24 September 2016


I'm very excited to share the details of this year's Christmaths event, which takes place in London on Thursday 22nd December 2016.

#christmaths15 was a great success (read about it here). We had an afternoon of CPD with brilliant speakers followed by food, drinks, puzzles and a quiz.

I know that many maths teachers are looking forward to the opening of the new maths gallery at the Science Museum, so I decided to organise a different type of Christmas event this year. Here's the plan:

3pm - 5pm
: Group visit to Mathematics: The Winton Gallery. Explore this exciting new gallery in the company of fellow maths teachers.

5pm - 7pm: We will have exclusive use of the Media Space Cafe at the Science Museum where you will be treated to a glass of fizz and a mince pie. The Big Fat Christmaths Quiz will return! Tickets for this reception are only £12. There are 130 spaces available and I expect these to go quickly so book now!

From 7pm: If anyone fancies a bit of festive socialising, we'll be going round the corner to The Hereford Arms afterwards. This isn't ticketed so you can just decide on the day if you'd like to come along.

For full details of the event and to buy tickets visit christmaths.co.uk. Please invite your friends and colleagues along too! All welcome.

17 September 2016

The Deadly Sins of Maths

A Twitter conversation with Ben Ward got me thinking about a display idea...

There are some misconceptions and mistakes that come up time and time again. Last week I set a lovely Don Steward quadratics homework for my Year 11s and was dismayed to see a number of them do this:
(x + 2)2 =  x2 + 4
When I returned the homeworks I talked to the whole class about this common mistake. I told them that it makes me cry every time I see it so they must never ever do it again! When I asked them why it was wrong, they were able to explain what had happened and tell me the correct way to do it (phew!).

When I next spot common misconceptions in my students' work, I'm going to tell the perpetrators that they've committed one of the deadly sins of maths, and point them in the direction of a classroom display. Making a big deal about these mistakes (in a half-jokey way that will stick in their heads) is a good way to lower the risk of students repeating the same mistake in an exam!
You can download my posters here (there are 20 posters to pick from - you may not agree with all my choices). I've also made a US-friendly version (using the word math instead of maths) which you can download here.

Some of these posters will make students stop and think - it might not be obvious to them what the mistake is.

In our teaching we should try to preempt common misconceptions - this is where clever questioning and well-written resources come into play. But sometimes we can't see mistakes coming - this is why effective marking and feedback are essential.
These days marking doesn't have to be handwritten - websites like Hegarty Maths can do it for you.

If you're looking for resources for highlighting and tackling common misconceptions, here are a few starting points:

I have a misconceptions page here that links to various websites and resources relating to common misconceptions.

If you use the 'deadly sins' idea, I'd love to hear how it goes!

Two days after creating this display, it was up on @jase_jwanner's classroom wall.  He has also suggested creating a students' display called 'Maths Heaven', where they write down the correct versions eg (-5)2=25.

11 September 2016

5 Maths Gems #63

Welcome to my 63rd update from the world of Maths EduTwitter. This is where I share some of the latest ideas and resources for teaching maths.

I don't know about you, but my first week of term felt like a month! The summer holidays now seem like a distant memory. The start of the school year is always exciting but exhausting... how long until half term?!

1. Corbett Maths Revision Cards
The brilliant John Corbett has been hard at work producing a fantastic set of revision cards for Higher and Foundation GCSE. These cards are designed for the new GCSE specification and can be ordered here. On the back of each card you'll find QR codes linking to revision videos and practice questions. The feedback on Twitter has been excellent - people love these!
2. Pythagoras and That
Thanks to @GuideCalculator for sharing a GCSE revision website: pythagorasandthat.co.uk. This website is very visually pleasing! There are loads of nice graphics that I'm going to borrow for lessons.
3. Pi Display
I stumbled upon a Pi display. It's 1000 digits so would be 27 metres long if you used the whole thing! When I tweeted about this, @PeterHTodd shared his πthon classroom display. It's π to 314 decimal places - he recites it on Pi day!

4. Year 7 Assessments
The resources from the White Rose Maths Hub are incredibly helpful. I wrote about the Schemes of Learning in Gems 58. My boss recently asked me to write an assessment for Year 7 and I was pleased to see that White Rose Maths Hub have already made one that I can borrow. Their assessments for primary and secondary are here. The collection is growing so do follow them for updates.

This question is taken from their Year 7 Autumn Paper A:

5. New Pixi Website
I'm pleased to see that superstar TES resource maker @pixi_17 has launched her own website. I wrote about her new GCSE revision booklets in Gems 58. It's worth taking some time to explore her resources, which are all free. Her collection is growing - for example she is producing a set of intervention booklets which I'm sure many schools will find helpful.
I've been back in the classroom since Monday. I already have lots to talk about - watch out for future blog posts about my folder experiment with Year 11, my launch of Times Table Rock Stars, and how I'm coping with the marking workload for the 31 students in my Year 12 class.

