Maths on Toast

Maths on Toast Bites

Maths on Toast is a family charity whose mission is to make maths a creative, enjoyable, human, social activity for families and communities. Maths on Toast want everyone to feel positive about maths – to feel that it is something they can do, and enjoy.

The charity holds regular library sessions and works with community groups. Now, to spread the word further, we have the launch of Maths on Toast Bites. I was delighted to attend the launch event, also attended by some of the children in the films. It is always so good to see children’s enjoyment in Maths.

The five films are now available on the website, use the dropdown menu and you can see from the children in the films how to make a hexaflexagon, construct a sturdy structure, make Platonic solids, step through a playing card and how to enjoy fun family maths.
Maths on Toast Bites Films

Maths on Toast ‘Bites’ …
Showing how maths is creative, fun and for everyone.

Maths on Toast – the family maths charity – today, May 16th, launches ‘Bites’, a series of short ‘How To’ creative maths videos presented by children aged between 8 and 11. Aimed at primary school children and their families, our group of enthusiastic ‘maths advocates’ demonstrates a range of fun, hands-on maths activities that families can try together.

The 5 short films, along with accompanying activity instructions, are available on Maths on Toast’s website.

Maths on Toast’s mission is to promote positive attitudes to maths. Bites will broaden children and their families’ view of what and where maths is, and show that maths can be creative family fun.

An instruction sheet for the activities demonstrated in each film is available to
download. Families can try them together at home – they could also be used in school or
community settings. Trying them, enjoying them, and being aware that this is maths,
will change the whole family’s perception of maths; learning together through play and
discovery will increase confidence and create positive memories of maths.

Lucy Davis, CEO, Maths on Toast
“Maths on Toast Bites illustrate perfectly that ‘maths is everywhere and for everyone’.
The films show fun, creative, hands-on activities that we hope will be shared far and
wide to inspire children and their families to look at maths in a different light and
explore the many possibilities that maths has to offer. The enjoyment of maths in its
many forms provide the first step to creating a positive attitude to maths that can help
counter maths anxiety and a lack of confidence in maths.”

Rashid Iqbal, CEO, The Winch
“Maths on Toast is showing that children love to learn when learning is child-centred,
and that we can nurture an intrinsic joy to mastering maths. I am always delighted to
see projects in action that assert the value of informal education and champion the
principles of community-driven pedagogical practices.”

Sebastian Thiel, Founder, Upshot Entertainment
“Working with Maths on Toast and the young people was beyond amazing! All of the
young people were fully engaged and found every maths game and activity extremely
fun. As someone who hated maths growing up, I was astonished to see how
fun maths can be, especially for young people.”

Mathematics & Further Mathematics – Risps

Jonny Griffiths Further RISPSJonny Griffiths investigative activities for the pure A Level Mathematics classroom are well known (details are below). He has now published Further Risps, forty rich tasks for the pure Further Mathematics classroom.

I thoroughly enjoyed his excellent session for London Maths, ATM and MA London Branch on Saturday 11th May, where teachers enjoyed working on these activities. two editions are available – a hard copy or pdf version. On this page you can see two trial activities, Further Risps 1 and 2.

The pdf not only provides the forty problems but also full teachers notes for each. The notes for each task begin with the topic or topics covered, identify the type of task, for example, introductory and state any preliminary knowledge required. This is a valuable resource for teaching Further Mathematics.

Investigating the first Risp on Matrices at the session this certainly would help students with fluency in finding the determinant of a matrix. Rich tasks like this can provide students with a greater understanding than just a traditional exercise and will hopefully stick for longer! The tasks very much remind me of Colin Foster’s wonderful Mathematical Etudes.

For the A Level collection (all free, you can optionally purchase an e book version for £1) use RISPS (Rich Starting Points), these open-ended investigative activities are for the A Level Pure Mathematics classroom. Note the helpful index by topic, choose a personal favourite of mine, Risp 21 Advanced Arithmagons for example and you will see not only the task but also teachers notes.

Alan Hudson exampleArithmagons provide a wonderful activity for making students of all ages think; I always tell my students that good mathematicians can go backwards!

(For a whole collection of Arithmagons activities see this post).
Also from Jonny Griffiths his companion sites on Statistics and Carom-Maths -activities to bridge the gap between A Level and University. You can find a resource collection from Jonny Griffiths on TES Resources.

