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2022 PA-N-1-1

Page history last edited by Brigit Minden 10 months ago

PA.N.1.1


PA.N.1.1 Develop and apply the properties of integer exponents, including a0 = 1 (with a0 ), to generate equivalent numerical and algebraic expressions
 


In a Nutshell

Students use previous knowledge of combining like terms, including terms with variables and exponents, to simplify products and quotients of numerical and algebraic terms including integer exponents. Students will be able to develop and apply properties of exponent rules to write equivalent expressions. When taking any base (a), when a  ≠ 0, students will discover the division of like bases with the same exponent presents a fraction equivalent to  1 but also simplifies to a(p-p) = a0 and therefore confirming any base (a  ≠ 0) to the power of zero, will equal one.

Student Actions

Teacher Actions

  • Develop ability to make conjectures, model and generalize by looking for patterns of exponents to develop a rule for the value of a number to the zero power.

  • Develop Mathematical Reasoning when exploring properties of and developing strategies for combining exponents in expressions containing products and quotients of algebraic monomial expressions, including the zero power rule.  

  • Develop a Deep and Flexible Conceptual Understanding when applying the properties of exponents to generate equivalent expressions, including negative exponents and the zero power rule.

  • Develop the Ability to Make Conjectures, Model, and Generalize by examining properties resulting from combinations of terms expressed with prime factorization and drawing conclusions of properties for simplifying with products/quotients of exponential expressions.

  • Develop Mathematical Reasoning by making justifiable conjectures between all exponent rules, including multiplying or dividing with the same base, negative exponent rule, and raising a power to a power. 
  • Support productive struggle by allowing students to look for patterns to make conjectures as to the “why” of exponent rules and writing out numbers in expanded form. This will allow students to develop the exponent rules within the context of the task. 

  • Use and connect mathematical representations to make connections between the students’ prior knowledge of prime factorization and the properties of exponents. Include prior knowledge of how to write repeated multiplication as exponents (3x3x3x3 = 34) as well as a non-zero number divided by itself simplifies to the value of 1 (4/4 = 1) 

  • Implement tasks that promote reasoning and facilitate the development of the exponent rules through student discovery. 

Key Understandings

Misconceptions 

  • Be able to know and apply the properties of exponents to generate equivalent expressions. This includes multiplying (42 x 45 = 47), dividing (75 / 73 = 72), raising a power to a power ( (34)2 = 38), converting negative exponents (5-2= 1/52  or 1/7-4 = 74), and zero power rule ( 80 = 1)

  • Understand the zero power rule and why anything to the zero power equals 1.

  • Understand the connection between prime factorization and exponent rules. 

  • Students may not realize (or forget) that any number to the zero power is 1 and incorrectly state that any number to the zero power is 0.

  • Students may interchange the rules of operating with exponents. For example, students will multiply exponents when the operation is multiplication, divide the exponents when the operation is division or take the exponent to the power when the power is taken to a power. 

  • Students may multiply the base and the exponent. For example, 26 is not equal to 12, it's 64.

  • Students may forget to use the reciprocal when working with negative exponents. 

  Knowledge Connections

Prior Knowledge

Leads to 

  • Raise rational numbers to positive integer exponents (7.N.2.4).

  • Represent patterns with whole-number exponents and evaluate powers with whole-number bases and exponents (6.N.2.4). 

  • Simplify polynomial expressions by adding, subtracting, or multiplying (A1.A.3.2). 

 

OKMath Framework Introduction

Pre-Algebra Introduction

 

 

 

 

 

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