Illustrative Math Alignment: Grade 8 Unit 7
Exponents and Scientific Notation
Lesson 1: Exponent Review
Use the following Media4Math resources with this Illustrative Math lesson.
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Math Example--Exponential Concepts--Laws of Exponents: Example 4 | Math Example--Exponential Concepts--Laws of Exponents: Example 4TopicExponents DescriptionThis example focuses on simplifying an expression with two negative exponents, resulting in a fraction. The problem involves simplifying x(-10) * x(-7), which results in x(-17) or 1/x17. This demonstrates how negative exponents combine and how the result can be expressed as a fraction with a positive exponent. |
Laws of Exponents |
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Math Example--Exponential Concepts--Laws of Exponents: Example 5 | Math Example--Exponential Concepts--Laws of Exponents: Example 5TopicExponents DescriptionThis example demonstrates the simplification of an expression using exponents with multiple terms. The problem involves simplifying x4 * x6 * x8, which results in x18. This showcases how the exponents of terms with the same base can be added when multiplying. |
Laws of Exponents |
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Math Example--Exponential Concepts--Laws of Exponents: Example 6 | Math Example--Exponential Concepts--Laws of Exponents: Example 6TopicExponents DescriptionThis example focuses on simplifying an expression with both negative and positive exponents. The problem involves simplifying x(-2) * x7 * x11, which results in x16. This demonstrates how positive and negative exponents interact when multiplying terms with the same base, and how they can be combined to yield a single positive exponent. |
Laws of Exponents |
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Math Example--Exponential Concepts--Laws of Exponents: Example 7 | Math Example--Exponential Concepts--Laws of Exponents: Example 7TopicExponents DescriptionThis example demonstrates the simplification of an expression using both positive and negative exponents. The problem involves simplifying x8 * x(-5) * x6, which results in x9. This showcases how positive and negative exponents interact when multiplying terms with the same base, and how they can be combined to yield a single positive exponent. |
Laws of Exponents |
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Math Example--Exponential Concepts--Laws of Exponents: Example 8 | Math Example--Exponential Concepts--Laws of Exponents: Example 8TopicExponents DescriptionThis example focuses on simplifying an expression with negative exponents and converting it to a fraction. The problem involves simplifying x2 * x * x(-5), which results in 1/x2. This demonstrates how positive and negative exponents interact when multiplying terms with the same base, and how the result can be expressed as a fraction. |
Laws of Exponents |
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Math Example--Exponential Concepts--Laws of Exponents: Example 9 | Math Example--Exponential Concepts--Laws of Exponents: Example 9TopicExponents DescriptionThis example demonstrates the simplification of an expression with multiple negative exponents and one positive exponent. The problem involves simplifying x(-6) * x(-5) * x7, which results in x(-4) or 1/x4. This showcases how positive and negative exponents interact when multiplying terms with the same base, and how the result can be expressed as a fraction. |
Laws of Exponents |
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Math Example--Exponential Concepts--Modeling Sums with Integer Exponents--Example 1 | Math Example--Exponential Concepts--Modeling Sums with Integer Exponents--Example 1
This is part of a collection of math examples that focus on exponents, exponential expressions, and exponential functions. |
Numerical Expressions |
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Math Example--Exponential Concepts--Modeling Sums with Integer Exponents--Example 2 | Math Example--Exponential Concepts--Modeling Sums with Integer Exponents--Example 2
This is part of a collection of math examples that focus on exponents, exponential expressions, and exponential functions. |
Numerical Expressions |
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Math Example--Exponential Concepts--Modeling Sums with Integer Exponents--Example 3 | Math Example--Exponential Concepts--Modeling Sums with Integer Exponents--Example 3
This is part of a collection of math examples that focus on exponents, exponential expressions, and exponential functions. |
Numerical Expressions |
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Math Example--Exponential Concepts--Modeling Sums with Integer Exponents--Example 4 | Math Example--Exponential Concepts--Modeling Sums with Integer Exponents--Example 4
