Adding and Subtracting with Scientific Notation

5 min

Narrative

This Math Talk focuses on operations with numbers written in scientific notation. It encourages students to think about powers of 10 and to rely on what they know about how the exponent of a power of 10 is related to the number of zeros to mentally solve problems. The strategies and understandings elicited here will be helpful later in the lesson when students compute with numbers in scientific notation.

Launch

Tell students to close their books or devices (or to keep them closed). Reveal one problem at a time. For each problem:

  • Give students quiet think time, and ask them to give a signal when they have an answer and a strategy.
  • Invite students to share their strategies and record and display their responses for all to see.
  • Use the questions in the Activity Synthesis to involve more students in the conversation before moving to the next problem. 

Keep all previous problems and work displayed throughout the talk.

Action and Expression: Internalize Executive Functions. To support working memory, provide students with sticky notes or mini whiteboards.
Supports accessibility for: Memory, Organization

Student Task

Decide mentally how many nonzero digits each number will have.

  • (3 × 109)(2×107)(3 \times 10^9)(2 \times 10^7)
  • (3 × 109)÷(2×107)(3 \times 10^9) \div (2 \times 10^7)
  • 3 ×109 +2×1073 \times 10^9 + 2 \times 10^7
  • 3 ×109− 2×1073 \times 10^9 - 2 \times 10^7

Sample Response

  • One nonzero digit. Sample reasoning: Multiplying 3 and 2 gives us 6, and the rest will just add a bunch of zeros.
  • Two nonzero digits. Sample reasoning: Dividing 3 by 2 gives us 1.5, and the rest will just move the decimal place and add a bunch of zeros.
  • Two nonzero digits. Sample reasoning: The 3 and the 2 have different place values and so when the values are added together, the 3 and 2 will remain as 2 separate digits and combine to make one digit of 5.
  • Three nonzero digits. Sample reasoning: The 3 and the 2 have different place values that differ by a factor of $, meaning they will be 2 places away from each other. When subtracted, we will have to “borrow” 2 times, resulting in 3 nonzero numbers.

Synthesis

To involve more students in the conversation, consider asking:

  • “Who can restate ‾\underline{\hspace{.5in}}’s reasoning in a different way?”
  • “Did anyone use the same strategy but would explain it differently?”
  • “Did anyone solve the problem in a different way?”
  • “Does anyone want to add on to ‾\underline{\hspace{.5in}}’s strategy?”
  • “Do you agree or disagree? Why?” “What connections to previous problems do you see?”
MLR8 Discussion Supports. Display sentence frames to support students when they explain their strategy. For example, “First, I ‾\underline{\hspace{.5in}} because . . . .” or “I noticed ‾\underline{\hspace{.5in}} so I . . . .” Some students may benefit from the opportunity to rehearse what they will say with a partner before they share with the whole class.
Advances: Speaking, Representing
Standards
Addressing
  • 8.EE.4·Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology.
  • 8.EE.A.4·Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology.

15 min

15 min

15 min