**Quickly get to grips with all the problem types in the maths curriculum**

You can teach:

- A fact
- A process
- A specific problem solution

You can guide them towards deep understanding, but that’s another ball game.

**Examples**

**Facts:**- Angles in a triangle sum to 180
- Angles in a quadrilateral sum to 360
- Angles on a straight line sum to 180

**Processes:**- Find missing angles in polygons by summing the angles you know, and subtracting the total from the angle sum of the shape
- Find the angle sum of any polygon by subtracting 2 from its number of sides, and then multiplying by 180

**Problems:**Take a look at the example problems below:

The facts and processes involved in finding the missing angles are pretty much the same each time, but the problems and their solutions become increasingly complex. Pupils understand ‘maths’ in terms of what questions they’re being asked to solve. Focus on one problem and show them how to solve it. Try a few examples together, then let them practice.

Introducing a slightly more complex problem can be a good way of challenging brighter students, but don’t be shocked (…you will be) when you find often even the most able can’t go from problem 2 to problem 3 without support; the fact that it looks different is enough to shut down most minds.

Building those kinds of thinking skills in pupils is a long term goal. In your first term, it’s important they experience success, so they believe they can learn something from you (they *do* want to, even if they say they don’t care).

Before you start, you need to very quickly get your head around the curriculum in terms of **facts**, **processes** and **problem types** that pupils need to know.

For most **facts** and **processes**, levelled/graded, see these maps and curriculum overview (there are still a few omissions and minor errors in the layout; they’re a work in progress):

For **problem types**… that’s a tougher one. Look at as many GCSE past papers as you can get your hands on, ask colleagues, see what the MEP (Mathematics Enhancement Programme – post with more detail here) has, Peter Bland has an exceptional catalogue of (higher) past papers and focus booklets here.

**In summary**

To plan a simple, bread and butter lesson in 20-30 minutes:

- Decide what problems you want to teach and copy paste some from the MEP resources
- Create some example problems where you can model
**exactly**how you want them to set working out in their books - A better lesson will have something upfront that asks the question ‘why’ this maths might be needed, and helps explain