PA.N.1.1 Develop and apply the properties of integer exponents, including a0 = 1 (with a 0 ), to generate equivalent numerical and algebraic expressions.
In a Nutshell
Students have developed the understanding of combining like terms, including terms with variables and exponents. Simplifying products and quotients of terms using exponents with a focus on like bases (or not), students will be able to apply a combination of exponent rules to write equivalent expressions by simplifying. When taking any base (b), when b ≠ 0, students will discover the division of like bases with the same exponent presents a fraction = 1 but also simplifies to b(p-p) = b0 and therefore confirming any base (b ≠ 0) to the power of zero, will equal one.
Student Actions
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Teacher Actions
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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.
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Develop Mathematical Reasoning when making a connection between the zero power rule being like a number divided by itself, therefore equaling 1 by working through several scenarios and examples illustrating this connection.
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Develop a Deep and Flexible Conceptual Understanding when applying the properties of exponents to generate equivalent expressions. This includes converting negative exponents and the zero power rule.
- Develop the Ability to Make Conjectures, Model, and Generalize by forming a connection between Prime Factorization and multiplication/division of exponential numbers through discussion with peers of specific scenarios.
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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.
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Key Understandings
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Misconceptions
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- 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);
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Understand how to write numbers in exponential form. For example, 2 × 2 × 2 can be written as 23
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Understand the connection between prime factorization and exponent rules
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Students sometimes do not realize (or forget) that any number to the zero power is 1. They commonly state that any number to the zero power is 0.
- Students often mix up the rules of operating with exponents. Students will multiply exponents when the operation is multiplication. Students will divide when the operation is division. Students will take the exponent to the power when the power is taken to a power.
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Students will sometimes multiply the base and the exponent. For example, 26 is not equal to 12, it's 64.
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Students may forget to use the reciprocal when working with negative exponents.
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OKMath Framework Introduction
Pre-Algebra Introduction
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