If you roll a die 30 times, should you get exactly five 6s? Most students say yes. Then they roll, and hardly anyone does. This investigation is set at a school fete game stall ("Roll a six, win a prize") with a die, coins and spinners.

How it runs

Three lessons of 45–60 minutes. Start with expected and observed results and expected frequency, like 1/6 of 30 = 5. Pairs predict, roll and tally. Pool the results (the sample data has 300 rolls) and draw a column graph with 1 line = 5 rolls. Class totals usually sit closer to the expected numbers than any one pair's, which leads into small and large numbers of trials.

Students look at simulator results from 10 to 10,000 flips and spin an unequal spinner. They judge whether games are fair, solve the Case of the Trick Die and decide whether the fete game is worth $1 when the player wins on 1 outcome and the stall on the other 5.

Maths covered

• MA3-CHAN-01: use the term frequency, distinguish frequency from probability, compare expected and observed frequencies after small and large numbers of trials (including outcomes that are not equally likely and digital simulators), and discuss fairness and randomness
• MA3-DATA-01: draw a column graph of pooled class results with a many-to-one scale (1 line = 5 rolls)
• Extension (Stage 4): the two-dice doubles investigation, with a 6 × 6 outcome table and the term "sample space", is clearly labelled (MA4-PRO-C-01)

Good to know

• Each pair needs a die (or the booklet's die net), a coin and a paperclip.
• Any free online simulator works, or =RANDBETWEEN(1,6) in a spreadsheet.
• Refreshed from my 2021 Theoretical vs Experimental Probability investigation. Maths Detectives characters and Keynote fonts included.