This is part of a collection of math examples that focus on exponents, exponential expressions, and exponential functions. |
Numerical Expressions |
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Math Example--Exponential Concepts--Modeling Sums with Integer Exponents--Example 5 | Math Example--Exponential Concepts--Modeling Sums with Integer Exponents--Example 5
This is part of a collection of math examples that focus on exponents, exponential expressions, and exponential functions. |
Numerical Expressions |
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Math Example--Exponential Concepts--Modeling Sums with Integer Exponents--Example 6 | Math Example--Exponential Concepts--Modeling Sums with Integer Exponents--Example 6
This is part of a collection of math examples that focus on exponents, exponential expressions, and exponential functions. |
Numerical Expressions |
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Math Example--Exponential Concepts--Modeling Sums with Integer Exponents--Example 7 | Math Example--Exponential Concepts--Modeling Sums with Integer Exponents--Example 7
This is part of a collection of math examples that focus on exponents, exponential expressions, and exponential functions. |
Numerical Expressions |
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Math Example--Solving Equations--Solving Equations with Angle Measures 2--Example 1 | Solving Equations with Angle Measures 2--Example 1TopicEquations |
Solving Multistep Equations and Applications of Quadrilaterals |
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Math Example--Solving Equations--Solving Equations with Angle Measures 2--Example 10 | Solving Equations with Angle Measures 2--Example 10TopicEquations |
Solving Multistep Equations and Applications of Quadrilaterals |
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Math Example--Solving Equations--Solving Equations with Angle Measures 2--Example 2 | Solving Equations with Angle Measures 2--Example 2TopicEquations |
Solving Multistep Equations and Applications of Quadrilaterals |
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Math Example--Solving Equations--Solving Equations with Angle Measures 2--Example 3 | Solving Equations with Angle Measures 2--Example 3TopicEquations |
Solving Multistep Equations and Applications of Quadrilaterals |
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Math Example--Solving Equations--Solving Equations with Angle Measures 2--Example 4 | Solving Equations with Angle Measures 2--Example 4TopicEquations |
Solving Multistep Equations and Applications of Quadrilaterals |
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Math Example--Solving Equations--Solving Equations with Angle Measures 2--Example 5 | Solving Equations with Angle Measures 2--Example 5TopicEquations |
Solving Multistep Equations and Applications of Quadrilaterals |
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Math Example--Solving Equations--Solving Equations with Angle Measures 2--Example 6 | Solving Equations with Angle Measures 2--Example 6TopicEquations |
Solving Multistep Equations and Applications of Quadrilaterals |
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Math Example--Solving Equations--Solving Equations with Angle Measures 2--Example 7 | Solving Equations with Angle Measures 2--Example 7TopicEquations DescriptionThis 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 |
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Math Example--Solving Equations--Solving Equations with Angle Measures 2--Example 8 | Solving Equations with Angle Measures 2--Example 8TopicEquations DescriptionThis 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 |
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Math Example--Solving Equations--Solving Equations with Angle Measures 2--Example 9 | Solving Equations with Angle Measures 2--Example 9TopicEquations |
Solving Multistep Equations and Applications of Quadrilaterals |
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MATH EXAMPLES--Teacher's Guide: Laws of Exponents | MATH EXAMPLES--Teacher's Guide: Laws of Exponents
This Teacher's Guide provides an overview of the 24 worked-out examples on the laws of exponents. This is part of a collection of teacher's guides. To see the complete collection of teacher's guides, click on this link. Note: The download is a PDF file.Related ResourcesTo see resources related to this topic click on the Related Resources tab above. |
Laws of Exponents |
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Math in the News: Issue 6--The BP Oil Spill, a Year Later | Math in the News: Issue 6--The BP Oil Spill, a Year Later
