27 August 2016

5 Maths Gems #62

Welcome to my 62nd update from the world of Maths EduTwitter. Here I summarise some of the latest ideas and resources for teaching maths.

1. A Brilliant Problem
If you have a Facebook account then it's definitely worth liking Brilliant.org's Facebook page for an ongoing flow of lovely maths problems in your news feed. I particularly like the problem below - I'd use it as a starter in a GCSE lesson.

2. Symbaloo
Emma Bell (@EJMaths) has created a very helpful Symbaloo of maths education websites. All you have to do is click on 'start using this webmix' and register for a free account. You can make it your homepage so whenever you open the internet you'll have a lovely set of maths websites, blogs, tools and resources to choose from. This will save teachers lots of time and help them discover new websites too.

3. Fraction Division
An approach to dividing fractions that doesn't involving 'flipping'... this method from @solvemymaths is worth a look.
4. Indices
@offpistemaths shared these indices questions from an Eton scholarship paper aimed at Year 8. I love these problems - more of our students should be given the opportunity to try challenging questions like this.
5. Interactive GCSE Questions
Here's a new free resource from MathsPad. These interactive GCSE exam-style questions are available for both Higher and Foundation. They would work well as daily lesson starters on an interactive whiteboard. It's easy to switch questions and display answers.

Summer is nearly over! A level and GCSE results days were particularly emotional and exciting for me this year (my first results at my new school). It's weird to think that this was our last GCSE results day with grades A* to U - next year we'll be seeing numerical grades for the first time. It's also weird to think that the coming school year will be the last time we teach C1 and C2, as modular A level comes to an end.

You might be interested in seeing the 'hardest' question on this year's Edexcel maths Higher GCSE, which was only answered correctly by 2.6% of students (thanks to @MathsEmporium for sharing this).
Earlier this week I went along for drinks at La Salle's #pieandmaths event - it was great to catch up with some Twitter friends and meet some new people. I'm really looking forward to #mathsconf8 in Kettering on 1st October (I've now submitted a workshop proposal) - book now!

Did you catch my recent post about Multiplying Negatives? If you're teaching addition and subtraction with negative numbers, you might like this post from @Ed_Realist.

I enjoyed reading these recent blog posts:

As the start of term approaches, you might find these 'back to school' posts helpful:

If you're not on Twitter then the start of the new school year might be a good time to join... The amount you gain from it is well worth the small investment of time. Email me for advice if you're not sure how to get started!
A Problem
I'll leave you with this lovely set of problems shared by @Mathematical_A, taken from 'A Square Peg in a Round Hole'. Find the fraction of the area of the quadrant occupied by each semicircle.

21 August 2016

Multiplying Negatives

"A negative times a negative is a positive". It's a hard one to explain. We all learnt it at school and practised it to the point of fluency, but it's not until we're asked why it works that we stop and think about it.

Numbers lines and visualisations are very helpful when teaching the addition and subtraction of negative numbers. But with multiplication and division it's not so clear.

Let's look at a few approaches and resources.

1 . Pattern Spotting
Draw a standard multiplication table and extend it backwards to include negative numbers. It's a straightforward pattern that all students should be able to spot and continue. Get students to do this using Colin Foster's activity on page 5 of his Negative Numbers chapter.
2. Multiplication Grids
Take two 2-digit numbers and multiply them together using grid multiplication. For simplicity, let's take 12 x 11:
Here we have written 12 as 10 + 2 and 11 as 10 + 1. But it would work just as well if we expressed those numbers differently. Instead, let's write 12 as 15 - 3 and 11 as 15 - 4. We should get the same answer:
This only works if -3 x -4 = 12. 

Note that this explanation requires students to first understand that positive x negative = negative. This is relatively straightforward to explain in terms of repeated addition. 

3. Proof
Here's a proof that is clear and accessible to us experienced mathematicians. I'm not sure how accessible it is to Year 7 students, but it's worth a go.
a and b are positive
a + (-a) = 0 
[a +(-a)]•b = 0•b 
a•b + (-a)•b = 0 
a•b is positive. Therefore (-a)•b is negative 

b + (-b) = 0 
(-a)•[b + (-b)] = (-a)•0
(-a)•b + (-a)•(-b) = 0
Since (-a)•b is negative, we conclude that (-a)•(-b) is positive.

