Illustrative Math Alignment: Grade 8 Unit 7

Overview

This comprehensive collection of 24 Math Examples focuses on the Laws of Exponents, providing educators with a rich resource to enhance their lesson plans. This set of downloadable images covers a wide range of skills related to exponent manipulation.

Overview

Overview

Overview

Overview

Overview

The "Comparing Fractions Products" collection from Media4Math offers a comprehensive set of examples designed to enhance students' understanding of comparing products of fractions. This collection is structured to gradually increase in complexity, allowing students to build their skills progressively. By analyzing a variety of examples, students can develop a deeper conceptual understanding and improve their ability to compare fractional products effectively.

This is a collection of definitions related to exponential concepts. This includes exponential functions, equations, and properties of exponents.

This is a collection of definitions related to exponential concepts. This includes exponential functions, equations, and properties of exponents.

This is part of a collection of math examples that focus on exponents, exponential expressions, and exponential functions.

This is part of a collection of math examples that focus on exponents, exponential expressions, and exponential functions.

This is part of a collection of math examples that focus on exponents, exponential expressions, and exponential functions.

This is part of a collection of math examples that focus on exponents, exponential expressions, and exponential functions.

This is part of a collection of math examples that focus on exponents, exponential expressions, and exponential functions.

This is part of a collection of math examples that focus on exponents, exponential expressions, and exponential functions.

This is part of a collection of math examples that focus on exponents, exponential expressions, and exponential functions.

This is part of a collection of math examples that focus on exponents, exponential expressions, and exponential functions.

This is part of a collection of math examples that focus on exponents, exponential expressions, and exponential functions.

This is part of a collection of math examples that focus on exponents, exponential expressions, and exponential functions.

This is part of a collection of math examples that focus on exponents, exponential expressions, and exponential functions.

This is part of a collection of math examples that focus on exponents, exponential expressions, and exponential functions.

This is part of a collection of math examples that focus on exponents, exponential expressions, and exponential functions.

This is part of a collection of math examples that focus on exponents, exponential expressions, and exponential functions.

This is part of a collection of math examples that focus on exponents, exponential expressions, and exponential functions.

Topic

Exponents

Description

This example demonstrates the simplification of an expression using the laws of exponents. The problem involves simplifying x2 * x3, which results in x5 by applying the law of exponents for multiplication. This step-by-step solution helps students understand how to combine like terms with exponents.

Topic

Exponents

Description

This example focuses on simplifying an expression with both positive and negative exponents. The problem involves simplifying x3 * x(-5) * x(-3), which results in x(-5) or 1/x5. 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.

Topic

Exponents

Description

This example demonstrates the simplification of an expression with both positive and negative exponents, including a zero exponent. The problem involves simplifying x(-10) * x10 * x(-2), which results in x(-2) or 1/x2. This showcases how positive and negative exponents interact when multiplying terms with the same base, and how zero exponents affect the result.

Topic

Exponents

Description

This example focuses on simplifying an expression with multiple negative exponents. The problem involves simplifying x(-1) * x(-5) * x(-3), which results in x(-9) or 1/x9. This demonstrates how negative exponents interact when multiplying terms with the same base, and how the result can be expressed as a fraction with a positive exponent in the denominator.

Topic

Exponents

Description

This example demonstrates the simplification of an expression involving division with exponents. The problem involves simplifying x3 / x2, which results in x. This showcases how exponents behave when dividing terms with the same base, illustrating the subtraction of exponents in division.

Topic

Exponents

Description

This example demonstrates the simplification of an expression involving division with negative exponents. The problem involves simplifying x(-5) / x6, which results in x(-11) or 1/x11. This showcases how negative and positive exponents interact when dividing terms with the same base, and how the result can be expressed as a fraction.

Topic

Exponents

Description

This example illustrates the simplification of an expression involving division with both positive and negative exponents. The problem involves simplifying x8 / x(-4), which results in x12. This demonstrates how positive and negative exponents interact when dividing terms with the same base, and how the result can yield a larger positive exponent.

Topic

Exponents

Description

This example focuses on simplifying an expression with negative exponents in both the numerator and denominator. The problem involves simplifying x(-7) / x(-5), which results in x(-2) or 1/x2. This demonstrates how negative exponents interact when dividing terms with the same base, and how the result can be expressed as a fraction.