I really hope to see all of you at #mathsconf8 in Kettering in three weeks. There are some excellent workshops lined up - check out the choices here. I'll be presenting on some new GCSE topics - if you're teaching Year 10 or 11 this year then do come along.
I'm really keen to launch my #christmaths16 event but a venue is keeping me waiting... Watch this space! 
Did you catch my latest post? I wrote about classic maths resources - it's been one of my most popular posts ever.

Also, check out the new series of posts on TES about the specifications and resources for the new GCSE.

If you're a fan of geeky stationery then you'll love the new Back 2 Skool range from Dunelm - it's very affordable too! 

I'll leave you with this question from Brilliant which might be helpful when teaching angles to Year 7. Can you spot the shortcut?

4 September 2016

Classic Resources

The Standards Unit was one of the first resources I was introduced to during my PGCE (I even have my own Standards Unit box at home - taking up far too much space!). It surprised me recently to hear that some maths teachers aren't aware of it. I think of it as a classic.

Perhaps the shift away from traditional university-based training towards more schools-based ITT means that there's less consistency in what teachers are told about during their training. I'm now a Lead Subject Mentor in a SCITT and will ensure that my trainees are made aware of all the best sources of maths resources - but of course that will be entirely based on my own opinion of what is the 'best'. There is no universal list of things that trainee maths teachers should be told about.

In this post I list five 'classic' maths resources. I assume that all maths teachers already know about these websites, but if you don't then you're about to discover some treasures!

1. CIMT  
The brilliant Mathematics Enhancement Programme from the Centre for Innovation in Mathematics Teaching offers an extensive collection of exercises for all key stages. I used this website so much in my NQT year that I ended up buying the set of textbooks to flick through (order form here).

Since then, Craig Barton has very helpfully provided links to CIMT's material on his website - organised by topic instead of by book, making it easier to locate what you're looking for (the answers are there too). For example if you're teaching vectors then you can access all the vectors material through this link, including worksheets, problems, activities and assessments.
The exercises and examples are all high quality so I often use extracts for my slides and classwork. For example, I've used the Place Value unit to help me plan my first week of lessons with Year 7.

CIMT's primary resources are excellent too, and may be suitable for some secondary students.
2. Standards Unit
Malcolm Swan's "Improving Learning in Mathematics" resources (known as the Standards Unit) are brilliant. For years I just used the activities at the back (often card sorts), but then I discovered that the lesson ideas and questioning prompts are also incredibly helpful.
mature_maths_trainee on TES has put the Standards Unit activities into a 'classroom ready' format, including PowerPoints and activities.
Other classic resources, including the Mathematics Assessment Project (which is like an American version of the Standards Unit), Bowland Maths and 'the Red Box' can be found at Shell Centre - see my post 'The Hidden Treasures of Shell Centre' for more about this.

Frank Tapson's resources at Teacher Resources Online are reliable classics. Highlights include Pages of Puzzles, Searches and Crossums and Codes and Ciphers. There are also plenty of curriculum resources, including great stuff for arithmetic, circles and trigonometry. I always find the 3D trigonometry questions very helpful.
Other treasures include a guide to multiplication methods, a formulary for mathematics (which includes a lovely clear list of mathematical symbols) and MisMaths - a collection of maths mistakes made in the media.

I particularly like the delightful dictionary exercises and vocabulary exercises.
4. TES
There are a few things that put people off using TES for resources: the large number of resources (they can be time consuming to search through), the fact that some resources aren't free (the vast majority are still free though), and the big variation in resource quality. But there are so many excellent resources on TES, I continue to use it fairly regularly.

I'm no expert resource maker, but whenever I make something that I think might be useful to other teachers I upload it to my TES 'shop'. I'd encourage every teacher to do the same. Collaboration is important in our profession - sharing resources ensures we don't all waste time reinventing the wheel.

Some popular TES maths resource authors include alutwyche, pixi_17 and SRWhitehouse. I can't list all the good authors here - there are hundreds of authors who make really great resources and share them on TES for free.
5. Nrich
The team at Cambridge have pulled together a wonderful collection of enriching maths problems for all ages. They are used all over the world. For example 'Right-angled midpoints' is taken from the collection 'Pythagoras' Theorem - Short Problems':
In my post 'Favourite Problems' I listed a number of websites that specialise in problems and puzzles - Nrich is considered to be one of the best.

And more...
I'm sure that experienced maths teachers reading this will have their own list of 'classics' - do let me know in the comments below. For example I know that GAIM tasks are very popular. If I were to list every wonderful maths resource website that I know of, this post would be incredibly long!

Some relatively new websites, such as Median Don StewardUnderground Mathematics and Corbett Maths are certainly modern classics - every new maths teacher should be aware of these resources, and many more.

Resources are not the most important thing we need to know about as maths teachers - subject knowledge and clarity of explanation come first - but high quality resources can enhance our teaching. So let's keep spreading the word about these classics.

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.