Perhaps start with a numerical example instead of a formal proof.
3 + (-3) = 0
Multiply everything by -4
3(-4) + (-3)(-4) = 0(-4) 
 -12 + (-3)(-4) = 0 
 (-3)(-4) must equal 12 to make this statement true. 

Further Reading
It's a good idea to read about a topic before you teach it, even relatively simple topics that you've taught many times before. Here are some helpful links:

I like this clip from Stand and Deliver:

The wording here is important. 'A negative times a negative equals a positive' is clearly preferable to 'two minuses make a plus'. The latter is confusing and may lead to misconceptions. An example of a common mistake is shown below (taken from mathmistakes.org via Nix the Tricks).
Tasks and Resources
Here are a few resource recommendations for this topic:

Colin Foster suggests that you ask students to make up ten multiplications and ten divisions each giving an answer of –8 (eg –2 × –2 × –2 or –1 × 8 etc).

The squaring and cubing (etc) of negatives is worth discussing - students should spot that an even power gives a positive value (eg what is the value of (-1)100?).

It may be worth exploring calculator behaviour too (ie some calculators require brackets when squaring a negative). It's important that students know how to use their calculator properly. There's a great resource from MathsPad for this - Using a Calculator: Odd One Out.

This topic is revisited in later years when students are practising substitution. For example, if a = 3, b = -2 and c = -5, find the values of: abc; bc2; (bc)2; a2b3 and so on. This Substitution Puzzle from mathsteaching.wordpress.com gets quite challenging.

Do let me know if you use an interesting method or resource for teaching the multiplication of negative numbers.

"Minus times minus results in a plus,
The reason for this, we needn't discuss"
- Ogden Nash

10 August 2016

5 Maths Gems #61

Welcome to my 61st update from the world of Maths EduTwitter. Here I summarise some of the latest ideas and resources for teaching maths.

I hope everyone is enjoying their summer break. I've been busy having lots of fun with my lovely daughters. We're going to stay on a farm near Hastings next week - looks like I might even get good weather! I'm starting to feel a bit nervous (and excited!) about A level and GCSE results - not long to wait now...

1. Magic
Thanks to Susan Russo (@Dsrussosusan) for sharing this Crystal Ball activity from @Yummymath. It's great fun! This might not work on a mobile - do try it on a computer if you can. Everyone likes a bit of mathematical sorcery... and the interesting bit is trying to figure out how it works.

2. Planet Nutshell
I spotted some good maths clips at Planet Nutshell. For example you could show this short proportional relationships video as part of a GCSE lesson (proportional graphs are featured on the new GCSE specification).

It's worth checking out the full range of videos. Short video clips can sometimes complement a lesson nicely.

3. Puzzles 
Through the @Team_Maths1 Twitter account I've been tweeting a Don Steward resource everyday using the hashtag #DonADay. In doing so I found the lovely activity 'Sacks' which I'd not seen before.

Do check out Don's latest set of number puzzles too.

I've also been enjoying the problems shared by Five Triangles (@Five_Triangles) recently. These two problems would work well at Key Stage 3 or 4:

a. Find x
b. The trapezium has height 22cm. The ratio of areas of triangles ⓐ to ⓑ is 4:5. Find area of shaded triangle.
4. Infinite Fractions
If you have 14 minutes spare for mathematical enrichment this summer, I recommend this video:

I really enjoyed this.

5. Planner 
I know this won't appeal to everyone, but if you're a fan of pretty stationery than you might want to design your own planner...  I've done it for the first time this year. The website is very easy to use and it's amazing how much you can customise - size, cover, binding, contents (which can include seating plans, mark sheets, behaviour logs etc...). If you want one for September I recommend ordering soon. I've been sent a code for 10% off (YDJ5PLX) which someone might benefit from. I love my new planner!

In case you missed them, here are my recent posts:

I also created a new page of classroom display ideas from various sources.

I was pleased that my blog was ranked second in Vuelio's Top 10 UK Education Blogs 2016.

Today I went to Bletchley Park with a lovely group of maths teachers from Twitter. We had a fantastic day and were treated to a special demonstration of an Enigma machine from @TeaKayB. If you haven't been to Bletchley Park before then I really recommend a visit.
La Salle have now confirmed the date of their next Pie and Maths event. It's on Tuesday 23rd August and you can book here. See Gems 37 for my write-up of last summer's event. I'm hoping to go along for the drinks this year.

#mathsconf8 is on Saturday 1st October in Kettering- I've now booked a room at the Premier Inn for the Friday night. Do come along to the conference - if you're not sure what happens at these conferences, here are some write-ups of past events: #mathsconf6, #mathsconf5, #mathsconf4, #mathsconf2015 and Gems 8.

