5 Maths Gems #47

Hello and welcome to my 47^th gems post. This is where I share five maths teaching ideas I've seen on Twitter.

1. Don's Multiple Choice
I often write about Don Steward's resources - it's worth checking his blog every now and then to see what he's added. This week I was browsing his 'practice and quiz questions' blog (which is separate to his main blog) when I noticed that he has started to produce excellent sets of multiple choice questions - here's an example:

 He has also produced some lovely 'odd one out' activities:

Both types of activity would work with technologies such as Plickers or Quick Key. Multiple choice questions are making a bit of a comeback at the moment - for more sources, see my post 'Multiple Choice Questions'.

2. Inequality Question
I really like this question from Steve Blades (@m4thsdotcom). Ask your students for the minimum and maximum value of abc to check their understanding of inequalities and integers.

I'll use this with my Year 11s - many of them struggled with the question below in their mock GCSE, which suggests a lack of fundamental understanding of inequality symbols. 

3. Math Wall of Shame

Thanks to Megan Schmidt (@Veganmathbeagle) for sharing Sara VanDerWerf's post 'Math Wall of Shame'. This post provides over 80 pictures including dodgy graphs and incorrect pricing - these are good for inspiring class discussion. Here's a couple of examples:

'Here's a cent, keep the change' 

4. Quick Cover 

Mathsbox is a fantastic website and it's very affordable at only £48 per year. It is full of useful resources and the recently added 'Quick Cover' lessons are a particularly good idea. These are designed for teachers to set as cover when they will be absent from a lesson. They include clear examples, plenty of practice questions and a jigsaw activity. Here's a couple of samples:

• Simplifying
• Expanding brackets

There's currently 23 Quick Cover lessons and the collection is growing. 

5. Access Maths

Access Maths is another excellent website with a wide range of worksheets, games and activities to explore. A new set of resources has just been added: Starters and Progress Tests for the new GCSE. 

Update
My post Five things you might not know about the new GCSE content #1 was well received. I promised a second post with five more facts about the new GCSE... I'm working on it but I think I've found some discrepancies between exam boards that I'm investigating. Watch this space!

There's been two announcements since my last gems post that you might be interested in. The first is that the date and venue has been set for researchED Maths and Science. It's on Saturday 11th June in Oxford. I think this will be a fantastic event. I have to attend a wedding reception in Kent that evening so I'll have to leave early, but will definitely be there in the morning. Tickets are likely to sell out quickly.

The second announcement was regarding new tests for times tables. We all agree that fluency in times tables is vital (as is conceptual understanding of multiplication) but there is disagreement over whether more Key Stage 2 tests are desirable.

It's also worth noting another change regarding testing (see above) - from 2017 Year 7 maths teachers will have three months to 'fix' students who did not 'pass' Key Stage 2...

It's been a hectic first week back at school but thankfully this weekend I didn't have any marking to do so I had the opportunity to visit the excellent Escher exhibition at Dulwich Picture Gallery. It finishes on 17th January so if you want to go then get tickets now! The gallery shop is full of mathsy gifts too.

I'll leave you with a nice demonstration of Pythagoras' Theorem from mathwarehouse.com.

Five things you might not know about the new GCSE content #1

This is the first of two posts listing changes to GCSE content that aren't widely known. If you're really familiar with the new GCSE specification then you probably already know all of this. But if you're worried that you might have missed something, read on.

1. Graph Transformations
No more stretching of functions. I missed this one so thanks to @MrBenWard for pointing it out today. This is an odd change - I can't see the rationale. Here's what's in and what's out:

I'm going to have to edit a lot of resources...

Don't forget that the featured transformations (ie reflections and translations) may also be applied to the graphs of y = sinx and y = cosx.

2. Trial and Improvement

Contrary to popular belief, trial and improvement hasn't gone! I thought it had until I saw these tweets from AQA:

AQA's Teaching Guidance says that "students should be able to use systematic trial and improvement to find approximate solutions of equations where there is no simple analytical method". 

