What Makes a Good Sample?

5 min

Teacher Prep
Setup
Display one problem at a time. Allow 30 seconds of quiet think time, followed by a whole-class discussion.

Narrative

This Math Talk focuses on division by powers of 10. It encourages students to think about ways to divide and to rely on the patterns when dividing by a power of 10 to mentally solve problems. The strategies elicited here will be helpful later in the lesson when students find means for various samples.

To find different strategies, students need to look for and make use of structure (MP7).

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

Find the value of each expression mentally.

  • 34,000÷1034,000\div10
  • 340÷100340\div100
  • 34÷1034\div10
  • 3.4÷1003.4\div100

Sample Response

  • 3,400. Sample reasoning: There are 100 tens in 1,000 and 34 hundreds in 34,000, so there are 34 hundred tens in 34,000.
  • 3.40. Sample reasoning: 100⋅3.4=340100 \boldcdot 3.4 = 340, so 340÷100=3.4340 \div 100 = 3.4.
  • 3.4. Sample reasoning:  There are 3 tens in 30 with 4 left over. Dividing this by 10 gives 410\frac{4}{10}.
  • 0.034. Sample reasoning: The decimal can be moved two places to the left.
Activity Synthesis (Teacher Notes)

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
Building On
  • 5.NBT.2·Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10.
  • 5.NBT.A.2·Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10.

15 min

15 min