Statistics and Probability
Material Type:
Lesson Plan
Middle School
  • 6th Grade Mathematics
  • Five Number Summary
  • Problem-Solving
    Creative Commons Attribution Non-Commercial
    Media Formats:

    Education Standards

    Characteristics Of Data

    Characteristics Of Data


    Students critique and improve their work on the Self Check from Lesson 13.

    Key Concepts

    Measures of spread (five-number summary) show characteristics of the data. It is possible to generate an appropriate data set with this information.

    Goals and Learning Objectives

    • Apply knowledge of statistics to solve problems.
    • Identify the five-number summary, and understand measures of center and use their properties to solve problems.
    • Track and review choice of strategy when problem solving.


    Lesson Guide

    Have students spend 10 minutes working alone to answer questions relevant to their solution.



    Review your work on the Self Check and think about these questions:

    • Did you find the five-number summary? How will these numbers help you determine some of the values in the data set?
    • What is the sum of the data?
    • How many data points are in each quartile?

    Math Mission

    Lesson Guide

    Discuss the Math Mission. Students will revise their work based on feedback.


    Revise your work based on the feedback you received.

    Revise Your Work

    Lesson Guide

    Have students work in pairs. Ask students to try the task again from scratch, this time combining their ideas.

    While students work in small groups, note:

    • Different student approaches to the task
    • Students' choice of problem-solving approaches
    • Students' choice of math

    Attend in particular to the students' mathematical decisions.

    • Do they track their progress in use of their chosen mathematics?
    • Do they notice if they have chosen a strategy that does not seem to be productive? If so, what do they do?
    • Do students see that the sum of the data must be 150?
    • Do students see that 0 and 28, 7 and 22, and two values adding to 23 (possibly 11 and 12) are all data values?
    • How do they justify their solution?

    Try not to make suggestions that move students toward a particular approach to this task. Instead, ask questions that help students to clarify their thinking. Have students consider these questions:

    • What do you already know? What do you need to know?
    • How can you represent the information in the box plot as a set of numbers?
    • How many data values are in each half? In each quartile?
    • What do you already know about box plots and measures of center and spread?

    SWD: Students with disabilities may have a more challenging time identifying areas of improvement to target in their self-check. Model for students how to plan for revisions in their strategy based on the feedback they are given.

    ELL: ELLs and other students may not recognize their progress. Point out the observations you have made about the misconceptions they have overcome and the achievements they have made with their math skills, math language, and terms.


    • Answers will vary. The data set must meet the following criteria:
      • 0 and 28 must be data values.
      • The middle pair of data values must add to 23.
      • 7 and 22 are data values.
      • The data set must add up to 150.
      • The 4 remaining numbers must be within the range of each quartile.

    Work Time

    Revise Your Work

    Work with your partner to revise your answer to the Self Check, based on the questions from the Opening and feedback from your partner.

    Self Check Problem:

    This box plot shows a summary of a data set of 10 measurements, each measured to the nearest inch.

    • Create a possible data set so that the mean of the data set is 15 inches.
    • Show your work and explain how you created the data set.

    Prepare a Presentation

    Lesson Guide

    Presentations will vary.

    Preparing for Ways of Thinking

    • Look for students who realized their self check numbers do not work and revised their work.
    • Look for students who have different data sets but still satisfy the specifications.
    • Find two students who disagreed when putting the data set together and have them explain the conversation they had and how they convinced each other on what data points to choose.

    Work Time

    Prepare a Presentation

    • Describe the feedback that you received from your teacher and your partner.
    • Explain how you revised your work based on that feedback.

    Make Connections

    Lesson Guide

    Organize a whole-class discussion to consider issues arising from the work students did to revise their work. You may not have time to address all the issues, so focus the class discussion on the issues most important for your students.

    • Have students who had strategies that didn't work share how and when they realized their strategy didn't work and what they did about it.
    • Have students share how they addressed the questions you identified specifically for them.
    • Have students ask questions and make observations as they view each other's work. SWD:

    Students with disabilities may have difficulty determining what information to review and study in preparation for the Unit Assessment. Create a study guide or template for students that outlines the key skills and concepts with which they must be familiar for the Unit Assessment.


    Questions to ask:

    • What part of the task was most difficult?
    • Did you and your partner ever disagree about a set of data values? How did you resolve your difference of opinion?

    Performance Task

    Ways of Thinking: Make Connections

    Take notes as your classmates present their work and discuss how they revised it.


    As your classmates present, ask questions such as:

    • Can you explain your strategy for deciding what values to include in your data set?
    • Did you revise your work based on the questions in the Opening? If yes, how?
    • What part of the task was the most difficult for you? Why?

    Reflect on Your Work

    Lesson Guide

    Have each student write a brief reflection before the end of class. Review the reflections to find out what students would do differently if they started the problem now.

    Work Time


    Write a reflection about the ideas discussed in class today. Use this sentence starter if you find it to be helpful.

    What I would do differently if I started yesterday’s problem now is …