Any trial and improvement questions in the new GCSE may be more challenging than what we're used to, so we can't rely on past exam questions and resources. Here's an example of a new specification trial and improvement question from AQA:

A solid has volume V = x³ + 2x² 

The volume of the solid is 90cm³ 

Work out the value of x to one decimal place. 

You must show your working.

Note that the question doesn't explicitly tell the student to use trial and improvement, which is a notable change from previous exam questions.

3. Compound Measures
The new specification lists pressure under compound measures - this is new to maths GCSE. The specification says, "Use compound units such as speed, rates of pay, unit pricing, density and pressure" - see Question 3 in this set of questions from justmaths.co.uk for an example.

In general students should be taught the importance of looking at units in compound measure questions. If speed is measured in km/h then we can see from the units that we need to divide distance by time to get speed. Using this approach students should be able to figure out how to answer any compound measure question even if they're not familiar with the context (eg if a question asks for population density in people/km² then they simply divide population by area - they know this by looking at the units, no formula required).

It's worth noting that students will need to know the equivalence of the notation m/s and ms^-1.

Peter Mattock has written a helpful blog post about teaching pressure. There are some pressure questions in the Toticity Mind the Gap Maths Toolkit which I reviewed here.

Example question from toticity.co.uk

4. Rounding

It was Mel's post 'GCSE 9-1 New content – Error Intervals' that first alerted me to error intervals and truncating so if you haven't read it then please do. These topics are fairly straightforward to teach, but a few of my top set Year 10 got a truncating question wrong when I tested them on it only a week later... They've been rounding for years and suddenly we're telling them not to round! 

Truncation practice

5. Systematic Counting

The specification says "Apply systematic listing strategies including use of the product rule for counting". Thanks to @MrMattock for drawing these changes to my attention through his blog post 'Multiplicative counting - the different types'.

AQA provides this example question:

"How many numbers between 100 and 200 have at least one digit that is 7?"

I'm not sure this kind of thing needs direct teaching - it just needs a logical approach. This second question from AQA requires the product rule - I think it might be worth spending a lesson or two on this (perhaps more if we extend to combinations and permutations - I will try to find out whether this necessary):

"Daniel has 10 shirts, 8 pairs of trousers and 5 pairs of socks.

a) How many different combinations of shirt, trousers and socks does he have? 

b) He chooses a shirt. How many combinations are there now?"

Apart from this lovely PowerPoint from newmrsc on TES, I don't have much in the way of resources for this topic so please send me anything that you have!

Formulae

Finally, just a reminder that your students will need to memorise more formulae than they used to. When the new GCSE was first announced this made the headlines:

"The new curriculum for GCSE maths will see pupils in England spending more classtime studying the subject and memorising mathematical formulae, such as Pythagoras's theorem."

Our students have always had to memorise Pythagoras' Theorem and plenty of other facts, theorems and formulae. I think that the impact of this change was exaggerated. Saying that, I will be annoyed when my students lose marks because they forget the quadratic formula... 

I'm pleased that students will no longer be required to memorise imperial to metric conversions because (unlike times tables, Ms Blower), it's entirely practical to look these up online if ever needed.

I hope that this post has been helpful. Don't forget I have a page of new GCSE resources and I've written various posts about new GCSE topics:

• New GCSE: Real Life Graphs 
• New GCSE: Tangents and Areas 
• New GCSE: Sequences 
• New GCSE: Inequalities
• Tricks and Tips 3: Quadratics 

Watch out for my next post when I'll list five more changes that you might not know about.

5 Maths Gems #46

Happy New Year and welcome to my 46^th gems post. This is where I share five maths teaching ideas I've seen on Twitter. 

1.  2016 Starters
Thanks to Dave Gale (@reflectivemaths) for sharing loads of great activities based on the number 2016 in his post '2016 Starters'.

Image: @IJTANEJA

2. Star Wars Puzzles

I've mentioned Emma's (@El_Timbre) puzzles before but they deserve another mention because she's now published a brilliant set of puzzles with a Star Wars theme... You can find these puzzles here, and while you're visiting Emma's blog do take a look at her EMMAths Awards 2015 too.