4/25/11. In this issue we discuss the BP oil spill one year after the spill. In particular we look at how damaging oil spills are to marine life and to oxygen levels in the water. This is part of the Math in the News collection. To see the complete collection, click on this link. Note: The download is a PPT file.Related ResourcesTo see resources related to this topic click on the Related Resources tab above. |
Data Analysis |
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VIDEO: Overview of Variables and Equations | VIDEO: Overview of Variables and Equations
What Is a Variable?A variable is a symbol, usually a letter, that can stand for different things. |
Variable Expressions, Applications of Equations and Inequalities and Variables and Unknowns |
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Paper-and-Pencil Quiz: Equations with Fractions (Easy) | Paper-and-Pencil Quiz: Equations with Fractions (Easy)
This is part of a collection of math quizzes on the topic of Equations with Fractions. To see the complete quiz collection on this topic, click on this link. Note: The download is the PDF version of the quiz (with answer key).Related ResourcesTo see additional resources on this topic, click on the Related Resources tab.Quiz LibraryTo see the complete collection of Quizzes, click on this link.ary">click on this link. |
Solving Fraction Equations |
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Paper-and-Pencil Quiz: Equations with Fractions (Hard) | Paper-and-Pencil Quiz: Equations with Fractions (Hard)
This is part of a collection of math quizzes on the topic of Equations with Fractions. To see the complete quiz collection on this topic, click on this link. Note: The download is the PDF version of the quiz (with answer key).Related ResourcesTo see additional resources on this topic, click on the Related Resources tab.Quiz LibraryTo see the complete collection of Quizzes, click on this link.ary">click on this link. |
Solving Fraction Equations |
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Paper-and-Pencil Quiz: Equations with Fractions (Medium) | Paper-and-Pencil Quiz: Equations with Fractions (Medium)
This is part of a collection of math quizzes on the topic of Equations with Fractions. To see the complete quiz collection on this topic, click on this link. Note: The download is the PDF version of the quiz (with answer key).Related ResourcesTo see additional resources on this topic, click on the Related Resources tab.Quiz LibraryTo see the complete collection of Quizzes, click on this link.ary">click on this link. |
Solving Fraction Equations |
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Paper-and-Pencil Quiz: Equations with Percents (Easy) | Paper-and-Pencil Quiz: Equations with Percents (Easy)
This is part of a collection of math quizzes on the topic of Equations with Percents. To see the complete quiz collection on this topic, click on this link. Note: The download is the PDF version of the quiz (with answer key).Related ResourcesTo see additional resources on this topic, click on the Related Resources tab.Quiz LibraryTo see the complete collection of Quizzes, click on this link.ary">click on this link. |
Solving Percent Equations |
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Paper-and-Pencil Quiz: Equations with Percents (Hard) | Paper-and-Pencil Quiz: Equations with Percents (Hard)
This is part of a collection of math quizzes on the topic of Equations with Percents. To see the complete quiz collection on this topic, click on this link. Note: The download is the PDF version of the quiz (with answer key).Related ResourcesTo see additional resources on this topic, click on the Related Resources tab.Quiz LibraryTo see the complete collection of Quizzes, click on this link.ary">click on this link. |
Solving Percent Equations |
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Paper-and-Pencil Quiz: Equations with Percents (Medium) | Paper-and-Pencil Quiz: Equations with Percents (Medium)
This is part of a collection of math quizzes on the topic of Equations with Percents. To see the complete quiz collection on this topic, click on this link. Note: The download is the PDF version of the quiz (with answer key).Related ResourcesTo see additional resources on this topic, click on the Related Resources tab.Quiz LibraryTo see the complete collection of Quizzes, click on this link.ary">click on this link. |
Solving Percent Equations |
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Paper-and-Pencil Quiz: Laws of Exponents (Easy) | Paper-and-Pencil Quiz: Laws of Exponents (Easy)
This is part of a collection of math quizzes on the topic of the Laws of Exponents. To see the complete quiz collection on this topic, click on this link. Note: The download is the PDF version of the quiz (with answer key).Related ResourcesTo see additional resources on this topic, click on the Related Resources tab.Quiz LibraryTo see the complete collection of Quizzes, click on this link.ary">click on this link. |
