Some more interesting / trickier questions using proof by induction. Answers to questions 4 and 6 provided which require much more work!

Lesson starter for a review lesson on Pythagoras’ Theorem. Includes addressing misconceptions and the area proof as a mini-extension. Good for use under a visualiser in front of the class.

Worksheet with coloured triangles to cut out that guides students through deriving the area of proof of Pythagoras’ Theorem.

Extension task finding averages from tables. Answers provided.

Starts off with basic (but creatively written!) compound interest questions, before moving on to some difficult multi-step questions on percentages. Answers provided.

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

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

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 tasks on indices. Answers provided.

Extension task on direct proportion that presents harder questions including connecting proportion to other formulae in GCSE.

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.

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

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

Scaffolded, fill-in-the-boxes worksheet on both simultaneous equations and trigonometry. Good as revision and for use under a visualiser.

Scaffolded, fill-in-the-boxes worksheet on the cosine rule. Good for use under a visualiser.

Scaffolded, fill-in-the-boxes worksheet on surds. Good for use under a visualiser.

Scaffolded, fill-in-the-boxes worksheet on finding midpoints and distances between 2D co-ordinates. Good for use under a visualiser.