ALEX Classroom Resource

  

Grade 8 Mathematics Module 1, Topic A: Exponential Notation and Properties of Integer Exponents

  Classroom Resource Information  

Title:

 Grade 8 Mathematics Module 1, Topic A: Exponential Notation and Properties of Integer Exponents

URL:

 https://www.engageny.org/resource/grade-8-mathematics-module-1-topic-overview

Content Source:

 EngageNY
Type: Lesson/Unit Plan

Overview:

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. 

Content Standard(s):
Mathematics
MA2019 (2019)
Grade: 8
3. Develop and apply properties of integer exponents to generate equivalent numerical and algebraic expressions.
Unpacked Content
Evidence Of Student Attainment:
Students:
  • Use their understanding of exponents as repeated multiplication to create equivalent expressions and justify integer exponent properties.
Teacher Vocabulary:
  • Integer Exponent
Knowledge:
Students know:
  • that whole number exponents indicate repeated multiplication of the base number and that these exponents indicate the actual number of factors being produced.
Skills:
Students are able to:
  • Develop integer exponent operations in order to generate equivalent expressions through addition, multiplication, division and raising a power by another power with expressions containing integer exponents.
Understanding:
Students understand that:
  • just as whole number exponents represent repeated multiplication, negative integer exponents represent repeated division by the base number.
  • The exponent can be translated (visually, listing out the factors) to represent the exact number of factors being repeated so that the use of integer exponent operations ("rules") can be proven/make sense.
Diverse Learning Needs:
Essential Skills:
Learning Objectives:
M.8.3.1: Define exponent, power, coefficient, integers, equivalent, and numerical expression.
M.8.3.2: Restate negative exponents as positive exponents in the form 1/x2 .
M.8.3.3: Restate zero exponents as 1 (x0 = 1).
M.8.3.4: Recognize to add exponents when multiplying terms with like bases (Property of product of powers).
M.8.3.5: Recognize to subtract exponents when dividing terms with like bases (Property of quotient of powers).
M.8.3.6: Compute a numerical expression with positive exponents.
M.8.3.7: Restate exponential numbers as repeated multiplication.
M.8.3.8: Compute problems with adding and subtracting integers.

Prior Knowledge Skills:
  • Define exponent, numerical expression, algebraic expression, variable, base, power, square of a number, and cube of a number.
  • Compute a numerical expression with exponents, with or without a calculator.
  • Restate exponential numbers as repeated multiplication.
  • Choose the correct value to replace each variable in the expression (Substitution).
  • Calculate the multiplication of single or multi-digit whole numbers, with or without a calculator.
  • Define integers, positive and negative numbers.
  • Demonstrate the location of positive and negative numbers on a vertical and horizontal number line.
  • Give examples of positive and negative numbers to represent quantities having opposite directions in real-world contexts.
  • Discuss the measure of centering of 0 in relationship to positive and negative numbers.
  • Discover that the opposite of the opposite of a number is the number itself.
  • Show on a number line that numbers that are equal distance from 0 and on opposite sides of 0 have opposite signs.
Tags: equivalent, exponents, expressions, integer, notation, numerical, properties
License Type: Custom Permission Type
See Terms: https://www.engageny.org/terms-of-use
For full descriptions of license types and a guide to usage, visit :
https://creativecommons.org/licenses
AccessibilityText Resources: Content is organized under headings and subheadings
Comments

There are six lessons in this topic.

This resource is free for teachers to access and use. All resources required for the lessons are available to print from the site. 

  This resource provided by:  
Author: Hannah Bradley
This site may contain links to other websites or content belonging to or originating from third parties or links to websites and features in banners or other advertising. Such external links are not investigated, monitored, or checked for accuracy, adequacy, validity, reliability, availability, or completeness by us. WE DO NOT WARRANT, ENDORSE, GUARANTEE, OR ASSUME RESPONSIBILITY FOR THE ACCURACY OR RELIABILITY OF ANY INFORMATION OFFERED BY THIRD-PARTY WEBSITES LINKED THROUGH THIS SITE.
Copyright © 2017, Alabama Learning Exchange
Alabama State Department of Education
Alabama State Department of Education