Laws of Exponents |
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Paper-and-Pencil Quiz: Laws of Exponents (Hard) | Paper-and-Pencil Quiz: Laws of Exponents (Hard)
This is part of a collection of math quizzes on the topic of the Laws of Exponents. To see the complete quiz collection on this topic, click on this link. Note: The download is the PDF version of the quiz (with answer key).Related ResourcesTo see additional resources on this topic, click on the Related Resources tab.Quiz LibraryTo see the complete collection of Quizzes, click on this link.ary">click on this link. |
Laws of Exponents |
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Paper-and-Pencil Quiz: Laws of Exponents (Medium) | Paper-and-Pencil Quiz: Laws of Exponents (Medium)
This is part of a collection of math quizzes on the topic of the Laws of Exponents. To see the complete quiz collection on this topic, click on this link. Note: The download is the PDF version of the quiz (with answer key).Related ResourcesTo see additional resources on this topic, click on the Related Resources tab.Quiz LibraryTo see the complete collection of Quizzes, click on this link.ary">click on this link. |
Laws of Exponents |
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Quizlet Flash Cards: Evaluating Quadratic Functions, Set 01 | Description Evaluate quadratic functions of the form f(x) = ax^2 + bx + c in this 20-flash card set. The values of a and b are in the range -10 to 10. Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards. Related ResourcesTo see other resources related to this topic, click on the Resources tab above. Quizlet LibraryTo see the complete Quizlet Flash Card Library, click on this Link to see the collection. |
Applications of Quadratic Functions |
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Quizlet Flash Cards: Evaluating Quadratic Functions, Set 02 | Description Evaluate quadratic functions of the form f(x) = ax^2 + bx + c in this 20-flash card set. The values of a and b are in the range -10 to 10. Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards. Related ResourcesTo see other resources related to this topic, click on the Resources tab above. Quizlet LibraryTo see the complete Quizlet Flash Card Library, click on this Link to see the collection. |
Applications of Quadratic Functions |
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Quizlet Flash Cards: Evaluating Quadratic Functions, Set 03 | Description Evaluate quadratic functions of the form f(x) = ax^2 + bx + c in this 20-flash card set. The values of a and b are in the range -10 to 10. Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards. Related ResourcesTo see other resources related to this topic, click on the Resources tab above. Quizlet LibraryTo see the complete Quizlet Flash Card Library, click on this Link to see the collection. |
Applications of Quadratic Functions |
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Quizlet Flash Cards: Evaluating Quadratic Functions, Set 04 | Description Evaluate quadratic functions of the form f(x) = ax^2 + bx + c in this 20-flash card set. The values of a and b are in the range -10 to 10. Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards. Related ResourcesTo see other resources related to this topic, click on the Resources tab above. Quizlet LibraryTo see the complete Quizlet Flash Card Library, click on this Link to see the collection. |
Applications of Quadratic Functions |
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Quizlet Flash Cards: Evaluating Quadratic Functions, Set 05 | Description Evaluate quadratic functions of the form f(x) = ax^2 + bx + c in this 20-flash card set. The values of a and b are in the range -10 to 10. Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards. Related ResourcesTo see other resources related to this topic, click on the Resources tab above. Quizlet LibraryTo see the complete Quizlet Flash Card Library, click on this Link to see the collection. |
Applications of Quadratic Functions |
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Quizlet Flash Cards: Evaluating Quadratic Functions, Set 06 | Description Evaluate quadratic functions of the form f(x) = ax^2 + bx + c in this 20-flash card set. The values of a and b are in the range -10 to 10. Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards. Related ResourcesTo see other resources related to this topic, click on the Resources tab above. Quizlet LibraryTo see the complete Quizlet Flash Card Library, click on this Link to see the collection. |
Applications of Quadratic Functions |
