Equations of the Form ax + b = c--Example 9 Topic Solving Equations Description An example of solving a two-step equation involving multiplication and addition demonstrates solving -2x + (-8) = 22 through inverse operations, specifically addition and division, to isolate x. This example demonstrates how to isolate the variable by first undoing any addition or subtraction, followed by division to find the solution.	Solving Two-Step Equations
Math Example: Solving Two-Step Equations of the Form ax - b = c--Example 1	Math Example: Solving Two-Step Equations of the Form ax - b = c--Example 1 Topic Solving Equations Description An example of solving a two-step equation involving multiplication and subtraction shows solving the equation 2x - 3 = 7 by isolating x through inverse operations. This example demonstrates how to isolate the variable by first undoing any addition or subtraction, followed by division to find the solution. Solving equations is a foundational skill in algebra, involving steps to isolate the variable and solve for its value. This collection of examples illustrates different methods for solving two-step equations, reinforcing the importance of order in arithmetic operations.	Solving Two-Step Equations
Math Example: Solving Two-Step Equations of the Form ax - b = c--Example 10	Math Example: Solving Two-Step Equations of the Form ax - b = c--Example 10 Topic Solving Equations Description An example of solving a two-step equation involving multiplication and subtraction demonstrates solving the equation -3x - (-12) = -42 by isolating x through inverse operations. This example demonstrates how to isolate the variable by first undoing any addition or subtraction, followed by division to find the solution. Solving equations is a foundational skill in algebra, involving steps to isolate the variable and solve for its value. This collection of examples illustrates different methods for solving two-step equations, reinforcing the importance of order in arithmetic operations.	Solving Two-Step Equations
Math Example: Solving Two-Step Equations of the Form ax - b = c--Example 2	Math Example: Solving Two-Step Equations of the Form ax - b = c--Example 2 Topic Solving Equations Description An example of solving a two-step equation involving multiplication and subtraction illustrates solving the equation 3x - 4 = 14 by isolating x with inverse operations. This example demonstrates how to isolate the variable by first undoing any addition or subtraction, followed by division to find the solution. Solving equations is a foundational skill in algebra, involving steps to isolate the variable and solve for its value. This collection of examples illustrates different methods for solving two-step equations, reinforcing the importance of order in arithmetic operations.	Solving Two-Step Equations
Math Example: Solving Two-Step Equations of the Form ax - b = c--Example 3	Math Example: Solving Two-Step Equations of the Form ax - b = c--Example 3 Topic Solving Equations Description An example of solving a two-step equation involving multiplication and subtraction demonstrates solving the equation -2x - 4 = 8 by isolating x using inverse operations. This example demonstrates how to isolate the variable by first undoing any addition or subtraction, followed by division to find the solution. Solving equations is a foundational skill in algebra, involving steps to isolate the variable and solve for its value. This collection of examples illustrates different methods for solving two-step equations, reinforcing the importance of order in arithmetic operations.	Solving Two-Step Equations
Math Example: Solving Two-Step Equations of the Form ax - b = c--Example 4	Math Example: Solving Two-Step Equations of the Form ax - b = c--Example 4 Topic Solving Equations Description An example of solving a two-step equation involving multiplication and subtraction explains solving the equation -x - 5 = 17 by isolating x with inverse operations. This example demonstrates how to isolate the variable by first undoing any addition or subtraction, followed by division to find the solution. Solving equations is a foundational skill in algebra, involving steps to isolate the variable and solve for its value. This collection of examples illustrates different methods for solving two-step equations, reinforcing the importance of order in arithmetic operations.	Solving Two-Step Equations
Math Example: Solving Two-Step Equations of the Form ax - b = c--Example 5	Math Example: Solving Two-Step Equations of the Form ax - b = c--Example 5 Topic Solving Equations Description An example of solving a two-step equation involving multiplication and subtraction shows solving the equation -7x - 6 = 43 by isolating x with inverse operations. This example demonstrates how to isolate the variable by first undoing any addition or subtraction, followed by division to find the solution. Solving equations is a foundational skill in algebra, involving steps to isolate the variable and solve for its value. This collection of examples illustrates different methods for solving two-step equations, reinforcing the importance of order in arithmetic operations.	Solving Two-Step Equations
Math Example: Solving Two-Step Equations of the Form ax - b = c--Example 6	Math Example: Solving Two-Step Equations of the Form ax - b = c--Example 6 Topic Solving Equations Description An example of solving a two-step equation involving multiplication and subtraction illustrates solving the equation 6x - (-2) = 38 by isolating x using inverse operations. This example demonstrates how to isolate the variable by first undoing any addition or subtraction, followed by division to find the solution. Solving equations is a foundational skill in algebra, involving steps to isolate the variable and solve for its value. This collection of examples illustrates different methods for solving two-step equations, reinforcing the importance of order in arithmetic operations.	Solving Two-Step Equations
