Education Technology

Middle Grades Math: Long Run

by Texas Instruments


  • Students will conduct simulations with multiple trials.
  • Students will use relative frequencies to compute experimental probabilities.
  • Students will informally explore the use of a simulation to observe long-run relative frequencies.




  • Law of Large Numbers
  • frequency
  • relative frequency
  • experimental probability
  • theoretical probability
  • scatter plot
  • connected scatter plot
  • trial
  • simulation

About the Lesson

This lesson involves investigating simulations used to observe long-run relative frequencies.
As a result, students will:

  • Simulate drawing blue and red marbles one at a time from a bag.
  • Generate a scatter plot of the relative frequencies of blue marbles.
  • Examine variations in the scatter plots generated by the simulations.
  • Determine and discuss any consistent patterns or trends found in the results of these simulations.