ALEX Classroom Resource

  

Power of a Quotient | Algebra 1: Module 2: Topic 5

  Classroom Resource Information  

Title:

 Power of a Quotient | Algebra 1: Module 2: Topic 5

URL:

 https://aptv.pbslearningmedia.org/resource/whro-video-classroom-mod2-topic5/power-of-a-quotient-algebra-1-module-2-topic-5/

Content Source:

 PBS
Type: Audio/Video

Overview:

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. 

Content Standard(s):
Mathematics
MA2019 (2019)
Grade: 7
Accelerated
14. Develop and apply properties of integer exponents to generate equivalent numerical and algebraic expressions. [Grade 8, 3]
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. i.e. 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:
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.
Mathematics
MA2019 (2019)
Grade: 8
Accelerated
2. Rewrite expressions involving radicals and rational exponents using the properties of exponents. [Algebra I with Probability, 2]
Unpacked Content
Evidence Of Student Attainment:
Students:
  • Convert from radical representation to using rational exponents and vise versa.
Teacher Vocabulary:
  • Radical
  • Rational exponent
  • Expression
Knowledge:
Students know:
  • the denominator of the rational exponent is the root index and the numerator is the exponent of the radicand. For example, 51/2=5 and 163/2=(161/2)3= (16)3=43=64.
  • The root index of the radical is the denominator of the rational exponent and the exponent of the radicand is the numerator of the rational exponent. For example, 4103= 103/4.
Skills:
Students are able to:
  • Rewrite expressions from radical representations to rational exponents and vice versa.
Understanding:
Students understand:
  • The meaning of rational exponents and how to convert between them and radical representations.
Diverse Learning Needs:
Tags: dividend, divisor, exponents, power, quotient
License Type: Public Domain
For full descriptions of license types and a guide to usage, visit :
https://creativecommons.org/licenses
AccessibilityAudio resources: includes a transcript or subtitles
Comments

This resource could be used as a before or an after the topic of a lesson.  Students could be encouraged to take notes.

  This resource provided by:  
Author: Kristy Lacks
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