Math Example: Solving Two-Step Equations of the Form ax - b = c--Example 7	Math Example: Solving Two-Step Equations of the Form ax - b = c--Example 7 Topic Solving Equations Description An example of solving a two-step equation involving multiplication and subtraction demonstrates solving the equation 10x - (-6) = 76 by isolating x through inverse operations. This example demonstrates how to isolate the variable by first undoing any addition or subtraction, followed by division to find the solution. Solving equations is a foundational skill in algebra, involving steps to isolate the variable and solve for its value. This collection of examples illustrates different methods for solving two-step equations, reinforcing the importance of order in arithmetic operations.	Solving Two-Step Equations
Math Example: Solving Two-Step Equations of the Form ax - b = c--Example 8	Math Example: Solving Two-Step Equations of the Form ax - b = c--Example 8 Topic Solving Equations Description An example of solving a two-step equation involving multiplication and subtraction explains solving the equation -x - (-5) = 71 by isolating x through inverse operations. This example demonstrates how to isolate the variable by first undoing any addition or subtraction, followed by division to find the solution. Solving equations is a foundational skill in algebra, involving steps to isolate the variable and solve for its value. This collection of examples illustrates different methods for solving two-step equations, reinforcing the importance of order in arithmetic operations.	Solving Two-Step Equations
Math Example: Solving Two-Step Equations of the Form ax - b = c--Example 9	Math Example: Solving Two-Step Equations of the Form ax - b = c--Example 9 Topic Solving Equations Description An example of solving a two-step equation involving multiplication and subtraction shows solving the equation -2x - (-8) = 22 by isolating x with inverse operations. This example demonstrates how to isolate the variable by first undoing any addition or subtraction, followed by division to find the solution. Solving equations is a foundational skill in algebra, involving steps to isolate the variable and solve for its value. This collection of examples illustrates different methods for solving two-step equations, reinforcing the importance of order in arithmetic operations.	Solving Two-Step Equations
Math Example: Solving Two-Step Equations of the Form x/a + b = c--Example 1	Math Example: Solving Two-Step Equations of the Form x/a + b = c--Example 1 Topic Solving Equations Description An example of solving a two-step equation with division and addition: x/5 + 3 = 7. The solution is detailed with inverse operations to isolate x. This example demonstrates how to isolate the variable by first undoing any addition or subtraction, followed by division to find the solution. Solving equations is a foundational skill in algebra, involving steps to isolate the variable and solve for its value. This collection of examples illustrates different methods for solving two-step equations, reinforcing the importance of order in arithmetic operations.	Solving Two-Step Equations
Math Example: Solving Two-Step Equations of the Form x/a + b = c--Example 10	Math Example: Solving Two-Step Equations of the Form x/a + b = c--Example 10 Topic Solving Equations Description An example of solving a two-step equation with division and addition: -x/3 + (-12) = -42. The solution follows each step using inverse operations to isolate x. This example demonstrates how to isolate the variable by first undoing any addition or subtraction, followed by division to find the solution. Solving equations is a foundational skill in algebra, involving steps to isolate the variable and solve for its value. This collection of examples illustrates different methods for solving two-step equations, reinforcing the importance of order in arithmetic operations.	Solving Two-Step Equations
Math Example: Solving Two-Step Equations of the Form x/a + b = c--Example 2	Math Example: Solving Two-Step Equations of the Form x/a + b = c--Example 2 Topic Solving Equations Description An example of solving a two-step equation with division and addition: x/4 + 4 = 14. It includes each step to isolate the variable using inverse operations. This example demonstrates how to isolate the variable by first undoing any addition or subtraction, followed by division to find the solution. Solving equations is a foundational skill in algebra, involving steps to isolate the variable and solve for its value. This collection of examples illustrates different methods for solving two-step equations, reinforcing the importance of order in arithmetic operations.	Solving Two-Step Equations
Math Example: Solving Two-Step Equations of the Form x/a + b = c--Example 3	Math Example: Solving Two-Step Equations of the Form x/a + b = c--Example 3 Topic Solving Equations Description An example of solving a two-step equation with division and addition: -x/3 + 4 = 8. The solution uses inverse operations to isolate x with careful handling of the negative sign. This example demonstrates how to isolate the variable by first undoing any addition or subtraction, followed by division to find the solution. Solving equations is a foundational skill in algebra, involving steps to isolate the variable and solve for its value. This collection of examples illustrates different methods for solving two-step equations, reinforcing the importance of order in arithmetic operations.	Solving Two-Step Equations
Math Example: Solving Two-Step Equations of the Form x/a + b = c--Example 4	Math Example: Solving Two-Step Equations of the Form x/a + b = c--Example 4 Topic Solving Equations Description An example of solving a two-step equation with division and addition: -x/6 + 5 = 17. The solution details each inverse operation step to isolate x. This example demonstrates how to isolate the variable by first undoing any addition or subtraction, followed by division to find the solution. Solving equations is a foundational skill in algebra, involving steps to isolate the variable and solve for its value. This collection of examples illustrates different methods for solving two-step equations, reinforcing the importance of order in arithmetic operations.	Solving Two-Step Equations
