Scientific Notation Is An Exponential Expression

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SWBAT solve word problems using Scientific Notation by identifying the correct math operation, and applying the operations correctly.

Big Idea

To Multiply! Divide! Add! or Subtract! , and how exponent laws apply to Scientific Notation.

Warm Up

15 minutes

The purpose of this Warm up is to remind students of the structure of the universe around us, and how scientific notation can be used to represent the size of extremely small and large numbers.  Students have previously been introduced to Scientific Notation in earlier grades. After reviewing the definition of Scientific Notation, the goal of this lesson is for students to be able to identify the correct math operation to apply to word problems, and how to perform those operations using Scientific Notation with and without technology.

I use the Powers of Ten video below to review the uses of Scientific Notation in the world around us.  I stop the video at eight minutes and 40 seconds.  I instruct the students to write down two facts from the video.  One large number, and one small number. Then I review the definition of Scientific Notation with the students by questioning how to write a number in Scientific Notation.  After I post all responses on the board, we clarify the definition of Scientific Notation as a number between 1 and 10, times 10 to a power. The number can be equal to 1, but not equal to 10.  As a class, we discuss that for small numbers, the power is negative and for large numbers, the power is positive.  I do a few extra examples with them to demonstrate converting between Scientific Notation and Standard Notation to clarify any misunderstandings even though this should be review from previous grades.



Guided Notes

15 minutes

Students should be able to convert between Scientific Notation and Standard Notation (Sometimes referred to as Normal or Decimal Notation).  After the warm up, the purpose of the Guided Notes is to relate the rules of the math operations to the Laws of Exponents.  

I start the Guided Notes with an important piece in this lesson.  A common problem that students have when performing math operations with Scientific Notation, is understanding how to rearrange the final answers or expressions to ensure that they are like terms or that the final answer is in Scientific Notation.  So that is the first skill that I have students practice.  I work a few of the problems with them, and then give them about five minutes to work on the other conversions.  

The second part of the Guided Notes is for students to understand what like terms mean, and realize that expressions must be like terms before finding the sum or difference.  Then I have students match like terms and practice the operations.  Students still have to be able to convert the final answer to Scientific Notation.  Sometimes it is necessary for students to convert problems to Like Terms before adding or subtracting and then state the final answer in Scientific Notation.  I model this problem for the students in number five of the second part.  I have a short video below explaining this section.

In the last part of the Guided Notes, I have students practice products and quotients.  I allow about five minutes for this section as well.  Final answers, again, must be in Scientific Notation.



Independent Practice- Word Problems

15 minutes

The Independent Practice is intended for the students to practice what they have learned in this lesson and apply it to different word problems. I allow students about 15 minutes to complete the Independent Practice. Then I have them trade papers and grade the assignment to hand in for me to assess their progress.

I first want students to identify what math operation to use from the key words in the problem. This goes back to the Language of Algebra lesson at the beginning of the year.  In number one, the problem states how far light travels in one second, and how far will it travel in five days? This is a multiplication problem.  Number two asks about how many people per square mile which is a ratio or a division problem.  Number three wants to know the total number of students which means to add.  The fourth problem ask for the difference of the distances, which means to subtract.  The final question is another product question.  It gives how much soft drink an average American drinks and wants to know how much all Americans drink in a year.

Besides using key words to identify math operations, students then must perform the operations.  Again, stating final answers in Scientific Notation.

After completing the Independent Practice, students are to work on the Exit Slip.   

Exit Slip

5 minutes

I use this Exit Slip as a formative assessment to check for student reflection on this lesson.  If time does not allow for all students to complete the Exit Slip, then it is assigned as homework. I first have them rate how many questions in the practice that were correct when checking with technology.  This gives me a quick assessment on the ability for each of them to perform the math operations using Scientific Notation.

This also brings the technology into the lesson, but not too early, so that students are not relying on it for answers instead of thinking on their own. I also want students to state why it is important to learn and think without the calculator, but yet at other times apply the technology. This is part of Mathematical Practice 5, applying the correct tools when needed.  Students need to be able to make those decisions, and take more ownership of their own learning, and not just providing input to get an answer with no reasoning or understanding.

In the final question, I want students to state how the exponent laws are applied to Scientific Notation.  I want students to recognize the following applies to both types of expressions:

  • To find the product of expressions, numbers are multiplied, and the exponents are added.
  • To find the quotient of expressions, numbers are divided, and the exponents are subtracted.
  • To find the sum or difference, the base and the exponent must be the same to combine like terms.

The only difference is that Scientific Notation always has a base of 10.