Illustrative Math Alignment: Grade 7 Unit 7

Expressions, Equations, and Inequalities

Lesson 11: Using Equations to Solve Problems

Use the following Media4Math resources with this Illustrative Math lesson.

Title	Body	Curriculum Topic
Math Clip Art--Rates and Tape Diagrams: Cooking 1	Math Clip Art--Rates and Tape Diagrams: Cooking 1 This is a collection of clip art images that show how to use tape diagrams to solve ratio and rate problems.	Ratios and Rates
Math Clip Art--Rates and Tape Diagrams: Cooking 10	Math Clip Art--Rates and Tape Diagrams: Cooking 10 This is a collection of clip art images that show how to use tape diagrams to solve ratio and rate problems.	Ratios and Rates
Math Clip Art--Rates and Tape Diagrams: Cooking 11	Math Clip Art--Rates and Tape Diagrams: Cooking 11 This is a collection of clip art images that show how to use tape diagrams to solve ratio and rate problems.	Ratios and Rates
Math Clip Art--Rates and Tape Diagrams: Cooking 2	Math Clip Art--Rates and Tape Diagrams: Cooking 2 This is a collection of clip art images that show how to use tape diagrams to solve ratio and rate problems.	Ratios and Rates
Math Clip Art--Rates and Tape Diagrams: Cooking 3	Math Clip Art--Rates and Tape Diagrams: Cooking 3 This is a collection of clip art images that show how to use tape diagrams to solve ratio and rate problems.	Ratios and Rates
Math Clip Art--Rates and Tape Diagrams: Cooking 4	Math Clip Art--Rates and Tape Diagrams: Cooking 4 This is a collection of clip art images that show how to use tape diagrams to solve ratio and rate problems.	Ratios and Rates
Math Clip Art--Rates and Tape Diagrams: Cooking 5	Math Clip Art--Rates and Tape Diagrams: Cooking 5 This is a collection of clip art images that show how to use tape diagrams to solve ratio and rate problems.	Ratios and Rates
Math Clip Art--Rates and Tape Diagrams: Cooking 6	Math Clip Art--Rates and Tape Diagrams: Cooking 6 This is a collection of clip art images that show how to use tape diagrams to solve ratio and rate problems.	Ratios and Rates
Math Clip Art--Rates and Tape Diagrams: Cooking 7	Math Clip Art--Rates and Tape Diagrams: Cooking 7 This is a collection of clip art images that show how to use tape diagrams to solve ratio and rate problems.	Ratios and Rates
Math Clip Art--Rates and Tape Diagrams: Cooking 8	Math Clip Art--Rates and Tape Diagrams: Cooking 8 This is a collection of clip art images that show how to use tape diagrams to solve ratio and rate problems.	Ratios and Rates
Math Clip Art--Rates and Tape Diagrams: Cooking 9	Math Clip Art--Rates and Tape Diagrams: Cooking 9 This is a collection of clip art images that show how to use tape diagrams to solve ratio and rate problems.	Ratios and Rates
Math Example--Solving Equations--One-Variable Equations: Example 1	One-Variable Equations: Example 1 Topic Equations	Solving Multistep Equations, Solving One-Step Equations and Solving Two-Step Equations
Math Example--Solving Equations--One-Variable Equations: Example 10	One-Variable Equations: Example 10 Topic Equations Description This example involves solving a one-variable equation that may include complex terms or require multiple steps to simplify. The equation might involve fractions, decimals, or variables on both sides. Solving it involves using inverse operations, distributing terms, and combining like terms to isolate the variable. This type of problem helps students refine their algebraic skills and understand the importance of systematic problem-solving. Checking the solution by substituting it back into the original equation is a crucial step to ensure accuracy.	Solving Multistep Equations, Solving One-Step Equations and Solving Two-Step Equations
Math Example--Solving Equations--One-Variable Equations: Example 11	One-Variable Equations: Example 11 Topic Equations	Solving Multistep Equations, Solving One-Step Equations and Solving Two-Step Equations
Math Example--Solving Equations--One-Variable Equations: Example 12	One-Variable Equations: Example 12 Topic Equations Description This example presents a one-variable equation that may involve variables on both sides. The solving process requires moving all terms involving the variable to one side and constants to the other. This often involves using the distributive property and combining like terms. The goal is to isolate the variable and solve for its value. This type of problem helps students develop their algebraic manipulation skills and understand the importance of maintaining balance in an equation. Checking the solution by substituting it back into the original equation is crucial to ensure accuracy.	Solving Multistep Equations, Solving One-Step Equations and Solving Two-Step Equations
Math Example--Solving Equations--One-Variable Equations: Example 13	One-Variable Equations: Example 13 Topic Equations Description This example involves solving a one-variable equation that might include complex expressions, such as those with parentheses or multiple terms. The solving process may require using the distributive property to eliminate parentheses and combining like terms to simplify the equation. After simplification, standard techniques are used to isolate the variable. This example reinforces the importance of following the order of operations and checking the solution for accuracy. Mastery of these skills is essential for tackling more advanced algebraic problems.	Solving Multistep Equations, Solving One-Step Equations and Solving Two-Step Equations
