Using Mean and MAD to Make Comparisons

5 min

Narrative

This Math Talk focuses on division of decimal values. It encourages students to think about how to divide mentally and to rely on patterns in the problems to mentally solve problems. The understanding elicited here will be helpful later in the lesson when students calculate means.

To divide the values, 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.

Representation: Internalize Comprehension. 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.

  • 42÷1242\div12
  • 2.4÷122.4\div12
  • 44.4÷1244.4\div12
  • 46.8÷1246.8\div12

Sample Response

  • 3.5. Possible strategy: 36÷12+6÷12=3.536\div12 + 6\div12=3.5

  • 0.2. Possible strategy: 2.4⋅10÷12=22.4\boldcdot 10\div12=2, and 2÷10=0.22\div10=0.2

  • 3.7. Possible strategy: 42÷12+ 2.4÷12=3.742\div12 + 2.4\div12=3.7

  • 3.9. Possible strategy: 42÷12+ 2.4÷12 + 2.4÷12=3.942\div12 + 2.4\div12 + 2.4\div12=3.9

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 _____ because . . . .” or “I noticed _____ 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
  • 6.NS.3·Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.
  • 6.NS.B.3·Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.
Building Toward
  • 6.SP.3·Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number.
  • 6.SP.A.3·Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number.

20 min

10 min