Finally, I'll leave you with this joke - I spotted it in a back issue of Chris Smith's weekly maths newsletter.

5 August 2016


Towards the end of the summer term I visited another school to deliver some training on the new GCSE.

I thought it might be helpful to share the slides and materials from this training session here, in case anyone wants to deliver a similar update at their school in September. It's a good time for maths departments to stop and think about whether they're on track with Year 11 and whether they're going to do anything differently with Year 10.

1. Example of GCSE questions
I started by asking the team to look at examples of exam questions and determine whether or not the questions were from new GCSE specimen papers. For example I included a question on moving averages from a Linked Pair paper (time series are on the new GCSE, but not moving averages).

This activity helped me get a sense of how familiar the team were with the new GCSE specification. You can download the questions here. The answers are in the slides, which you can download at the end of this post.

2. Misconceptions
I then talked through ten key points which were mainly drawn from the two posts I wrote:

It's worth noting that whenever I ask the question 'has this topic gone from GCSE?', the exam boards are careful not to commit to anything. They are allowed to include questions on topics that aren't specifically mentioned in their specification, as long as the text in the question provides enough information for students to work it out for themselves.

For example Edexcel lists stem and leaf diagrams and frequency polygons in their GCSE (9-1) Mathematics Content Guidance FAQs, so I'd definitely teach these topics if my students were going to sit the Edexcel exams. AQA does not specify these topics in their Teaching Guidance, but this doesn't guarantee they won't come up. If students are asked to interpret a stem and leaf diagram in an AQA paper, the question will have to clearly explain how to read a stem and leaf diagram before asking students to do so.

3. New topics
I attempted to list all the topics that are new to Higher and Foundation tier (as best I could - there is no definitive list!). The list of new Foundation topics is a concern - I struggle to understand why some of these topics are considered suitable for Foundation tier.
4. Exam Structure, Tiering and Grading 
I talked about exam structure (three papers, the first of which is before half term) and grading. No one can predict grade boundaries and I won't attempt to do so, but two points did come up:

Beware the drop
If you enter students for the Higher tier and they only manage to get a handful of marks, they may well get a U. Bear in mind that the Higher tier paper will no longer start with a load of 'easy' questions like it used to, so some students may well struggle with the entire paper. If they barely pick up any marks, they will fall off the bottom of the grade boundaries and end up with a U when they may have picked up a Grade 3 or 4 from the Foundation tier. I've seen speculation that this cut-off point on the Higher tier will be anywhere between 10% and 20%, but this is totally unknown at the moment. The suggestion is that 'borderline' students would be safer on the Foundation tier, but please don't quote me on that!

50% A and A* content
This is a really important quote, taken from Edexcel's Guide to Edexcel GCSE Mathematics (9-1):
"Previously, 25% of questions were targeted at A/A*, but now 50% of questions in each paper are targeted at the equivalent grades, 7–9".
That's quite a ramp up in difficultly level!

At my training session, a teacher suggested that the grade boundary for a Grade 6 is unlikely to be higher than 50%, because a student who gets more than 50% of the marks on the Higher tier exam has clearly accessed some Grade 7 - 9 material.

I have no idea about grade boundaries but if you're interested in reading more, have a look at Mel's post 'Grading Part 1' and Phil McBride's post 'This time I am mainly excited by... evoking discussions'.

4. Resources
I talked about new GCSE resources - there are many resources to share so this is just a few highlights:

  • The exam boards have provided some great resources - including numerous sets of practice exam papers - so do check out their websites. For example I really like AQA's 20 minute topic tests.
  • Small subscriptions can get you access to excellent resources - MathsPad is one of my favourites.
  • Free resources - such as those from Don Steward - continue to be really helpful.
  • I've collated resources and links for new GCSE topics here.
  • Mel's exam questions by topic are very helpful. 
  • Read my post about the Mind the Gap Maths Toolbox for more ideas.

At my training session I also showed some examples of revision workbooks. Most of my Year 10s bought a workbook to prepare for their end of year exams. There are plenty of resources available for students to buy on Amazon including revision guides, revision cards and sets of practice papers. This might be a good use of pupil premium money for Year 11s who can't afford to buy these resources themselves.
Note that Edexcel are now making a selection of printed past papers available for you to use for mock exams. These will save schools both time and money. Preparing papers for mocks is a hassle so this is a really good idea!

