IXL Ad

Illustrative Math-Media4Math Alignment

 

 

Illustrative Math Alignment: Grade 6 Unit 1

Expressions and Equations

Lesson 6: Write Expressions Where Letters Stand for Numbers

Use the following Media4Math resources with this Illustrative Math lesson.

Thumbnail Image Title Body Curriculum Nodes
Math Example--Solving Equations--Solving Equations Using Triangle Properties: Example 5 Math Example--Solving Equations--Solving Equations Using Triangle Properties: Example 5 Solving Equations Using Triangle Properties: Example 5

Topic

Equations

Description

This example focuses on solving equations involving isosceles triangles centered in a circle. The problem presents two equations: z - y = 20 and z + y = 120, where z and y represent angles in the isosceles triangles. The goal is to solve this system of equations to find the values of z and y, utilizing properties of isosceles triangles and circles. 

 Applications of Equations and Inequalities and Applications of Triangles
Math Example--Solving Equations--Solving Equations Using Triangle Properties: Example 6 Math Example--Solving Equations--Solving Equations Using Triangle Properties: Example 6 Solving Equations Using Triangle Properties: Example 6

Topic

Equations

Description

This example explores solving equations involving triangles that share a vertex at the center of a circle. We are presented with two equations: 

x + y = 75 and z + y = 110, where x, y, and z represent angles in the triangle

The goal is to solve this system of equations to find the values of x, y, and z, utilizing properties of isosceles triangles. Since each of the triangles is isosceles, we know that z + 55 + 55 = 180 and therefore, z = 70°. We substitute this into one of the equations:

70 + y = 110

7 = 40°

 Applications of Equations and Inequalities and Applications of Triangles
Math Example--Solving Equations--Solving Equations Using Triangle Properties: Example 7 Math Example--Solving Equations--Solving Equations Using Triangle Properties: Example 7 Solving Equations Using Triangle Properties: Example 7

Topic

Equations

Description

This example focuses on solving equations involving isosceles triangles with a common vertex and base. We are given two angles, 62° and 99°, and need to find the unknown angle x. This problem demonstrates how to use the properties of isosceles triangles and the sum of angles in a triangle to solve for an unknown angle. 

Key properties to consider: 

 Applications of Equations and Inequalities and Applications of Triangles
Math Example--Solving Equations--Solving Equations Using Triangle Properties: Example 8 Math Example--Solving Equations--Solving Equations Using Triangle Properties: Example 8 Solving Equations Using Triangle Properties: Example 8

Topic

Equations

Description

This example involves solving an equation using the properties of a trapezoid with an embedded parallelogram and applying the exterior angle theorem. We are given two angles, 30° and 110°, and need to find the unknown angle x. This problem demonstrates the application of multiple geometric concepts to solve a complex equation. 

Key properties to consider: 

 Applications of Equations and Inequalities and Applications of Triangles
Math Example--Solving Equations--Solving Equations Using Triangle Properties: Example 9 Math Example--Solving Equations--Solving Equations Using Triangle Properties: Example 9 Solving Equations Using Triangle Properties: Example 9

Topic

Equations

Description

This example focuses on solving equations using the properties of a kite and applying the exterior angle theorem. We are given one angle of 30° and two unknown angles, y and x. The goal is to set up and solve equations to find the values of y and x using the properties of kites and the exterior angle theorem. 

Key properties to consider: 

 Applications of Equations and Inequalities and Applications of Triangles
Math Example--Solving Equations--Solving Equations with Angle Measures--Example 1 Math Example--Solving Equations--Solving Equations with Angle Measures--Example 1 Solving Equations with Angle Measures--Example 1

Topic

Equations

 Solving Multistep Equations and Applications of Angles and Planes
Math Example--Solving Equations--Solving Equations with Angle Measures--Example 10 Math Example--Solving Equations--Solving Equations with Angle Measures--Example 10 Solving Equations with Angle Measures--Example 10

Topic

Equations

 Solving Multistep Equations and Applications of Angles and Planes
Math Example--Solving Equations--Solving Equations with Angle Measures--Example 11 Math Example--Solving Equations--Solving Equations with Angle Measures--Example 11 Solving Equations with Angle Measures--Example 11

