**Developing inquiry from students' questions**

These are the questions and observations of a year 8 mixed attainment class. They show students asking about notation, grappling with the difference between the meanings of 'probability' and 'outcome', suggesting changes to the prompt and making assertions about the theoretical probability of getting two heads and two tails on four coins. The class went on to create sample spaces for two and four coins. Pascal's triangle proved useful in extending the prompt to other even numbers of coins (see one page of the inquiry flipchart below). The class worked out the probabilities as follows:

**Number of coins** | **Required outcome** | **Probability of required outcome** |

2 | 1H 1T | ^{1}/_{2} |

4 | 2H 2T | ^{3}/_{8} |

6 | 3H 3T | ^{5}/_{16} |

8 | 4H 4T | ^{70}/_{256} |

The class ended the inquiry by studying patterns in Pascal's triangle. The highest attaining students derived the binomial expansion for the first few cases of (*x *+ 1)^{n}.