5 Maths Gems #44

Hello and welcome to my 44^th gems post. This is where I share maths teaching ideas I've seen on Twitter.

1. Problems by Topic
I've often featured links to problem solving resources in my posts but these are rarely organised by topic. This means we have to trawl through mixed packs of problems to find something suitable for our lessons. Bravo to Leanne Shaw (@LeanneShawAHS) for creating a very helpful new website of problem solving activities grouped by topic. This growing collection includes both full lessons and shorter tasks. The picture below shows the resources listed under 3D Shapes so you get an idea how this website works. It's well worth exploring.

2. Concept Maps
Thanks to Greg Coleman (@MrK5Math) for sharing his Concept Maps which are designed to help students develop their understanding of mathematical vocabulary. Have a read of Greg's post for more on this, including templates.

Concept maps by Greg Coleman

3. Exam Skills
Thanks to @thefeelosopher for sharing the interesting resource pictured below. This is used to analyse the skills that contribute to students' success in maths GCSE exams. I've not seen anything like this before and thought my readers might be interested as it raises some discussion points.

I wonder whether a similar analysis might be helpful in Year 7 - for example at the end of the first term students could be given feedback against criteria such as:

• Do they know their times tables? 
• Is their handwriting legible? 
• Do they ask for help when stuck? 
• Do they make good notes in class? 
• Do they do sufficient practice in class? 

This would help teachers and parents identify potential barriers to progress. Do let me know if your school does something like this.

4. Puzzles 
I love the excellent puzzles that Emma Bell (@El_Timbre) has been sharing. Check out her blog to see the collection.

5. Lost Questions
Back in Gems 18 I featured a lovely idea for teaching factorisation - this was taken from Chris Smith's (@aap03102) newsletter. He puts something like this on the board:

When the class arrives he demands to know who rubbed the questions off the board. When no-one confesses he asks his students to figure out what the questions were.

Last week Michael Allan (@mrallanmaths) tried this activity and found it worked well - he shared a picture of his board on Twitter. 

This prompted Keith Morrison (@MrKMorrison) to try the same idea for division and multiplication.

During #mathsTLP on Sunday there was a discussion about other topics that this might work for. There were some really good ideas - I particularly like the suggestion that this could be used when introducing integration in C1.

Update
I wrote a review of some resources for new GCSE topics - if you teach Year 10 and you missed it then do have a look.

I also updated my mathsy gifts page in time for Christmas.

I attended the Debating Education event at Michaela on Saturday. It was an interesting day and all the debates were thought-provoking. The Andrew Old vs Bruno Reddy debate on mixed ability was particularly relevant to maths and is something I do intend to blog about at some point.

Tickets for the CPD element of my Christmaths Party have sold out. You still have a few days left to buy tickets for the evening party - join us for a fun night of mathsy merriment.

School
School is going well, though very busy - I'm incredibly lucky to have two Inset days coming up, the second of which is a 'Christmas shopping' day off (to make up for an extra Inset that was added at the start of term). It's perfect timing for a break.

I'm really enjoying teaching Year 10 - we had a good go at all the new sequences GCSE content. I ended the topic with these two puzzles from @jase_wanner which worked very well. In the first activity students have to fill in the gaps and in the second activity students are looking for the odd one out.

Year 11 is my big challenge because they're doing Linked Pair GCSE which has a lot more content than normal GCSE. This content (Flow Charts, AER, Linear Programming etc) is new to me. I only see my Year 11 class three times a week which doesn't give me enough time to teach all the content in sufficient depth. I really am feeling the time pressure and have never taught topics so quickly before. Tight time constraints don't allow for effective teaching so I'm very pleased that my school is looking to increase the allocation of maths on the timetable next year. As a result I think we'll probably be looking to recruit new maths teachers so if you fancy coming to work with me (based in Epsom, Surrey) then do get in touch.

And finally...
Prompted by some recommendations I read on Twitter, I'm very much enjoying playing the excellent Sumaze puzzle app on my phone at the moment. I'm also really looking forward to going to Just for Graphs this weekend, and am very grateful to my husband for offering to come with me.

I passed half a million views of my blog last week - thanks very much for reading!

I'll leave you with this lovely visualisation of prime factorisation which was shared on @edfromo's brilliant Google Plus.

