# Introductory session

## Activity 1

### Look at a situation: where is the maths?

Look at the photographs called *Building a school with bottles
in Honduras* on handout 1. This is presented as a context - no
problems are posed. Make a list of things you notice about the
situation. What mathematical questions occur to you? You might begin
by asking questions that start:

- How many ...?
- What would happen if ....?

Now set yourself a problem and use mathematics to tackle it.

## Activity 2

### Look at the Key Stage 3 Key Processes

Try to relate the work you have just done to the modelling cycle
flowchart on *Handout 2* . How well does it fit? **Simplify and
represent the situation**

- What specific problems did you pose?
- What simplifications and representations did you create?
- What choices did you make of information, methods and tools?

**Analyse and solve the model you've made:**

- What variables did you use?
- What information did you collect, or estimate?
- What relations between them did you formulate?
- What did you need to calculate, and how?

**Interpret and evaluate the results:**

- What did you learn about the situation? Were the results plausible?

**Communicate and reflect on your findings:**

- How could you best explain your analysis to someone else?
- What connections can you see to other problems?

## Activity 3

### Discuss some pedagogical implications

- How can you help pupils to become more aware of the Key Concepts in the Programmes of Study?
- How can you help pupils become more aware of the importance of
the Key Processes shown in the modelling cycle on
*Handout 2?* - Should you explicitly discuss these goals with pupils?
- Should you gradually introduce pupils to the modelling cycle in pupil-friendly language?

## Activity 4

### Observe a lesson

Now watch Frank's lesson on Building a School with plastic
bottles. As you watch the lesson, ask yourself: **Which Key
Processes can you see in the work of these pupils?** Can you see
them: **Simplifying and representing the situation?**

- What problems did they identify?
- What simplifications and representations did they create?
- What choices did they make of information, methods and tools?

**Analysing and solving the model they've made?**

- Which variables did they consider?
- What information did they collect, or guess?
- What relationships did they formulate?
- What calculations did they make?

**Interpreting and evaluating the results?**

- What did they learn about the situation?
- Were their results plausible?

**Communicating and reflecting on the findings?**

- How did they explain their analyses?
- What connections did they see to other problems?

## Activity 5

### Plan a lesson using one of the problems

Now it is your turn to plan a lesson using the Building a School situation. Discuss how you will:

- introduce the situation to pupils;
- introduce the idea of the modelling cycle;
- organise the classroom and the resources needed;
- answer the question "Why are we doing this in maths?";
- conclude the lesson in a way that gives pupils a better understanding of the nature of mathematical processes.

This is the end of the *Introductory session.* After you have
tried out your lesson with your own pupils, return for the
*Follow-up session* . Resources to support the lesson, and a
suggested lesson plan, can be found in the *Into the classroom
session* .