5. Checklist and Scheme of Work
I finished my session by issuing the team with this topic checklist and asking them to tick off what they'd covered in Year 10 so they could identify which topics they still had left to cover in Year 11.

My school is about halfway through the list. Given that we only have until early May, and that our students go off timetable twice during the year for mocks, I think we're all feeling the time pressure! Thankfully our Year 11s will have nine lessons a fortnight next year - this will help considerably.

I shared my scheme of work - you can download it here but bear in mind that most of the links won't work as they're linked to documents on my school's network.

6. Slides
As far as I know, the content of my training session applies equally to Edexcel, AQA and OCR. My slides contain a number of graphics from Edexcel's excellent Guide to Edexcel GCSE Mathematics (9-1). The slides for this session (which took around one hour) are here and you're very welcome to borrow them if you feel that your team needs an update in September.

1 August 2016

Misspelt Words Display

I've had a go at making a classroom display of commonly misspelt maths words. I saw something similar at the front of a geography classroom once. I like displays that are useful for students.

I've made two versions. The first version is in the style of a chalkboard and highlights the 'tricky' parts of the words.
You can download the PDFs of these posters here (there are 25 posters in total).

The second version is perhaps a bit more printer-friendly because it's got a white background. Each poster features a simple graphic to represent the word.
You can download the PDFs of these posters here.

I made these posters using my free Canva account. I've been using Canva for a while to make graphics and posters - it's incredibly easy to use. If you're planning to make a new set of displays for September, you might find it helpful.

Edit 1:
Thanks to Emile Pinco ‏(@EmilePinco) for combining my two versions and editing the format to produce a far better creation!  You can download Emile's version here.

Edit 2: 
Thank you to Daria Kohls (@DaK_74) who has adapted these posters for science - download them here. Please pass these on to your science colleagues.

27 July 2016

Divisibility Rules

In the last lesson of term my students played a few rounds of a Countdown type game, and were particularly stumped by this problem:
I managed to do it pretty quickly and briefly experienced one of those lovely moments of appearing, to my students at least, to be a maths genius. Of course all I did was spot that 531 divides by 9, then it was straightforward. Have a go.

A colleague asked me how I'd done it so quickly and I told her that I'd used divisibility rules. She said that she'd never taught divisibility rules because she'd never seen it specified on a scheme of work. It strikes me that this is a helpful bit of mathematical knowledge that many secondary maths teachers don't teach. Do you teach it? In what year? Most resources for this topic are aimed at primary children but I think we should probably revisit it at Key Stage 3.

I was aware that my Year 10s didn't know the divisibility rules, so I covered them as part of the 'Factors and Multiples' topic this year (ie alongside prime factorisation, highest common factor etc). It's a good way to review the fundamentals of multiplication and to develop fluency and efficiency with numbers. To my Year 10s the rules seemed like 'new' maths that they'd not seen before (or if they had, they couldn't recall it), so it made an interesting and suitably challenging lesson.

I also ran a session on divisibility rules with some smart Year 3s and 4s at a local primary school this year. They picked it up well, and again I saw it as a good way to develop their understanding of multiplication and their number fluency.

So it's a topic that works well with any age group, from Key Stage 2 to Key Stage 4. Let's take a quick look at the rules and resources.

The Rules
Most children will easily be able to determine whether a number is divisible by 2, 5 or 10. The neat 'tricks' are for 3 (the digit sum is divisible by 3) and 9 (the digit sum is divisible by 9). Once we know whether a number divides by 3, we know whether it divides by 6 (ie all even multiples of 3 are multiples of 6). For divisibility by 4 there are two alternatives: either check whether the last two digits divide by 4, or halve the number and see if your answer is even (the four times table being double the two times table). The seven key tests are shown in the graphic below (there are loads of nice graphics for this on google images).

I didn't bother teaching the rule for divisibility by 7 because it's not straightforward. Rather then memorise this rule I thought my students would be better off just checking for divisibility by 7 with long division.

If you're interested in all the rules, from 1 - 30 and beyond, check out the Wikipedia page Divisibility rule.

I found a mixture of uninspiring worksheets and bizarre activities when I searched for resources online (the more unusual activities included Divisibility Rock n' RuleNFL divisibility dance and I'll take, you take...).

For the interactive whiteboard we have Vectorkids: divisibility rulesDivisibility TestDelightfully Divisible and this simple divisibility game.

