I was sent a private message on twitter from a teacher asking for some more advice on which task to use to start with for the children in his class. As a consequence I decided to write this blog, outlining in brief the content of each task.

The Mathematics Apprenticeship tasks are all non-standard activities, requiring the children to organise and carry out extended tasks. They also require children to consider the ‘real-world’ effectiveness of their solutions. It is difficult to narrow down the specific objectives that are covered in each activity; however, I hope this blog helps to outline the basic context and mathematical content of each task.

The tasks generally speaking get progressively more difficult. I try to match the task chosen to the areas of the curriculum that my class have recently covered. A general outline for each task is included below:

**Sandwich Task**

Designing a menu for a stall at a music festival, ordering the necessary ingredients and pitching the proposal to the festival organiser.

*Ratio calculations; calculating percentage discounts; scaling calculations.*

**Classroom Design**

Designing a new group room for a primary school, producing a to-scale diagram and matching costings document. The pitch is done to a school-leader or governor.

*Finding areas of rectangular and non-rectangular surfaces; a range of multi-step calculations involving money and measures.*

**BBC Broadcasting**

Carrying out a research project on behalf of the BBC, presenting findings and recommendations to a BBC commissioner.

*Collecting, interpreting and presenting an extended set of data.*

**Fruit Stall**

Designing a stock ordering system for a fruit stall, ensuring that the correct number of baskets of fruit are ordered and that stock remains fresh, whilst minimising costs.

*A context for extended division and multiplication; considering a range of factors to minimise costs.*

**Adventure Park**

To select a range of activities for a new Adventure Park within a set budget, considering the costs to build and run each activity. Teams must present their plan, which will include details such as toilet blocks and car parking spaces, for their new park to the CEO of Venturemax.

*A context for extended calculations involving large monetary amounts; calculating percentages; scaling multiplication.*

**Action Research**

To carry out a research project into one of two possible essay titles, exploring one aspect of mathematics learning in detail. Groups must write an extended report to present their findings.

*Opportunity for reflection into the learning process in mathematics, spanning different curriculum areas.*

**MI5 Security**

To use a range of variables to produce two security codes for the Head of Secret Service Headquarters; to produce a to-scale diagram of the office, with security features included. The security proposal is presented to an MI5 official.

*Using letters to replace unknown numbers; experimenting with formulas to produce different products; using measures including angle.*

**Garden Design**

To produce a garden design to fulfil a given brief. Groups must produce a to-scale diagram and a detailed costings document, balancing the considerations of quality and cost. The proposals are to be presented to a member of the Marks family.

*Extended area and perimeter calculations; calculations involving money and measures.*

**Gadgets Task**

From the given information, each group needs to decide on the most profitable gadgets for Teknofad to invest in. Children have to consider the cost of both the initial investment in each product, and the potential profits based on different sales figures, when presenting their work to the manager of Teknofad.

*Calculating profits using fixed and variable costs and revenue forecasts; considering different probabilities; presenting data in the most appropriate form.*

**Football Data**

Given a range of OPTA Sports information, groups have to analyse the key factors in determining the success of a Premiership football team. They then have to present their findings and recommendations to a member of the League Manager’s Association.

*Analysing and presenting data, including the use of scatter graphs.*

**Educational Resources**

The children have to write an educational resource for children at a specific stage of learning, in the process reflecting on what constitutes effective learning in mathematics. They will present their work to you, the teacher.

*Opportunity for reflection into the learning process in mathematics, spanning different curriculum areas.*