ALEX Classroom Resources

   View Standards     Standard(s): [MA2019] ACC-7 (7) 14 :

14. Develop and apply properties of integer exponents to generate equivalent numerical and algebraic expressions. [Grade 8, 3]

[MA2019] REG-8 (8) 3 :

3. Develop and apply properties of integer exponents to generate equivalent numerical and algebraic expressions.

Explore the relationship between graphic patterns and their mathematical representation. This video focuses on how fractals can be a visual representation of positive exponents. This video was submitted through the Innovation Math Challenge, a contest open to professional and nonprofessional producers.

   View Standards     Standard(s): [MA2019] ACC-7 (7) 14 :

14. Develop and apply properties of integer exponents to generate equivalent numerical and algebraic expressions. [Grade 8, 3]

[MA2019] REG-8 (8) 3 :

3. Develop and apply properties of integer exponents to generate equivalent numerical and algebraic expressions.

Determine the relationship between graphic patterns and what they represent mathematically. This video focuses on how fractals can be a visual representation of negative exponents, which are a way to express repeated division. This video was submitted through the Innovation Math Challenge, a contest open to professional and nonprofessional producers.

   View Standards     Standard(s): [MA2019] ACC-7 (7) 14 :

14. Develop and apply properties of integer exponents to generate equivalent numerical and algebraic expressions. [Grade 8, 3]

[MA2019] REG-8 (8) 3 :

3. Develop and apply properties of integer exponents to generate equivalent numerical and algebraic expressions.

[MA2019] ACC-8 (8) 2 :

2. Rewrite expressions involving radicals and rational exponents using the properties of exponents. [Algebra I with Probability, 2]

In this program, we learn that the power of a quotient is equal to the quotient obtained when the dividend and divisor are each raised to the indicated power separately before the division is performed. 

   View Standards     Standard(s): [MA2019] (6) 15 :

15. Write, read, and evaluate expressions in which letters represent numbers in real-world contexts.

a. Interpret a variable as an unknown value for any number in a specified set, depending on the context.

b. Write expressions to represent verbal statements and real-world scenarios.

c. Identify parts of an expression using mathematical terms such as sum, term, product, factor, quotient, and coefficient.

d. Evaluate expressions (which may include absolute value and whole number exponents) with respect to order of operations.

[MA2019] ACC-7 (7) 14 :

14. Develop and apply properties of integer exponents to generate equivalent numerical and algebraic expressions. [Grade 8, 3]

[MA2019] REG-8 (8) 3 :

3. Develop and apply properties of integer exponents to generate equivalent numerical and algebraic expressions.

[MA2019] ACC-8 (8) 2 :

2. Rewrite expressions involving radicals and rational exponents using the properties of exponents. [Algebra I with Probability, 2]

[MA2019] AL1-19 (9-12) 1 :

1. Explain how the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for an additional notation for radicals using rational exponents.

[MA2019] AL1-19 (9-12) 2 :

2. Rewrite expressions involving radicals and rational exponents using the properties of exponents.

Apply your critical thinking skills to learn about multiplication and division of exponents. This interactive exercise focuses on positive and negative exponents and combining exponents in an effort to get you to recognize patterns and determine a rule.

This resource is part of the Math at the Core: Middle School collection.

   View Standards     Standard(s): [MA2015] AL1 (9-12) 32 :

32 ) Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. [F-IF8]

a. Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context. [F-IF8a]

b. Use the properties of exponents to interpret expressions for exponential functions. [F-IF8b]

Example: Identify percent rate of change in functions such as y = (1.02)^t, y = (0.97)^t, y = (1.01)^12t, and y = (1.2)^t/₁₀, and classify them as representing exponential growth and decay.

[MA2015] ALT (9-12) 13 :

13 ) Use the structure of an expression to identify ways to rewrite it. [A-SSE2]

Example: See x⁴ - y⁴ as (x²)² - (y²)², thus recognizing it as a difference of squares that can be factored as (x² - y²)(x² + y²).

[MA2019] ACC-7 (7) 14 :

14. Develop and apply properties of integer exponents to generate equivalent numerical and algebraic expressions. [Grade 8, 3]

[MA2019] REG-8 (8) 3 :

3. Develop and apply properties of integer exponents to generate equivalent numerical and algebraic expressions.

[MA2019] AL1-19 (9-12) 5 :

5. Use the structure of an expression to identify ways to rewrite it.

Example: See x⁴ - y⁴ as (x²)² - (y²)², thus recognizing it as a difference of squares that can be factored as (x² - y²)(x² + y²).

[MA2019] AL1-19 (9-12) 24 :

24. Distinguish between situations that can be modeled with linear functions and those that can be modeled with exponential functions.

a. Show that linear functions grow by equal differences over equal intervals, while exponential functions grow by equal factors over equal intervals.

b. Define linear functions to represent situations in which one quantity changes at a constant rate per unit interval relative to another.

c. Define exponential functions to represent situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another.

[MA2019] AL1-19 (9-12) 25 :

25. Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).

Students will apply their critical thinking skills to learn about multiplication and division of exponents. This interactive exercise focuses on positive and negative exponents and combining exponents in an effort to help students recognize patterns and determine a rule.

This resource is part of the Math at the Core: Middle School collection.

   View Standards     Standard(s): [MA2019] REG-8 (8) 3 :

3. Develop and apply properties of integer exponents to generate equivalent numerical and algebraic expressions.

In Module 1, Topic A, students begin by learning the precise definition of exponential notation where the exponent is restricted to being a positive integer. In Lessons 2 and 3, students discern the structure of exponents by relating multiplication and division of expressions with the same base to combining like terms using the distributive property, and by relating multiplying three factors using the associative property to raising a power to a power.

Lesson 4 expands the definition of exponential notation to include what it means to raise a nonzero number to a zero power; students verify that the properties of exponents developed in Lessons 2 and 3 remain true. Properties of exponents are extended again in Lesson 5 when a positive integer, raised to a negative exponent, is defined. In Lesson 5, students accept the properties of exponents as true for all integer exponents and are shown the value of learning them, i.e., if the three properties of exponents are known, then facts about dividing numbers in exponential notation with the same base and raising fractions to a power are also known. 

   View Standards     Standard(s): [MA2019] ACC-7 (7) 14 :

14. Develop and apply properties of integer exponents to generate equivalent numerical and algebraic expressions. [Grade 8, 3]

[MA2019] REG-8 (8) 3 :

3. Develop and apply properties of integer exponents to generate equivalent numerical and algebraic expressions.

In this activity from Khan Academy, students will review the common properties of exponents that allow them to rewrite powers in different ways. For example, x²⋅x³ can be written as x⁵. This activity has embedded videos, practice problems with immediate checks for the correctness of answers, and an explanation option. This review can be assigned to Google Classroom. 

Khan Academy is a free resource for teachers. Teachers can sign up for a free account to access additional resources

   View Standards     Standard(s): [MA2019] ACC-7 (7) 14 :

14. Develop and apply properties of integer exponents to generate equivalent numerical and algebraic expressions. [Grade 8, 3]

[MA2019] REG-8 (8) 3 :

3. Develop and apply properties of integer exponents to generate equivalent numerical and algebraic expressions.

In this MathPlanet lesson, students will learn the properties of exponents. The students will learn to multiply powers, apply the power of a power property, divide exponents, raise a quotient to a power, and what to do with a negative exponent. This lesson includes a video lesson and can be added to Google Classroom.