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Quizlet Flash Cards: Evaluating Quadratic Functions, Set 07 | Description Evaluate quadratic functions of the form f(x) = ax^2 + bx + c in this 20-flash card set. The values of a and b are in the range -10 to 10. Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards. Related ResourcesTo see other resources related to this topic, click on the Resources tab above. Quizlet LibraryTo see the complete Quizlet Flash Card Library, click on this Link to see the collection. |
Applications of Quadratic Functions |
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Quizlet Flash Cards: Evaluating Quadratic Functions, Set 08 | Description Evaluate quadratic functions of the form f(x) = ax^2 + bx + c in this 20-flash card set. The values of a and b are in the range -10 to 10. Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards. Related ResourcesTo see other resources related to this topic, click on the Resources tab above. Quizlet LibraryTo see the complete Quizlet Flash Card Library, click on this Link to see the collection. |
Applications of Quadratic Functions |
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Quizlet Flash Cards: Evaluating Quadratic Functions, Set 09 | Description Evaluate quadratic functions of the form f(x) = ax^2 + bx + c in this 20-flash card set. The values of a and b are in the range -10 to 10. Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards. Related ResourcesTo see other resources related to this topic, click on the Resources tab above. Quizlet LibraryTo see the complete Quizlet Flash Card Library, click on this Link to see the collection. |
Applications of Quadratic Functions |
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Quizlet Flash Cards: Evaluating Quadratic Functions, Set 10 | Description Evaluate quadratic functions of the form f(x) = ax^2 + bx + c in this 20-flash card set. The values of a and b are in the range -10 to 10. Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards. Related ResourcesTo see other resources related to this topic, click on the Resources tab above. Quizlet LibraryTo see the complete Quizlet Flash Card Library, click on this Link to see the collection. |
Applications of Quadratic Functions |
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Quizlet Flash Cards: Solving Quadratic Equations by Factoring, Set 01 | Solve quadratic equations by factoring in this 20-flash card set. The values of the quadratic equation terms are in the range -10 to 10. Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards. Related ResourcesTo see the complete collection of Quizlet Flash Cards on this topic, click on this link: https://bit.ly/3cwZzXj |
Factoring Quadratics and Quadratic Equations and Functions |
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Quizlet Flash Cards: Solving Quadratic Equations by Factoring, Set 02 | Solve quadratic equations by factoring in this 20-flash card set. The values of the quadratic equation terms are in the range -10 to 10. Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards. Related ResourcesTo see the complete collection of Quizlet Flash Cards on this topic, click on this link: https://bit.ly/3cwZzXj |
Factoring Quadratics and Quadratic Equations and Functions |
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Quizlet Flash Cards: Solving Quadratic Equations by Factoring, Set 03 | Solve quadratic equations by factoring in this 20-flash card set. The values of the quadratic equation terms are in the range -10 to 10. Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards. Related ResourcesTo see the complete collection of Quizlet Flash Cards on this topic, click on this link: https://bit.ly/3cwZzXj |
Factoring Quadratics and Quadratic Equations and Functions |
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Quizlet Flash Cards: Solving Quadratic Equations by Factoring, Set 04 | Solve quadratic equations by factoring in this 20-flash card set. The values of the quadratic equation terms are in the range -10 to 10. Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards. Related ResourcesTo see the complete collection of Quizlet Flash Cards on this topic, click on this link: https://bit.ly/3cwZzXj |
Factoring Quadratics and Quadratic Equations and Functions |
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Quizlet Flash Cards: Solving Quadratic Equations by Factoring, Set 05 | Solve quadratic equations by factoring in this 20-flash card set. The values of the quadratic equation terms are in the range -10 to 10. Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards. Related ResourcesTo see the complete collection of Quizlet Flash Cards on this topic, click on this link: https://bit.ly/3cwZzXj |
Factoring Quadratics and Quadratic Equations and Functions |
