**Goals**

- The students understand and can articulate why an experiment must be repeated multiple times in order to be confident about the results;
- Persistence: the students quickly realize that the deviation in the throws is due to the difference in weight of the dice. The question however is how often the dice needs to be thrown in order to confidently say what amount of pips (side of a dice) was thrown the most;
- The students learn to consistently perform a task (namely to repeatedly throw the dice in the same way);
- The students practice working together (making use of each other’s actions, coming to agreements within the group, division of tasks);
- The students learn to accurately record their observations (are the measurements recorded in a way that their meaning is clear?).

**Duration **

60 minutes

**Work form**

Groups of four to five students

**Preparation and necessities**

- Forms (one per group);
- Dice (each group receives four ordinary and one weighted dice which can be found in toy stores or online);
- Cups used to throw the dice (one per group

**Introduction/orientation**

Each group receives five dice (of which one is heavier) and a cup with which the dice are thrown. The amount of pips thrown must be systematically tallied. The goal is to show with which value (the number of pips) something is wrong (because of the weighted dice, a certain number of pips or specific side of the dice will be thrown above average, but you won’t inform them). Before the dice are thrown, the worksheet should first be discussed and the tasks within the group assigned. For the latter, you can let the students themselves determine and assign the tasks as a group or you can inform the students what tasks need to be fulfilled: one student throws, another records the results, another controls whether the results are accurately being recorded and two children count the number of pips. Each group constructs a plan on how they intend to prove that something is wrong.

**Activity**

The students throw all the dice at once over the table using a cup. After each throw, the values or number of pips are tallied in the first column of the worksheet. After five attempts, the number of times each pip was thrown is recorded in the second column. Following ten attempts, the same is reiterated for the third column and so on. They repeat this process until they think they have figured out the cause of the deviation. After how many attempts do the students suspect the cause and after how many attempts are they confident about their claim? The conclusion may only be based on the statistics of throwing the dice and not by close inspection of the dice itself (because the heavier side of the weighted dice is visibly different).

**Wrapping up**

Discussion of results: when and after how many throws could the students confidently claim that something was off with one of the values and what was that based on?

Relation to the Higgs boson: This exercise illustrates why particles must repeatedly be collided in the LHC before knowing for certain that the Higgs boson was indeed found. In science, in order to prove something, reproducibility of the experiment and results are vital.

Evaluation of activity: The weighted dice shows visible deviation from the normal dice. Because of this, the students often find it difficult to see the experiment through to the end, since the students already can assume which side will occur more often, despite understanding the importance of repeating an experiment. However, this very dilemma is reflective of real research: you might already know the answer to your question, but nevertheless you will have to repeat the experiment in order to confidently support your claim.

The researchers that were involved in coming up with this game show just how many times they threw the dice before they were certain of their case. This is illustrated below in the diagrams which you could present to the class.

**Tips**

- It is important that the students can articulate the fact that there is a significant difference between the claims after 5, 10 and 25 attempts;
- Emphasise the notion that it all comes down to providing evidence;
- After a few minutes, you may want to pause the activity to ask whether the students have encountered any problems and whether the tallying of pips is going well.