An extension lesson which introduces basic group theory (without the formalisation) applied to symmetries of a square. Cut-outs provided: students should stick pairs of squares back-to-back so that the numbers line up on either side. Answers to the worksheet also provided.

Worksheet that guides students through the derivation of the sine and cosine rules. Answers provided.

Extension that works with linear and quadratic sequences, finishing with using quadratic sequences to find expressions for sums of positive integers. Answers provided.

Extension on Sample Space Diagrams that generalises the class “sum of two spinners” setup to spinners with n numbers on each. Answers provided.

Extension on transformations that works with reflections algebraically. Answers provided.

An extension task that guides students through sketching quadratic graphs using completing the square, ending with the case for general a, b and c where “a” can be positive or negative. Answers provided.

An extension on Pythagoras’ theorem, including multi-step problems. Answers provided.

Worksheet that guides students through the (now standard A level maths) proof that root 2 is irrational. Also included is a generalisation to root c, where c is non-square.

Extension task which guides students through the derivation of the pi x r x l formula for the curved surface area of a cone. Answers provided.

Probability Trees Extension, including the classic “Hannah’s Sweets” question from Edexcel GCSE. Answers provided.

Extension which combines pie charts, algebra and sequences. Answers provided.

An extension worksheet guiding students through calculations involving modular arithmetic. Answers provided.

Great as an extension or end-of-year lesson for a bright set. Three investigations on iterating averages on a set of numbers, ideas of dividing by zero and working with logic gates.

A full lesson on finding limits of sequences, with starter, powerpoint and higher/foundation worksheets. Great as an extension lesson for a bright GCSE set that’s flying through the syllabus or for anyone who wants a taste of university-style maths.

Extension tasks on indices. Answers provided.

A creative extension for the topic of Histograms, which brighter students can often find quite boring. Asks students to think about what one might look like in higher dimensions!

I owe this one to my teacher training mentor that introduced me to the dice game Greed. Brilliant game which kids love playing, then this worksheet follows on by guiding students through the calculations of probabilities involved. Good for an extension lesson after a sequence of lessons on probability. Answers provided.

Worksheet guiding students through spider diagrams which demonstrate solutions to iterations. Answers provided.

A detailed investigation that finds precisely under what conditions fractions produce recurring decimals, building on the GCSE topic of algebraic proof. Suitable for brighter GCSE students who might be looking ahead to maths A level and beyond! Answers provided.

Short extension task linking factorising single brackets to highest common factors and simplifying complex expression involving indices.