Mastering Powers of 10: Multiplication and Division

PreAlgebra Grades High School 9:02 Video
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Lesson Description

Learn how to efficiently multiply and divide by powers of 10 using decimal placement and exponents. This lesson plan provides clear explanations, examples, and practice problems to solidify understanding.

Video Resource

Multiplying and Dividing by Powers of 10 | Math with Mr. J

Math with Mr. J

Duration: 9:02
Watch on YouTube

Key Concepts

  • Powers of 10
  • Decimal Placement
  • Exponential Notation
  • Multiplying and Dividing by Powers of 10
  • Standard Form

Learning Objectives

  • Students will be able to multiply and divide whole numbers and decimals by powers of 10.
  • Students will be able to convert between standard form and exponential notation for powers of 10.
  • Students will be able to explain why moving the decimal point is an effective strategy when multiplying and dividing by powers of 10.
  • Students will be able to determine if the answer should increase or decrease in value

Educator Instructions

  • Introduction (5 mins)
    Begin by introducing the concept of powers of 10 and their importance in mathematics. Briefly review place value and the decimal system. Show the video 'Multiplying and Dividing by Powers of 10 | Math with Mr. J' to introduce the topic.
  • Guided Practice (15 mins)
    Work through several examples from the video with the students, emphasizing the rule of moving the decimal point. Model the thinking process of deciding whether the answer should increase or decrease in value.
  • Independent Practice (15 mins)
    Provide students with a worksheet containing various multiplication and division problems involving powers of 10. Include problems in both standard and exponential notation. Encourage them to check their answers and discuss any difficulties they encounter.
  • Wrap-up and Review (5 mins)
    Summarize the key concepts of the lesson. Address any remaining questions and provide a brief overview of how this skill relates to other mathematical concepts, such as scientific notation.

Interactive Exercises

  • Decimal Dash
    Create a game where students race to correctly move the decimal point in a series of problems displayed on the board.
  • Power of 10 Card Sort
    Prepare cards with expressions like '10^3', '1000', '10 to the power of 3' and have students match equivalent expressions.

Discussion Questions

  • Why does moving the decimal point work when multiplying or dividing by powers of 10?
  • How does exponential notation simplify working with large numbers?
  • In what real-world scenarios might you need to multiply or divide by powers of 10?
  • Explain the difference between standard and exponential form
  • What happens if you move the decimal the wrong way?

Skills Developed

  • Decimal manipulation
  • Problem-solving
  • Critical thinking
  • Understanding of exponential notation

Multiple Choice Questions

Question 1:

What is 5.25 x 10^3?

Correct Answer: 5250

Question 2:

What happens to the value of a number when you divide it by 10?

Correct Answer: Decreases

Question 3:

Which of the following is equal to 1000?

Correct Answer: 10^3

Question 4:

What is 125 / 10^2?

Correct Answer: 1.25

Question 5:

What does 10^0 equal?

Correct Answer: 1

Question 6:

Multiplying by 10^4 is the same as moving the decimal point how many places?

Correct Answer: 4

Question 7:

What is 0.75 x 10^2?

Correct Answer: 75

Question 8:

Which direction do you move the decimal when multiplying by a power of 10?

Correct Answer: Right

Question 9:

What is 900 / 10^3?

Correct Answer: 9

Question 10:

The exponent in 10^5 tells you to multiply 10 by itself how many times?

Correct Answer: 5

Fill in the Blank Questions

Question 1:

Multiplying by 1000 is the same as multiplying by 10 to the power of ____.

Correct Answer: 3

Question 2:

Dividing by 10^2 means moving the decimal point two places to the ____.

Correct Answer: left

Question 3:

When you multiply a number by a power of 10, the value of the number ____.

Correct Answer: increases

Question 4:

10^4 is equal to ____ in standard form.

Correct Answer: 10000

Question 5:

Moving the decimal point to the right makes the number bigger. This happens when we are _________.

Correct Answer: multiplying

Question 6:

650 divided by 10^1 equals ____.

Correct Answer: 65

Question 7:

Another way to write 10 x 10 x 10 is _________.

Correct Answer: 10^3

Question 8:

The number of zeros in the number 10,000 is ____.

Correct Answer: 4

Question 9:

0.5 multiplied by 10^3 equals ____.

Correct Answer: 500

Question 10:

When you divide a number by a power of 10, you move the decimal point to the _______.

Correct Answer: left

Educational Standards

PA.N.1.1:Develop and apply the properties of integer exponents, including a^0 = 1 (with a ≠ 0), to generate equivalent numerical and algebraic expressions. PA.N.1.2:Express and compare approximations of very large and very small numbers using scientific notation.

Teaching Materials

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