Topic

Equations

 Solving Multistep Equations and Applications of Angles and Planes
Math Example--Solving Equations--Solving Equations with Angle Measures--Example 12 Math Example--Solving Equations--Solving Equations with Angle Measures--Example 12 Solving Equations with Angle Measures--Example 12

Topic

Equations

 Solving Multistep Equations and Applications of Angles and Planes
Math Example--Solving Equations--Solving Equations with Angle Measures--Example 13 Math Example--Solving Equations--Solving Equations with Angle Measures--Example 13 Solving Equations with Angle Measures--Example 13

Topic

Equations

 Solving Multistep Equations and Applications of Angles and Planes
Math Example--Solving Equations--Solving Equations with Angle Measures--Example 14 Math Example--Solving Equations--Solving Equations with Angle Measures--Example 14 Solving Equations with Angle Measures--Example 14

Topic

Equations

 Solving Multistep Equations and Applications of Angles and Planes
Math Example--Solving Equations--Solving Equations with Angle Measures--Example 15 Math Example--Solving Equations--Solving Equations with Angle Measures--Example 15 Solving Equations with Angle Measures--Example 15

Topic

Equations

 Solving Multistep Equations and Applications of Angles and Planes
Math Example--Solving Equations--Solving Equations with Angle Measures--Example 2 Math Example--Solving Equations--Solving Equations with Angle Measures--Example 2 Solving Equations with Angle Measures--Example 2

Topic

Equations

 Solving Multistep Equations and Applications of Angles and Planes
Math Example--Solving Equations--Solving Equations with Angle Measures--Example 3 Math Example--Solving Equations--Solving Equations with Angle Measures--Example 3 Solving Equations with Angle Measures--Example 3

Topic

Equations

 Solving Multistep Equations and Applications of Angles and Planes
Math Example--Solving Equations--Solving Equations with Angle Measures--Example 4 Math Example--Solving Equations--Solving Equations with Angle Measures--Example 4 Solving Equations with Angle Measures--Example 4

Topic

Equations

 Solving Multistep Equations and Applications of Angles and Planes
Math Example--Solving Equations--Solving Equations with Angle Measures--Example 5 Math Example--Solving Equations--Solving Equations with Angle Measures--Example 5 Solving Equations with Angle Measures--Example 5

Topic

Equations

 Solving Multistep Equations and Applications of Angles and Planes
Math Example--Solving Equations--Solving Equations with Angle Measures--Example 6 Math Example--Solving Equations--Solving Equations with Angle Measures--Example 6 Solving Equations with Angle Measures--Example 6

Topic

Equations

 Solving Multistep Equations and Applications of Angles and Planes
Math Example--Solving Equations--Solving Equations with Angle Measures--Example 7 Math Example--Solving Equations--Solving Equations with Angle Measures--Example 7 Solving Equations with Angle Measures--Example 7

Topic

Equations

 Solving Multistep Equations and Applications of Angles and Planes
Math Example--Solving Equations--Solving Equations with Angle Measures--Example 8 Math Example--Solving Equations--Solving Equations with Angle Measures--Example 8 Solving Equations with Angle Measures--Example 8

Topic

Equations

 Solving Multistep Equations and Applications of Angles and Planes
Math Example--Solving Equations--Solving Equations with Angle Measures--Example 9 Math Example--Solving Equations--Solving Equations with Angle Measures--Example 9 Solving Equations with Angle Measures--Example 9

Topic

Equations

 Solving Multistep Equations and Applications of Angles and Planes
Math Example: Solving Quadratic Equations with Algebra Tiles--Example 1 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--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--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 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 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 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 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 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 Math Example: Solving Two-Step Equations of the Form ax + b = c--Example 1

This is part of a collection of math examples that show how to solve two-step equations that involve combinations of addition, subtraction, multiplication, and division.

 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 Math Example: Solving Two-Step Equations of the Form ax + b = c--Example 10

This is part of a collection of math examples that show how to solve two-step equations that involve combinations of addition, subtraction, multiplication, and division.

