7.6(I): Determine experimental and theoretical probabilities related to…

Is It Fair? Chance and Probability Grades 6–7

Is a six harder to roll? Which bag gives the best chance of a red? Why does horse 7 always win? Can you design a fair game? Four lessons with dice, coins, counters and spinners where students test their hunches and find out what chance really does.

• Is a six harder to roll? 50–60 min

  Teams roll a die 30 times and get lopsided results, then pool the whole class's rolls and watch every face settle close to one-sixth. Students place events on a probability scale from 0 to 1, write probabilities as fractions, decimals and percents, and explain why experimental probability gets closer to theoretical probability with more trials.

• Which bag would you pick from? 50–60 min

  To win a prize you must pull a red counter from one of four bags. Teams find that the bag with the most red counters gives the worst chance, and that two bags with different numbers of counters give exactly the same chance. Students find and compare probabilities, use the complement, and test their predictions by drawing with replacement.

• Why does horse 7 always win? 50–60 min

  Teams play a horse race where horses numbered 2 to 12 move when the sum of two dice matches their number. Horse 7 wins again and again, and horse 2 and horse 12 hardly move. Students build the 36-outcome sample space in a table, find probabilities of compound events, and explain why sums in the middle are more likely.

• Can you design a fair game? 50–60 min

  Teams test three two-player games with coins, dice and spinners, and find that a game that sounds fair, odd or even products of two dice, gives one player three times the chance of the other. Using tree diagrams and tables, students find the probability of each player winning, then design, test and defend a fair game of their own.