“Pig game” is a simple dice game which in its basic form is playable with just a single dice. You win by being the first player to achieve a certain number of points.

To play you'll need 2 to 10 players, one 6-sided dice, and a pencil and some paper for keeping score.

The teacher organizes the class into four or five groups, each acting as a team. Each group rolls a dice to determine the order of play, with the highest number of points going first, followed by the next highest, and so on. If possible, use a large dice made from soft material so the activity can take place with students standing and moving.

The first team rolls the dice and scores the number of points shown, provided they do not roll a 1. If the team rolls a 1, their turn ends, and they lose all the points accumulated during that turn, passing the die to the next team. Team members must decide collectively whether to continue rolling and risk rolling a 1 (and losing their points) or end their turn and keep the points earned.

Scores can be recorded on the whiteboard or blackboard. Play continues from team to team until a winner is determined. The first team to accumulate 50 or more points wins the game.

(Adapted from https://www.dicegamedepot.com/dice-n-games-blog/pig-dice-game-rules/)

Students sit in a semicircle, facing the teacher, and discuss what is the best strategy to win the “Pig game”. Children can express their opinion, make experiments or demonstrations.

• Express greater or lower degree of uncertainty relative to occurring events resulting from random experiments through terms such as ‘likely’ or ‘probable’.

• Compare the results of a random experience based on its likelihood.

• Produce, collect and organize data in order to understand simple probabilistic models.

Materials:

• Empty matchboxes

• Solid color marbles (many colors)

• Dices

Preparation for the lesson:

The teacher should prepare a set of boxes, ensuring there are several identical boxes for each type.

Type 1: A match box with 1 dice inside

Type 2: A match box with 3 marbles inside, one white and the other two blue (we propose two diferent shades of blue)

Type 3: A match box with 4 marbles inside, 2 pairs of marbles with the same colors (we show a box with 2 red and 2 green marbles).

Figure 1. Examples of boxes of type 1 (left side), type 2 (center) and type 3 (right side).

Data and Probability is fundamental to understanding today’s world, although not traditionally a core subject in early years mathematics. Simple games provide children with opportunities to explore random phenomena and their patterns, introducing ways of thinking and communicating about events characterized by uncertainty and chance.

Exploratory learning from an experimental set-up.

Language – oral and visual communication.

Almost all the steps of the lesson are comprehensible to most special needs students who have well-preserved cognitive abilities. The lesson does not comprise written explanations, and the long instructions, which are difficult for the target group’s students (TGSt), are very few.

The role of the special needs teacher or the assistant teacher is to help TGSt in case they are not able to cope with some of the tasks or steps.

Unlikely

Likely

Probable

Equally probable

Phase 1: Presenting the context (see appendix 1)

Children are presented to the three types of boxes. The teacher organizes the students into small groups (between 2 and 4 children). Each group is arbitrarily assigned a box. Each box is associated with a game.

Game 1: Close box type 1 properly, shake it for a few seconds and place the box upright so that the dice inside can rest against the bottom and top of the inside of the box (see figure 2). Open the box. If the sum of the points on the two exposed faces is even you win, if is odd you lose.

Figure 2. Example of outcome of game 1. In this case, the exposed faces are 4 (headed front) and 1 (at the top), whose sum is 5, an odd number - meaning the player loses the game.

Game 2: Close box 2 properly, shake it for a few seconds and place the box upright so that the marbles inside are aligned with the bottom of the box (see figure 3). Open the box. If the white marble is between the blue marbles you win, otherwise you lose.

Game 3: Close box 3 properly, shake it for a few seconds and place the box upright so that the marbles inside are aligned with the bottom of the box (see figure 4). Open the box. If the red marble are together you win, otherwise you lose.

Figure 4. Example of outcome of game 3. In this case, the red marbles are alternated with the green ones meaning the player loses the game.

10 minutes

 

Phase 2: Formulating the problem

In this phase, each group has a box of one of the three types, so there are several groups for game 1, several for game 2 and several for game 3.  

Each group will have to analyze the game they have been assigned in order to answer the following question: Is the game fair?

At this stage, the teacher should discuss with the students what it means ‘a fair fair’, based on the understandings expressed by the students. They should realize that being fair means having equal chances of winning and losing. It is appropriate to use expressions such as ‘equally probable’.

The teacher can ask each group about the game they have been given, whether it seems, at first glance, fair or not and why.

10 minutes

 

Phase 3: Exploring the games

Now the working groups are invited to explore the game they have been assigned by repeating a set of trials, recording the result (win or lose) for each one. The roles of performing the trials and recording can rotate among all the members of the group so that everyone participates actively.

The registers can take the form shown in figure 5, or any other form with pedagogical interest. It is important that, in total, each group does a sufficiently large number of tests so that a pattern can emerge (lets say, 50 or 60 trials). Each pair of tester/recorder students can carry out a series of 10 tests, rotating these functions within the group. The other members should ensure that each trial takes place in a way to avoid bias.

Figure 5. Example of record of an hypothetical outcome of a set of 50 trials.

Teachers should bear in mind that, effectively, games 1 and 3 are fair, with the probability of winning equal to the probability of losing. In game 2 the probability of losing is substantially higher then the probability of winning, and thus game 2 is not fair (see annex 1). However, one should not forget that equal probability of results does not imply the mandatory equality of wins and losses when repeating the experiment a certain number of times. Chance, in itself, is unpredictable and the probabilistic model inherent to the random experience only reveals itself after a large number of repetitions. 

The example in figure 5 is perfectly plausible as a result of 50 repetitions of games 1 or 3. Only a very ‘well-behaved chance’ would produce 25 wins and 25 losses in 50 trials. However, for those willing to see, the fairness between wins and losses is there and will be so much more visible the higher the number trials. In a fair game, such as the cases of game 1 and game 3, one can expect a small advantage of either outcomes (win or lose) in a large set of trials. In the case of game 2 a significant difference between the number of gains and the number of losses is expected, with obvious benefit for the latter.

30 minutes

 

Phase 4:  Discussion of results

At this stage, the teacher asks the groups to share their results from each game. It may be interesting to combine the totals from the different groups that played each game to obtain overall totals for each one. With a larger number of trials, it is expected that the fairness or unfairness of the games will become more evident. The class should conclude that:

•  games 1 and 3 are fair, while game 2 is not.

•  in games 1 and 3, winning and losing are equally probable results.

• In game 2 is more likely to lose than it is to win.

20 minutes

Students should try to find an explanation for why games 1 and 3 are fair, while game 2 is not. To guide their reflection, the following questions can be asked for each game:

• How many possible outcomes are there?

• For how many we have a winner combination and for how many we have a loser combination?

15 minutes

Appendix1