PA.N.1.3 Multiply and divide numbers expressed in scientific notation, express the answer in scientific notation.
In a Nutshell
Scientific notation does not have variables, but they are products of a coefficient and an exponent term with a base of 10. As students multiply and divide scientific notation values, they should be treating the decimal value as a product or quotient of coefficients, then applying their prior knowledge of exponent rules of products and quotients for the like bases of 10. Students should come to the realization that their work may not result in a valid scientific notation expression and will need to be rewritten correctly.
Student Actions
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Teacher Actions
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Develop Ability to Make Conjectures, Model and Generalize when exploring and discussing the properties of exponents to generate equivalent expressions. This includes multiplying, dividing, raising a power to a power, converting negative exponents, and the zero power rule.
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Develop the Ability to Communicate Mathematically by writing the rules in words to help explain how the expression is being simplifies.
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Develop Mathematical Reasoning when working with negative exponents while looking for connections as to why negative exponents can be simplified by using the reciprocal. Ex. 3^-3 is equivalent to 1/27.
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Develop Accurate and Procedural Understanding when analyzing problems involving multiplying and dividing numbers in scientific notation. This includes putting the answer in proper scientific notation.
- Apply and Adapt a variety of appropriate strategies to solve real-world problems using scientific notation.
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- Implement meaningful tasks that promote reasoning and understanding where students explore tasks allowing them to generalize and state the rules of exponents. Allow students to write each expression in expanded notation, so they will make the connection between the rule and the computations in expanded form. This will support their understanding of the rule and make it unnecessary for them to memorize the rules.
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Use and connect prior knowledge of negative exponents to the rules of dividing exponents by posing purposeful questions and providing examples..
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Implement meaningful tasks that promote reasoning and problem solving by providing students with real world contexts when they are multiplying and dividing in scientific notation.
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Key Understandings
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Misconceptions
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Students may forget to check the result of product or quotient to ensure it is written in correct scientific notation. Additional steps might be needed to convert the result into scientific notation.
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Students might leave off significant digits when writing the product or quotient in scientific notation.
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OKMath Framework Introduction
Pre-Algebra Introduction
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