Illustrative Math Alignment: Grade 6 Unit 1
Expressions and Equations
Lesson 4: Practice Solving Equations and Representing Situations with Equations
Use the following Media4Math resources with this Illustrative Math lesson.
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Definition--Equation Concepts--The Unknown | The UnknownTopicEquations DefinitionThe unknown is the variable in an equation that needs to be solved for. DescriptionThe unknown in an equation represents the value that needs to be determined. For example, in the equation x + 3 = 7 x is the unknown. Identifying and solving for the unknown is a core aspect of algebra. In real-world applications, finding the unknown is crucial for solving problems in various fields such as science, engineering, and finance. Understanding how to identify and solve for the unknown helps students develop problem-solving skills and apply mathematical concepts to real-life situations. |
Variables and Unknowns |
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Definition--Equation Concepts--Transitive Property of Equality | Transitive Property of EqualityTopicEquations DefinitionThe Transitive Property of Equality states that if a = b and b = c, then a = c. DescriptionThe Transitive Property of Equality is a fundamental principle in mathematics. It states that if one quantity equals a second quantity, and the second quantity equals a third, then the first and third quantities are equal. For example, if x = y and y = z then x = z This property is used to justify steps in solving equations and proving mathematical statements. |
Applications of Equations and Inequalities |
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Definition--Equation Concepts--True Equation | True EquationTopicEquations DefinitionA true equation is an equation that holds true for the given values of the variable(s). DescriptionA true equation is an equation that is valid for specific values of the variable(s). For example, the equation 2 + 3 = 5 is true because both sides are equal. Identifying true equations is important in verifying the correctness of mathematical statements. In real-world applications, recognizing true equations helps in ensuring the accuracy of mathematical models and solutions. Understanding true equations helps students develop critical thinking and analytical skills. |
Applications of Equations and Inequalities |
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Definition--Equation Concepts--Two-Step Equation | Two-Step EquationTopicEquations DefinitionA two-step equation requires two operations to solve. DescriptionTwo-step equations involve performing two operations to isolate the variable. For example, solving 2x + 3 = 7 requires subtracting 3 from both sides and then dividing by 2 to find x = 2. These equations are common in algebra and require a systematic approach to solve. In real-world applications, two-step equations are used in problem-solving scenarios such as calculating costs or determining measurements. Understanding how to solve two-step equations helps students develop critical thinking and problem-solving skills. |
Solving Two-Step Equations |
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Definition--Equation Concepts--Variable Expression | Variable ExpressionTopicEquations DefinitionA variable expression is a mathematical phrase involving variables, numbers, and operation symbols. DescriptionVariable expressions consist of variables, numbers, and operations such as addition, subtraction, multiplication, and division. For example, 3x + 4 is a variable expression. These expressions are used to represent quantities and relationships in algebra. |
Variable Expressions |
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Definition--Equation Concepts--Visual Models for Equations | Visual Models for EquationsTopicEquations DefinitionVisual models for equations use graphical representations to illustrate the relationships between variables. DescriptionVisual models for equations include graphs, charts, and diagrams that represent the relationships between variables. For example, a graph of the equation y = 2x + 3 shows a straight line with a slope of 2 and a y-intercept of 3. These models help in understanding and interpreting equations. |
Applications of Equations and Inequalities |
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INSTRUCTIONAL RESOURCE: Math Examples 13 | INSTRUCTIONAL RESOURCE: Math Examples--Equations with Fractions
The complete set of 13 examples that make up this set of tutorials. This is part of a collection of math examples for a variety of math topics. To see the complete collection of these resources, click on this link. Note: The download is a PPT file.Library of Instructional ResourcesTo see the complete library of Instructional Resources , click on this link. |
Solving Fraction Equations |
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INSTRUCTIONAL RESOURCE: Math Examples 14 | INSTRUCTIONAL RESOURCE: Math Examples--Equations with Percents
The complete set of 42 examples that make up this set of tutorials. This is part of a collection of math examples for a variety of math topics. To see the complete collection of these resources, click on this link. Note: The download is a PPT file.Library of Instructional ResourcesTo see the complete library of Instructional Resources , click on this link. |
Solving Percent Equations |
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INSTRUCTIONAL RESOURCE: Math Examples 34 | INSTRUCTIONAL RESOURCE: Math Examples--One-Variable Equations
The complete set of 21 examples that make up this set of tutorials. This is part of a collection of math examples for a variety of math topics. To see the complete collection of these resources, click on this link. Note: The download is a PPT file.Library of Instructional ResourcesTo see the complete library of Instructional Resources , click on this link. |
Applications of Equations and Inequalities |
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INSTRUCTIONAL RESOURCE: Tutorial: Solving Addition and Subtraction Equations | INSTRUCTIONAL RESOURCE: Tutorial: Solving Addition and Subtraction Equations
Learn how to solve addition and subtraction equations using column addition and subtraction techniques. This is part of a collection of math tutorials on a variety of math topics. To see the complete collection of these resources, click on this link.Library of Instructional ResourcesTo see the complete library of Instructional Resources , click on this link. |
Addition Expressions and Equations and Subtraction Expressions and Equations |
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INSTRUCTIONAL RESOURCE: Tutorial: Writing and Solving Division Equations | INSTRUCTIONAL RESOURCE: Tutorial: Writing and Solving Division Equations
This tutorial provides an overview of solving division equations, with the focus on one- and two-step equations. This is part of a collection of math tutorials on a variety of math topics. To see the complete collection of these resources, click on this link.Library of Instructional ResourcesTo see the complete library of Instructional Resources , click on this link. |