Resources for New GCSE Topics

If you follow my blog then you'll know that over summer I spent a lot of time setting up a new GCSE support page. In doing so I found that there are some topics (such as Error Intervals and Frequency Trees) which currently have very few teaching resources.

Free vs Subscription Resources
The resources I recommend in my libraries are all available for free. The teachers behind free websites like m4ths.com and Corbett Maths are adding new GCSE content all the time. The exam boards are also being very helpful - I've already made use of both AQA and OCR's excellent new resources.

There's also a number of high quality resource providers who charge a small subscription fee. These include MathsPad, MathsBox, Teachit Maths and Just Maths. These subscriptions are well worth considering. The picture below shows an extract from a MathsPad activity that I used yesterday with my top set Year 10 - it's a great activity but it's only available with a subscription (£3 per month).

Of course it should be your school that pays for any subscriptions, not you. I know school budgets are tight, but if your department doesn't have any new GCSE maths textbooks then it does need to ensure that teaching resources are available.

Toticity
Last week I discovered a company called Toticity. My eyes lit up when I saw that they're selling a 'Mind the Gap Maths Toolbox' which is full of resources for new GCSE topics. I was particularly pleased to see that one of their free samples is on Iteration - this a topic for which resources are few and far between.

In this post I provide a review of the Toolbox, which is available to your school for a one-off payment of £95 + VAT.

Sequences
I've just finished teaching the new sequences content - it was very enjoyable. There's some great sequences resources listed in my algebra library, but when I taught triangular numbers and 'Fibonacci-type sequences' I couldn't find any resources at all. It's a shame I didn't have the Toticity Toolbox last week because there's a lovely Fibonacci worksheet in there, plus some nice activities for triangular numbers.

Fibonacci-type sequence questions
from the Mind the Gap Maths Toolbox

Under-resourced topics
Under-resourced topics such as Frequency Trees, Error Intervals and Invariant Points are all covered in the Mind the Gap Maths Toolbox - extracts from these worksheets are shown below. What a relief to finally have some resources for these topics!

Compound Measures
Compound measure worksheets are presented as a series of proportionality puzzles. Students start with puzzles like the example shown below - here students are told that the horizontal functions must be the same and the vertical functions must be the same.

This leads onto speed problems, such as the example shown below.

We are also given both density and pressure problems, which follow the same format.

I like this logical approach to proportional thinking, it reminds me of ratio tables.

Area under a Graph
In August I wrote a post about finding the area under a graph. In my post I talked about using the Trapezium Rule to find the area under a curve, but I didn't mention graphs like the example pictured below.

This doesn't require the Trapezium Rule but does require that students either know how to calculate the area of a trapezium or realise that they can split the area into a rectangle and a triangle. The Mind the Gap Maths Toolbox provides a preliminary worksheet to help students develop the necessary skills - an extract is shown below. They use shapes before they move onto graphs. I like this.

Diagrams and Scaffolding
The worksheets in the Mind the Gap Toolbox contain a lot of algorithmic diagrams. Workings have to follow a defined structure. For example the format below is used for all the questions on finding the midpoint of a line.

Another example is shown below - this is taken from a rounding worksheet. I've not seen this approach before. In order to use this worksheet in a lesson on rounding I'd probably have to use this representation throughout my teaching of the topic. Instead I use a straightforward number line and I'm not sure I want to change that.

Have a look at Page 2 of this free sample resource on perpendicular lines to see what I mean about the use of lots of algorithmic diagrams. These approaches are interesting but I'm not sure they will appeal to everyone.

Design
I like the design of all the worksheets in the Mind the Gap Maths Toobox - they are user-friendly and well formatted. Answers are provided. There's little in the way of problem solving or stretch and challenge - these worksheets are very much designed for fluency practice. I'll use these worksheets in addition to (but not instead of) rich tasks that develop problem solving skills.

The diagrams and flowcharts used throughout most of the worksheets provide a lot of scaffolding. This makes some of the challenging new content more accessible, for example through the use of grids for expanding triple brackets. The approaches used (the very distinctive methodologies) might not appeal to everyone but are worth a look.

I'm very pleased that I have a new set of practice worksheets and am really looking forward to getting stuck in with all the new GCSE topics. Even iteration! Do have a look at toticity.co.uk for free samples, a list of new topics and an order form.