Math Example--Solving Equations--One-Variable Equations: Example 14	One-Variable Equations: Example 14 Topic Equations Description This example deals with solving a one-variable equation that may involve more complex algebraic expressions, such as nested parentheses or fractional coefficients. The solving process requires careful application of the distributive property and combining like terms. After simplifying the equation, inverse operations are used to isolate the variable. This example highlights the importance of precision in algebraic manipulation and the necessity of verifying solutions by substituting them back into the original equation to ensure correctness.	Solving Multistep Equations, Solving One-Step Equations and Solving Two-Step Equations
Math Example--Solving Equations--One-Variable Equations: Example 15	One-Variable Equations: Example 15 Topic Equations Description This example involves solving a one-variable equation that may include complex terms or require multiple steps to simplify. The equation might involve fractions, decimals, or variables on both sides. Solving it involves using inverse operations, distributing terms, and combining like terms to isolate the variable. This type of problem helps students refine their algebraic skills and understand the importance of systematic problem-solving. Checking the solution by substituting it back into the original equation is a crucial step to ensure accuracy.	Solving Multistep Equations, Solving One-Step Equations and Solving Two-Step Equations
Math Example--Solving Equations--One-Variable Equations: Example 16	One-Variable Equations: Example 16 Topic Equations	Solving Multistep Equations, Solving One-Step Equations and Solving Two-Step Equations
Math Example--Solving Equations--One-Variable Equations: Example 17	One-Variable Equations: Example 17 Topic Equations Description This example presents a one-variable equation that may involve variables on both sides. The solving process requires moving all terms involving the variable to one side and constants to the other. This often involves using the distributive property and combining like terms. The goal is to isolate the variable and solve for its value. This type of problem helps students develop their algebraic manipulation skills and understand the importance of maintaining balance in an equation. Checking the solution by substituting it back into the original equation is crucial to ensure accuracy.	Solving Multistep Equations, Solving One-Step Equations and Solving Two-Step Equations
Math Example--Solving Equations--One-Variable Equations: Example 18	One-Variable Equations: Example 18 Topic Equations Description This example involves solving a one-variable equation that might include complex expressions, such as those with parentheses or multiple terms. The solving process may require using the distributive property to eliminate parentheses and combining like terms to simplify the equation. After simplification, standard techniques are used to isolate the variable. This example reinforces the importance of following the order of operations and checking the solution for accuracy. Mastery of these skills is essential for tackling more advanced algebraic problems.	Solving Multistep Equations, Solving One-Step Equations and Solving Two-Step Equations
Math Example--Solving Equations--One-Variable Equations: Example 19	One-Variable Equations: Example 19 Topic Equations Description This example deals with solving a one-variable equation that may involve more complex algebraic expressions, such as nested parentheses or fractional coefficients. The solving process requires careful application of the distributive property and combining like terms. After simplifying the equation, inverse operations are used to isolate the variable. This example highlights the importance of precision in algebraic manipulation and the necessity of verifying solutions by substituting them back into the original equation to ensure correctness.	Solving Multistep Equations, Solving One-Step Equations and Solving Two-Step Equations
Math Example--Solving Equations--One-Variable Equations: Example 2	One-Variable Equations: Example 2 Topic Equations	Solving Multistep Equations, Solving One-Step Equations and Solving Two-Step Equations
Math Example--Solving Equations--One-Variable Equations: Example 20	One-Variable Equations: Example 20 Topic Equations Description This example involves solving a one-variable equation that may include complex terms or require multiple steps to simplify. The equation might involve fractions, decimals, or variables on both sides. Solving it involves using inverse operations, distributing terms, and combining like terms to isolate the variable. This type of problem helps students refine their algebraic skills and understand the importance of systematic problem-solving. Checking the solution by substituting it back into the original equation is a crucial step to ensure accuracy.	Solving Multistep Equations, Solving One-Step Equations and Solving Two-Step Equations
Math Example--Solving Equations--One-Variable Equations: Example 21	One-Variable Equations: Example 21 Topic Equations	Solving Multistep Equations, Solving One-Step Equations and Solving Two-Step Equations
