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Math activity

Dice Probability Lab

Roll a die and see what numbers come up! Track which numbers you roll the most. Some numbers might be your lucky numbers!

Hands OnAbout 20 minutesScreen-freeParent help expected

Materials and setup

How this changes by age

Pre-K (ages 3–4)

Roll a die and see what numbers come up! Track which numbers you roll the most. Some numbers might be your lucky numbers!

Difficulty 1 of 3

Steps

  1. Roll a die 20 times. After each roll, say the number out loud.
  2. Color in a square on a chart for each number you roll (like a bar graph).
  3. After 20 rolls, look at your chart. Which number came up the most? The least?
  4. Guess: if you roll again, what number do you think will come up? Roll and see!
  5. Talk about: 'Every number can come up! We cannot be sure which one.'
  6. Tell a grown-up one thing that surprised you.

Learning objectives

  • Collect and record data from repeated random events
  • Compare frequencies of different outcomes
  • Understand that random events are unpredictable

Kindergarten (ages 5–6)

Explore probability by rolling dice and flipping coins. Predict what will happen, test it, and see if your predictions were close.

Difficulty 2 of 3

Steps

  1. Flip a coin 20 times. Record heads (H) or tails (T) each time.
  2. Count: how many heads? How many tails? Were they close to equal?
  3. Predict: 'If I roll a die, will I get a 6?' Discuss: it is hard to know for sure!
  4. Roll two dice 20 times. Add the numbers. Which sum came up most?
  5. Talk about 'likely' (probably will happen) and 'unlikely' (probably will not happen). Is rolling a 7 on one die likely or unlikely? (Impossible!)
  6. Tell a grown-up one thing that surprised you.

Learning objectives

  • Collect data from coin flips and dice rolls
  • Use words like likely, unlikely, certain, and impossible
  • Compare predicted outcomes to actual results

Early elementary (ages 6–8)

Compare theoretical probability (what should happen) to experimental probability (what actually happens). Roll dice many times and see if results match the math.

Difficulty 2 of 3

Steps

  1. Theoretical probability: a die has 6 faces, each equally likely. P(rolling a 4) = 1/6. P(rolling even) = 3/6 = 1/2.
  2. Roll a die 60 times. Record every result in a table.
  3. Calculate experimental probability: if you rolled a 4 twelve times, P(4) = 12/60 = 1/5.
  4. Compare theoretical (1/6) to experimental (1/5). Are they close? Why might they differ?
  5. Two-dice experiment: roll 2 dice 50 times, record the sum. Why does 7 come up most often? (There are more ways to make 7.)
  6. Challenge: list all possible sums from two dice. How many ways can you make each sum? Create a chart.
  7. In one sentence, tell a parent or sibling what surprised you today.

Learning objectives

  • Calculate theoretical probability as favorable outcomes over total outcomes
  • Calculate experimental probability from collected data
  • Compare theoretical and experimental probability and explain differences

Upper elementary (ages 8–10)

Design probability experiments to test predictions. Calculate compound probabilities, create sample space diagrams, and explore the Law of Large Numbers.

Difficulty 3 of 3

Steps

  1. Create the complete sample space for rolling two dice: a 6x6 grid showing all 36 possible outcomes.
  2. Calculate the theoretical probability of: rolling a sum of 7, rolling doubles, rolling a sum greater than 9.
  3. Roll two dice 100 times and record results. Calculate experimental probabilities. How close to theoretical?
  4. Law of Large Numbers: graph your running average after every 10 rolls. Does it get closer to the theoretical probability as you roll more?
  5. Compound probability: P(rolling 6 AND then flipping heads) = 1/6 x 1/2 = 1/12. Design and test this experiment.
  6. Write a probability report: state your hypothesis, describe your experiment, present theoretical vs. experimental data with graphs, and explain what you learned.

Learning objectives

  • Create sample space diagrams for compound events
  • Calculate and compare theoretical and experimental compound probabilities
  • Demonstrate understanding of the Law of Large Numbers through experimentation

Safety and evidence note

Read the full activity before beginning. An adult should supervise tools, heat, food, outdoor work, movement, and experiments as appropriate. Completion records that the activity was done; the child’s explanation, work sample, photo, or demonstration is stronger evidence of learning than a completion check alone.

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