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Stop or Dare

All you need for this game is a pack of cards. While you play the game, think about strategies that will increase your chances of winning.

Snail Trails

This is a game for two players. You will need some small-square grid paper, a die and two felt-tip pens or highlighters. Players take turns to roll the die, then move that number of squares in a straight line. Move only vertically (up/down) or horizontally (across), never diagonally. You can cross over the other player's trails. You can trace over the top of the other player's trails. You can cross over a single trail of your own, but can never cross a pair of your trails (side-by-side) or trace over your own trail. To win, you must roll the exact number needed to finish in the target square. You can never pass through the target square. The game ends when a player ends his/her trail in the target square, OR when a player cannot move without breaking any of the rules.

Game of PIG - Sixes

Can you beat Piggy in this simple dice game? Can you figure out Piggy's strategy, and is there a better one?

Cosy Corner

Age 11 to 14 Challenge Level:

Why do this problem?

This problem offers an opportunity to explore and discuss two types of probability: experimental and theoretical. The simulation generates lots of experimental data quickly, freeing time to focus on predictions, analysis and justifications.

Possible approach

Demonstrate the interactivity a few times, explaining that to win, at least one corner needs to contain a red ball.
Invite students to estimate the probability of winning. Allow students some thinking and discussion time in pairs before bringing them together to state their initial conjectures.
Students may find this Recording Sheet useful, to work out the different possible outcomes.
Record their conjectures on the board and then run the interactivity a few hundred times. Then revisit students' conjectures and discuss which ones matched the experimental data, before rounding the activity off by discussing which methods for recording the different combinations were both successful and efficient.

Key questions

Are there efficient systems for recording the different possible combinations?
What counts as a different outcome?
If the red balls are in the same position but a blue and yellow ball swap places, does that count as a different outcome?

Possible support

An alternative problem for exploring theoretical and experimental probability is Flippin' Discs

Possible extension

A follow-up problem could be Two's Company


Teachers may want to use this recording tool to gather the results of other similar experiments that their students are carrying out: