25 May 2019

5 Maths Gems #111

Welcome to my 111th gems post. This is where I share some of the latest news, ideas and resources for maths teachers.

1. Multiplication Tasks
In a Twitter chat on multiplication I saw two nice resources shared. First, Sharon Malley (@mathsmumof2) mentioned these 7 Times Table Reasoning Activities by krisgreg30 on TES. These tasks require children to use known facts to reason how to solve other calculations.

Second, Jonathan Hall (@StudyMaths) shared a lovely task he designed for his Year 7s to get them thinking a bit deeper.

2. MathByExample
Three years ago I wrote about AlgebraByExample in Gems 54. This set of tasks prompts students to analyse and explain misconceptions in algebra problems.

The team at SERP Institute (@SERPInstitute) have now launched their MathByExample website. The tasks are similar to AlgebraByExample but they are for topics that children meet at Key Stage 2.
There are loads of great tasks to explore on this website. In each case children are given a correct answer and an incorrect answer with questions about each one, and then they are asked to solve similar problems themselves.

The question prompts help children develop a better understanding of each concept.

3. Compound Area
Amie Albrecht (@nomad_penguin) shared a smart way to take a standard textbook-style exercise and add a higher level of thinking. Instead of just completing the exercise, pupils are asked to consider the features and difficultly level of each problem before deciding which problems to solve.

4. Linear Sequences
Thanks to Dan Lewis (@4301maths) for sharing a series of tasks on linear sequences.

Follow Dan on Twitter for more like this, including examples of his pupils' work.

5. Question Generators
Thanks to Jonathan Payne (@DrPMaths) who has built a collection of helpful question generators.

For example if you are creating some angle questions for your explanations or for your pupils to practise, then you can use his missing angles generator to create a set of customised questions.

And here's one that creates arithmagons.

I've been busy making more GCSE revision resources. This is the last time I'll do this for a while because next year I'll only be teaching Key Stage 3.

Because the non-calculator revision mats and the calculator revision mats I recently made went down well with pupils, I was asked by a colleague to make another set. So now I have a second set of calculator revision mats. Again, they have four levels of difficulty so you can pick the right level for your pupils.
I also made a Higher and Foundation 'Spot the Mistake' revision activity for something a bit different.

I also made a couple of revision mats with topics that might come up on AQA Paper 2. These are just a collation of questions taken from Maths Genie. Because these are 'temporary' resources (ie designed specifically to prepare for AQA Paper 2 June 2019), these are not on TES but are linked through Adam Creen's blog. Every year Adam pulls together all the 'between-paper' resources on his blog for easy access.

Don't forget you can use my breakfast resources as pre-exam warm-ups before Paper 2 and Paper 3. And my GCSE revision post continues to be the place where I collate all free GCSE revision resources (with the exception of the 'between-exam' resources that have a limited shelf-life).


I was delighted to announce this week that I will be teaming up with Craig Barton to offer two full day training courses in late October. Visit mathscpd.weebly.com for all the information. Bookings are already going well.

My recent post 'Calculator Woes' rung true with many teachers. It was selected as a Schools Week 'Top Blog of the Week' by Amir Arezoo and featured in Ollie Lovell's weekly Twitter takeaways. I think there's quite a serious problem with calculator skills across the country and I really hope to see teachers try to remedy this by getting lots of Year 6s and Year 7s involved in MEI's Calculator Crunch next month.

Thanks to Teresa Robinson at The Russell Education Trust who used my post to create a lesson on calculator skills.

Thanks also to @pgonlinepub for sharing a free worksheet on the 'Top 5 calculator hacks for GCSE Maths'.

Yesterday I had coffee with Simon Singh, the author of my favourite maths book. We discussed what parents can do to encourage and support their mini-mathematicians at home. Simon mentioned the coding app Box Island. When I got home I downloaded for my daughters. It's awesome!

By the way, if you don't currently receive the MA's eNewsletter then you can sign up here. I've been working with Ed Southall to relaunch it. From now on it will include an exclusive monthly puzzle for your pupils to try - one for primary and one for secondary. Sign up now!

I'll leave you with this graph, shared on Twitter by @lizardbill, which is probably the best example I have ever seen of a really really bad graph. There are more amusingly terrible graphs in the thread.

Enjoy half term!

22 May 2019

Marvellous Maths Teaching

I have exciting news! I'm teaming up with Craig Barton to deliver a brand new training course for maths teachers this October. 'Marvellous Maths Teaching' offers a full day of high quality maths CPD.

Your school or college will only have to pay £90 + booking fee to send you on this course, which makes it an absolute bargain - many other one day training courses are considerably more expensive. Even better, we're running both a Northern Leg (at the home of White Rose Maths in Halifax) and a Southern Leg (at my awesome new school in Sutton). So basically we're going on tour, and we're very excited about it.

Check out the full programme, and if this looks like something you might benefit from then get your absence/training request in quickly - there are only 100 places available on each course.

We can't wait to get started on this! It's going to be great. For more information and to book a place, visit mathscpd.weebly.com. Hope to see you there!

16 May 2019

Calculator Woes

One of the Year 11 classes I teach is what we call a withdrawal group. They all got a Grade 0 in their Higher GCSE mock back in November so we moved them to Foundation tier. This was definitely the right decision. I teach them for two double periods a week. The pupils in this particular group are very complex. Trying to teach them has been the most challenging thing I have ever done. I'm crossing my fingers that they all get a Grade 4 this summer.

Last week I attempted to engage this class in a revision lesson with one of the revision mats I recently made. This required calculators, which I lent them. This particular revision mat was deliberately designed to identify gaps in their knowledge of how to use basic calculator functions. I very quickly discovered that there were indeed many gaps. In this post I hope to help teachers of similar GCSE classes be aware of things to look out for and address.

The first question to cause me concern was this one on multiplying fractions:
The answer they wrote down was 4.2. There are two worrying things about this: 
  1. that they don't recognise that the answer should be greater than 21 (an area model would be a good way to demonstrate this)
  2. after almost five years of using calculators at secondary school, they don't know where the mixed number key is. 
Their answer of 4.2 came from them inputting the fraction ½ and then using the cursor to move back and put a three in front of it. The calculator sees this as 3 x ½ rather than the intended 3 + ½. 

In this country (though apparently not all others), writing 3½ means 'three and a half' and we call it a 'mixed number' - I'm pretty sure my pupils know this much. But when I went round and corrected each of them individually they all swore blind that they had never before been shown the mixed number button.
Now, I have been teaching teenagers long enough to know that the old 'we've never been taught this' line is normally nonsense. However in this case it may well be true. When we teach fraction arithmetic we do so in lessons that deliberately don't involve calculators. So unless these pupils have had a 'calculator skills' lesson then perhaps they haven't been shown it.

The second question to cause me concern was this one:
Thankfully all but one pupil wrote down the correct answer without using a calculator because they have some understanding of place value (phew!). The pupil who got it wrong wrote one seventh. 
He could have typed 7% in his calculator and then pressed the S-D button and it would have done it for him. The percentage button simply divides by 100. It's nothing special but it's there if they need it. For example, think about the various ways to do this question: 
We know that the most efficient thing to type into your calculator is 43 x 1.16. If pupils are not au fait with multipliers then perhaps they can type 16% x 43 instead, making use of the percentage button, and then add their answer to 43.

Do they do this? Hell no. Interestingly this is a topic where most students working at Grades 1 - 3 are very good at non-calculator methods. They will have done a lot of work on using multiplicative reasoning to find 10%, 5% and 1%. I'm super pleased that they can do this, but it's frustrating to see them use this method when they have a calculator at their disposal.

The next question that alerted me to a knowledge gap was this one:
There were two issues here: 1. not knowing where the cube root button is (I've known pupils to do 3√64 in the past) and 2. not following the order of operations. Some of them wrote 15 x 4, having worked out the cube root of 64 on their calculator after asking me the whereabouts of the button. I reminded them that their calculator has 'been taught the order of operations and understands it well', so we can trust it to correctly evaluate the multiplication first if we type in the whole calculation in one go. The problem of course comes with something like this:
In this case the calculator does indeed follow the order of operations, so if you type -32 then it will correctly square the three before multiplying it by negative one. But of course that's not what we wanted it to do. So if we insist on squaring negative three using a calculator, then we must put it in brackets. In fact if using a calculator I'd suggest putting all substituted values in brackets ie typing in 5(-3)2 -2(-3). I'd prefer to see this one done without a calculator really though. 

Evaluating the square of a negative incorrectly using a calculator is a problem that persists. We know that GCSE students make this mistake all the time when asked to plot quadratic graphs. They end up with weird looking 'parabolas'. I remind them that they know they've gone wrong if their graph isn't symmetrical. Pupils must use brackets if they use a calculator to square a negative! I feel like I've said this a million times and I will keep saying it until I'm blue in the face. 

The next question is one that I deliberately included in the resource to draw my pupils' attention to a useful calculator button. In my question about prime numbers, most of them assumed that 51 is prime. I pointed out that using the FACT button will show the prime factorisation of that number, which is rather exciting.  If they're asked to write a number as a product of primes it will probably be in the non-calculation paper, but it's still helpful to know this function. It gave me the opportunity to have a helpful conversation with my pupils about what prime numbers are. 

I think they were impressed by this button. 'This button is peng, fam'.

I had shown them it before, back in January. I'd also shown them the button they can use for time conversions. They were impressed then too, but had clearly forgotten all about these buttons which is unfortunate.

The final question of interest is this one on standard form.
Like fractions, standard form is often taught in a non-calculator context. And even if we have a calculator, it doesn't help us convert between standard form and ordinary numbers. However, if we're asked to use standard form in a calculation and we have a calculator to hand, it might be helpful to know how to use the x10x button. 

On reflection, this resource ended up being more than just a revision mat. It helped me identify and address significant gaps in calculator knowledge, albeit much more last minute than I would have liked. They should have been using these buttons for years. 

I should mention that when I took on this class at Christmas there were even more gaps in their calculator knowledge. At first they weren't making use of the Ans button. Plus, to do say 5.72 they would type 5.7 x 5.7 because they didn't know about the x2 button. So we have made some progress. 

Ironically, as they left the classroom I reminded them that they should bring compasses and a protractor to their maths exam and they told me that they don't need to because it is all provided for them in a pencil case. 'Oh. In that case just make sure you bring your calculator. It has to be the one you've been using for the last five years - the one you know how to use'. 'Nah miss - they provide calculators too, we'll just use whatever they give us'. 


This lesson got me thinking. I have a feeling that many schools don't do enough with calculators. In every school where I've taught Year 7 we haven't used calculators at all for the entire year - this is such a shame when there are many opportunities to explore and make sense of numbers in Year 7 using calculators. Also, although we need to build fluency with arithmetic in Year 7, I am convinced we should allow calculators for topics such as angles. It makes sense, and pupils like it.

Pupils need to be explicitly shown how to use their calculators throughout secondary school - I think that teachers often assume pupils already know the main keys. We need to bear in mind that much of it may not be obvious to a novice.

If you currently teach Year 6 or Year 7 then you might want your class to take part in MEI's Calculator Crunch in June. In this challenge there will be nine daily problems to solve using a calculator. MEI will be providing two lesson plans too.

There are lots of fun 'know your calculator' activities in my resource library. These are great, but we must make sure that calculator use is embedded throughout the topics we teach too, not just covered separately. I'm sure that some schools already do this really well.


Note that the calculator pictures in this post are from my 'peng' Casio fx-83GTX which was kindly given to me by Science Studio (and engraved with Mrs Morgan, which I love!). The buttons I've featured are in the same position on the Casio fx-83GT and fx-85GT (the ubiquitous calculators in the current Year 11 cohort).

11 May 2019

5 Maths Gems #110

Welcome to my 110th gems post. This is where I share some of the latest news, ideas and resources for maths teachers.

1. TES Author
When we did the latest round of TES Maths Panel reviews, my fellow panelist Damian Watson discovered the wonderful free resources of TES author cparkinson3. This author's PowerPoints are really well designed - they are slick and professional with neatly animated worked examples plus exercises with solutions.

For example check out the two lessons on volume of prisms - one for Foundation tier and one for Higher tier.
This resource on curve sketching is excellent.
I really like the bar modelling lesson too.

Check out the full collection. I've added them all to my resource libraries.

2. Vectors in Transformations
There's been some updates to BossMaths including changes to their Geogebra applets. The rotations applet now lets you show and hide tracing paper. You can also use vectors as an alternative to using tracing paper. I like this idea - I find using tracing paper a bit unsatisfactory so I will try vectors next time I teach this.

The enlargements applet now lets you show vectors from the centre to a vertex simply by clicking the vertex. This is useful if you use vectors for enlargements (which is particularly helpful for negative enlargements) - I blogged about this here.

3. SATs Support
I know this is a bit late for Year 6 teachers because SATs are next week, but these resources might be helpful to teachers of other year groups, and to Year 6 teachers next year.

Mr Morgs (@_mrmorgs) shared a PowerPoint explaining the language used in the KS2 Maths SATs. This follows on from his detailed analysis of exam language. This is really interesting and comes with lots of advice for teachers. I hope that one day someone does a similarly detailed analysis of the language used in GCSE maths exams.
Greg Chantler (@gregchantler) put all Key Stage 2 SATs arithmetic questions together in a PowerPoint and split them by curriculum year. Each question comes with discussion prompts.
4. Defend Yourself
Amie Albrecht (@nomad_penguin) shared a new idea for an activity. Students are assigned to a representation or method and have to try to explain why it's best. I think this would prompt rich discussion and thinking.
5. Shifting Times Tables
This activity from Miss Konstantine (@GiftedBA) provides a really clear representation of linear sequences as 'shifting times tables'.
Here we can see the four times table (4n) highlighted in the first row, then we see that the times table has been shifted down by one in the second row, meaning the nth term of the sequence is 4n - 1. I love the visualisation here. Check out Miss Konstantine's regularly updated blog for lots of great maths activities and resources.

My blog has been receiving record number of visitors in the last couple of weeks. I guess a lot of people are using my GCSE revision resources page and my recently published post on Foundation revision resources.

I've recently uploaded two sets of revision mats to TES. I made these at work when I realised it's hard to find suitable resources for students who are working at a Grade 1 or 2. Most GCSE resources are inaccessible to them, and this can result in disengagement and sometimes bad behaviour. So I made A3 revision mats that are more accessible, and while I was doing that I made similar resources for other classes. So there are four levels of difficulty. You can download these resources here:

I also made some Foundation workouts which are particularly 'print budget friendly'.

GCSE exams are just round the corner now. Don't forget that last year I made breakfast revision resources for all three exams. These can be used either on the morning of the exams or in the lessons leading up to them. 
Last week I published by 5th Annual Gem Awards. Do check it out if you missed it so you can see all the best gems of the year.
Congratulations to Emma McCrea on the publication of her new book 'Making Every Maths Lesson Count'. This is an excellent book for maths teachers.

Here are some other things you might have missed:
  • In 2017 I published a post on approaches to answering AQA GCSE ratio questions. It's one of my most popular posts with over 20,000 reads. I've now made a lesson to accompany this post.
  • Adam Boxer (@adamboxer1) shared a post on observing expert teaching which includes an 'expert teaching observation form'. I contributed to this post by testing the form out in a maths lesson.
  • Richard Tock (@TickTockMaths) published a number of new lessons including some on indices which draw a lot of ideas from my Topics in Depth CPD. Check them out on his blog
  • One of my Year 11s was flummoxed by rotational symmetry last week so I used the FlashMaths rotational symmetry tool to show him how it works. This has been around for a very long time so I was surprised that a lot of teachers on Twitter hadn't seen it before.
Don't forget that there are a number of events in the summer term that are now open for booking (see my events listings here). I will be presenting at researchED Rugby 2019, the Complete Mathematics Conference, the MEI Conference and the Kent and Medway Secondary Maths Conference. Speaking of events, I also have something a bit different to announce soon - watch this space.

I'll leave you with this video on why zero is the naughtiest and most important number from BBC Ideas.

5 May 2019

Gem Awards 2019

Last week it was resourceaholic.com's fifth birthday! It's become a tradition for me to mark the anniversary of my blog by publishing an annual 'Gem Awards' post. Here I look back at all the ideas I've shared in my gems posts over the last year and choose some of my favourites. Each category has a winner and a special mention.

1. Best GCSE Support
This award goes to the website BossMaths which I first blogged about in last May in Gems 89. This free site made by maths teachers has over 200 lessons matched to the GCSE specification, each with examples, practice exercises, misconceptions, and exam-style problems. I blogged about it again in Gems 103 when I discovered that a number of lessons contain examples and non-examples.

I love this website because it ridiculously easy to use (no login is required and you can navigate in seconds using the search tool) and covers the entire secondary maths curriculum. I use this website quite often - I borrow bits and pieces from lessons to include in mine.
Special mention to David Morse who won the 'Best New GCSE Resources' Gem Award last year. He continues to produce high quality resources and has recently re-launched his website, as featured in Gems 106.

2. Best New Blog
This award goes to maths teacher Mr Rowlandson (@Mr_Rowlandson) who has been writing his blog "Pondering Planning in Mathematics" since December 2017. He has organised his blog posts into series - so far we have 'Interconnected Maths', 'Lessons Learned From Shanghai' and 'Planning Thought'. He writes very well and always gives me lots to think about. He shares lesson ideas, reflections and related research. I absolutely loved his two most recent posts: Thinking About Corresponding Angles and Thinking About Calculating Areas of Circles. These are well worth a read if you are interested in task design in general, and also very helpful if you are planning lessons on either of these two topics (they come with helpful PowerPoints to download). In fact I think that these PowerPoints would be good for department meeting CPD.
Special mention to Chris McGrane (@ChrisMcGrane84) for his blog 'Get Out of My Swamp' where he shares thoughts and reflections on learning episodes, and his website Starting Points where he shares tasks and ideas.

3. Best App 
This award goes to MEI for their brilliant Sumaze series. These apps are such good fun for everyone, including maths teachers. If you've never played Sumaze! and Sumaze! 2 then do have a go (warning - they're addictive). Sumaze! is a problem-solving puzzle game suitable for A level mathematicians and above, and its sequel Sumaze! 2 is suitable for GCSE mathematicians and above. I was delighted when MEI launched Sumaze! Primary which is perfect for my seven year old daughter. We had loads of fun playing it.
Special mention to the Key Cards GCSE Maths Revision App from Simply Effective Education. Last month I downloaded a load of GCSE maths revision apps to check (so I'd know which apps to recommend to my students). This one stood out as particularly high quality.

4. Best CPD
This award goes to Teresa Robinson (@teresaarob1) for her brilliant Joint Maths/Science CPD.

Schools often want the maths department to support other subjects, but it can be hard to figure out the best way to do it. I was very pleased when Mel (@Just_Maths) wrote a blog post sharing Teresa's excellent CPD that maths teachers can do alongside science teachers.
Teresa followed this up with a second post: maths CPD to support business studies teachers. Again, it's really high quality.

In the 'Best CPD' category, special mention also to Craig Barton's podcast. It won the CPD Award two years ago and is still going strong. Craig has continued to interview a wide range of brilliant guests from the world of education. This CPD is really accessible for busy teachers (I listen on the way to work), and is always full of great advice, ideas and reflections.

5. Best Time Saving Tool for Teachers
This award goes to Hannah (@missradders) for her Planning Padlet. She made this for the teachers in her department but shared it publicly so other teachers can benefit. It's a good idea to make this your homepage on your work computer. It provides instant access to a large number of quality websites that teachers can use when planning lessons. It's very well organised, regularly updated and easy to use.
Special mention to Jonathan Hall (@StudyMaths) for his GCSE Grade Boundaries page and his GCSE Countdown page on MathsBot.com. I blog about MathsBot all the time - it's full of great tools for teachers. I teach a lot of Year 11 this year and I've lost count of the number of times I've used the exam countdown and grade boundaries pages. It's so helpful to know I can access that information instantly when I need it - a great time saver.

6. Best Animations
I don't like to give an award to the same person twice, but this one is going to have to go to MathsPad again! Since they got the 2018 Gem Award for Best New Online Tool, they've added more interactive resources to help teachers with their explanations. Recent additions include tools and slides for plans and elevationscontainer filling, pie charts and 3D Pythagoras. I find these really helpful. As I've said many times before, if you have the budget then MathsPad is well worth subscribing to.
Special mention to BossMaths (@boss_maths) for the ready-to-use Geogebra resources which are built into a number of their lessons. When I tweeted about numberless protractors, Sudeep from BossMaths replied straight away with a handy numberless protractor applet that he made using Geogebra.

7. Best New Website
This award goes to Jonathan Hall for the website nonexamples.com that I first blogged about in Gems 95. There are four sections on this website: Compare, Odd One Out, Frayer Model and Multiple Choice Quiz.
Like Jonathan's other websites, it's very easy to use. For example when I was explaining exterior angles to my students, I showed them this:
Special mention to Craig Barton's website variationtheory.com. This is one of a set of websites hosted by Craig where teachers can submit their own resources to share with other teachers (see also SSDDs, Venns and Diagnostic Questions). Variationtheory.com hosts a large number of useful tasks - for example the exercise on deciding whether to add or subtract simultaneous equations made me realise that part of my explanation needed to be improved. I particularly like the 'Fill in the Gaps' resources that have recently been added to the site.
8. Best Puzzles
This award goes to teacher Catriona Shearer (@Cshearer41) for the excellent hand drawn geometric puzzles she shares on Twitter on a regular basis.
These beautiful puzzles are really fun for maths teachers and would provide a good challenge for students too. It was wonderful to see them featured in Alex Bellos's Monday Puzzle column in The Guardian in January.

The 'special mention' for this award category goes to this puzzle which I featured in Gems 104:
This was shared by a colleague of Tom Bennison (@DrBennison) and prettified by puzzle master Ed Southall (@solvemymaths). Given it's a square, find the marked angle. I really like this - it doesn't require any knowledge beyond primary school angle facts but it's really satisfying to solve. 

9. Mathematics Award
This award goes to Nicholas Rougeux's (@rougeux) stunning interactive recreation of Byrne's 1847 edition of Euclid's Elements. I love this - it's wonderful. Check out Gems 101 for more on this.
Special mention to Mathigon, which won my 2015 Gem Award for Best Website. The new content on this site is brilliant, including the interactive history of maths timeline. Check out Gems 106 for more on Mathigon.

10. Lifetime Achievement Award
My previous lifetime achievement awards have gone to Don Steward, John Corbett and Jonathan Hall. This year my lifetime achievement award goes to the wonderfully talented Chris Smith (@aap03102).

Chris teaches maths at Grange Academy in Kilmarnock and contributes absolutely tonnes to the global maths teaching community. His weekly maths newsletter goes to around 3000 subscribers and is guaranteed to cheer up my Fridays. His resources are brilliant and his jokes are terrible. Chris won Scottish Teacher of the Year 2018 which was very well deserved. Chris has a pivotal role Maths Week Scotland, runs an annual maths camp for his students, does crazy things on Pi Day, and lots more.

If you haven't listened to Chris being interviewed by Craig Barton on the podcast then you must - he is so incredibly positive and passionate, it really makes you remember and appreciate the joy of maths teaching. Chris is also an inspirational public speaker and I very much hope to see him speak in both Scotland and England in the near future.
As well as being full of brilliant ideas, Chris is a wonderfully kind and generous person. He is an inspirational teacher and he makes a massive contribution to the maths community. No doubt he will continue to do so for years to come. On behalf of all maths teachers I'd like to thank Chris for everything he does. What a superstar. 


There are many people who I've not mentioned here who have helped to fill my gems posts with resources and ideas over the past year. Thank you to all of them for their ongoing contribution to maths education. I really appreciate the lengths people go to share their work as widely as possible so that we all benefit. I've been on Twitter for five years now and continue to feel privileged to be part of such a welcoming and generous community. Thank you also to the people who have encouraged and supported me over the last year - it's been really tough at times, but there's been lots of highlights (LateMaths, Humble Pi and Big MathsJam to name but a few).

If you're new to my blog and you enjoyed this post then visit my Gems Archive you'll find an index of 109 gems posts - they are all full of great ideas and resources. Also listen to my Gems podcast with Craig Barton where we discuss some hidden gems. You might also want to check out the Gem Awards 2018Gem Awards 2017, Gem Awards 2016 and Gem Awards 2015 to see who has won awards previously.

Happy 5th birthday resourceaholic.com. Thank you to my readers for all the support!