Paired activity. Suitable for KS4. This activity attempts to get students to think about frequency density and how it is used in the construction of a histogram. The is a distinctly 'puzzle' feel to this task, which can take a good half-hour working in pairs.

A chance to practice expansion of brackets and factorisation within the context of a simple algebraic result that can be spotted and then proved.

You need to revise simultaneous equations at the start of the A Level course, but you wish to take account of your students' prior learning and differing abilities. This task will accomplish this for you, and introduce some ideas of proof too.

An activity to test students' understanding of independence. Could be a useful starter for an S1 lesson on probability. Set in the context of a school with Venn diagrams. Part of a collection of A Level Statistics activities at www.making-statistics-vital.co.uk

Where do the compound angle formulae come from? This activity is a route in to this question that does not involve drawing triangles, but rather seeing what happens when we combine simpler functions.

Students like being given a sheet containing one or two howlers for them to uncover. Here's problem where the answer contains an error - and it's an important one to resolve.

Given four facts about a triangle, only three of which are true at any one time, how many triangles can you make? Great practice for the Sin Rule, Cos Rule, and some logic too.

Forgetting to change one's calculator from degrees mode to radians mode is likely to be a familiar error for your students. Here this is turned into an activity that tests how to solve general trig equations.

The pdf collects together into a single document the 40 investigatory tasks from the popular Risp website created by Jonny Griffiths at www.risps.co.uk. These activities are all pure maths ones, and are written for the A Level Maths syllabus. They represent excellent practise on problem-solving. There are 151 pages, and hyperlinks enable easy navigation.

A 'game&' using cards to generate practice with using the Product, Chain, and Quotient Rules. The exponential and ln functions are differentiated too. An excellent poster activity.

How to start on the calculus? A key question - one answer is here. An approach through pattern- spotting that should bring all your students with you.

A chance to use the Remainder Theorem and Factor Theorem in the context of a simple result from number theory that provides a motivation for the work. The acitivty proved to be happily effective with my AS students. This starter once again provides good practice, here in the use of the Remainder Theorem, with proving a conjecture as an end point in view to provide a motivation. The final result when viewed as a theorem might be scorned as ordinary, yet the proof of the Remainder Theorem itself can look fairly trivial at times, while it remains surprisingly useful.

Given three expressions, find a way to make each one the odd one out. Designed here for revising C4, but the method can be used for any topic.

Statistics activity suitable for KS4/KS5. A Powerpoint document, with a range of possible ways to measure spread, as discussed by a hive of bees. Written from the point of view of the MEI A Level syllabus.

A practical introduction to this famous problem, including a proof of the six colour theorem. Enrichment activity for A level Maths. Powerpoint bridging from A Level to University. Could be used in Extracurricular Maths Group. Part of a wider set of activities at www.carom-maths.co.uk

A way to introduce implicit differentiation in a way that your students can picture. There are also some curious graphs to catch their attention! Provides a useful reference to numerical methods too, if your students have studied these.

Sometimes a problem becomes a lot more interesting when turned around the other way. Here is a standard (and maybe a little dull?) Binomial question that livens up when reversed.

When you start with sequences, there are a number of different behaviours that you want your student to encounter. This activity gives rise to most of the kinds of sequence you want to examine, and their classification makes for good practice. Includes: convergent, divergent, periodic, bounded.

Given some clues about which parametric curve you are dealing wiith, can you find the missing constants?

When does the nth term of a sequence equal the sum of the first n terms? A chance to consolidate the formulae for summing arithmetic and geometric sequences. Periodic sequences make an appearance too...

Paired or Group activity. Suitable for KS4 GCSE Statistics and KS5, S1Here is a chance to cut up bars in your head and reorganise them in various ways. The mean, median and mode and the various ways in which they might be ordered are all part of it.