The purpose of this activity is to engage students in solving a problem involving probability, proportional reasoning and expected number, within context.

The background knowledge and skills that need to be established before and/or during this activity are outlined in the diagram below:

Click to show example questions for each heading

In approaching this activity, the students will need to make assumptions. Making different assumptions will mean that their final solutions are not likely to be exactly the same. The students might need to be reassured that this does not mean any solution is wrong, rather that it fits a different interpretation of the context. When discussing the assumptions the students will need to make, there is an opportunity to discuss the practicalities of the context and how mathematical calculations can be used to guide rather than dictate our actions.

This activity may be carried out with step by step guidance, or by allowing the student to follow their own method of solution. The approach should be chosen in sympathy with students' skills and depth of understanding.

Janet has an after school job delivering flyers and the local advertiser (free newspaper).

She has a total of 126 letterboxes to deliver to with different combinations of no circulars, advertiser only and ones happy to take anything.

So that she doesn’t have to carry extra weight, Janet has recorded how many of each type of letterbox on her delivery route.

Takes flyers and advertiser | 63 |

Advertiser only | 42 |

No Flyers, no advertiser | 21 |

If her delivery route is extended to include a further 60 letterboxes, how many advertisers should she expect to deliver?

### The arithmetic approach (show more)

- The student is able to calculate proportions and to use these to solve and expected number problem, with guidance.

### The conceptual approach (show more)

- The student is able to calculate proportions and to use these to solve and expected number problem.