Bellwork Teacher selected Prior Knowledge Over the last few days we have been working with exponents and also learning about scientific notation.

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1 Course: 8 th Grade Math DETAIL LESSON PLAN Student Objective 8EEA4 Perform operations (+, -, x, ) with numbers expressed in scientific notation Some problems may include one number written in standard form and the other in scientific notation such as x 10⁴ Students may also be asked to interpret scientific notation that has been generated by technology 8EEA3 Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other Calculator No Lesson Lesson 324 Replacement Lesson (Perform Operations in Scientific Notation) Tonight s Homework Teacher selected Bellwork Teacher selected Prior Knowledge Over the last few days we have been working with exponents and also learning about scientific notation Introduction Today, we will start with a step-by-step review of how to convert between standard form and scientific notation Then we will move on to something new We will learn to multiply, divide, add, and subtract two numbers written in scientific notation Let s start our review with a real world example of how scientists rewrite numbers so that they are easier to use Show brief PowerPoint: Lesson 324 Intro Why Learn about Scientific Notation? Teacher Input Review bellwork Review homework Pass out student notes Complete Part 1 which is a review on converting between standard form and scientific notation (20 minutes max) Complete Part 2 of the lesson Allow students to complete you try problems throughout the lessons Extra problems are provided for student practice at the end of the lesson Good practice for 8EE3 and 8EE4 Assessment Observe students as they work on you try problems and classwork Closure 1 In scientific notation, the first number is? Greater than or equal to 1, but less than 10 2 The second number is always a power of 10 3 Give me an example of a number correctly written in scientific notation Answer will vary 4 572,000,000 Which number does the decimal go after when writing a large number in scientific notation? First whole number How do you determine the correct power of 10? Count the number of jumps from the end until you get to the decimal 6 What kind of exponent will really small numbers have in scientific notation Negative

2 Lesson Part 1 Let s review how to convert between Standard Form Scientific Notation

3 Student Notes Standard Form Scientific Notation Scientific Notation It s a short cut way of writing really big numbers and really small numbers A number written in Scientific Notation is made up of 3 parts: Writing a LARGE number in Scientific Notation 980,000,000 You try! Write in Scientific Notation form: 6,300,000 = 800,300 =

4 Writing a SMALL number in Scientific Notation You try! Write in Scientific Notation form: = = Changing Scientific Notation back to Standard Form 888 x 10⁸ 59 x 10 ⁸ You Try! Write in Standard Form: 169 x 10⁵ = 23 x 10 ⁴ =

5 Lesson Part 2 Performing Operations with Scientific Notation Examples:

6 Student Notes Operations with Scientific Notation Multiplying Multiplying in Scientific Notation Step 1: Multiply the decimal numbers Step 2: Then add the exponents of the powers of 10 Step 3: Place the new power of 10 with the decimal in scientific notation form Step 4: IF the number is not in scientific form, you need to move the decimal so that it is behind the first digit and count the number of places the decimal moves If the decimal moves left, increase the exponent by the number of moves Example (26 ) (63 ) Step 1: Multiply the decimal numbers Step 2: Add the exponents Step 3: Put the new decimal number with the new exponent in scientific notation form Step 4: IF the number is not in scientific form, you need to move the decimal so that it is behind the first digit and count the number of places the decimal moves If the decimal moves left, increase the exponent by the number of moves In this case, the decimal point moves one place left, so add 1 to the exponent Guided Practice a (25 x ) (3 x ) = You Try! b (44 x ) (39 x ) =

7 Dividing in Scientific Notation Step 1: Divide the decimal numbers Operations with Scientific Notation Dividing Step 2: Then subtract the exponents of the powers of 10 Step 3: Place the new power of 10 with the decimal in scientific notation form Step 4: IF the number is not in scientific form, you need to move the decimal so that it is behind the first digit and count the number of places the decimal moves If the decimal moves left, increase the exponent by the number of moves Example (123 ) (24 ) Step 1: Divide the decimal numbers Step 2: Subtract the exponents Step 3: Put the new decimal number with the new exponent in scientific notation form Step 4: IF the number is not in scientific form, you need to move the decimal so that it is behind the first digit and count the number of places the decimal moves If the decimal moves left, increase the exponent by the number of moves Guided Practice a (576 ) (32 ) = You Try! b (3 ) (8 ) =

8 Operations with Scientific Notation Adding or Subtracting When you are asked to add or subtract two numbers expressed in scientific notation you need to be a little more careful Both powers of ten must be the same Adding or Subtracting in Scientific Notation Step 1: If needed, use what you know about the below rule to make adjustments so that the powers of ten are the same Step 2: Add or subtract the decimal numbers as asked Step 3: Place the power of 10 with the decimal in scientific notation form Step 4: IF the number is not in scientific form, you need to move the decimal so that it is behind the first digit and count the number of places the decimal moves If the decimal moves left, increase the exponent by the number of moves Example (44 ) (71 ) Step 1: If needed, make adjustments so that the powers of ten are the same Both are the same No adjustments needed Step 2: Add or subtract the decimal numbers as asked 5 Step 4: Place the power of ten with the decimal in scientific notation form Step 4: IF the number is not in scientific form, you need to move the decimal so that it is behind the first digit and count the number of places the decimal moves If the decimal moves left, increase the exponent by the number of moves

9 Example (412 ) (394 ) Step 1: If needed, make adjustments so that the powers of ten are the same In this case they are not the same ( ) so we must adjust one of them It doesn t matter which one you adjust I will change the to a power of 4 Step 2: Add or subtract the decimal numbers as asked Step 3: Put the new decimal number with the exponent in scientific notation form Step 4: IF the number is not in scientific form, you need to move the decimal so that it is behind the first digit and count the number of places the decimal moves If the decimal moves left, increase the exponent by the number of moves Guided Practice Note: When subtracting, adjust the exponent which will not make your coefficients negative! a (53 x ) (22 x ) = You Try! b (14 x ) (46 x ) =

10 Name: Operations with Scientific Notation obj 8EEA3, Period: 8EEA4 Try These! Simplify each of the following Multiply 1) Divide 2) 3) A typical dwarf sperm whale, the planet s smallest whale species, weighs about pounds A blue whale, the planet s largest whale, might weigh pounds How many times heavier is the blue whale than the dwarf sperm whale? Add or Subtract 4) 5) Challenging! 6) 7) 8) Michelle used a calculator to multiply the following numbers Her calculator displayed the answer below What do you think her calculator is displaying? 144E24

11 Answer Key Operations with Scientific Notation obj 8EEA3, 8EEA4 Try These! Simplify each of the following Multiply 1) Answer: Divide 2) Answer: 3) A typical dwarf sperm whale, the planet s smallest whale species, weighs about pounds A blue whale, the planet s largest whale, might weigh pounds How many times heavier is the blue whale than the dwarf sperm whale? Answer: times larger Add or Subtract 4) 5) Answer: Answer: Challenging! 6) 7) Answer: or Answer: or 8) Michelle used a calculator to multiply the following numbers Her calculator displayed the answer below What do you think her calculator is displaying? 144E24 Answer: