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PA-N-1-2

Page history last edited by Tashe Harris 6 years, 2 months ago

PA.N.1.2 Express and compare approximations of very large and very small numbers using scientific notation.

In a Nutshell

With real-world applications, students will find writing numbers that represent large values (number of inches to the moon) or very small numbers (size of a grain of salt, in inches) to be difficult, as a standard number. Students will make connections between movement of the decimal and the concept of multiplying or dividing by a power of 10. The discovery of the usefulness of scientific notation should be developed by students as a convenient way to write very large or small numbers. Students should also realize scientific notation that use positive exponents represent much larger standard numbers and those with negative exponents represent smaller standard numbers. This will help students compare numbers written in scientific notation and as standard numbers.

Student Actions	Teacher Actions
Develop Mathematical Reasoning as students discuss and compare how to write very large or small numbers in a readable manner just as in science. Develop Accurate and Procedural Fluency when converting from scientific notation to standard form by interpreting the power of ten being multiplied by the coefficient. Students will also develop accurate and procedural fluency when converting from standard form to scientific notation. Develop Strategies for Problem Solving when operating with scientific notation to find the solution to a real world problems. Develop Mathematical Reasoning when determining the difference between a negative exponent and a negative coefficient while solving problems written in scientific notation. Develop Accurate and Procedural Fluency when recognizing scientific notation as it appears on a calculator screen. Be able to interpret scientific notation when it is shown on a calculator. For example, 2.3456E6 is 2.3456 x 10⁶.	Pose purposeful questions to allow students to explain and understand that when a base does not show an exponent it is assumed to be to the first power. Use and connect place value in base ten with the movement of the decimal point when evaluating scientific notation. Implement meaningful tasks that allow students to make the connection between repeated multiplication or division and converting from scientific notation and standard form. Pose purposeful questions specifically including examples involving negative exponent values. Use and connect the order of operations when working with evaluating or simplifying expressions, emphasizing the importance of grouping symbols. Pose purposeful questions to ensure understanding that the concept of significant digits originated from the science field out of necessity as a way to enhance the degree of accuracy.
Key Understandings	Misconceptions
Students must come to the realization that scientific notation is a way to write very large or very small numbers in a readable manner developed by scientists. Students will develop the understanding that the number is written with a coefficient between 1 and 10 and multiplied by a power of ten; Students will be able to convert from scientific notation to standard form by interpreting the power of ten being multiplied by the coefficient; Ensure students can convert from standard form to scientific notation	Students may think when writing numbers in scientific notation that they should move the decimal the position after the first zero instead of the first whole number. Students often mistake the exponent as the number of zeros to put on the end of the coefficient instead of realizing it represents the number of times they should multiply by ten. Ex. 2.5 x 10⁵ would be written by a student as 2,500,000 instead of the proper form of 250,000. When writing numbers in scientific notation, students may interpret the negative exponent as a negative number. Ex. 4^-2 as -16 instead of 1/16.