3. Order of Operations
Teaching the order of operations? This gif will definitely make your students laugh! Thanks to @k8nowak for sharing.

4.  New GCSE Exam Questions

You've probably already seen these, but if not then you don't want to miss them... Mel (@Just_Maths) has produced a set of resources for those of us teaching the new GCSE. She has collated GCSE questions by topic from the sample materials of all exam boards. Thank you Mel! Very helpful.

• Higher questions by topic 
• Foundation questions by topic
• Both tiers: questions by topic

5. The Progression of Multiplication
Do watch this six minute video about multiplication from Graham Fletcher (@gfletchy). It's excellent.


Resolutions
I'm not one for New Year's Resolutions - in fact, this image from parenting blog hurrahforgin.com sums it up nicely.

Saying that, if I were to make resolutions relating to my professional life as opposed to my personal life, then this graphic from @sylviaduckworth provides a really nice approach.

Over Christmas...
In case you missed them, here's the three blog posts I wrote over Christmas:

• Dates for the Diary - events for maths teachers in 2016
• Top of the Blogs - some of my favourite blog posts from 2015
• #christmaths15 - a write-up of my event

If you teach A level then you'll probably appreciate these posts about the upcoming changes to the specifications:

• 2017 Spec by Stuart Price (@sxpmaths)
• New AS-Level Further Mathematics 2017 by Tom Bennison (@DrBennison)

Over the Christmas holidays I spent many many hours working my way through a mountain of mock exam marking. To be honest I'm slightly concerned by some of my Year 11's results so I now need to do something pretty spectacular to improve the situation... Help!

Over Christmas I've absolutely loved spending lots of quality time with my daughters. I'll really miss them when term starts.

My youngest - 1.5 years old and still hasn't
slept through the night! What a monkey.

Have a great first week back at work! Thanks for reading.

Dates for the Diary

2015 has been the most eventful year of my teaching career to date. I returned to work from maternity leave in January and took on a Lead Practitioner role at a new school six months later. I continued to be a busy blogger and tweeter throughout the year and was chuffed that my efforts were recognised at the UK Blog Awards in April. During 2015 I attended numerous education events including maths conferences, TeachMeets, debates and my very own Christmaths party. Although it's tempting to write a long and rambling reflection of all the events of the year, instead I've decided to look at what 2016 has to offer. There's loads going on in the year ahead and this post lists a few highlights. Full listings can be found here.

January
Back to school and the chaos starts all over again. If your school is kind enough to let you out for a day, I reckon La Salle's National Maths Education Symposium on Thursday 21st January is worth a look. The programme is excellent.

I'm incredibly jealous of anyone who is able to attend the next Peterborough Maths Network event. They've only managed to line up the most awesome person in the maths education - Don Steward! This event takes place after school on 19th January and you'd be foolish to miss it.

It's also my birthday on 6th January... just saying.

February

It's a leap year! Did you see this tweet from Matt Parker? I ♥ numbers.

Sure, 2016 is not divisible by 5 like 2015, but it is divisible by EVERY OTHER SINGLE-DIGIT NUMBER. 4th time ever. Max possible until 2520.

— Matt Parker (@standupmaths) December 27, 2015

March and April
Have you noticed how short the Spring Term is? Easter falls early in 2016. As a result there's an awful lot going on during March.

The National Mathematics Teacher Conference (#mathsconf6) in Peterborough on Saturday 5th March will be a highlight. I've already booked my train ticket and my hotel room. I love these conferences. If you haven't attended one before then read my write-up of the last conference to get an idea of what goes on.

I'm also really looking forward to Julia Smith's (@tessmaths) Easter Maths Camp which is on 28th and 29th March in sunny St Osyth, Essex. There's all sorts of lovely activities lined up - contact Julia if you want to get involved.

As always, the ATM and MA are holding their conferences over the Easter holidays. The ATM's Easter Conference 2016 is in Warwick from Tuesday 29th March to Friday 1st April and the MA Annual Conference 2016 takes place in Oxford from Friday 1st April to Sunday 3rd April. Both have excellent programmes. Hopefully when my children are older I'll be able to attend one of these residential conferences.

A couple of weeks into the Summer Term is Maths in the Sticks. This event is organised by Stuart Price (@sxpmaths) and is aimed at A level maths teachers. It will involve CPD and a roast dinner at a beautiful boarding school in the Surrey Hills. I've tried the roast dinner - it's delicious! The event programme sounds very good too - I'm looking forward to this one.

May
We're all far too busy with our exam classes to attend events during May...

June
The second half of the summer term is best time of year for CPD. Most of us have some gained time after our exam classes leave so things are a bit less hectic. To start we have researchED Maths and Science on Saturday 11th June in Oxford. No doubt this will be outstanding event - tickets are likely to sell out quickly.

I'll be speaking at LIME Oldham on 20th June - if you're not familiar with LIME events then do check out their website for information. A week later I'll be attending the National Mathematics Teacher Conference (#mathsconf7) in Manchester, and a week after that is the MEI Conference in Bath. Last year I presented at the MEI Conference and absolutely loved it (see my write-up here) so if you get the chance to go, I really recommend it.

July and August
I'll be presenting on A level resources at the annual FMSP Key Stage 5 Teachers Conference in London on 8th July - details to follow.

Tom Bennison (@DrBennison) is organising an East Midlands KS5 Mathematics Conference on 9th August at the University of Nottingham. With the upcoming implementation of new Key Stage 5 specifications, A level CPD is going to take centre stage over the next two years. Tom is planning what sounds like an excellent event - I will share details when they are announced.

September to December
#mathsconf8 takes place in Manchester on 1st October - it's a bit of a trek for me but I wouldn't miss it!

I'm sure there'll be lots more Autumn Term events announced closer to the time. Maybe even a #christmaths16... And (fingers crossed) I really hope to organise something when the new maths gallery opens at the Science Museum. Watch this space.

Quick - get these dates in your diary now!

Throughout the year there's loads of fantastic local events organised by bodies such as the Further Maths Support Programme and the Maths Hubs. I haven't listed everything here, but there's always plenty going on for maths teachers so do find out what's happening in your area.

I look forward to seeing you at an event in 2016.

Happy New Year!

Top of the Blogs

This post recommends ten maths education blog posts from 2015.

Post: Taking Back the F Word
Author: Ed Southall (@solvemymaths)
Why you should read it: To see that you don't need gimmicks to make maths fun. You just need really good questions.

Post: US vs. UK: Mathematical Terminology
Author: Ben Orlin (@benorlin)
Why you should read it: Because it's both entertaining and interesting, like all of Ben's posts.

Post: Maths everywhere
Author: Bodil Isaksen (@BodilUK)
Why you should read it: Because it gives you a taste for how maths is taught at Michaela. It's unusual, controversial and fascinating.

Post: 10 things you might not have realised about the new Primary Maths curriculum
Author: Michael Tidd (@MichaelT1979)
Why you should read it: It's essential that Key Stage Three teachers know what's going on at Key Stage Two.

Post: In Praise of Being Boring
Author: Dani Quinn (@danicquinn)
Why you should read it: How would you feel if your students described your lessons as boring? Does it matter? Dani's perspective is interesting - she describes "a satisfying boredom that is part of the journey to a worthwhile goal".

Post: The Pain of Problem Solving...

Author: Andy Lyons (@mrlyonsmaths)
Why you should read it: To learn about Andy's practical approach to developing problem solving skills in reluctant students.

Post: A Singapore-UK standoff: textbook round
Author: Bodil Isaksen (@BodilUK)
Why you should read it: To see how different two maths textbooks can be.

Post: Maths Mindsets: My Y10s
Author: Tom Sherrington (@headteacherguru)
Why you should read it: You will find yourself nodding along, picturing your own students for each of the mindsets Tom describes. We have our work cut out...

Post: Supercalifragilistic First Time I Taught Quotient
Author: Dan Draper (@MrDraperMaths)
Why you should read it: Dan's honest and witty style of writing is always a pleasure to read. "The way I was slapping some maths words on the board at the start of a lesson, never to be seen or heard of again, does nothing to improve literacy". His new approach to literacy in maths lessons is spot on.

Post: 10 reasons why it's a great time to be a maths teacher
Author: Ed Southall (@solvemymaths)
Why you should read it: To remind yourself why being a maths teacher is awesome. Read it the day before the start of term and you'll turn up at work raring to go.

✭✭✭✭✭

I've limited myself to ten posts here, but I could keep going all day! The fact that most of my favourite bloggers aren't even mentioned here is testament to how much excellent maths blogging has taken place during 2015. I learn so much from these blogs and I really appreciate the time and effort that is put into sharing insights and ideas.

If you want to start reading education blogs but you don't know where to start, I recommend following the Maths Echo Chamber (@MathsEcho) which automatically shares links to all new UK maths blog posts.

I hope you've found my list helpful. I'd love to know what your favourite posts from 2015 were, so please share!

#christmaths15

It's hard to know what to write about #christmaths15 because I'm still a bit overwhelmed by it all.

A few months ago I decided that I wanted to run an event which would provide an opportunity for teachers to talk about the new GCSE. Importantly, I didn't want it to be an event just for tweeters - I wanted it to be open to anyone who had an interest. Originally I was thinking of a cross between a TeachMeet and #pieandmaths (which I wrote about here) - a combination of CPD and a social event. I've always enjoyed throwing parties and Christmas seemed like the ideal time to do so.

Once I started contacting potential venues, I realised that it was going to be far more difficult than I originally thought. I couldn't find a large, well-located pub function room that had AV facilities and was available for free hire for a whole afternoon and evening. I searched high and low and was about to give up when I stumbled upon Pause Bar, which is a function venue located in the City of London - my stomping ground when I worked in Banking.

I was required to order food in advance which meant I had to charge for tickets - this wasn't ideal because I was hoping to make it a free event, but I decided to take a gamble that people would be willing to pay. I booked it at half-term, putting down a hefty deposit which wiped out my meagre savings. I instantly regretted it! The pressure was on.

Over the following month my husband was subjected to constant updates - 'I just sold another ticket! Wooo!' and 'I haven't sold a ticket in 2 days! This is a disaster' - that kind of thing. Thankfully it did sell out pretty quickly, showing that there is strong demand for events like this. I ended up with a waiting list.

I had a lot of decisions to make - speakers, food, drinks, music, puzzles, quizzes, handouts... My budget was pretty tight so it was all very DIY (it took forever to print the programmes on my home printer!). I did my best to make it all as slick and professional as possible. AQA very kindly provided materials relating to the new GCSE (and free pens!). Emma Bell (@El_Timbre) provided puzzles and Rob Beckett (@RBeckett_Yd) brought along copies of Chalkdust Magazine. I couldn't afford a DJ so did a playlist myself, and I wrote my own quiz (which is here, if you'd like a go! Answers available on request). From the £25 ticket price, £2.50 went straight to EventBrite and around £22 went on food, drink and service. With the remainder I bought everyone a Lindt teddy!

Thankfully things went well on the day. The venue looked pretty, sparkling with Christmas lights. The welcome drinks went down well and the food was very nice. People seemed to have a good time. Most importantly, the CPD was very well received. There were a couple of problems -  the wifi was intermittent and some people couldn't see the screen from their seat. I'm hugely sorry about these things. Otherwise I think it was a success. I was incredibly anxious in the weeks leading up to the event so I'm very relieved it went quite smoothly on the day.

The speakers were brilliant. I knew they would be. I am hugely grateful to all of them. I will write another post about the key ideas I took from their sessions, and I will share their presentations if I can.

Who bought me a Jägerbomb at 6.30pm?! You know who you are! I had no chance of surviving the night in one piece after that. Mel (@Just_Maths) was on top form too, getting in round after round of Baby Guinness. For the last couple of hours there were only a dozen of us left but we had such an awesome time.

Tweeters enjoying the party

Sambuca with Tom Quilter of pinpointlearning.co.uk. (Rob Smith photoboming!)

I really enjoyed chatting to so many lovely people - I can't list them all here but they know who they are. Huge thanks to my friends who helped me set everything up at the start of the event, those who bought me drinks and those who called me a taxi at the end of the night. Thank you also to everyone who either came to the event or supported me in some way (particularly my long-suffering husband!).

I was given a card which was signed by my guests - I'm incredibly touched by this. I will treasure it.

I can't make any promises that I'll run another event next year! At times I was really stressed about it all. It was certainly the biggest project I've ever taken on. Hosting a party is hard work and at times I said 'never again', but I know what I'm like - I can't resist! I'm not sure about the venue though, and the jury's out on whether it will be summer or Christmas. Watch this space!

Finally, here's a Storify of the tweets from before, during and after the event. It's lovely to read through and see how much people enjoyed themselves. I'm really chuffed.

Merry Christmas everyone! From a very tired but happy @mathsjem.

5 Maths Gems #45

Hello and welcome to my 45^th gems post. This is where I share five maths teaching ideas.

1. Circumference
Don Steward has been writing lots of brilliant posts lately so do keep an eye on his blog. I love two of his recent posts - Pi Development and Circle: Introducing Circumference. The latter features animations such as this:

and a really nice set of circumference questions.

2. Pinpoint Learning
Causing quite a stir on Twitter over the last two weeks, @tom_quilter's new website pinpointlearning.co.uk provides students with personalised question booklets based on exam results. It's perfect for after a mock exam. You simply upload students' marks and the website automatically produces individual booklets featuring question on the topics that students need to work on. The website is free and is set up for Edexcel papers, so if you've recently done an Edexcel mock then do give it a go. I've seen many tweets from teachers who've already tried it and speak very highly of it.

3. Five Minute Mock Analysis
When you return mock exams to students you might like to use this excellent Five Minute Mock Paper Analysis from @MathedUp. The file is editable so you can customise it for your school.

4. C4 Integration
I'm teaching C4 integration to my Further Maths class at the moment. We've just done Volumes of Revolution and I enjoyed making use of props to explain the concept. Thanks to an idea from Chris Smith (@aap03102), I used paper decorations to demonstrate how a solid is formed when a plane is rotated around the x axis.

I used these alongside gifs such as those shown below.

I also enjoyed using constant characters for the first time. This is an idea from @edenspresence that I featured back in Gems 22. Students who forget the 'plus c' in their answers are asked to decorate a constant character. Hopefully this will encourage them not to forget again and will make an interesting display for the classroom wall. Here's a couple of examples of what my students came up with:

5. Snowflakes
These Star Wars snowflake designs are brilliant and even feature characters from the latest films.

Here's a video about how to fold them:



If you're planning to do some snowflake activities at school in the last week of term then it's a great opportunity to talk about fractals - read Gems 16 for more on this.

Snowflakes can be a bit tricky to make so you might like these Paper Snowflake Cutting Tips. And this video (shared by @WycHighMaths) from Vi Hart is awesome:

It's only one week until #christmaths15! How exciting. You can still buy evening tickets if you want to join us for the party. The party includes a maths quiz, puzzles, food and a disco - partners and friends are very welcome.

If you teach Year 10 then do check out my recent post about real-life graphs.

Right, I have mock marking to do and Christmas cards to write so I better get on. I'll leave you with this nice question from @OCR_Maths - what fraction is unshaded?

New GCSE: Real Life Graphs

I have a feeling that I still haven't identified all the new GCSE content. This makes me nervous. I glanced through a textbook last week and spotted a few topics that aren't on my list. For example, I know there's new content for quadratic graphs, but I didn't know that students will also be required to identify the roots of cubic graphs (see example question below). The specification simply says 'recognise, sketch and interpret graphs of ... simple cubic functions'. Previously students have only been required to recognise the shape of cubics - roots didn't come up until A level. Now I've spotted this content in the textbook, I'll need to adjust my plans to ensure I have time to cover this at some point in the next 18 months. The time pressure is increasing.

A question from Edexcel GCSE (9 - 1) Mathematics: Higher Student Book 

Real Life Graphs
I've just taught linear graphs to my Year 10s. My scheme of work tells me that I now have to teach 'real life graphs'. But what does that mean? In this post I will attempt to clarify what comes under this title.

The previous GCSE specification said that students had to 'construct linear, quadratic and other functions from real-life problems and plot their corresponding graphs'. Examples included conversion graphs, 'ready reckoners' (whatever they are...) and distance time graphs.

Here's the relevant extract from the new specification:

The wording is different to the previous specification but it's broadly the same content, with perhaps more emphasis on interpreting contextual graphs. AQA's excellent Teaching Guidance gives us a more detailed description:

There's a lot here! The first four points follow on from linear graphs - for example students will have to interpret a y-intercept as a fixed charge. AQA gives this example question:

There's some great new resources for this kind of graph in AQA's Bridging Unit: Resource Pocket 3. The support provided by AQA is fantastic.

Modelling

The most common examples of 'graphs showing real-life situations in geometry' are those that model water flow. In AQA's sample assessment materials (Question 23 in Higher Paper 3) students are shown a graph representing the depth of water in a container over time. They are asked to identify the corresponding container from a selection (shown below). They are then asked to estimate a rate of change, requiring them to calculate the gradient of a tangent to the curve.

It's worth spending a couple of lessons developing the skills required for the first part of this question (ie identifying the correct container). Thankfully there's plenty of good resources for this topic.

In previous years I've used a 'filling up a bath' card sort (I adapted this from a treasure hunt I found on TES). I don't often use card sorts but I remember this one working well. There's also a good real life graph card sort from Nuffield.

I'm really keen to use Desmos Water Line - this is an online lesson in which students graph the rate at which containers fill with water. They also create their own containers to graph. Desmos lessons are absolutely brilliant so if you have access to tablets or computers then do give it a try. For me it will be a rare but worthwhile visit to the IT Room.

The classic Red Box is full of excellent graphing activities - it's a shame that the image quality isn't great.

Kinematics Graphs
Although I'm teaching real life graphs next week, I'm planning to leave kinematic graphs until I teach compound measures. This will then lead onto rates of change and area under a graph, which I've already blogged about. It doesn't make sense to do kinematic graphs before teaching speed.

We have plenty of resources for distance time graphs. AQA's Bridging Unit has some good questions (extract above). Interpreting Distance-Time Graphs from the Mathematics Assessment Project is excellent. I also like this commentary activity from Transum - The Hurdles Race.

I don't have much on speed time graphs, apart from those listed in my post about finding the area under a graph and those available from Toticity's Mind the Gap Maths Toolbox.

Exponential Graphs
The Higher Tier specification includes contextual exponential graphs. An example question from my Edexcel textbook is shown below. I plan to cover this kind of graph when I teach growth and decay (eg compound interest) next year.

My Plan
Next week I'm teaching 'real life graphs', but what exactly will I teach? Having looked through the new GCSE specification, the sample assessment materials, AQA's Teacher Guidance and a couple of new GCSE textbooks, I now have a clearer idea of what I need to cover. It's taken a lot of effort to determine that I need to do a lesson or two on contextual linear graphs and a couple of lessons on modelling. I'll come back to kinematic graphs, rates of change and areas under graphs after I've done compound measures. I just hope I'll have enough time to cover everything.

Proportional graphs also seem to come up a lot in the new GCSE. Often a context is given in the question. I'll teach these in January when I cover ratio and proportion. @fmaths42 recently wrote a useful post about these graphs which is worth a read.

I hope that this post has been helpful in clarifying the GCSE content on real life graphs. Do let me know if I've missed anything. Don't forget I have a whole page of new GCSE support here.