Division Expressions and Equations |
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INSTRUCTIONAL RESOURCE: Tutorial: Writing and Solving Multiplication Equations | INSTRUCTIONAL RESOURCE: Tutorial: Writing and Solving Multiplication Equations
This tutorial provides an overview of writing and solving multiplication equations. The focus is on one- and two-step equations. This is part of a collection of math tutorials on a variety of math topics. To see the complete collection of these resources, click on this link.Library of Instructional ResourcesTo see the complete library of Instructional Resources , click on this link. |
Multiplication Expressions and Equations |
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Math Example--Quadratics--Calculating the Discriminant: Example 1 | Calculating the Discriminant: Example 1TopicQuadratics |
Quadratic Formula |
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Math Example--Quadratics--Calculating the Discriminant: Example 10 | Calculating the Discriminant: Example 10TopicQuadratics DescriptionThis example illustrates a quadratic with two real roots. The discriminant being positive indicates that there are two real solutions to the equation. This scenario helps students recognize the significance of repeated roots and their graphical representation. For a complete collection of math examples related to Quadratics click on this link: Math Examples: Quadratics Collection. |
Quadratic Formula |
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Math Example--Quadratics--Calculating the Discriminant: Example 2 | Calculating the Discriminant: Example 2TopicQuadratics |
Quadratic Formula |
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Math Example--Quadratics--Calculating the Discriminant: Example 3 | Calculating the Discriminant: Example 3TopicQuadratics DescriptionThis example demonstrates a quadratic equation with one distinct real root, highlighting the relationship between the coefficients and the resulting discriminant. By calculating the discriminant, students can identify the nature of the roots, which is crucial for solving quadratics effectively. Skills involved include algebraic manipulation and understanding the graphical implications of roots. For a complete collection of math examples related to Quadratics click on this link: Math Examples: Quadratics Collection. |
Quadratic Formula |
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Math Example--Quadratics--Calculating the Discriminant: Example 4 | Calculating the Discriminant: Example 4TopicQuadratics DescriptionThis example illustrates a quadratic with two real roots. The discriminant being positive indicates that there are two real roots. This scenario helps students recognize the significance of repeated roots and their graphical representation. For a complete collection of math examples related to Quadratics click on this link: Math Examples: Quadratics Collection. |
Quadratic Formula |
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Math Example--Quadratics--Calculating the Discriminant: Example 5 | Calculating the Discriminant: Example 5TopicQuadratics DescriptionThis example demonstrates a quadratic equation with no distinct real roots, highlighting the relationship between the coefficients and the resulting discriminant. By calculating the discriminant, students can identify the nature of the roots, which is crucial for solving quadratics effectively. Skills involved include algebraic manipulation and understanding the graphical implications of roots. For a complete collection of math examples related to Quadratics click on this link: Math Examples: Quadratics Collection. |
Quadratic Formula |
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Math Example--Quadratics--Calculating the Discriminant: Example 6 | Calculating the Discriminant: Example 6TopicQuadratics DescriptionThis example illustrates a quadratic with a double real root. The discriminant being zero indicates that there is exactly one real solution to the equation. This scenario helps students recognize the significance of repeated roots and their graphical representation. For a complete collection of math examples related to Quadratics click on this link: Math Examples: Quadratics Collection. |
Quadratic Formula |
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Math Example--Quadratics--Calculating the Discriminant: Example 7 | Calculating the Discriminant: Example 7TopicQuadratics DescriptionIn this example, the quadratic equation results in two roots, demonstrating the cases where the discriminant is positive. This provides insights into scenarios where quadratic equations intersect the x-axis twice. Skills in algebra are focused on interpreting complex solutions and their geometric implications. For a complete collection of math examples related to Quadratics click on this link: Math Examples: Quadratics Collection. |
Quadratic Formula |
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Math Example--Quadratics--Calculating the Discriminant: Example 8 | Calculating the Discriminant: Example 8TopicQuadratics DescriptionThis example illustrates a quadratic with two real roots. The discriminant being positive indicates that there are two real solutions to the equation. This scenario helps students recognize the significance of two roots and their graphical representation. For a complete collection of math examples related to Quadratics click on this link: Math Examples: Quadratics Collection. |
Quadratic Formula |
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Math Example--Quadratics--Calculating the Discriminant: Example 9 | Calculating the Discriminant: Example 9TopicQuadratics DescriptionThis example demonstrates a quadratic equation with two distinct real roots, highlighting the relationship between the coefficients and the resulting discriminant. By calculating the discriminant, students can identify the nature of the roots, which is crucial for solving quadratics effectively. Skills involved include algebraic manipulation and understanding the graphical implications of roots. For a complete collection of math examples related to Quadratics click on this link: Math Examples: Quadratics Collection. |
Quadratic Formula |
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Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 1 | Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 1
This is part of a collection of math examples that focus on ratios, proportions, and percents. |
Proportions |
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Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 10 | Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 10
This is part of a collection of math examples that focus on ratios, proportions, and percents. |
Proportions |
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Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 11 | Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 11