5 Maths Gems #43

Hello and welcome to my 43^rd gems post. This is where I share some of the best ideas I've seen on Twitter.

1. Vocabulary
Maria Howard (@MrsHsNumeracy) has created a new resource to assess and develop students' literacy. Maria's Mathematical Literacy Assessment for Year 7 is one of the best vocabulary resources I've seen. Two extracts are shown below but you must look through the whole assessment to appreciate how good this is.

Reflecting on the importance of developing literacy in maths lessons, Maria says, "I realised I needed to assess their level of understanding of Mathematical vocabulary, that way I would know what words I needed to teach them and embed them in their everyday Mathematical conversations in class". 

I look forward to seeing the literacy resources that Maria plans to create for Year 9 and Key Stage 4. I think these will be incredibly useful.

Do check out the rest of Maria's website too - it's a goldmine of resources for numeracy across the curriculum.

2. Addition
I liked Cristina Milos' (@surreallyno) recent tweet showing an expanded form of addition. This explanation will help students understand why we 'carry ones' when we do long addition.

3. New Resources
I'm so pleased that Don Steward has started creating new resources again, including the lovely common dechocolateater.

The clever people at MathsPad continue to produce wonderful new resources too - here's one of their latest activities (subscription is only £3 per month).

4. Returning Tests
If you haven't yet discovered #maths TLP then you're missing out. Every Sunday night hundreds of maths teachers take part in our weekly 'Twitter Lesson Planning' hour, sharing ideas and resources for lessons in the week ahead. A few weeks ago Mark Horley (@mhorley) asked this question:

I expect that many of us feel that the lessons in which we return assessments could be better. I don't look forward to these lessons at all.

Mark was inundated with excellent ideas so he wrote a blog post about it which you can read here. It's worth a read.

Speaking of Mark's blog, I'd like to draw your attention to another of his posts - Finding the nth term - in which he shared a lovely resource for linear sequences. This resource is all about patten spotting - students compare each sequence to a previous sequence in order to identify the nth term.

5. Animations
Thanks to Siobhan Allen (‏@SiobhanA1969) for sharing this animation of the volume of a cone - I've not seen this one before.

This led me to discover a nice collection of gifs including this one on the surface area of a cylinder.

Thanks also to Ed Southall (@solvemymaths) for sharing Don Steward's angle bisection animation. I've never seen this method before. It featured in Don's presentation which you can read about in Ed's post.

There are more mathematical animations in my post Animations and Simulations.

Update
I uploaded some fantastic new Pret Homeworks today. If you've not seen Pret homeworks before then check out this post which explains all. Last week I created a new page of A level Mechanics Resources. I also had a post published on the new blog Starter for Five which provides advice to new teachers.

I've been a bit quiet on the blogging and tweeting front this week because it was my eldest daughter's 4th birthday on Wednesday, plus work continues to be very busy.

Happy birthday mini-Morgan

Timetabling Maths
I'm really interested in timetabling and curriculum design. In my opinion my school doesn't have enough maths on the timetable. I'm often rushing through topics. My GCSE students have significant gaps in their conceptual knowledge and I think the main cause of this is that they haven't had enough time to master topics at Key Stage 3. But I do wonder how other schools fit it all in - if you increase the number of maths lessons, what gets dropped from the timetable? I'd appreciate it if you'd email me to let me know how it works at your school. If you have loads of maths lessons, what subjects are absent from the curriculum?

I recently did two 24 hour Twitter polls to find out how much time is spent teaching maths in Years 10 and 7. Here are the results:

The Mathematical Association did a Sixty Second Survey which had a similar number of respondents but provides more detail:

Without the context (eg type of school) both sets of results are of limited value, but they do provide some starting points.

It appears that many schools have increased the number of lessons at Key Stage 4 in response to the change in GCSE specification. Although my sample size is small, I believe that schools with only three hours a week of maths lessons at Key Stage 3 and 4 are behind the national average.

Do let me know your thoughts and experiences.

#chrismaths15
I'm very excited about my upcoming event and am pleased to announce that Colin Hegarty will now be speaking too. I'll publish a full programme soon. For information and tickets, see christmaths.weebly.com.