Dot Plots

5 min

Teacher Prep
Setup
Students in groups of 2. A couple of minutes of partner collaboration, followed by a minute to compare responses with another group.

Narrative

This Math Talk focuses on calculating percentages from parts of a whole. It encourages students to think about percentages and to rely on what they know about division to mentally solve problems. The understanding elicited here will be helpful later in the lesson when students describe how common a value is in a data set as a percentage.

To calculate percentages mentally, students need to look for and make use of structure (MP7). In describing their strategies, students need to be precise in their word choice and use of language (MP6). 

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.

Student Task

Find each value as a percentage.

  • 18 out of 50
  • 7 out of 20
  • 6 out of 60
  • 12 out of 30

Sample Response

  • 36%. Sample reasoning: By doubling both values, 18 out of 50 is the same percentage as 36 out of 100, which is 36%.
  • 35%. Sample reasoning: By multiplying both values by 5, 7 out of 20 is the same as 35 out of 100, which is 35%.
  • 10%. Sample reasoning: By dividing both values by 6, 6 out of 60 is the same percentage as 1 out of 10. Then, multiplying those by 10, it is the same percentage as 10 out of 100, or 10%.
  • 40%. Sample reasoning: By dividing both values by 3, 12 out of 30 is the same percentage as 4 out of 10. Then, multiplying those by 10, it is the same percentage as 40 out of 100, or 40%.
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?”

When examining displays of data, it can help to consider frequencies as percentages to determine how often certain values, or ranges of values, appear in the data set.

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.SP.4·Display numerical data in plots on a number line, including dot plots, histograms, and box plots.
  • 6.SP.B.4·Display numerical data in plots on a number line, including dot plots, histograms, and box plots.

10 min

20 min