Making Statistics Vital has some tasks which are excellent for the A Level specification, look at this task on World Wide Statistics for example which includes the task with answers and a spreadsheet with data for 191 countries.

Making Statistics Vital

…and on the subject of bargains – note the free/cheap Maths books available!

Mathematical Miscellany #28

MEI Calculator Crunch

MEI – Calculator Crunch

This coming June MEI’ summer challenge, the Calculator Crunch will be helping Year 6s get ‘calculator-ready’ for secondary school, and additionally provide extra practice for Year 7s.

Note the dates – from 10 to 20 June, on each school day, MEIMaths will tweet a question a day for students to work on. PDFs of the questions will also be available from MEI’s page for display on whiteboards and to print as hand-outs. MEI has designed the problems not only to practise using a basic or scientific calculator but to develop mathematical thinking skills. Lesson plans will also be provided.

On the subject of MEI and Primary Maths, don’t forget their latest wonderful Sumaze! Primary app, one of a series of three apps in the series. All highly recommended, these problem-solving games cover a wide range of ages. Sumaze! which explores arithmetic, inequalities, the modulus function, logarithms, powers and primes is a problem-solving puzzle game suitable for A level mathematicians and above. Its sequel, Sumaze! 2, which explores fractions, decimals, percentages, primes and digits is suitable for those studying GCSE Mathematics and above.

For some more practise with calculators, perhaps try this calculator exercise from ADA Maths. Students can check that they can key in all the calculations correctly by answering the questions and checking their answers. ADA Maths is a free Mathematics Question Bank with no login required. The creator is Sam Powell, a mathematics teacher from the UK, working in Australia. All questions have answers, some have a fuller solution and a video explanation. Several categories of questions are available; look at Algebra for example and we see some nice use of colour in presenting a solution to a problem expanding double brackets (select Show Solutions) These examples could be helpful for students when revising.
ADA Project Algebra

Desmos AQA LDS Cars
In February of this year, I was very pleased to see that we can use Desmos for Statistics. Tom Bennison has written a large data set (AQA-Cars) resource using the Desmos statistics visualisation functions. It really is very easy to copy and paste into Desmos and display boxplots. Tom’s resource includes questions for students. It strikes me we should use the large data sets with younger year groups, using Desmos (or GeoGebra) makes it very easy to investigate such data when we are teaching boxplots and other Statistics topics.

Tom Bennison A Level Question a day

Tom Bennison – Year 13 Exam Question a Day

Tom has been busy, see also his Year 13 Exam Question a Day with questions up to June 13th. Tom has used Sample Assessment Materials from the awarding bodies’ websites so students can find mark schemes using the reference for any question. This will be a very useful resource for revision now and also in future. I do like the way we can easily see the topic for each question.

TeachItMaths Proof review

TeachitMaths Proof review sheet

Following my post on Proof resources, looking further through TeachIt Maths proof resources, I see many gems. Rather good for year 11 Higher GCSE students is this Higher Level Proof review sheet.

Maths Week London
In June we have for London teachers, Maths Week London. You can still register for this event, there are a limited number of welcome packs remaining.

Coming in November 2019, we have Maths Week England.


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

Proof CrashMATHS

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 is OCR’s section check in on Proof. OCR Check in test-Proof

maths genie

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.

Proof by Induction - Plymouth University notes

Plymouth University – Proof by Induction

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

For older students, 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

Underground maths review question

Building Blocks

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.

CIMT mixed 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!

CIMT Proof

Nrich Collection

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!

Nrich - Proof

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.


Don Steward

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?

Edexcel proof question

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.

Have you seen…?#7

These wonderful, and reassuring A level notes for students from Mathsbox?

Have you seen…?6 was about the Pure Mathematics notes:
From the excellent MathsBox site, brilliant timing for this wonderful free resource: Pure Mathematics A Level Notes. The notes have a very comprehensive set of clear and well-explained examples which I am sure will appeal to students.

We now have Statistics and Mechanics notes as well.

Free A LEVEL MATHS – Statistics and Mechanic Notes

Mathsbox has many free samples to try, one of the best value subscription sites around in my opinion.