Math Example--Solving Equations--One-Variable Equations: Example 22	One-Variable Equations: Example 22 Topic Equations Description This example presents a one-variable equation that may involve variables on both sides. The solving process requires moving all terms involving the variable to one side and constants to the other. This often involves using the distributive property and combining like terms. The goal is to isolate the variable and solve for its value. This type of problem helps students develop their algebraic manipulation skills and understand the importance of maintaining balance in an equation. Checking the solution by substituting it back into the original equation is crucial to ensure accuracy.	Solving Multistep Equations, Solving One-Step Equations and Solving Two-Step Equations
Math Example--Solving Equations--One-Variable Equations: Example 23	One-Variable Equations: Example 23 Topic Equations Description This example involves solving a one-variable equation that might include complex expressions, such as those with parentheses or multiple terms. The solving process may require using the distributive property to eliminate parentheses and combining like terms to simplify the equation. After simplification, standard techniques are used to isolate the variable. This example reinforces the importance of following the order of operations and checking the solution for accuracy. Mastery of these skills is essential for tackling more advanced algebraic problems.	Solving Multistep Equations, Solving One-Step Equations and Solving Two-Step Equations
Math Example--Solving Equations--One-Variable Equations: Example 24	One-Variable Equations: Example 24 Topic Equations Description This example deals with solving a one-variable equation that may involve more complex algebraic expressions, such as nested parentheses or fractional coefficients. The solving process requires careful application of the distributive property and combining like terms. After simplifying the equation, inverse operations are used to isolate the variable. This example highlights the importance of precision in algebraic manipulation and the necessity of verifying solutions by substituting them back into the original equation to ensure correctness.	Solving Multistep Equations, Solving One-Step Equations and Solving Two-Step Equations
Math Example--Solving Equations--One-Variable Equations: Example 25	One-Variable Equations: Example 25 Topic Equations Description This example involves solving a one-variable equation that may include complex terms or require multiple steps to simplify. The equation might involve fractions, decimals, or variables on both sides. Solving it involves using inverse operations, distributing terms, and combining like terms to isolate the variable. This type of problem helps students refine their algebraic skills and understand the importance of systematic problem-solving. Checking the solution by substituting it back into the original equation is a crucial step to ensure accuracy.	Solving Multistep Equations, Solving One-Step Equations and Solving Two-Step Equations
Math Example--Solving Equations--One-Variable Equations: Example 26	One-Variable Equations: Example 26 Topic Equations	Solving Multistep Equations, Solving One-Step Equations and Solving Two-Step Equations
Math Example--Solving Equations--One-Variable Equations: Example 27	One-Variable Equations: Example 27 Topic Equations	Solving Multistep Equations, Solving One-Step Equations and Solving Two-Step Equations
Math Example--Solving Equations--One-Variable Equations: Example 3	One-Variable Equations: Example 3 Topic Equations	Solving Multistep Equations, Solving One-Step Equations and Solving Two-Step Equations
Math Example--Solving Equations--One-Variable Equations: Example 4	One-Variable Equations: Example 4 Topic Equations Description This example likely demonstrates solving a more complex one-variable equation. It may involve multiple steps, such as combining like terms, using the distributive property, or dealing with fractions or decimals. The solving process typically includes isolating the variable on one side of the equation by performing inverse operations on both sides. This type of problem enhances students' algebraic manipulation skills and prepares them for more advanced equation solving. The specific solution would involve carefully following the order of operations and checking the final answer by substituting it back into the original equation.	Solving Multistep Equations, Solving One-Step Equations and Solving Two-Step Equations
Math Example--Solving Equations--One-Variable Equations: Example 5	One-Variable Equations: Example 5 Topic Equations Description This example likely showcases a more challenging one-variable equation. It may involve variables on both sides of the equation, requiring students to consolidate like terms before solving. The problem might also include parentheses, necessitating the use of the distributive property. Solving this equation would involve carefully balancing operations on both sides, possibly dealing with negative numbers or fractions. This type of problem helps students develop their algebraic reasoning skills and reinforces the importance of maintaining equation balance throughout the solving process.	Solving Multistep Equations, Solving One-Step Equations and Solving Two-Step Equations
Math Example--Solving Equations--One-Variable Equations: Example 6	One-Variable Equations: Example 6 Topic Equations	Solving Multistep Equations, Solving One-Step Equations and Solving Two-Step Equations
