Statistical Questions

5 min

Teacher Prep
Setup
Access to inch rulers and a class dot plot. Students in groups of 2. After data is collected, give students 1 minute of quiet work, followed by a whole-class discussion. 

Narrative

The purpose of this Warm-up is for students to review how to represent measurements on a dot plot and how to interpret the data.

Launch

Arrange students in groups of 2. Distribute rulers marked in inches to each group, and ensure that each student has a pencil.

Display the large class dot plot prepared before class for all to see and access. Tell students to measure the length of their pencil to the nearest 14\frac14 inch and record their measurement as a dot on the class dot plot. Give each student a dot sticker as a way to record their measurement.

When the class data is recorded, give students 1 minute of quiet work time. Then, ask partners to briefly share their responses and follow with a whole-class discussion. 

Student Task

  1. Measure your pencil to the nearest 14\frac14-inch. Then, plot your measurement on the class dot plot.
  2. What is the difference between the longest and shortest pencil lengths in the class?
  3. What is the most common pencil length?
  4. Find the difference in lengths between the most common length and the shortest pencil.

Sample Response

Answers vary. There may or may not be one most common pencil length, depending on the distribution of the data.

Activity Synthesis (Teacher Notes)

The purpose of the discussion is for students to recognize the usefulness of the dot plot structure. 

Ask a student to share their responses for each of the questions. Record and display their reasoning for all to see. After the student shares, ask the class if they agree or disagree and why. Some discussion may arise about the interpretation of the most common pencil size. It is ok to allow some ambiguity at this time.

To involve more students in the conversation, consider asking some of the following questions: 

  • Who can restate ___’s reasoning in a different way?
  • Did anyone have the same response but would explain it differently?
  • Did anyone find the difference between the shortest and longest lengths in a different way?
  • Does anyone want to add on to _____’s reasoning?
Anticipated Misconceptions

Some students may struggle with subtracting the shortest pencil length from the longest. Ask if they could use the horizontal axis to find the difference (for example, by adding up from the shorter length to the longer one). 

Standards
Building On
  • 5.MD.2·Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. <em>For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally.</em>
  • 5.MD.B.2·Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. <span>For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally.</span>
Addressing
  • 6.SP.B·Summarize and describe distributions.
  • 6.SP.B·Summarize and describe distributions.

15 min

15 min