 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 Math Example: Solving Two-Step Equations of the Form ax + b = c--Example 2

This is part of a collection of math examples that show how to solve two-step equations that involve combinations of addition, subtraction, multiplication, and division.

 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 Math Example: Solving Two-Step Equations of the Form ax + b = c--Example 3

This is part of a collection of math examples that show how to solve two-step equations that involve combinations of addition, subtraction, multiplication, and division.

 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 Math Example: Solving Two-Step Equations of the Form ax + b = c--Example 4

This is part of a collection of math examples that show how to solve two-step equations that involve combinations of addition, subtraction, multiplication, and division.

 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 Math Example: Solving Two-Step Equations of the Form ax + b = c--Example 5

This is part of a collection of math examples that show how to solve two-step equations that involve combinations of addition, subtraction, multiplication, and division.

 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 Math Example: Solving Two-Step Equations of the Form ax + b = c--Example 6

This is part of a collection of math examples that show how to solve two-step equations that involve combinations of addition, subtraction, multiplication, and division.

 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 Math Example: Solving Two-Step Equations of the Form ax + b = c--Example 7

This is part of a collection of math examples that show how to solve two-step equations that involve combinations of addition, subtraction, multiplication, and division.

 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 Math Example: Solving Two-Step Equations of the Form ax + b = c--Example 8

This is part of a collection of math examples that show how to solve two-step equations that involve combinations of addition, subtraction, multiplication, and division.

 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 Math Example: Solving Two-Step Equations of the Form ax + b = c--Example 9

This is part of a collection of math examples that show how to solve two-step equations that involve combinations of addition, subtraction, multiplication, and division.

 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 Math Example: Solving Two-Step Equations of the Form ax - b = c--Example 1

This is part of a collection of math examples that show how to solve two-step equations that involve combinations of addition, subtraction, multiplication, and division.

 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 Math Example: Solving Two-Step Equations of the Form ax - b = c--Example 10

This is part of a collection of math examples that show how to solve two-step equations that involve combinations of addition, subtraction, multiplication, and division.

 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 Math Example: Solving Two-Step Equations of the Form ax - b = c--Example 2

This is part of a collection of math examples that show how to solve two-step equations that involve combinations of addition, subtraction, multiplication, and division.

 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 Math Example: Solving Two-Step Equations of the Form ax - b = c--Example 3

This is part of a collection of math examples that show how to solve two-step equations that involve combinations of addition, subtraction, multiplication, and division.

 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 Math Example: Solving Two-Step Equations of the Form ax - b = c--Example 4

This is part of a collection of math examples that show how to solve two-step equations that involve combinations of addition, subtraction, multiplication, and division.

 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 Math Example: Solving Two-Step Equations of the Form ax - b = c--Example 5

This is part of a collection of math examples that show how to solve two-step equations that involve combinations of addition, subtraction, multiplication, and division.

 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 Math Example: Solving Two-Step Equations of the Form ax - b = c--Example 6

This is part of a collection of math examples that show how to solve two-step equations that involve combinations of addition, subtraction, multiplication, and division.

 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 Math Example: Solving Two-Step Equations of the Form ax - b = c--Example 7

This is part of a collection of math examples that show how to solve two-step equations that involve combinations of addition, subtraction, multiplication, and division.

 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 Math Example: Solving Two-Step Equations of the Form ax - b = c--Example 8

This is part of a collection of math examples that show how to solve two-step equations that involve combinations of addition, subtraction, multiplication, and division.

 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 Math Example: Solving Two-Step Equations of the Form ax - b = c--Example 9

This is part of a collection of math examples that show how to solve two-step equations that involve combinations of addition, subtraction, multiplication, and division.

 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 Math Example: Solving Two-Step Equations of the Form x/a + b = c--Example 1

This is part of a collection of math examples that show how to solve two-step equations that involve combinations of addition, subtraction, multiplication, and division.

 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 Math Example: Solving Two-Step Equations of the Form x/a + b = c--Example 10

This is part of a collection of math examples that show how to solve two-step equations that involve combinations of addition, subtraction, multiplication, and division.

 Solving Two-Step Equations