Topic

Exponents

Description

This example demonstrates the simplification of an expression involving multiplication and division with exponents. The problem involves simplifying (x2 * x3) / x4, which results in x. This showcases how exponents behave when multiplying and dividing terms with the same base, illustrating the addition and subtraction of exponents in a single expression.

Topic

Exponents

Description

This example focuses on simplifying an expression involving multiplication and division with both positive and negative exponents. The problem involves simplifying (x-3 * x5) / x6, which results in x-4 or 1/x4. This demonstrates how positive and negative exponents interact when multiplying and dividing terms with the same base, and how the result can be expressed as a fraction.

Topic

Exponents

Description

This example demonstrates the simplification of an expression involving multiplication and division with both positive and negative exponents. The problem involves simplifying (x6 * x-10) / x2, which results in x-6 or 1/x6. This showcases how positive and negative exponents interact when multiplying and dividing terms with the same base, and how the result can be expressed as a fraction.

Topic

Exponents

Description

This example focuses on simplifying an expression with negative exponents using exponent rules. The problem involves simplifying x(-3) * x4, which results in x1 or simply x. This demonstrates how positive and negative exponents interact when multiplying terms with the same base.

Topic

Exponents

Description

This example demonstrates the simplification of an expression involving multiplication and division with both positive and negative exponents. The problem involves simplifying (x5 * x9) / x-6, which results in x20. This showcases how positive and negative exponents interact when multiplying and dividing terms with the same base, and how dividing by a negative exponent can lead to a larger positive exponent.

Topic

Exponents

Description

This example focuses on simplifying an expression involving multiplication and division with negative exponents. The problem involves simplifying (x(-3) * x(-5)) / x5, which results in 1/x13. This demonstrates how negative exponents interact when multiplying and dividing terms with the same base, and how the result can be expressed as a fraction with a positive exponent in the denominator.

Topic

Exponents

Description

This example demonstrates the simplification of an expression involving multiplication and division with both positive and negative exponents. The problem involves simplifying (x6 * x(-7)) / x(-9), which results in x8. This showcases how positive and negative exponents interact when multiplying and dividing terms with the same base, and how dividing by a negative exponent can lead to a positive result.

Topic

Exponents

Description

This example focuses on simplifying an expression involving multiplication and division with both positive and negative exponents. The problem involves simplifying (x(-5) * x9) / x(-6), which results in x10. This demonstrates how positive and negative exponents interact when multiplying and dividing terms with the same base, and how dividing by a negative exponent can lead to a larger positive exponent.

Topic

Exponents

Description

This example demonstrates the simplification of an expression involving multiplication and division with negative exponents. The problem involves simplifying (x(-2) * x(-6)) / x(-8), which results in 1. This showcases how negative exponents interact when multiplying and dividing terms with the same base, and how they can cancel out to yield a result of 1.

Topic

Exponents

Description

This example demonstrates the simplification of an expression resulting in a negative exponent. The problem involves simplifying x5 * x(-6), which results in x(-1) or 1/x. This showcases how positive and negative exponents interact and how the result can be expressed as a fraction.

Topic

Exponents

Description

This 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.

Topic

Exponents

Description

This 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.

Topic

Exponents

Description

This 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.

Topic

Exponents

Description

This 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.

Topic

Exponents

Description

This 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.

Topic

Exponents

Description

This 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.

Topic

Comparing Fractions

Topic

Comparing Fractions

Description

This example illustrates the process of comparing the products of fractions. The image shows a scenario where two fractions are multiplied and their products are compared to determine which is greater. The mathematical concept involves understanding how to multiply fractions and compare the resulting products. Key skills include fraction multiplication, simplification, and comparison. Solving this problem often requires an algorithmic method where fractions are multiplied and then compared, or a visual model might be employed to provide a clearer understanding of the size of each product relative to the other.

Topic

Comparing Fractions

Description

This example focuses on comparing the products of fractions. The image depicts a fraction product compared to a whole number. The concept involves multiplying fractions and comparing the results to see which is larger or smaller. Skills required include multiplying fractions, simplifying them, and comparing the numerical outcomes. This problem can be solved using a straightforward algorithm where each fraction is multiplied, and the products are compared, or through a visual model that helps illustrate the relative sizes and relationships between the products.