Roving Ranges

Sixth Grade Poster Problem
Statistics and Probability

In this poster problem, students will demonstrate their understanding of the central idea in the Grade 6 Standards in Statistics and Probability: Statistical questions anticipate variability. When you roll four dice and add, you can’t know exactly what you will get, but you can still predict a lot about the result.

Students will also get practice with underlying concepts and tools: the collection of results forms a distribution; the distribution has a center and spread; and we can display distributions usefully in graphs, especially in box plots. Students use all of these together to make decisions and explain them coherently.

Here, they’ll be making decisions in a simple dice game. You roll four dice and add: what will you get? Of course, you can’t know exactly, but suppose, before you rolled, you had to state a range of results—the minimum and maximum values you expect. If you’re right, you get some points. If you’re wrong, you get nothing.

And here’s the kicker: the number of points you get depends on the range. The wider the range you allow, the fewer points you get.

Learning Objectives:

  • Students collect data and display them as a distribution
  • Students make mathematically sound decisions based on the distributions
  • Students can articulate why their decisions make sense

Common Core State Standards for Mathematics:


  • Lots of dice. As written, the directions call for 4 dice per student. With that many dice, students can work in parallel and work more quickly.
  • Note:

    This poster problem, as written, does not teach how to make a box plot. Students should know the mechanics of making a box plot before doing this lesson. This lesson will, however, give students a chance to practice making box plots and using them to make decisions.

The Lesson Plan:

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Lesson Plan



Project funding provided by The William and Flora Hewlett Foundation and S.D. Bechtel Jr. Foundation.

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