Math Example: Solving Two-Step Equations of the Form x/a + b = c--Example 5	Math Example: Solving Two-Step Equations of the Form x/a + b = c--Example 5 Topic Solving Equations Description An example of solving a two-step equation with division and addition: -x/7 + 6 = 43. The solution carefully applies inverse operations to solve for x. This example demonstrates how to isolate the variable by first undoing any addition or subtraction, followed by division to find the solution. Solving equations is a foundational skill in algebra, involving steps to isolate the variable and solve for its value. This collection of examples illustrates different methods for solving two-step equations, reinforcing the importance of order in arithmetic operations.	Solving Two-Step Equations
Math Example: Solving Two-Step Equations of the Form x/a + b = c--Example 6	Math Example: Solving Two-Step Equations of the Form x/a + b = c--Example 6 Topic Solving Equations Description An example of solving a two-step equation with division and addition: x/6 + (-2) = 38, showing each step to isolate x through inverse operations. This example demonstrates how to isolate the variable by first undoing any addition or subtraction, followed by division to find the solution. Solving equations is a foundational skill in algebra, involving steps to isolate the variable and solve for its value. This collection of examples illustrates different methods for solving two-step equations, reinforcing the importance of order in arithmetic operations.	Solving Two-Step Equations
Math Example: Solving Two-Step Equations of the Form x/a + b = c--Example 7	Math Example: Solving Two-Step Equations of the Form x/a + b = c--Example 7 Topic Solving Equations Description An example of solving a two-step equation with division and addition: x/10 + (-6) = 76. Each inverse operation is shown to solve for x. This example demonstrates how to isolate the variable by first undoing any addition or subtraction, followed by division to find the solution. Solving equations is a foundational skill in algebra, involving steps to isolate the variable and solve for its value. This collection of examples illustrates different methods for solving two-step equations, reinforcing the importance of order in arithmetic operations.	Solving Two-Step Equations
Math Example: Solving Two-Step Equations of the Form x/a + b = c--Example 8	Math Example: Solving Two-Step Equations of the Form x/a + b = c--Example 8 Topic Solving Equations Description An example of solving a two-step equation with division and addition: -x/9 + (-5) = 71. The solution includes each inverse operation needed to isolate x. This example demonstrates how to isolate the variable by first undoing any addition or subtraction, followed by division to find the solution. Solving equations is a foundational skill in algebra, involving steps to isolate the variable and solve for its value. This collection of examples illustrates different methods for solving two-step equations, reinforcing the importance of order in arithmetic operations.	Solving Two-Step Equations
Math Example: Solving Two-Step Equations of the Form x/a + b = c--Example 9	Math Example: Solving Two-Step Equations of the Form x/a + b = c--Example 9 Topic Solving Equations Description An example of solving a two-step equation with division and addition: -x/2 + (-8) = 22, detailing the inverse operations step-by-step to solve for x. This example demonstrates how to isolate the variable by first undoing any addition or subtraction, followed by division to find the solution. Solving equations is a foundational skill in algebra, involving steps to isolate the variable and solve for its value. This collection of examples illustrates different methods for solving two-step equations, reinforcing the importance of order in arithmetic operations.	Solving Two-Step Equations
Math Example: Solving Two-Step Equations of the Form x/a - b = c--Example 1	Math Example: Solving Two-Step Equations of the Form x/a - b = c--Example 1 Topic Solving Equations Description An example of solving a two-step equation with division and subtraction: x / 5 - 3 = 7 using two inverse operations to isolate x. This example demonstrates how to isolate the variable by first undoing any addition or subtraction, followed by division to find the solution. Solving equations is a foundational skill in algebra, involving steps to isolate the variable and solve for its value. This collection of examples illustrates different methods for solving two-step equations, reinforcing the importance of order in arithmetic operations.	Solving Two-Step Equations
Math Example: Solving Two-Step Equations of the Form x/a - b = c--Example 10	Math Example: Solving Two-Step Equations of the Form x/a - b = c--Example 10 Topic Solving Equations Description An example of solving a two-step equation with division and subtraction: -x / 3 - (-12) = -42 with two inverse operations to isolate x. This example demonstrates how to isolate the variable by first undoing any addition or subtraction, followed by division to find the solution. Solving equations is a foundational skill in algebra, involving steps to isolate the variable and solve for its value. This collection of examples illustrates different methods for solving two-step equations, reinforcing the importance of order in arithmetic operations.	Solving Two-Step Equations

Illustrative Math Alignment: Grade 7 Unit 7

Expressions, Equations, and Inequalities

Lesson 9: Dealing with Negative Numbers

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