If you're looking for a well structured worksheet pack, this is quite good.

This simple PowerPoint sets out the rules and contains practice activities mainly drawn from this homeschool website. It's nothing special but feel free to borrow and adapt it. It didn't take a whole lesson so it's worth adding some more challenging problems, such as this task from Don Steward.
Don Steward also has slides on divisibility rules, full of lovely challenging problems.

Why do the rules work?
The ancient Greeks knew rules for divisibility by 2, 3, 5 and 9 in the third century BC.

So why does the digit sum of multiples of three divide by three? Sal Khan explains here...


He has a similar video for divisibility by 9.

Do let me know about your experiences of teaching divisibility rules and any resource recommendations. If you've not taught it before, have a go next year. It's useful knowledge and well worth teaching.

24 July 2016

5 Maths Gems #60

Welcome to my 60th update from the world of Maths EduTwitter. Here I summarise some of the latest ideas and resources for teaching maths.

1. Perpendicular Gradient
I love this gif demonstrating the relationship between gradients of perpendicular lines, shared by Simon Pampena (@mathemaniac).

Geogebra fans will be pleased to see that Tim Brzezinski ‏(@dynamic_math) made 'Slope Triangle Rotation' to explore this further.

2. Metric Units
Next time I teach a lesson on units I'm going to show this five minute video on the history of the metric system. I think it's really interesting.

I discovered this on YouTube after watching The mathematical secrets of Pascal’s triangle which was shared by Cliff Pickover (@pickover).

3. Calculus Puzzles
A level teachers will like this Chalkdust post 'Puzzles about calculus' by Matthew Scroggs (@mscroggs).
4. Displays
Twitter continues to be a great place to share classroom display ideas. I saw two ideas last week that I particularly like. First, check out Sarah Carter's (@mathequalslove) fantastic mathematical welcome sign
Second, Claire Mazurkiewicz (‏@MrsMazzy) put an A level twist on Mel's (@Just_Maths) popular maths periodic table display. I rarely see displays designed for A level classrooms - read about it and download the file here.
5. Shadow Shapes
The image below has been going round the internet for years (original source unknown). I wrote about it last February in Gems 23. I now use it whenever I teach plans and elevations.
Phil Bruce (@pbrucemaths) was inspired by this image to make a PowerPoint of five more examples. You can download it from his blog here, under "shadow shapes".
My last day of term was on Friday (hurrah!)... I know some of you are still at school for a couple more days (nearly there!).

In case you missed any of my recent posts, here they are:

I've used VideoScribe to make a welcome video for Year 7 and an expectations video for Year 11 (you can watch both here) - I did something similar for my first lessons last year and it worked quite well.

If you didn't make it to researchED Maths and Science back in June then you might like to watch some videos of the presentations here.

Please follow @Team_Maths1 if you haven't already - I use this account to tweet maths resources, and my partner in crime Lucy tweets articles and maths jokes. We also offer a resource clinic - ask us for help and we will do what we can to find a suitable maths resource for your lesson.

Do check out the hashtag #DonADay too.

I'll probably blog a bit less frequently than usual over the summer holidays (I've got lots of school work to do... I also hope to make a start on organising #christmaths16... and I want to spend lots of time with my daughters). But I will be using the hashtag #summerblogread to tweet links to posts that you might have missed over the years.

It looks like La Salle are organising another Pie and Maths (see Gems 37 for my write up of the last one) so - depending on the date - I might be there for some summer socialising.

I'll leave you with this question from brilliant.org. There are various approaches (it's pretty straightforward if you can do basic trigonometry) but the solution is interesting. Check out the replies to my tweet here to follow the discussion.

17 July 2016

Looking Ahead

So how was your 2015/16? Careers have their ups and downs. This was the best year of my teaching career so far, thanks to a wonderful set of colleagues.

I got my new timetable on Friday which means I can now start thinking about what I need to do over summer to prepare for September. My school has increased the time allocated to maths for most year groups, so this is where we now stand in terms of the number of one hour lessons per fortnight:
I think this will work well. It differs from allocations at other schools - discussions on Twitter this year have shown that there is little consistency in maths timetabling across the country. 

The changed allocations at my school mean that most maths teachers will be teaching fewer classes next year, but seeing their classes more often. This has clear advantages in terms of relationship building and teacher workload (eg a reduction in test marking, parents evenings and so on). However it has come at a cost - our class sizes are now very large (from what I've gathered on Twitter, we have larger 'bottom sets' than most other schools) - this worries me.

