Got Data?

10 min

Teacher Prep
Setup
2 minutes of quiet work time followed by a whole-class discussion.

Narrative

The purpose of this Warm-up is to review students’ prior knowledge about representation of numerical data. Students may be familiar with line plots from previous grades but unfamiliar with the term dot plot, which is what will be used in this unit and beyond. Students learn that both terms are commonly used for the same type of diagram.

Students examine a dot plot of data and consider which contexts may make sense for the data shown. Then students invent their own context for the data and interpret what additional data in that set would mean in their context.

This is an opportunity to see how students make sense of a data representation in the context of situations (MP2).

Launch

Display the image and data for all to see.

  • 0
  • 0.25
  • 0.5
  • 0.5
  • 0.75
  • 0.75
  • 0.75
  • 1
  • 1
  • 1.5
  • 1.5
  • 1.5
  • 1.5
  • 1.75
  • 1.75
  • 1.75
  • 2
  • 2.25
  • 2.25
  • 2.5
  • 2.5

A dot plot, labeled 0 to 4 by ones with tick marks every quarter. Beginning with 0 and counting by point 2 5, the number of dots above each increment is 1, 1, 2, 3, 2, 0, 4, 3, 1, 2, 2.

Ask students what they notice and wonder about the image. Students may notice:

  • There are 21 dots over the number line.
  • The data match the dots over the number line.
  • Some of the dots are over fractional values.
  • Some values have no dots.

Students may wonder:

  • What do the dots and data represent?
  • Why are there no dots over 1.25 or after 2.5?
  • Why are there so many dots over 1.5?
  • Is this a line plot?

If not mentioned by students, remind them that the display is interpreted like a line plot. Tell students that this is called a dot plot, and that line plots use Xs and dot plots use dots, but the meaning is very similar.

Give students 2 minutes of quiet work time to complete the task, followed by a whole-class discussion.

Student Task

Here is a dot plot for a data set.

A dot plot, labeled 0 to 4 by ones with tick marks every quarter. Beginning with 0 and counting by point 2 5, the number of dots above each increment is 1, 1, 2, 3, 2, 0, 4, 3, 1, 2, 2.

 

  1. Determine if each of these would be an appropriate label to represent the data in the dot plot? Be prepared to explain your reasoning.

    1. Number of children per class.
    2. Distance between home and school, in miles.
    3. Favorite subject in school.
    4. Weight of elephants, in pounds.
    5. Points received on a homework assignment.

  2. Think of another label that can be used with the dot plot.

    1. Write it below the scale of the dot plot. Be sure to include the unit of measurement.
    2. In your scenario, what does one dot represent?
    3. In your scenario, what would a data point of 0 mean? What would a data point of 3143\frac 14 mean?

Sample Response

  1. Sample responses:
    1. No. We cannot have partial children.
    2. Yes. The distances are reasonable for the context and can be fractional.
    3. No. The dot plot shows numerical values, not lists of school subjects.
    4. No. The unit of measurement (pounds) does not work with the context. Elephants weigh much more than several pounds.
    5. Yes. A teacher could grade a homework assignment on a scale of 1 to 4 and assign partial points.
  2. Sample responses:
    1. Time spent napping, in hours.
    2. A dot represents the length of a nap (in hours) on one day.
    3. A day without a nap. A nap that lasts 3.25 hours.
Activity Synthesis (Teacher Notes)

The purpose of the discussion is for students to understand how to read a dot plot, including what dots represent in context.

Invite students to share their responses to each scenario presented in the first question, and ask a few students to explain their reasoning for each.

Invite a few students to share another label that they think could be used with the set of data and what each dot would represent. Based on each response, ask the class these questions:

  • “What would a data point of 0 mean in the context mentioned?”
  • “What would a data point of 3143\frac 14 mean in the context mentioned?”
Standards
Building On
  • 5.MD.B·Represent and interpret data.
  • 5.MD.B·Represent and interpret data.
Building Toward
  • 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.

20 min

10 min