Math Example--Solving Equations--One-Variable Equations: Example 7	One-Variable Equations: Example 7 Topic Equations Description This example presents a one-variable equation that may involve variables on both sides. The solving process requires moving all terms involving the variable to one side and constants to the other. This often involves using the distributive property and combining like terms. The goal is to isolate the variable and solve for its value. This type of problem helps students develop their algebraic manipulation skills and understand the importance of maintaining balance in an equation. Checking the solution by substituting it back into the original equation is crucial to ensure accuracy.	Solving Multistep Equations, Solving One-Step Equations and Solving Two-Step Equations
Math Example--Solving Equations--One-Variable Equations: Example 8	One-Variable Equations: Example 8 Topic Equations Description This example involves solving a one-variable equation that might include complex expressions, such as those with parentheses or multiple terms. The solving process may require using the distributive property to eliminate parentheses and combining like terms to simplify the equation. After simplification, standard techniques are used to isolate the variable. This example reinforces the importance of following the order of operations and checking the solution for accuracy. Mastery of these skills is essential for tackling more advanced algebraic problems.	Solving Multistep Equations, Solving One-Step Equations and Solving Two-Step Equations
Math Example--Solving Equations--One-Variable Equations: Example 9	One-Variable Equations: Example 9 Topic Equations Description This example deals with solving a one-variable equation that may involve more complex algebraic expressions, such as nested parentheses or fractional coefficients. The solving process requires careful application of the distributive property and combining like terms. After simplifying the equation, inverse operations are used to isolate the variable. This example highlights the importance of precision in algebraic manipulation and the necessity of verifying solutions by substituting them back into the original equation to ensure correctness.	Solving Multistep Equations, Solving One-Step Equations and Solving Two-Step Equations
Math Example--Solving Equations--Solving Equations with Angle Measures 2--Example 1	Solving Equations with Angle Measures 2--Example 1 Topic Equations	Solving Multistep Equations and Applications of Quadrilaterals
Math Example--Solving Equations--Solving Equations with Angle Measures 2--Example 10	Solving Equations with Angle Measures 2--Example 10 Topic Equations	Solving Multistep Equations and Applications of Quadrilaterals
Math Example--Solving Equations--Solving Equations with Angle Measures 2--Example 2	Solving Equations with Angle Measures 2--Example 2 Topic Equations	Solving Multistep Equations and Applications of Quadrilaterals
Math Example--Solving Equations--Solving Equations with Angle Measures 2--Example 3	Solving Equations with Angle Measures 2--Example 3 Topic Equations	Solving Multistep Equations and Applications of Quadrilaterals
Math Example--Solving Equations--Solving Equations with Angle Measures 2--Example 4	Solving Equations with Angle Measures 2--Example 4 Topic Equations	Solving Multistep Equations and Applications of Quadrilaterals
Math Example--Solving Equations--Solving Equations with Angle Measures 2--Example 5	Solving Equations with Angle Measures 2--Example 5 Topic Equations	Solving Multistep Equations and Applications of Quadrilaterals
Math Example--Solving Equations--Solving Equations with Angle Measures 2--Example 6	Solving Equations with Angle Measures 2--Example 6 Topic Equations	Solving Multistep Equations and Applications of Quadrilaterals
Math Example--Solving Equations--Solving Equations with Angle Measures 2--Example 7	Solving Equations with Angle Measures 2--Example 7 Topic Equations Description This example demonstrates solving equations involving angle measures in a kite. A kite has two pairs of adjacent congruent angles. In this case, we have angles represented as (x+50)°, (x+50)°, (y+20)°, and y°. To solve this problem, we apply two key principles: the sum of angles in a quadrilateral is 360°, and the sum of the angles of a triangle is 180°. You can use the triangle equation to solve for y. Once you determine the value for y, you can use that to find x using either the triangle or the quadrilateral equation. In the solution shown, the triangle equation is used.	Solving Multistep Equations and Applications of Quadrilaterals
Math Example--Solving Equations--Solving Equations with Angle Measures 2--Example 8	Solving Equations with Angle Measures 2--Example 8 Topic Equations Description This example illustrates solving equations involving angle measures in a kite. The kite has two known angles of 70° and 40°, and two unknown angles represented as (x+y)°. To solve this problem, we look at the triangles formed by one of the diagonals of the kite and use the triangle equation. First solve for x with the top triangle. Once you find x, use that value to solve for y in the bottom triangle. You could also use the quadrilateral equation to solve for y.	Solving Multistep Equations and Applications of Quadrilaterals
Math Example--Solving Equations--Solving Equations with Angle Measures 2--Example 9	Solving Equations with Angle Measures 2--Example 9 Topic Equations	Solving Multistep Equations and Applications of Quadrilaterals
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	Solving Equations with Angle Measures--Example 10 Topic Equations	Solving Multistep Equations and Applications of Angles and Planes