This is part of a collection of math examples that focus on ratios, proportions, and percents. |
Proportions |
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Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 12 | Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 12
This is part of a collection of math examples that focus on ratios, proportions, and percents. |
Proportions |
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Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 13 | Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 13
This is part of a collection of math examples that focus on ratios, proportions, and percents. |
Proportions |
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Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 14 | Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 14
This is part of a collection of math examples that focus on ratios, proportions, and percents. |
Proportions |
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Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 15 | Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 15
This is part of a collection of math examples that focus on ratios, proportions, and percents. |
Proportions |
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Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 16 | Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 16
This is part of a collection of math examples that focus on ratios, proportions, and percents. |
Proportions |
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Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 17 | Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 17
This is part of a collection of math examples that focus on ratios, proportions, and percents. |
Proportions |
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Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 18 | Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 18
This is part of a collection of math examples that focus on ratios, proportions, and percents. |
Proportions |
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Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 19 | Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 19
This is part of a collection of math examples that focus on ratios, proportions, and percents. |
Proportions |
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Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 2 | Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 2
This is part of a collection of math examples that focus on ratios, proportions, and percents. |
Proportions |
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Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 20 | Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 20
This is part of a collection of math examples that focus on ratios, proportions, and percents. |
Proportions |
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Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 21 | Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 21
This is part of a collection of math examples that focus on ratios, proportions, and percents. |
Proportions |
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Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 22 | Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 22
This is part of a collection of math examples that focus on ratios, proportions, and percents. |
Proportions |
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Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 23 | Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 23
This is part of a collection of math examples that focus on ratios, proportions, and percents. |
Proportions |
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Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 24 | Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 24
This is part of a collection of math examples that focus on ratios, proportions, and percents. |
Proportions |
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Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 25 | Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 25
This is part of a collection of math examples that focus on ratios, proportions, and percents. |
Proportions |
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Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 26 | Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 26
This is part of a collection of math examples that focus on ratios, proportions, and percents. |
Proportions |
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Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 27 | Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 27
This is part of a collection of math examples that focus on ratios, proportions, and percents. |
Proportions |
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Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 28 | Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 28
This is part of a collection of math examples that focus on ratios, proportions, and percents. |
Proportions |
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Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 29 | Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 29
This is part of a collection of math examples that focus on ratios, proportions, and percents. |
Proportions |
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Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 3 | Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 3
This is part of a collection of math examples that focus on ratios, proportions, and percents. |
Proportions |
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Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 30 | Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 30
This is part of a collection of math examples that focus on ratios, proportions, and percents. |
Proportions |
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Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 31 | Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 31
This is part of a collection of math examples that focus on ratios, proportions, and percents. |
Proportions |
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Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 32 | Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 32
This is part of a collection of math examples that focus on ratios, proportions, and percents. |
Proportions |
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Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 33 | Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 33
This is part of a collection of math examples that focus on ratios, proportions, and percents. |
Proportions |
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Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 34 | Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 34
This is part of a collection of math examples that focus on ratios, proportions, and percents. |
Proportions |