Teaching Year 7 (my only Key Stage 3 class) will be my big challenge next year. We're moving to a quasi-mastery curriculum and, without any proper training or guidance, I think we'll all find this difficult. Half a term of fractions, eek! 

My other classes are Year 11, Year 12 and Year 13. It's funny to think that this will be the last year that we will teach C1 and C2. Just when I was starting to get the hang of it...

I'll be taking my top set Year 10 through to Year 11 next year. I intend to continue with regular low stakes quizzes (as discussed here).

I still have a lot of GCSE content to get through and fear that there will be very little (if any) time for revision and exam preparation in lessons after Easter. This means I need to think carefully about how to use lessons and homeworks effectively throughout the year.

I intend to trial using ring binders instead of exercise books with this class next year. It might be a disaster, but I use so many worksheets that I'm no longer convinced that it makes sense to use exercise books. I'll report back on how it goes...

I recently delivered some training on the new GCSE which I'll blog about next week.

My school now leads a SCITT, which means (with my Lead Practitioner hat on) I'll be much more involved in teacher training. Next year I will be a 'Lead Subject Mentor', meaning I'm in charge of maths-specific training and assessment for our cohort of maths trainees. I'm excited about this - it's exactly what I want to focus on. It's a good career development opportunity for me.

We have five new teachers (of which three are NQTs) joining my department next year, plus at least one trainee. That will keep us all busy! I'll be mentoring one of our NQTs and assessing an NQT in another subject.

Numeracy Initiative
I've been put in charge of whole school numeracy next year. To get an idea of where I stand on numeracy, read Dani Quinn's excellent post Headaches Across the Curriculum: what’s the point in whole-school numeracy?.

The way I see it, the best thing I can do for my students is increase their fluency when working with numbers - from that flows the all-important confidence. So I'm going to use my numeracy budget to start a big push on times tables for Year 7. We will subscribe to Times Tables Rockstars and promote it through a launch assembly, an after school 'Rock Gods' club, competitions and prizes, and dedicated time in maths lessons and afternoon registrations. If all goes well we'll have a large proportion of our Year 7s loving numbers by the end of the year! 

I look forward to spending some quality time with my family this summer. My eldest daughter Maddie starts primary school in September.

I'm a Year 12 form tutor so will have 32 personal statements to review and 32 references to write over summer (my tutor group is unusually big for Sixth Form). I've not done this before and I have a feeling it will take me ages, so I definitely don't want to leave it all until September.

Over summer I'll also be starting to plan my one-day subject knowledge enhancement sessions for the SCITT, and I've signed up for some paid proofreading work for an A level textbook (just to make ends meet). I'm not yet sure if I'll have my own classroom to tidy and decorate but if so then I'll do that when I go into school on GCSE results day - thanks to Twitter I'm never short of display ideas!

Lots to look forward to! Do let me know how your year went and what you've got planned for next year. I know that some of you have already broken up but for those of us still going - enjoy the final days of the school year! Nearly time for a well-earned rest.

13 July 2016

Mathsy Gifts: The Sequel

A couple of years ago I wrote a post about mathsy gifts for teachers. Today's post is a sequel - it features a small selection from the vast range of cool, beautiful and quirky mathsy gifts available from Etsy. Be warned, if you're based in the UK and you actually want to buy any of this, much of it ships from the US.

1. Shot glasses from 'Designer Science Gifts' Etsy seller CognitiveSurplus

2. Pi bow tie from 'Fun Fandom Bows' Etsy seller dexlarprice

3. Cookie cutters from 'Literary, Anatomical & Custom cookie cutters' Etsy seller BoeTech (some of their cookie cutters are bizarre).

4. Math dress for children from Etsy seller Hunter and Fox
5. Triangle Club Poster for a maths classroom from quirky Etsy seller cakeswithfaces

6. Graph Paper Towel (a tea towel!) from Etsy seller of 'Mindful and Playful Home Goods' dirtsastudio. Check out their full range of products - they have lovely stuff for English teachers too.
7. Maths Rocks Tank Top from Etsy seller TheGunsofBrixton1979

8. Pi Poster - one of many beautiful posters from Etsy seller QuantumPrints

9. A Guide to Regular Polygons from Etsy seller JamesBrownPrints.

10. Maths Teacher Shoes - are you brave enough to wear these?! From Etsy seller ibleedheART

Isn't the internet wonderful?