Note that following my session at Maths Conf Mini2 – August 2021, a new post on Proof will be published shortly.

There are some excellent resources available for teaching Proof. I have created a collection here.

Poof Worksheet – crashMATHS

From crashMATHS a **Proof worksheet and solutions** are available for A Level. There are proof questions on the A Level Maths Practice Papers available, including a rather nice question on the recently added **Bronze set C for Edexcel**.

A very valuable resource for A Level Maths is OCR’s **section check in on Proof** and for Further Maths: OCR Check in test-Proof

Maths Genie – Proof by Contradiction

For **A Level** and also **GCSE** questions by topic, **Maths Genie** is a go-to site, try **Proof at AS Level** or **A Level** – proof by Contradiction or **GCSE**.

Plymouth University – Proof by Induction

For Further Mathematicians, these **very clear notes with exercises from Plymouth University** include **Proof by Induction**.

Underground Maths has many **Proof resources**; perhaps try these proof sorts, **Proving the laws of logarithms** or **Proving the quadratic formula**. Or try this **review question**…

Building Blocks – Proof, Andy Lutwyche –

I have mentioned a favourite TES author, **Andy Lutwyche** in many posts; in his excellent **Building Blocks series** which have questions to take students through the various skills required for each topic, we have one for **Proof**.

From CIMT who are one of my favourite sites for a reason – see this **GCSE additional unit on Proof**. A favourite site because if you are ever short of examples it is highly likely you will find something on CIMT who have everything from **resources for little people** to **Advanced Level** and **everything in between**!

Nrich has this collection **Reasoning, Justifying, Convincing and Proof** for Lower Secondary. A search on **Nrich on Proof** returns a wonderful selection for all ages and stages. We have tasks to introduce **ideas of proof to younger children** (see also **Mastering Mathematics: Developing Generalising and Proof**) to **preparation for STEP** examinations. The **STEP resources** include Proof by Induction, useful for Further Mathematics Students.

Also from Nrich, try this **Interactive Proof Sorter** example which works on my phone as well as on my laptop. This would make a good starter – if you want to give out paper copies for students to work on as they come in, you can easily fit 4 copies to an A4 page!

**Teachit Maths**, though a subscription site offers an extensive **collection of activities** as free pdf files. A **search on Proof** returns some great resources. I do like this **Worksheet on Proof** which has 20 varied tasks aimed at older students 16-18, though some would be accessible to younger students. Full teachers notes on solutions are provided. In the task illustrated here, a full proof is given and students asked to explain each step.

From Don Steward on **Median**, we have many wonderful **proof resources**. Try **always and never** or **multiple proofs**. Why just multiply out brackets when we can do a little proof?

On Dr Frost’s site, it is possible to browse all his excellent **resources by topic** so if, for example, we search on KS2/3/4 then Algebra, we see **Algebraic Proofs**. Under Proof the Year 9 file PowerPoint file is excellent for high ability students, you will also see a very useful worksheet on counter-examples. I do like **Dr Frost’ Full Coverage resources** which are compilations of GCSE questions (GCSE – UK qualification taken at age 15-16). Answers are provided at the end of the document. Explore this outstanding site full of very high-quality resources, all Dr Frost’s clear indexing make the resources simple to find.

**MathsBot** is another superb site and very easy to find questions by topic, the **GCSE Exam Style Questions** are a good example. Select any filters and note the many question topics.

This **search of TES resources** returns several highly rated free resources on proof. Try **Algebraic Proof – Expressions and Proofs** from James Clegg, the worksheet “teases out expressions to show certain situations (e.g. the sum of 2 consecutive odd numbers) and features options on an “answer grid” at the bottom of the page.” There are also some questions to try.

Maths4Everyone – Algebraic Proof Workbook

From the excellent Maths4Everyone this **Algebraic Proof (Workbook with Solutions)** has numerous problems to try as well as very clear examples. Answers are provided – highly recommended (as are all the resources on **Maths4Everyone** by David Morse). A new navigation system is currently under development on the site, we see that many **proof resources** are on the site.